Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell’s law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.

ANALYSIS OF THE DYNAMIC BEHAVIOR OF A GRIFFITH PERMEABLE CRACK IN PIEZOELECTRIC MATERIALS WITH THE NON-LOCAL THEORY

The dynamic behavior of a Griffith permeable crack under harmonic anti-plane shear waves in the piezoelectric materials is investigated by use of the non-local theory. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near the crack tips. By means of Fourier transform, the problem can be solved with a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. These equations are solved with the Schmidt method and numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularities are present at the crack tip. The finite hoop stress and the electric displacement depend on the crack length, the lattice parameter of the materials and the circle frequency of the incident waves. This enables us to employ the maximum stress hypothesis to deal with fracture problems in a natural way.

INVESTIGATION OF THE SCATTERING OF ANTI-PLANE SHEAR WAVES BY TWO GRIFFITH CRACKS USING THE NON-LOCAL THEORY

In this paper, the scattering of harmonic antiplane shear waves bytwo finite cracks is studied using the non-local theory. The Fouriertransform is applied and a mixed boundary value prob- lem isformulated. Then a set of triple integral equations is solved using anew method, namely Schimidt's method. This method is more exact andmore reasonable than Erigen's for solving this Kind of problem. Theresult of the stress near the crack tip was obtained. Contrary to theclassical elas- Ticity solution, it is found that no stresssingularity is present at the crack tip, which can explain theProblem of macroscopic and microscopic mechanics.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen's for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

INVESTIGATION OF A GRIFFITH CRACK SUBJECT TO UNIFORM TENSION USING THE NON-LOCAL THEORY BY A NEW METHOD

Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual-integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's a one Sor solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present ar the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.

THE SCATTERING OF HARMONIC ELASTIC ANTI-PLANE SHEAR WAVES BY A FINITE CRACK IN INFINITELY LONG STRIP USING THE NON-LOCAL THEORY

In this paper, the scattering of harmonic anti-plane shear wavesby a finite crack in infinitely long strip is studied using thenon-local theory. The Fourier transform is applied and a mixedboundary value problem is formulated. Then a set of dual integralequations is solved using the Schmidt method instead of the first orthe second integral equation method. A one-dimensional non-localkernel is used instead of a two-di- mensional one for the anti-planedynamic problem to obtain the stress occurring at the crack tips.Contrary to the classical elasticity solution, it is found that nostress singularity is present at the crack tip. The non-local dynamicelastic solutions yield a finite hoop stress at the crack tip, thusallowing for a fracture criterion based on the maximum dynamic stresshypothesis. The finite hoop stress at the crack tip depends on thecrack length, the width of the strip and the lattice parameters.

GURTIN-TYPE VARIATIONAL PRINCIPLES FOR DYNAMICS OF A NON-LOCAL THERMAL EQUILIBRIUM SATURATED POROUS MEDIUM

Based on the porous media theory and by taking into account the efects of the pore fuid viscidity, energy exchanges due to the additional thermal conduction and convection between solid and fuid phases, a mathematical model for the dynamic-thermo-hydro-mechanical coupling of a non-local thermal equilibrium fuid-saturated porous medium, in which the two constituents are assumed to be incompressible and immiscible, is established under the assumption of small de- formation of the solid phase, small velocity of the fuid phase and small temperature changes of the two constituents. The mathematical model of a local thermal equilibrium fuid-saturated porous medium can be obtained directly from the above one. Several Gurtin-type variational principles, especially Hu-Washizu type variational principles, for the initial boundary value problems of dy- namic and quasi-static responses are presented. It should be pointed out that these variational principles can be degenerated easily into the case of isothermal incompressible fuid-saturated elastic porous media, which have been discussed previously.

Solutions for a class of Hamiltonian systems on time scales with non-local boundary conditions

In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems.Compared with the known results,this work establishes the variational structure in an appropriate Sobolev’s space.Then,by applying the mountain pass theorem and symmetric mountain pass theorem,the existence and multiplicity of the solutions are obtained.Finally,some examples with numerical simulation results are given to illustrate the correctness of the results obtained.

The “Non-Locality” of Entangled States Is Seeming Phenomenon

EPR raised fundamental problems of non-locality (NL) in the case of entangled states (ES) 82 years ago. These problems were not solved until now. EPR and their followers used and would continue to use calculation methods that were available at that time. However, we can easily explain this observable NL as a trivial result of conservation laws (CL) within modern quantum mechanics (MQM). But application of CL requires materialistic descriptions of reality in a micro world in contrast to so-called quantum measurement theory (QMT), which was created mainly in the times of EPR and is widely accepted until now. We have to use a materialistic description, just as many physicists who actually work with high precision do by default. In this article, practical examples are given for real, precise measurements of wave functions of molecules and crystals, which, of course, were not known to EPR and were not noticed by their followers. We should acknowledge that QMT is merely an unneeded complication of simple relations of MQM. NL is the seeming result of these complications.

NEW STRAIN GRADIENT THEORY AND ANALYSIS

A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.

Non-local theory solution to two collinear limited-permeable mode-I cracks in a piezoelectric/piezomagnetic material plane

The non-local theory solution to two collinear limited-permeable mode-1 cracks in a piezoelectric/piezomagnetic medium was investigated by using the generalized Almansi＇s theorem and the Schmidt method in the present paper. The problem was for- mulated through Fourier transformation into two pairs of dual integral equations, in which the unknown variables are the dis- placement jumps across the crack surfaces. For solving the dual integral equations, the displacement jumps across the crack surfaces were directly expanded as a series of Jacobi polynomials. Numerical examples were provided to show the effects of the crack length, the distance between the two collinear cracks, the lattice parameter, the electric permittivity and the magnetic permeability of the air inside the crack on the stress fields, the electric displacement fields and the magnetic flux fields near the crack tips in a piezoeleetric/piezomaguetic medium. Different from the classical solutions, the present solution exhibits no stress, electric displacement and magnetic flux singularities at the crack tips in a piezoelectric/piezomagnetic medium.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

Reflection of thermo-elastic wave in semiconductor nanostructures nonlocal porous medium

The current work is an extension of the nonlocal elasticity theory to fractional order thermo-elasticity in semiconducting nanostructure medium with voids.The analysis is made on the reflection phenomena in context of three-phase-lag thermo-elastic model.It is observed that,four-coupled longitudinal waves and an independent shear vertical wave exist in the medium which is dispersive in nature.It is seen that longitudinal waves are damped,and shear wave is un-damped when angular frequency is less than the cut-off frequency.The voids,thermal and non-local parameter affect the dilatational waves whereas shear wave is only depending upon non-local parameter.It is found that reflection coefficients are affected by nonlocal and fractional order parameters.Reflection coefficients are calculated analytically and computed numerically for a material,silicon and discussed graphically in details.The results for local(classical)theory are obtained as a special case.The study may be useful in semiconductor nanostructure,geology and seismology in addition to semiconductor nanostructure devices.

An improved theoretical procedure for the pore-size analysis of activated carbon by gas adsorption

Amorphous carbon materials play a vital role in adsorbed natural gas(ANG) storage. One of the key issues in the more prevalent use of ANG is the limited adsorption capacity, which is primarily determined by the porosity and surface characteristics of porous materials. To identify suitable adsorbents, we need a reliable computational tool for pore characterization and, subsequently, quantitative prediction of the adsorption behavior. Within the framework of adsorption integral equation(AIE), the pore-size distribution(PSD) is sensitive to the adopted theoretical models and numerical algorithms through isotherm fitting. In recent years, the classical density functional theory(DFT) has emerged as a common choice to describe adsorption isotherms for AIE kernel construction. However,rarely considered is the accuracy of the mean-field approximation(MFA) commonly used in commercial software. In this work, we calibrate four versions of DFT methods with grand canonical Monte Carlo(GCMC) molecular simulation for the adsorption of CH_4 and CO_2 gas in slit pores at 298 K with the pore width varying from 0.65 to 5.00 nm and pressure from 0.2 to 2.0 MPa. It is found that a weighted-density approximation proposed by Yu(WDA-Yu) is more accurate than MFA and other non-local DFT methods. In combination with the trapezoid discretization of AIE, the WDA-Yu method provides a faithful representation of experimental data, with the accuracy and stability improved by 90.0% and 91.2%, respectively, in comparison with the corresponding results from MFA for fitting CO_2 isotherms. In particular, those distributions in the feature pore width range(FPWR)are proved more representative for the pore-size analysis. The new theoretical procedure for pore characterization has also been tested with the methane adsorption capacity in seven activated carbon samples.

Post-Newtonian parameter γ in generalized non-local gravity

We investigate the post-Newtonian parameter 7 and derive its formalism in generalized non-local （GNL） gravity, which is the modified theory of general relativity （GR） obtained by adding a term m2n-2 R -nR to the Einstein-Hilbert action. Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields ~i in addition to the metric tensor g μ v, the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters 9,, we can compare our expressions and results with those in Hohmann and Jarv et al. （2016）, as well as current observational constraints on the values of γ in Will （2006）. Hence, we draw restrictions on the nonminimal coupling terms F- around their background values.

Effect of Matter Distribution on Relativistic Time Dilation

Context: Derivations for the relativity formulations for the Lorentz are conventionally based on continuum mechanics. Purpose: This paper derives the formulations from a particle perspective. Approach: A non-local hidden-variable (NLHV) approach is adopted, based on the specific particle structures of the Cordus Theory. Findings: The Lorentz and relativistic Doppler formulations are shown to be derivable from a NLHV particle perspective. Unexpectedly, the equations contain an additional term relating to the difference in the distribution of matter (fabric density) between situations. For a homogenous fabric, which is the assumption of general relativity, the conventional formulations are recovered. Originality: The novel contribution is deriving the relativistic formulation from a NLHV theory. Also novel is the identification of the fabric density as a term in the Lorentz. Implications: It is predicted that inertial frames of reference are only situationally equivalent in the special case where they also have the same fabric density. We find against the cosmological principle with its assumption of homogeneity. The resulting situational theory of relativity has further implications for interpreting gravitational interactions at the galactic scale and larger.

A Physical Explanation for Particle Spin

CONTEXT The spin of a particle is physically manifest in multiple phenomena. For quantum mechanics (QM), spin is an intrinsic property of a point particle, but an ontological explanation is lacking. In this paper we propose a physical explanation for spin at the sub-particle level, using a non-local hidden-variable (NLHV) theory. APPROACH Mechanisms for spin were inferred from the Cordus NLHV theory, specifically from theorised structures at the sub-particle level. RESULTS Physical geometry of the particle can explain spin phenomena: polarisation, Pauli exclusion principle (Einstein-Podolsky-Rosen paradox), excited states, and selective spin of neutrino species. A quantitative derivation is provided for electron spin g-factor g = 2, and a qualitative explanation for the anomalous component. IMPLICATIONS NLHV theory offers a candidate route to new physics at the sub-particle level. This also implies philosophically that physical realism may apply to physics at the deeper level below QM. ORIGINALITY The electron g-factor has been derived using sub-particle structures in NLHV theory, without using quantum theory. This is significant as the g-factor is otherwise considered uniquely predicted by QM. Explanations are provided for spin phenomena in terms of physical sub-structures to the particle.

Asymmetrical Genesis by Remanufacture of Antielectrons

Problem: The asymmetrical genesis problem concerns why the universe should have an abundance of matter over antimatter. Purpose: This paper shows how the baryogenesis and leptogenesis asymmetries may both be resolved. Approach: Design methods were used to develop a conceptual mechanics for the remanufacturing processes that transform particles in the decay processes. This was based on the structures for the photon, electron, antielectron, proton and antineutrino as previously identified as logical necessities for the beta decay process, and represented as a non-local hidden-variable design with discrete fields. Findings: The solution is given in terms of a mechanics that defines the transformation of discrete field structures in particles. The genesis problem is shown to be solvable. The mechanics describes pair production of an electron and antielectron from two initial photons, and subsequent remanufacture of the antielectron into a proton. It is predicted that two antineutrinos would be emitted, which are testable and falsifiable. The theory identifies that the role of the antineutrinos is to remove the antimatter handed field structures. The original electron and proton may bond to form a simple hydrogen atom, or combine via electron capture to form a neutron and hence heavier nuclides. The subsequent preponderance of the matter pathways in the genesis production sequence is also addressed and is explained as domain warfare between the matter and antimatter species. Originality: The concept of remanufacture of antielectrons into protons, with emission of antineutrinos, is novel. Extensions of the theory explain the nuclides. Consequently the theory explains from pair production up to nuclear structure, which is also original.

Unification Might Be Achievable by a Hypothesis of Instantaneous Time-Jumps during Photon and Graviton Interactions (A Brief Note)

Quantum theory according to the Copenhagen interpretation holds that, when a quantum interaction is observed (i.e., “measured”), the observer’s measuring devices temporarily become a part of the quantum system. Relativity theory holds that the event clock of the absorbed or emitted photon or graviton is frozen in time relative to all clocks outside the observed system. If we harmonize both theories, this would appear to imply that time continuity must be interrupted at each instant of observed photon or graviton interaction with matter. It is as if a segment of space-time is clipped out during each such observed interaction. If so, we must dispense with the notion of an absolutely smooth and continuous space-time and replace it with an observation-dependent, discontinuous, relativistic/quantum space-time. Mathematical physicists should be able to model this hypothesis (call it a “time-jump hypothesis”) and its inherent discontinuous space-time in their further efforts at unification.