This paper investigates FinFET transistor technology, aiming to address limitations in conventional planar CMOS transistors. The motivation stems from the escalating demandfor high-performance, low-power devices in sub-10nm technology nodes. The challenges of short-channel effects, leakage currents,and scalability constraints in planar CMOS transistors have prompted exploration into novel architectures like FinFETs. This research provides an indepth analysis of FinFETs’ threedimensional structure, fabrication, materials, and design considerations. We evaluate their advantages and limitations compared to traditional transistors in terms of power consumption, speed, and scalability. Our approach involves comparative studiesutilizing simulations, material analysis, and empirical data. By merging theory with practical insights, this paper aims to offera comprehensive view of FinFET technology’s potential and challenges in modern semiconductor applications. In conclusion,this study sheds light on FinFET transistors, emphasizing their fabrication, design, and performance characteristics. It highlightstheir promise as a solution to semiconductor industry challenges, paving the way for next-generation electronic devices.

This study applies Density Functional Theory(DFT), using the B3LYP functional, and via ab initio Restrict Hartree-Fock (RHF) methods, to study the infrared spectrum of steroid 17-Iodo-androst-16-ene. The spectrum was obtained viacomputational methods ab initio RHF and DFT. Optimization of molecular structure via UFF (Universal Force Field), followed by PM3 (Parametric Method 3), with geometric optimization,obtaining the spectrum of other basis sets of steroid 17-Iodo-androst-16-ene. The study this steroid was chosen because it can could act as aromatase enzyme inhibitors and this phenomenon could be translated as good compounds to treat breast cancer. The B3LYP functional always presents the lowest thermal energy than the RHF in all calculated bases, however the RHF always presents the highest Entropy than the B3LYP, in all the calculated basis sets. The normalized spectrum calculated in the B3LYP/SVP functional/basis set have harmonic frequency with peaks 3,241.83 cm−1, 100% and 3,177.535 cm−1 at 43.304% absorbance. The study has so far been limited to computational methods compatible with the theory of quantum chemistry.

Based on the experimental facts of angle-resolved photoemission spectroscopy (ARPES) and neutron scattering in high-temperature superconductors, a unified theoretical framework centered around polyhedron quantum-well-confinedelectrons is presented for superconductivity. According to the crystal structure of superconducting materials, the new theory can analytically determine the fundamental properties in copper- and iron-based superconductors, including the Fermi surface structure, the superconducting energy-gapsymmetry and value, the superconducting transition temperature, and the spin resonance peaks and parity, the predictions of the theoryare in good agreement with experiments. Furthermore, our research provides new insights into the microscopic nature of magnetism,spin, and the Ginzburg-Landau order parameter.

A novel chiral electron-hole (CEH) pairing mechanism is proposed to account for non-BCS superconductivity. In contrast to BCS Cooper pairs, CEH pairs exhibit a pronounced affinity to antiferromagnetism for superconductivity. The gap equations derived from this new microscopic mechanism are analyzed for both s- and d-wave superconductivity, revealing marked departures from the BCS theory. Unsurprisingly, CEH naturally describes superconductivity in strongly-correlated systems, necessitating an exceedingly large coupling parameter ($lambda>1$ for s-wave and $lambda>pi/2$ for d-wave) to be efficacious. The new mechanism provides a better understanding of various non-BCS features, especially in cuprate and iron-based superconductors. In particular, CEH, through quantitative comparison with experimental data, shows promise in solving long-standing puzzles such as the unexpectedly large gap-to-critical-temperature ratio $Delta_0/T_c$, the lack of gap closure at $T_c$, superconducting phase diagrams, and a non-zero heat-capacity-to-temperature ratio $C/T$ at $T=0$ (i.e., the ``anomalous linear term''), along with its quadratic behavior near $T=0$ for d-wave cuprates.

We present a description of plane Poiseuille flow of non-Newtonian time-independent fluid based on symmetric equations, which take into account both the longitudinal motion and rotation of the vortex tubes. This model has analytical solution in the form of the two-parametric velocity distribution, which is in good agreement with velocimetry data in microchannels. The advantage of this approach is that, in contrast to the Ostwald-de Waele power law, it provides a more accurate approximation of experimental velocity profiles for different Reynolds numbers by model profiles corresponding to the same viscosity parameter. We believe that this simple model can be useful for making adequate estimates for the parameters of non-Newtonian time-independent fluids in engineering hydrodynamics.

The development of energy-efficient, high-density three-dimensional (3D) magnonic devices has garnered significant interest due to their potential for revolutionizing information processing and storage technologies. Building upon recent findings on spin-wave modes in magnetochiral nanotubes with axial and circumferential magnetization, this study investigates the effects of tailored geometries and magnetic configurations on the spin-wave properties of these nanostructures.By employing advanced simulation techniques, experimental methods, and theoretical analysis, we explore the interplay between geometry, magnetization, and spin-wave dynamics in magnetochiral nanotubes. Our results reveal that specific combinations of geometrical parameters and magnetic configurations lead to enhanced spin-wave properties, paving the way for the design of novel 3D magnonic devices with improved performance and energy efficiency.Furthermore, we demonstrate the potential of these optimized magnetochiral nanotubes for various applications, including logic nanoelements and vertical through-chip vias in 3D magnonic device architectures. This study not only advances our understanding of spin-wave dynamics in magnetochiral nanotubes but also provides a foundation for the development of next-generation magnonic devices.

The RLC circuit is generalized in such a way that the capacitor has longitudinal form and the components are all in series with the voltage source . The medium in capacitor is dielectric with the index of refraction n. The change of the amount of charges on the left and right sideof the capacitor generate in medium special radiation which is not the Cerenkov radiation, no the Ginzburg transition radiation but the originalradiation which must be confirmed in laboratories.We have calculated the spectral form of the radiation. It depends on the dielectric constant n of the capacitor medium. The defect in medium is involved in the spectral form and can be compared with the original medium. Such comparison is the analog of the Heyrovsky-Ilkovic procedure in the electro-chemistry (Heyrovsky et al., 1965).

In my previous preprint about SRWS-zeta theory[Y.Ueoka,viXra:2205.014,2022],I proposed an approximation of rough averaged summation of typical critical Greenfunction for the Anderson transition in the Orthogonal class. In this paper, I removea rough approximate summation for the series of the typical critical Greenfunction by replacing summation with integral. Pade approximant is used to takea summation. The perturbation series of the critical exponent nu of localizationlength from upper critical dimension is obtained. The dimensional dependence ofthe critical exponent is again directly related with Riemann zeta function. Degree offreedom about lower critical exponent improve estimate compared with previousstudies. When I fix lower critical dimension equal to two, I obtained similar estimateof the critical exponent compared with fitting curve estimate of the criticalexponent[E.Tarquini et al.,PhysRevB.95(2017)094204].

Based on the real-space Mott insulator model, we establish a unifiedpairing, coherent and condensate mechanism of superconductivity. Motivatedby Dirac's magnetic monopole and Maxwell's displacement current hypothesis,we demonstrate that electric and magnetic fields are intrinsicallyrelevant. An isolated proton or electron creates an electric field,whereas a quantized proton-electron pair creates a magnetic field.The electric dipole vector of the proton-electron pair is the Ginzburg-Landauorder parameter in the superconducting phase transition. The Pierce-likedimerization pairing transition of the electron-proton electric dipolelattice leads to the symmetry breaking of the Mott insulating stateand the emergence of superconducting and magnetic states. This theoreticalframework can comprehensively explain all superconducting phenomena.Our research sheds new light on electron spin, magnetic monopoles,and the symmetry of Maxwell's equations.

There are three different ways of counting microstates for indistinguishable particles and distinguishable energy levels. Two of them correspond to Bosons and Fermions (and anyons, which interpolate between the two), but the third one, which is not considered so far, is when we require a `dual' of the Exclusion Principle to hold: in each energy level (state) there must exist at least one particle. I call this `the Inclusion Hypothesis' and propose the statistics as a possibility of existence of a third kind of particles.

In my previous paper about Statistical Random Walk Summation(SRWS) theory[1], I proposed a new expansion of typical critical Green function for the Anderson transition in the Orthogonal class. In this paper, I perform an approximate summation for the series of the typical critical Green function. Pad'e approximant is used to take a summation. The new approximate expression of the critical exponent nu of localization length is obtained. The dimensional dependence of the critical exponent is directly related with Riemann zeta function. Thus, the number theory and the critical phenomena of the Anderson transition is connected. Therefore I call this method as zeta-Pad'e SRWS theory. Existence of lower critical dimension is understood as the infinite existence of prime numbers. Besides it, analogy with statistical mechanics also becomes clear.

We continue to consult the Ekagi-Dutch-English-Indonesian Dictionary by J. Steltenpool. In this short note, we remove all the multiple countings of an entry in a letter's section which have gone in in the companion paper "Along the side of the Onsager's solution, the Ekagi language; viXra: 2205.0065[Condensed Matter]". We draw the natural logarithm of the number of entries, denoted as f, normalised, starting with a letter vs the natural logarithm of the rank of the letter, denoted as k. We find that $\frac{lnf}{lnf_{max}}$ vs $\frac{lnk}{lnk_{lim}}$ is matched by the graph of the reduced magnetisation vs the reduced temperature of the exact Onsager solution of the two dimensional Ising model in the absence of the external magnetic field

I propose a method to study the Anderson transition in the orthogonal symmetryclass. This method employs a virtual lattice characterised by an arbitraryspectral dimension instead of a concrete lattice with a given integer or fractal dimension.This method makes it possible to simulate numerically infinite size systemon a computer. Moreover, the computational complexity does not increaseexponentially as the dimensionality increases. Thus, we can avoid the curse ofdimensionality. Also, we can estimate the critical exponent numerically withoutresorting to the finite size scaling method often used in previous numerical studiesof critical phenomena.

The focus of the work deals with the analysis of the action sites of four exobiological nanomolecules, determined by the distribution of electrical charges around the nanomolecules atoms called: ASi, CSi, GSi and TSi. The Van der Waals radius distribution calculations have been determined via ab initio Hartree-Fock methods, Unrestricted and Restrict (UHF and RHF) in the set of basis used Effective Core Potential (ECP) minimal basis, and CC-pVTZ (Correlation-consistent valenceonly basis sets triple-zeta). The study has so far been limited to computational ab initio methods. The results are compatible with the theory of quantum chemistry, but their comprovation experimental verification depend on advanced techniques for their synthesis, obtaining in laboratory for experimental biochemical.

I suggest a new explicit formula for dimensional dependence of the critical exponent of the Anderson transition considering high dimensional asymptotic behavior and using the multi-points summation method. Asymptotic expansion at infinite dimension is estimated from numerical data. Combining known asymptotic series at two dimension and infinite dimension using the multi-points summation method, I obtained useful approximation formula for the critical exponent in the Orthogonal class.

We consult Ekagi-Dutch-English-Indonesian Dictionary by J. Steltenpool. Here we count all the Ekagi head words initiating with a letter. We draw the natural logarithm of the number of words, normalised, starting with a letter vs the natural logarithm of the rank of the letter. We find that the words underlie a magnetisation curve. The magnetisation curve i.e. the graph of the reduced magnetisation vs the reduced temperature is the exact Onsager solution of the two dimensional Ising model in the absence of external magnetic field.

The work focused on determining the Infrared spectroscopy (IRS) of the two compounds calculated are from two esters (compounds C1 and C2) from 2,3,4,5-Tetrahydro-oxepine derivatives, here called C1 and C2. The IRS was obtained via computational methods ab initio Restricted Hartree-Fock. Optimization of molecular structure via UFF, followed by PM3, RHF/EPR-II and RHF/STO-6G, thus obtaining a stable structure, in STP. The molecule was obtained, whose composition is C: 81.7%; H: 7.1%; N: 3.4%; O: 7.8%, 411.53536 g, and molecular formula: C28H29NO2 for C1 and C: 70.6%; H: 7.4%; N: 10.3%; O: 11.7%, 544.68439 g, and molecular formula: C32H40N4O4. The highest vibrational absorbance frequency peaks for the C1 and C2 molecule are found at the frequency of 1793.58 cm-1, 1867.14 cm-1 and 1956.39 cm-1, for C1 and 1368.99 cm-1, 1409.43 cm-1 and 1790.47 cm-1, for C2, respectively. Limitations our study has so far been limited to computational simulation via quantum mechanics (QM) an applied theory. Our results and calculations are compatible with the theory of QM.

We consult an Arabic dictionary: "al-Mujam al-w\'{a}fi" or, "adhunik arabi-bangla abhidhan" by Dr. M. Fazlur Rahman. We draw the natural logarithm of the number of words, normalised, starting with a letter vs the natural logarithm of the rank of the letter. We find that the words underlie a magnetisation curve. The magnetisation curve i.e. the graph of reduced magnetisation vs reduced temperature is the exact Onsager solution of two dimensional Ising model in the absence of external magnetic field.

We propose a modified phenomenological equation for heat and impurity fluxes in solids by analogy with the Cattaneo-Vernotte concept. It leads to the second-order elliptical equations describing the evolution of temperature and impurity profiles with finite rate of propagation. The comparison of transfer peculiarities in the framework of parabolic and elliptic equations is discussed.

Proton nuclear magnetic resonance (1H NMR) is the application of nuclear magnetic resonance in NMR spectroscopy with respect to 1H within the molecules of a substance, in order to determine the structure of its molecules. The work focused on determining the 1H NMR spectrum of the molecule here called Xalapa, in homage of the city of Xalapa, the capital city of the Mexican state of Veracruz and the name of the surrounding municipality. The 1H NMR spectrum was obtained via computational methods ab initio Restricted Hartree-Fock. Optimization of molecular structure via UFF, followed by PM3, RHF/EPR-II and RHF/STO-6G, thus obtaining a stable structure, in STP, NMR via the GIAO(Gauge-Independent Atomic Orbital) method. The IUPAC name of the molecule was obtained, whose composition is C: 81.7%; H: 7.1%; N: 3.4%; O: 7.8%, formula weight: 411.53536 g, and molecular formula: C28H29NO2. Limitations our study has so far been limited to computational simulation via quantum mechanics (QM) an applied theory. Our results and calculations are compatible with the theory of QM, but their physical experimental verification depends on experimental data that should be laboratory for experimental biochemical.

We study A Dictionary of Modern Italian by John Purves. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,$\beta H$=0) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising model with four nearest neighbours in absence of external magnetic field. H is external magnetic field, $\beta$ is $\frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the Boltzmann constant. Moreover, we compare the Italian language with other Romance languages. These are the Spanish, the Basque and the Romanian languages respectively. On the top of it, we compare A Dictionary of Modern Italian with Dictionary of Law and Administration, 2000, by National Law Development Foundation. We find a tantalizing similarity between the Modern Italian and the jargon of law and administartion.

Coupled equations describing diffusion and cross-diffusion of tracer particles in hard-sphere suspensions are derived and solved numerically. In concentrated systems with strong excluded volume and viscous interactions the tracer motion is subdiffusive. Cross diffusion generates transient perturbations to the host-particle matrix, which affect the motion of the tracer particles leading to nonlinear mean squared displacements. Above a critical host-matrix concentration the tracers experience clustering and uphill diffusion, moving in opposition to their own concentration gradient. A linear stability analysis indicates that cross diffusion can lead to unstable concentration fluctuations in the suspension. The instability is a potential mechanism for the appearance of dynamic and structural heterogeneity in suspensions near the glass transition.

We study the Webster's Universal Spanish-English Dictionary by Geddes and Grosset. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,$\beta H$=0) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising model with four nearest neighbours in absence of external magnetic field. H is external magnetic field, $\beta$ is $\frac{1}{k_{B}T}$ where, T is temperature and $k_{B}$ is the Boltzmann constant. Moreover, We compare the Spanish language with two other Romance languages, the Basque and the Romanian languages respectively. On the top of it, we compare the Spanish-English Dictionary with A Dictionary of Geography of Oxford University Press by Susan Mayhew and find a tantalizing similarity between the Spanish and the jargon of Geography.

Majorana fermion solution is obtained from the self-consistent effective Hamiltonian theory. The ground state is conjectured to be a non-empty vacuum with 2 fermions, one for each type. The first type is the original charged fermion and the second type the chiral charge-less Majorana fermion. The Marjorana fermion is like a shadow of the first fermion cast by the non-empty vacuum.

An effective hard-sphere model of the diffusion and cross-diffusion of salt in unentangled polymer solutions is developed. Given the viscosity, sedimentation coefficient and osmotic pressure of the polymer, the model predicts the diffusion and cross-diffusion coefficients as functions of the polymer concentration and molecular weight. The results are compared with experimental data on NaCl diffusion in aqueous polyethylene glycol solutions, showing good agreement at polymer molecular weights up to 400\,g/L. At higher molecular weights the model becomes less accurate, likely because of the effects of entanglement. The tracer Fickian diffusivity can be written in the form of a Stokes-Einstein equation containing the solution viscosity. For NaCl diffusion in polyethylene glycol solutions, the Stokes-Einstein equation breaks down as the polymer size increases. Using Batchelor's viscous correction factor to determine an effective viscosity experienced by the salt ions within the polymer matrix leads to much closer agreement with experiment.

The work characterizes develop a single layer bioinorganic membrane using nano-molecule Kurumi C13H20BeLi2SeSi / C13H19BeLi2SeSi, is well characterize computationally. As its scientific name 3-lithio-3-(6-{3-selena 8-beryllatricyclo [3.2.1.02,⁴]oct-6-en-2-yl}hexyl)-1-sila-2-lithacyclopropane. The work was based on a molecular dynamics (MD) of 1ns, using the CHARMM22 force field, with step 0.001 ps. Calculations indicate that the final structure, arrangement have the tendency to form a single layer micellar structure, when molecular dynamics is performed with a single layer. However, when molecular dynamics were carried out in several layers, indicates the behavior of a liotropic nematic liquid crystal order. Kurumi features the structure polar-apolar-polar predominant. Limitations our study has so far been limited to computational simulation via quantum mechanics e molecular mechanics (QM/MM), an applied theory. Our results and calculations are compatible and with the theory of QM/MM, but their physical experimental verification depend on advanced techniques for their synthesis, obtaining laboratory for experimental biochemical. Going beyond imagination, the most innovative and challenging proposal of the work advances the construction of a structure compatible with the formation of a “new DNA”, based now on the kurumi molecule.

We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and the complete single fermion excitation energy spectrum is constructed using the non-interacting fermions that are eigenstates of the quadratic matrix related to the system Hamiltonian. Connection to the Riemann Hypothesis is discussed.

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in quadratic form which can then be exactly solved. The theory can be constructed within density functional theory framework and a self-consistent scheme is proposed for solving the exact density functional theory. We apply the theory to structurally disordered system and a symmetric and asymmetric Hubbard dimer and corresponding lattice models and the the single fermion excitation spectra show a persistent gap due to the fermionic entanglement induced pairing condensate. For disordered system, density of state at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase and a sharp resonance is predicted as the gap is not dependent on the temperature of the system. For the symmetric Hubbard model, the gap for both half filling and doped case suggests quantum phase transition between the AFM and SC is a continuous phase transition.

We study a Garo to English School Dictionary. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,$\beta H=0.02$) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising model with four nearest neighbours with $\beta H=0.02$. $\beta$ is $\frac{1}{k_{B}T}$ where, T is temperature, H is external magnetic field and $k_{B}$ is the Boltzmann constant.

We study the Oxford Dictionary Of Social Work and Social Care. We draw the natural logarithm of the number of entries, normalised, starting with a letter vs the natural logarithm of the rank of the letter, normalised. We conclude that the Dictionary can be characterised by BP(4,$\beta H=0.01$) i.e. a magnetisation curve for the Bethe-Peierls approximation of the Ising model with four nearest neighbours with $\beta H=0.01$. $\beta$ is $\frac{1}{k_{B}T}$ where, T is temperature, H is external magnetic field and $k_{B}$ is the tiny Boltzmann constant.

The Coulomb and Yukawa potentials of particles are derived from the Schwinger field theory at zero and the finite temperature. At the same time the correction to the Coulomb potential is determined for the two charges interacting in the photon black-body sea by the photon exchange mechanism. The running coupling constant is determined in dependence on the mean free path of photons in the photon sea. The relation to the Cooper pairs and phonon-phonon interaction at finite temperature is discussed.

We review the recently proposed universal concept of dynamic complexity and its new mathematics based on the unreduced interaction problem solution. We then consider its progress-bringing applications at various levels of complex world dynamics, including complex-dynamical nanometal physics and living condensed matter, unreduced nanobiosystem dynamics and the integral medicine concept, causally complete management of complex economical and social dynamics, and the ensuing concept of truly sustainable world governance.

In this work, we have studied the effects from increasing the strength of the applied electric field on the charge transport of hydrogenated graphitic fibers. Resistivity measurements were carried out for direct currents in the nA - mA range and for temperatures from 1.9 K to 300 K. The high-temperature non-ohmic voltage-current dependence is well described by the nonlinear random resistor network model applied to systems that are disordered at all scales. The temperature-dependent resistivity shows linear, step-like transitions from insulating to metallic states as well as plateau features. As more current is being sourced, the fiber becomes more conductive and thus the current density goes up. The most interesting features is observed in high electric fields. As the fiber is cooled, the resistivity first decreases linearly with the temperature and then enters a plateau region at a temperature T ~ 260 − 280 K that is field-independent. These observations on a system made out of carbon, hydrogen, nitrogen, and oxygen atoms suggest possible electric-field induced superconductivity with a high critical temperature that was predicted from studying the role of chirality on the origin of life.

We report transport and magnetization measurements on graphites that have been hydrogenated by intercalation with an alkane (octane). The temperature-dependent electrical resistivity shows anomalies manifested as reentrant insulator-metal transitions. Below T ∼ 50 K, the magnetoresistance data shows both antiferromagnetic (AFM) and ferromagnetic (FM) behavior as the magnetic field is decrease or increased, respectively. The system is possibly an unconventional magnetic superconductor. The irreversibility observed in the field-cooled vs. the zero-field cooled data for a sufficiently high magnetic field suggests that the system might enter a superconducting state below Tc ∼ 50 K. Energy gap data is obtained from nonlocal electric differential conductance measurements. An excitonic mechanism is likely driving the system to the superconducting state below the same T ∼ 50 K, where the gap is divergent. We find that the hydrogenated carbon fiber is a multiple gap system with critical temperatures estimates above room temperature. The temperature dependence of the superconducting gap follows the flat-band energy relationship, with the flat band gap parameter linearly increasing with the temperature above Tc ∼ 50 K. Thus, we find that either a magnetic or an electric field can drive this hydrogenated graphitic system to superconducting state below Tc ∼ 50 K. In addition, AF spin fluctuations creates pseudogap states above Tc ∼ 50 K.

The dependence of the critical temperature of high temperature superconductors of various families on their composition and structure is proposed. A clear dependence of the critical temperature of high temperature superconductors on the sequence number of the constituent elements, their valency, and the structure of the crystal lattice is revealed.

Were analyzed boundary conditions for kinetic equations describing the dynamics of electrons in the metal. Boundary condition of the Fuchs and boundary condition of Soffer are considered. Were taken into account the Andreev conditions for almost tangential moving electrons. It is shown that the Soffer boundary condition does not satisfy this condition. It was proposed the boundary condition that satisfies the Andreev condition. It is shown that this boundary condition in the limiting case passes into the mirror--diffuse Fuchs boundary condition.

The kinetic equation for electrons in polycrystalline metal has been considered. This kinetic equation takes into account, along with collisions of electrons with impurities the collisions of electrons with the boundaries of the grains. We analyze the influence of a scattering of electrons on the boundaries of the grains on his electric properties.

This article presents a novel Hamiltonian architecture based on vertex types and empires for demonstrating the emergence of aperiodic order (quasicrystal growth) in one dimension by a suitable prescription for breaking translation symmetry. At the outset, the paper presents different algorithmic, geometrical, and algebraic methods of constructing empires of vertex configurations of a given quasi- lattice. These empires have non-local scope and form the building blocks of the new lattice model. This model is tested via Monte Carlo simulations beginning with randomly arranged N tiles. The simulations clearly establish the Fibonacci configuration, which is a one dimensional quasicrystal of length N, as the final relaxed state of the system. The Hamiltonian is promoted to a matrix operator form by performing dyadic tensor products of pairs of interacting empire vectors followed by a summation over all permissible configurations. A spectral analysis of the Hamiltonian matrix is performed and a theoretical method is presented to find the exact solution of the attractor configuration that is given by the Fibonacci chain as predicted by the simulations. Finally, a precise theoretical explanation is provided which shows that the Fibonacci chain is the most probable ground state. The proposed Hamiltonian is a one dimensional model of quasicrystal growth.

A phenomenological theory of diffusion and cross-diffusion of tracer particles in con- centrated hard-sphere suspensions is developed within the context of Batchelor's theory of multicomponent diffusion. Expressions for the diffusion coeffcients as functions of the host particle volume fraction are obtained up to the close-packing limit. In concen- trated systems the tracer diffusivity decreases because of the reduced pore space available for diffusion. Tracer diffusion, and segregation during sedimentation, ceases at a critical trapping volume fraction. The tracer diffusivity can be modelled by a Stokes-Einstein equation with an effective viscosity that depends on the pore size. The tracer cross- diffusion coeffcient increases near the glass transition and diverges in the close-packed limit.

The distribution of free charges within fluids or plasma is often modeled using linearized Poisson-Boltzmann equation (PBE). However, this author has recently shown that the usual boundary conditions (BC), namely the Dirichlet condition and the Neumann condition cannot be used to solve the PBE due to some physical reasons. This author has used the BC of `mixed' type to obtain the physical solution to the 1-D PBE and derived the charged density distribution $\rho_e$ within {\it rectangular} and {\it cylindrical} geometries before. Here the 1-D formulae of $\rho_e$ (i) within, (ii) between and (iii) outside {\it spherical} geometries has been derived. The result shows that the electric field is high at the surface of small objects, immersed in electrolyte solution. These formulae could be very useful in explaining similar physical situations that are found in nature or made in the laboratories.

The Richardson thermal effect is considered for the situation where the thermal electrons are inserted into the homogenous magnetic field. The electron flow in magnetic field produces the synchrotron radiation. We calculate the spectral distribution of the synchrotron photons.

An approximate solution of the expected value of the direction of an arbitrary electron on the generalized Ising model (Ising model in which the energy with the external magnetic eld and the energy of the interaction between the electrons take an arbitrary value) was obtained. Actually, considering application to the information system, we calculated each electron spin state as 0or1 instead of -1or1. As a result, even if the number of each spin increased, the error did not increase and it fell within 2%. If the expected value of the spin state is 0.1 to 0.9, the expected value can be obtained within an error range of 2% regardless of whether the energy value is positive or negative. The calculation amount of the approximate solution is obtained by the calculation amount of the square of N multiplied by 10 times. It can be expected as application of network analysis and the like. We also posted python source code.

A theory describing the processes of atomic diffusion in a nonequilibrium state with nonuniform distributions of components in a defect-impurity system of silicon crystals is proposed. Based on this theory, partial diffusion models are constructed and simulation of a large number of experimental data is curried out. A comparison of the simulation results with the experiments confirms the correctness and importance of the theory developed. The book will useful for researchers, engineers, and advanced students in semiconductor physics, microelectronics, and nanoelectronics. Practical application of the theoretical ideas formulated in the book allows finding cheaper solutions in the manufacturing of semiconductor devices and integrated microcircuits.

We derive the photon power spectrum, including the radiative corrections, generated by charged particle moving within 2D graphene sheet with implanted ions forming dielectric medium. It enables the experimental realization of the Vavilov-Cherenkov radiation. The relation of the Vavilov-Cherenkov radiation to light emission diode (LED) is discussed. LED dielectric sheets can be the crucial components of detectors in experimental particle physics. So, the article represents the unification of graphene physics with the physics of elementary particles.

The use of N-S equation is of outmost important for everyday life: airplanes, ships, underwater ships, etc. So, the Clay Institute promises 1 000 000 dollars for a good solution. Present paper is about Estonian author confidence, that he have solved the problem.

This article explores an implementation of the 2D Ising model using the Metropolis algorithm in the Python programming language. The goal of this work was to explore the scope of behaviours this model can demonstrate through a simplistic implementation on a relatively low-end machine. The Ising model itself is particularly interesting as it demonstrates relatively complex behaviours of ferromagnetics e.g. the second-order phase transition in spite of its simplicity. To study the specifics of this model several parameters were measured (namely the net magnetization and energy, the specific heat and correlation function) and a visualization of the grid was implemented. The simulations demonstrated an easily observable phase transition near critical temperature on a 100 × 100 Ising grid with the measured parameters behaving nearly as predicted by the exact solution developed for this model.

A study of a silicon n-p-n structure used as a cold emission cathode. Such a device is able to emit electrons in low external field and also to internally control the intensity of emission.

The Eyring’s rate process theory and free volume concept are employed to treat protons (or other particles) transporting through a 2D (two dimensional) crystal like graphene and hexagonal boron nitride. The protons are assumed to be activated first in order to participate conduction and the conduction rate is dependent on how much free volume available in the system. The obtained proton conductivity equations show that only the number of conduction protons, proton size and packing structure, and the energy barrier associated with 2D crystals are critical; the quantization conductance is unexpectedly predicted with a simple Arrhenius type temperature dependence. The predictions agree well with experimental observations and clear out many puzzles like much smaller energy barrier determined from experiments than from the density function calculations and isotope separation rate independent of the energy barrier of 2D crystals, etc.. Our work may deepen our understandings on how protons transport through a membrane and has direct implications on hydrogen related technology and proton involved bioprocesses.

A theory of tracer diffusion in hard-sphere suspensions is developed by using irreversible thermodynamics to obtain a colloidal version of the Kedem-Katchalsky equations. Onsager reciprocity yields relationships between the cross diffusion coefficients of the particles and the reflection coefficient of the colloidal suspension. The theory is illustrated by modelling a self-forming colloidal membrane that filters tracer impurities from the pore fluid.

Electrostatic problems are widely solved using two types of boundary conditions (BC), namely, the Dirichlet condition (DC) and Neumann condition (NC). The DC specifies values of electrostatic potential ($\psi$), while the NC specifies values of $\nabla \psi$ at the boundaries. Here we show that DC and NC may not produce equivalent solutions to a given problem; we demonstrate it with a particular problem: 1-D linearized Poisson-Boltzmann equation (PBE), which has been regularly used to find the distribution of ionic charges within electrolyte solutions. Our findings are immediately applicable to many other problems in electrostatics.

To date, the Hubbard model and its strong coupling limit, the t-J model, serve as the canonical model for strongly correlated electron systems in solids. Approximating the Coulomb interaction by only the on-site term (Hubbard U-term), however, may not be sufficient to describe the essential physics of interacting electron systems. We develop a more complete model in which all the next leading order terms besides the on-site term are retained. Moreover, we discuss how the inclusion of these neglected interaction terms in the Hubbard model changes the t-J model.

The effect of the electron sound absorption in a conducting medium (metal) was previously considered on the assumption of the Fermi-surface deformation under the action of the sound wave. In the present work will be considered another approach to the problem based on dynamic (kinetic) interaction of the electron gas with the lattice vibrations. The analysis is carried out for the case of arbitrary degeneration degree of the solid-state plasma.

In the present work the problem of the attenuation of longitudinal sound oscillations in a conducting medium are considered. The proposed approach is based on the dynamic interaction of electron gas with the lattice vibrations. This interaction is manifested in the modification of kinetic equation for electrons. The process is accompanied by generation of an electric field.

A novel effective Hamiltonian in the subspace of singly occupied states is obtained by applying the Gutzwiller projection approach to a generalized Hubbard model with the interactions between two nearest-neighbor sites. This model provides a more complete description of the physics of strongly correlated electron systems. The system is not necessarily in a ferromagnetic state as temperature T->0 at any doping level. The system, however, must be in an antiferromagnetic state at the origin of the doping-temperature plane. Moreover, the model exhibits superconductivity in a doped region at sufficiently low temperatures. We summarize the studies and provide a phase diagram of the antiferromagnetism and the superconductivity of the model in the doping-temperature plane here. Details will be presented in subsequent papers.

The second Stokes's problem about the behavior of rarefied gas filling half-space, when limiting the half-space the plane performs harmonic oscillations in its plane is considered. Continuum mechanics equations with the slip are used. It is shown that in quadratic in the velocity of wall approximation in gas have taken place the temperature effects due to influence of viscous dissipation. In this case there is a temperature difference between the surface of the body and the gas away from the surface.

The Poisson-Boltzmann equation (PBE) gives us very simple formula for charge density distribution $(\rho_e)$ within ionic solutions. PBE is widely solved by specifying values to electrostatic potential ($\psi$) at different boundaries; this type of boundary condition (BC) is known as Dirichlet condition (DC). Here we show that DC cannot be used to solve the PBE, because it leads to unphysical consequences. For example, when we change the reference for $\psi$, the functional forms of $\psi$ and $\rho_e$ change in non-trivial ways i.e. it changes the physics, which is not acceptable. Our result should have far reaching effects on many branches of physical, chemical and biological sciences.

A theory describing the processes of atomic diffusion in a nonequilibrium state with nonuniform distributions of components in a defect?impurity system of silicon crystals is proposed. Based on this theory, partial diffusion models are constructed, and simulation of a large number of experimental data are curried out. A comparison of the simulation results with the experiment confirms the correctness and importance of the theory developed.

The present work describes the equilibrium configuration of the caramboxin molecule studied using the Hartree-Fock (HF) and Density functional theory (DFT) calculations. With the DFT calculations, the total energy for the singlet state of caramboxin molecule has been estimated to be -933.3870701 a.u. Furthermore, the binding energy of the caramboxin molecule has been estimated to be 171.636 kJ/mol. The carambola or star fruit is a fruit used for human consumption in juices, desserts, pastries, custards, jellies, or even in natural consumption. Recent research indicates that it has great toxicity for people with kidney failure, and may even lead to death. Experiments demonstrated that it has glutamatergic effects, which means that it affects the function of the neurotransmitter glutamate, thus explaining the neurological effects. Our calculations indicate that the main active sites in carambox are the -OH (alcohols) groups, and the two carboxyl (-COOH) groups.

The Hall effect, especially integer, fractional and anomalous quantum Hall effect, has been addressed with the Eyring's rate process theory and free volume concept. The basic assumptions are that the conduction process is a common rate controlled "reaction" process that can be described with Eyring's absolute rate process theory; the mobility of electrons should be dependent on the free volume available for conduction electrons. The obtained Hall conductivity is clearly quantized as e^2/h with prefactors related to both the magnetic flux quantum number and the magnetic quantum number via azimuthal quantum number, with and without an externally applied magnetic field. This article focuses on two dimensional (2D) systems, but the approaches developed in this article can be extended to 3D systems

We consider the Kapitza-Dirac configuration for the generation of the standing waves. Electrons are then diffracted by standing waves and Bragg equation is valid. The situation is considered also in a plane and in the three dimensions. The electron-photon system forms the electron-photon superconductor. The Kapitza-Dirac effect is then applied to silicene.

Chemical reaction dynamics are usually tackled within the framework of Quantum Mechanics which can be computationally demanding. Here we suggest to use the energy-dependent Hamilton-Jacobi description with a classical reactive force field to obtain the most probable path. This may enable to calculate the reaction rate.

This work checks the Pauli equation with the description of the magnetic field and found a possible missing term in it. We propose a fixed Pauli equation, where the application in density functional theory explains the observed magnetic susceptibilities for Al, Si, and Au with applying directly magnetic fields. The possible shape of the Lagrangian describing the charged particle with an external magnetic field is also discussed.

Linearized Poisson-Boltzmann equation (PBE) gives us simple expressions for charge density distribution (ρ_e) within fluids or plasma. A recent work of this author shows that the old boundary conditions (BC), which are usually used to solve PBE, have serious defects. The old solutions turned out to be non-unique, and violates charge conservation principle in some cases. There we also derived the correct formula of ρ_e for a finite, rectangular geometry, using appropriate BCs. Here we consider some other types of geometries and obtain formula of ρ_e, which may be useful to analyse different experimental conditions.

We show that the unreduced, mathematically rigorous solution of the many-body problem with arbitrary interaction, avoiding any perturbative approximations and "exact" models, reveals qualitatively new mathematical properties of thus emerging real-world structures (interaction products), including dynamic multivaluedness (universal non-uniqueness of ordinary solution) giving rise to intrinsic randomness and irreversible time flow, fractally structured dynamic entanglement of interaction components expressing physical quality, and dynamic discreteness providing the physically real space origin. This unreduced interaction problem solution leads to the universal definition of dynamic complexity describing structure and properties of all real objects. The united world structure of dynamically probabilistic fractal is governed by the universal law of the symmetry (conservation and transformation) of complexity giving rise to extended versions of all particular (correct) laws and principles. We describe then the unique efficiency of this universal concept and new mathematics of complexity in application to critical problems in life sciences and related development problems, showing the urgency of complexity revolution.

We show the existing solution of Poisson-Boltzmann equation (PBE) to violate charge conservation principle, and then derive the correct formula for charge density distribution $(\rho_e)$ in a fluid. We replaced unphysical old boundary conditions with some conditions that have never been used. Our result demonstrates that PBE cannot explain the formation of `Electric Double Layer' (EDL); it follows that the present physical interpretation of `Debye length' $(\lambda_D)$ is wrong, too.

New conduction equations are derived on the basis of Eyring’s rate process theory and free volume concept. The basic assumptions are that electrons traveling from one equilibrium position to the other may obey Eyring’s rate process theory; the traveling distance is governed by the free volume available to each electron by assuming that electrons may have a spherical physical shape with an imaginative effective radius. The obtained equations predict that the superconductivity happens only when electrons form certain structures of a relative small coordinate number like Cooper pair at low temperatures; If each electron has a large coordinate number such as 8 when electrons form the body-centered-cubic (bcc) lattice structure like Wigner crystal, the predicted conductivity decreases instead increases when temperatures approach to zero. The electron condensation structures have a big impact on the conductivity. A sharp conductivity decrease at low temperatures, probably due to an Anderson transition, is predicted even when the Cooper pair is formed and the electrons can only travel short distances; While the Mott transition appears when crystalline structures like Wigner crystal form. On the other hand, the electron pairing or called the strong spin-spin coupling is predicted to induce Kondo effect when electrons are assumed to travel a very short distance. The Anderson localization seems to have a lot of similarities as Kondo effect such as electron pairing and low traveling distances of electrons at low temperatures. The Cooper pair that is the essence of BCS theory for superconductivity and the spin-spin coupling that is the cause for Kondo effect seem to contradict each other, but are seamlessly united in our current conductivity equations. The topological insulators become the natural occurrences of our equations, as both Kondo insulator and superconductivity share a same physical origin–the electron pairs, but the electrons just travel different distances at these two cases. A material containing an element of a high electro-negativity (or high ionization energy) and an element of a low electro-negativity(or low ionization energy) may form a good topological insulator and superconductor. Any magnetic element, like Iron, Nickel, and Cobalt, that has unpaired electrons and can induce Kondo effect as a dopant, could be a very good superconductor candidate once it is synthesized together with other proper elements of low electro- negativity (for example forming pnictide superconductors). The numbers of both conduction and valence electrons and the volume of a material under investigation have positive impacts on the conductivity. Any method that may increase the numbers of both conduction and valence electrons may move the superconductivity transition temperatures to higher regions. Any method that may reduce the volume of the material like external pressure seems to lower transition temperatures, unless that the applied pressure is so high that the electron density between the chemical bonds increases. The derived equations are in good agreement with the currently observed experimental phenomena. The current work may shed light on the mechanisms of superconductivity, presenting clues on how to move the superconductivity transition temperatures to higher regions.

We derive the electro-osmotic velocity profile in a micro-channel using a recently corrected charge density distribution within an electrolytic solution. Previous distribution did not take care of charge conservation principle while solving Poisson-Boltzmann equation and needed modification, hence the velocity profile also needs modification that we do here. Helmholtz-Smoluchowskii velocity scale is redefined, which accommodates Debye length parameter in it, unlike old definition.

Presence of a charged wall distributes like charges (co-ions) and unlike charges (counter-ions) differently within an electrolytic solution. It is reasonable to expect that counter-ions have more population near the wall, while co-ions are abundant away from it; experiments and simulations support this. An analytical formula for the net charge-density distribution has been used widely since almost hundred years, was obtained by solving the Poisson-Boltzmann equation. However, the old formula shows excess counter-ions everywhere, cannot account for the missing co-ions satisfactorily, and clearly violates charge conservation principle. Here, I correct the distribution formula from fundamental considerations. The old derivation expresses charge-density distribution as a function of electrostatic potential through Boltzmann distribution, but missed a crucial point that the indefinite nature of electrostatic potential makes charge-density indefinite as well. We must tune electrostatic potential by adding suitable constant until the integral of charge-density becomes consistent with the net charge present in solution; old theory did not do it, that I do here. This result demonstrates how to reconcile a definite quantity to an indefinite one, when they are related. I anticipate, this result is going to have far reaching impacts on many fields like colloid science, electro-kinetics, bio-technology etc. that use the old theory

Based on the thirteen similarities of structures of lattice, electron, and strong correlation Hamiltonian between CMR (colossal magnetoresistance) manganites and the high-Tc cuprates, this paper concludes that the Hamiltonian of the high-Tc cuprates and CMR manganites are the same. Based on uniform and quantitative explanations for fifteen experimental facts, this paper concludes that the pseudogap and CMR of manganites are caused completely by formation of Cooper pairs, consisting of two oxygen 2pσ holes in MnO2 plane

We correct the solution of Poisson-Boltzmann equation regarding charge distribution in an electrolytic solution bounded by walls. Considering charge conservation principle properly, we show that the gradient of electrostatic potential at different walls are strictly related, and cannot be assigned independent values, unlike old theory. It clarifies some cause and effect ideas: distribution turns out to be independent of the initial polarity of walls; the accumulated charges in liquid usually induce opposite polarity on the wall surface, forms `Electric Double Layer' (EDL), contrary to the common belief that a charged wall attracts counter-ions to form EDL. Distribution depends only on the potential difference between walls and the net charge present in the solution, apart from Debye length.

I eliminate hundred years old notion of `plug-flow' in electro-osmosis, which was predicted by incomplete `electric double layer' (EDL) theory. A recently developed `electric triple layer' (ETL) theory removes some serious shortcomings of EDL theory regarding conservation of electric charge, and when applied to electro-osmosis, shows that the velocity profile is not `plug-like' at all, but more like a parabola; it agrees with experiments and molecular dynamical simulation (MDS) results. Also, I redefine ‘Helmholtz-Smoluchowski velocity-scale’, which clears certain misunderstandings regarding representation of flow direction, and accommodates solution and geometrical properties within it. I describe some novel electro-osmotic flow controlling mechanisms. The entire electrokinetic theory must be modified using these concepts.

I correct hundred years old theory of charge distribution within an electrolytic solution surrounded by charged walls. Existing theory always implies excess amount of counter-ions (having polarity unlike walls) everywhere in the solution domain; so it cannot handle a solution that possesses excess ions of other type (co-ions) or is electrically neutral as a whole. Here, in the corrected distribution, counter-ions dominate near the walls, while the rest of the domain is allowed to be dominated by co-ions; the algebraic sum gives the net charge present, which can be of any sign and magnitude that makes theory quite general. This clarifies and raises many important concepts: a novel concept of `Electric Triple Layer' (ETL) replaces `Electric Double Layer' (EDL) theory; widths of electric layers can be calculated accurately instead of estimating by Debye length scale etc.

Kirchhoff's law of thermal emission demands that all cavities contain blackbody, or normal, radiation which is dependent solely on the temperature and the frequency of observation, while remaining independent of the nature of the enclosure. For over 150 years, this law has stood as a great pillar for those who believe that gaseous stars could emit a blackbody spectrum. However, it is well-known that, under laboratory conditions, gases emit in bands and cannot produce a thermal spectrum. Furthermore, all laboratory blackbodies are constructed from nearly ideal absorbers. This fact strongly opposes the validity of Kirchhoff's formulation. Clearly, if Kirchhoff had been correct, then laboratory blackbodies could be constructed of any arbitrary material. Through the use of two cavities in temperature equilibrium with one another, a thought experiment is presented herein which soundly refutes Kirchhoff's law of thermal emission.

Vanadium doped diamond-like carbon films prepared by unbalanced magnetron sputtering have been investigated by X-ray and ultraviolet photoelectron spectroscopy measurements for the purpose of revealing electronic structures including values of work function on the surfaces. In addition to these photoelectron measurements, X-ray diffraction measurements have been performed to characterize the crystal structures.

Calculating free energy differences is a topic of substantial interest and has many applications including chemical reactions which are used in organic chemistry, biochemistry and medicines. In equilibrium free energy methods that are used in molecular simulations, one molecule is transformed into another to calculate the energy difference. However, when the compared molecules have different number of atoms, these methods cannot be directly applied since the corresponding transformation involves breaking covalent bonds which will cause a phase transition and impractical sampling. Thus, Quantum Mechanical Simulations, which are significantly more demanding computationally, are usually combined to calculate free energies of chemical reactions. Here we show that the free energies can be calculated by simple classical molecular simulations followed by analytic or numerical calculations. In this method each molecule is transformed into its replica with the VDW and Coulomb terms of the different atoms relaxed in order to eliminate the partition function difference arising from these terms. Then, since each transformed system can be treated as non interacting systems, the remaining difference in the (originally highly complex) partition function can be directly calculated. Since molecular force fields can often be automatically generated and the calculations suggested here are rather simple the method can form a basis for automated free energy computation of chemical reactions.

In this work, Kirchhoff’s law (Kirchhoff G. Monatsberichte der Akademie der Wissenschaften zu Berlin, sessions of Dec. 1859, 1860, 783–787) is being revisited not only to mark its 150th anniversary but, most importantly, to highlight serious overreaching in its formulation. At the onset, Kirchhoff’s law correctly outlines the equivalence between emission and absorption for an opaque object under thermal equilibrium. This same conclusion had been established earlier by Balfour Stewart (Stewart B. Trans. Royal Soc. Edinburgh, 1858, v. 22(1), 1–20). However, Kirchhoff extends the treatment beyond his counterpart, stating that cavity radiation must always be black, or normal: depending only on the temperature and the frequency of observation. This universal aspect of Kirchhoff’s law is without proper basis and constitutes a grave distortion of experimental reality. It is readily apparent that cavities made from arbitrary materials (epsilon < 1) are never black. Their approach to such behavior is being driven either by the blackness of the detector, or by black materials placed near the cavity. Ample evidence exists that radiation in arbitrary cavities is sensitive to the relative position of the detectors. In order to fully address these issues, cavity radiation and the generalization of Kirchhoff’s law are discussed. An example is then taken from electromagnetics, at microwave frequencies, to link results in the resonant cavity with those inferred from the consequences of generalization.

Through the reevaluation of Kirchhoff’s law (Robitaille P. M. L. IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267), Planck’s blackbody equation (Planck M. Ann. der Physik, 1901, v. 4, 553–356) loses its universal significance and becomes restricted to perfect absorbers. Consequently, the proper application of Planck’s radiation law involves the study of solid opaque objects, typically made from graphite, soot, and carbon black. The extension of this equation to other materials may yield apparent temperatures, which do not have any physical meaning relative to the usual temperature scales. Real temperatures are exclusively obtained from objects which are known solids, or which are enclosed within, or in equilibrium with, a perfect absorber. For this reason, the currently accepted temperature of the microwave background must be viewed as an apparent temperature. Rectifying this situation, while respecting real temperatures, involves a reexamination of Boltzmann’s constant. In so doing, the latter is deprived of its universal nature and, in fact, acts as a temperature dependent variable. In its revised form, Planck’s equation becomes temperature insensitive near 300 K, when applied to the microwave background.

It has been advanced, on experimental (P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267) and theoretical (P.-M. Robitaille, Progr. Phys., 2006, v. 2, 22–23) grounds, that blackbody radiation is not universal and remains closely linked to the emission of graphite and soot. In order to strengthen such claims, a conceptual analysis of the proofs for universality is presented. This treatment reveals that Gustav Robert Kirchhoff has not properly considered the combined effects of absorption, reflection, and the directional nature of emission in real materials. In one instance, this leads to an unintended movement away from thermal equilibrium within cavities. Using equilibrium arguments, it is demonstrated that the radiation within perfectly reflecting or arbitrary cavities does not necessarily correspond to that emitted by a blackbody.

Since the days of Kirchhoff, blackbody radiation has been considered to be a universal process, independent of the nature and shape of the emitter. Nonetheless, in promoting this concept, Kirchhoff did require, at the minimum, thermal equilibrium with an enclosure. Recently, the author stated (P.-M. Robitaille, IEEE Trans. Plasma Sci., 2003, v. 31(6), 1263–1267; P.-M. Robitaille, Progr. in Phys., 2006, v. 2, 22–23), that blackbody radiation is not universal and has called for a return to Stewart’s law (P.-M. Robitaille, Progr. in Phys., 2008, v. 3, 30–35). In this work, a historical analysis of thermal radiation is presented. It is demonstrated that soot, or lampblack, was the standard for blackbody experiments throughout the 1800s. Furthermore, graphite and carbon black continue to play a central role in the construction of blackbody cavities. The advent of universality is reviewed through the writings of Pierre Prévost, Pierre Louis Dulong, Alexis Thérèse Petit, Jean Baptiste Joseph Fourier, Siméon Denis Poisson, Frédérick Hervé de la Provostaye, Paul Quentin Desain, Balfour Stewart, Gustav Robert Kirchhoff, and Max Karl Ernst Ludwig Planck. These writings illustrate that blackbody radiation, as experimentally produced in cavities and as discussed theoretically, has remained dependent on thermal equilibrium with at least the smallest carbon particle. Finally, Planck’s treatment of Kirchhoff’s law is examined in detail and the shortcomings of his derivation are outlined. It is shown once again, that universality does not exist. Only Stewart’s law of thermal emission, not Kirchhoff’s, is fully valid.

Through the formulation of his law of thermal emission, Kirchhoff conferred upon blackbody radiation the quality of universality [G. Kirchhoff, Annalen der Physik, 1860, v. 109, 275]. Consequently, modern physics holds that such radiation is independent of the nature and shape of the emitting object. Recently, Kirchhoff’s experimental work and theoretical conclusions have been reconsidered [P. M. L. Robitaille. IEEE Transactions on Plasma Science, 2003, v. 31(6), 1263]. In this work, Einstein’s derivation of the Planckian relation is reexamined. It is demonstrated that claims of universality in blackbody radiation are invalid.

We derived the energy gap of superconductor close to Tc, without using the usual methods of creation-annulation operators CC+. our approximations ar in good agreement with the numerical estimates and theoretical results.

The structure of crystal cells in two and three dimensions is fundamental for many material properties. In two dimensions atoms (or molecules) often group together in triangles, squares and hexagons (regular polygons). Crystal cells in three dimensions have triclinic, monoclinic, orthorhombic, hexagonal, rhombohedral, tetragonal and cubic shapes. The geometric symmetry of a crystal manifests itself in its physical properties, reducing the number of independent components of a physical property tensor, or forcing some components to zero values. There is therefore an important need to efficiently analyze the crystal cell symmetries. Mathematics based on geometry itself offers the best descriptions. Especially if elementary concepts like the relative directions of vectors are fully encoded in the geometric multiplication of vectors.

A new interactive software tool is described, that visualizes 3D space group symmetries. The software computes with Clifford (geometric) algebra. The space group visualizer (SGV) originated as a script for the open source visual CLUCalc, which fully supports geometric algebra computation. Selected generators (Hestenes and Holt, JMP, 2007) form a multivector generator basis of each space group. The approach corresponds to an algebraic implementation of groups generated by reflections (Coxeter and Moser, 4th ed., 1980). The basic operation is the reflection. Two reflections at non-parallel planes yield a rotation, two reflections at parallel planes a translation, etc. Combination of reflections corresponds to the geometric product of vectors describing the individual reflection planes. We first give some insights into the Clifford geometric algebra description of space groups. We relate the choice of symmetry vectors and the origin of cells in the geometric algebra description and its implementation in the SGV to the conventional crystal cell choices in the International Tables of Crystallography (T. Hahn, Springer, 2005). Finally we briefly explain how to use the SGV beginning with space group selection. The interactive computer graphics can be used to fully understand how reflections combine to generate all 230 three-dimensional space groups. <b>Mathematics Subject Classification (2000).</b> Primary 20H15; Secondary 15A66, 74N05, 76M27, 20F55 . <b>Keywords.</b> Clifford geometric algebra, interactive software, space groups, crystallography, visualization.

The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone PC application based on the visualization software CLUCalc. We first explain the unique geometric algebra structure behind the SGV. In the second part we review the main features of the SGV: The GUI, group and symmetry selection, mouse pointer interactivity, and visualization options.We further introduce the joint use with the International Tables of Crystallography, Vol. A [7]. In the third part we explain how to represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a new compact geometric algebra group representation symbol, which allows to read off the complete set of geometric algebra generators. For clarity we moreover state explicitly what generators are chosen. The group symbols are based on the representation of point groups in geometric algebra by versors.

This paper establishes an algorithm for the conversion of conformal geometric algebra (GA) [3, 4] versor symbols of space group symmetry-operations [6–8, 10] to standard symmetry-operation symbols of crystallography [5]. The algorithm is written in the mathematical language of geometric algebra [2–4], but it takes up basic algorithmic ideas from [1]. The geometric algebra treatment simplifies the algorithm, due to the seamless use of the geometric product for operations like intersection, projection, rejection; and the compact conformal versor notation for all symmetry operations and for geometric elements like lines and planes. The transformations between the set of three geometric symmetry vectors <i>a,b,c</i>, used for generating multivector versors, and the set of three conventional crystal cell vectors <b>a,b,c</b> of [5] have already been fully specified in [8] complete with origin shift vectors. In order to apply the algorithm described in the present work, all locations, axis vectors and trace vectors must be computed and oriented with respect to the conventional crystall cell, i.e. its origin and its three cell vectors.

This set of instructions shows how to successfully display the 17 two-dimensional (2D) space groups in the interactive crystal symmetry software Space Group Visualizer (SGV) [6]. The SGV is described in [4]. It is based on a new type of powerful geometric algebra visualization platform [5]. The principle is to select in the SGV a three-dimensional super space group and by orthogonal projection produce a view of the desired plane 2D space group. The choice of 3D super space group is summarized in the lookup table Table 1. The direction of view for the orthographic projection needs to be adapted only for displaying the plane 2D space groups Nos. 3, 4 and 5. In all other cases space group selection followed by orthographic projection immediately displays one cell of the desired plane 2D space group. The full symmetry selection, interactivity and animation features for 3D space groups offered by the SGV software become thus also available for plane 2D space groups. A special advantage of this visualization method is, that by canceling the orthographic projection (remove the tick mark of Orthographic View in drop down menu Visualization), every plane 2D space group is seen to be a subgroup of a corresponding 3D super space group.

We study the aperiodic signal transmission in a static nonlinearity in the context of aperiodic stochastic resonance. The performance of a nonlinearity over that of the linear system is defined as the transmission efficacy. The theoretical and numerical results demonstrate that the noise-enhanced transmission efficacy effects occur for different signal strengths in various noise scenarios.

We refined the concepts of electric current and fluxoid, and London’s equation that specify quantum phenomena of moving electrons and magnetic flux in a closed circuit similar to a superconducting ring, so as not to violate the uncertainty principle. On this basic the relation between the electron motion and magnetic flux in a superconductor has been theoretically investigated by means of Faraday’s law and/or canonical momentum relation. The fact that minimum unit of the quantized magnetic flux is hc/2e does not mean the concurrent motion of the two electrons in a Cooper pair as is known so far. However, it is shown to be related with independent motion of the each electron in a superconducting state.

Maxwell equations for electromagnetic waves propagating in dispersive media are studied as they are, without commonplace substituting a scalar function for electromagnetic field. A method of variables separation for the original system of equation is proposed. It is shown that in case of planar symmetry variables separate in systems of Cartesian and cylindric coordinates and Maxwell equations reduce to one-dimensional Schr¨odinger equation. Complete solutions are obtained for waves in medium with electric permittivity and magnetic permeability given as ϵ = e^−κz, µ = c^−2e^−λz. keywords: Maxwell equations, dispersive media, complete solutions PACS numbers: 41.20.Jb, 42.25 .Bs Keywords: Maxwell equations, dispersive media, complete solutions

We investigate the nature of the superconducting current from the Maxwell's displacement current. We argue that the conduction current density term of the Maxwell's equations is physically untrue, and it should be eliminated from the equations. Essentially, both the superconducting current and conduction current are originated from the Maxwell's displacement current characterizing the changes of electric field with time or space. Therefore, there are no electrons tunnel through the insulating layer of the Josephson junction. It is shown that the conventional static magnetic field is, in fact, the static electric field of the intrinsic electron-ion electric dipoles in the materials. The new paradigm naturally leads to unification of magnetic and electrical phenomena, while at the same time realizing the perfect symmetry of the Maxwell's equations. Moreover, it is well confirmed that the Dirac's magnetic monopole is indeed the well-known electron. This research is expected to shed light on the high-temperature superconductivity.

Through a convenient mathematical approach for the Navier-Stokes equation, we obtain the quadratic dependence $v^{2}$ of the drag force $F_{D}$ on a falling sphere, and the drag coefficient, $C_{D}$, as a function of the Reynolds number. Viscosity effects related to the turbulent boundary layer under transition, from laminar to turbulent, lead to the tensorial integration related to the flux of linear momentum through a conveniently choosen control surface in the falling reference frame. This approach turns out to provide an efficient route for the drag force calculation, since the drag force turns out to be a field of a non-inertial reference frame, allowing an arbitrary and convenient control surface, finally leading to the quadratic term for the drag force.

Particles on a plate form Chladni patterns when the plate is acoustically excited. To better understand these patterns and their possible real-world applications, I present a new analytical and numerical study of the transition between standard and inverse Chladni patterns on an adhesive surface at any magnitude of acceleration. By spatial autocorrelation analysis, I examine the effects of surface adhesion and friction on the rate of pattern formation. Next, I explore displacement models of particles translating on a frictional surface with both adhesive and internal particle-plate frictions. In addition, I find that both adhesion and damping forces serve as exquisite particle sorting mechanisms. Finally, I discuss the possible real-world applications of these sorting mechanisms, such as separating nanoparticles, organelles, or cells.

The article shows that in case if the photon is viewed as a particle moving in empty space the zero value of chemical potential of equilibrium electromagnetic radiation cannot be explained basing only on first principles of statistical physics. On the contrary, to explain the chemical potential of equilibrium electromagnetic radiation being equal to zero is rather simple if the photon is considered as a quasi-particle that is the way to describe collective motion of a system consisting of particles whose number is a fixed value. Collective motions of the particles of mentioned system are interpreted in the article as oscillations of an electromagnetic eld that corresponds to observation data of modern astronomy, according to which the space, that fills the gaps, both between massive objects and between massive particles forming them, should be attributed to characteristics of a continuous medium.

It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of introducing Proca equations include an alternative description of superconductivity, via extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible extension of Proca equation using biquaternion number. Further implications and experiments are recommended.

Emergent physics refers to the formation and evolution of collective patterns in systems that are nonlinear and out-of-equilibrium. This type of large-scale behavior often develops as a result of simple interactions at the component level and involves a dynamic interplay between order and randomness. On account of its universality, there are credible hints that emergence may play a leading role in the Tera-ElectronVolt (TeV) sector of particle physics. Following this path, we examine the possibility of hypothetical highenergy states that have fractional number of quanta per state and consist of arbitrary mixtures of particles and antiparticles. These states are similar to "un-particles", massless fields of non-integral scaling dimensions that were recently conjectured to emerge in the TeV sector of particle physics. They are also linked to "unmatter", exotic clusters of matter and antimatter introduced few years ago in the context of Neutrosophy. The connection between 'unmatter' and 'unparticle' is explained in details in this paper. Unparticles have very odd properties which result from the fact that they represent fractional field quanta. Unparticles are manifested as mixed states that contain arbitrary mixtures of particles and antiparticles (therefore they simultaneously evolve "forward" and "backward" in time). From this, the connection with unmatter. Using the fractal operators of differentiation and integration we get the connection between unparticle and unmatter. 'Unmatter' was coined by F. Smarandache in 2004 who published three papers on the subject.

Besides matter and antimatter there must exist unmatter (as a new form of matter) in accordance with the neutrosophy theory that between an entity <A> and its opposite <AntiA> there exist intermediate entities <NeutA>. Unmatter is neither matter nor antimatter, but something in between. An atom of unmatter is formed either by (1): electrons, protons, and antineutrons, or by (2): antielectrons, antiprotons, and neutrons. At CERN it will be possible to test the production of unmatter. The existence of unmatter in the universe has a similar chance to that of the antimatter, and its production also difficult for present technologies.

In a gradient of magnetic field, magnetic dipoles of air are attracted toward the region of intense field. So, the air pressure is more in the regions of more intense field. The formed pressure gradient exerts a net force on a body placed in the air in this gradient of magnetic field toward the region of low pressure or the region having weaker field. This is like what takes place in the process of sink-float separation. To establish the presented theory we need only to perform diamagnetism experiment in vacuum (according to the presented guidelines)to see if it will cease.(I'm ready to prepare for such an experiment in any university as a guest researcher).