Energy Stable Nodal DG Methods for Maxwell’s Equations of Mixed-Order Form in Nonlinear Optical Media

In this work,we develop energy stable numerical methods to simulate electromagnetic waves propagating in optical media where the media responses include the linear Lorentz dispersion,the instantaneous nonlinear cubic Kerr response,and the nonlinear delayed Raman molecular vibrational response.Unlike the first-order PDE-ODE governing equations considered previously in Bokil et al.(J Comput Phys 350:420–452,2017)and Lyu et al.(J Sci Comput 89:1–42,2021),a model of mixed-order form is adopted here that consists of the first-order PDE part for Maxwell’s equations coupled with the second-order ODE part(i.e.,the auxiliary differential equations)modeling the linear and nonlinear dispersion in the material.The main contribution is a new numerical strategy to treat the Kerr and Raman nonlinearities to achieve provable energy stability property within a second-order temporal discretization.A nodal discontinuous Galerkin(DG)method is further applied in space for efficiently handling nonlinear terms at the algebraic level,while preserving the energy stability and achieving high-order accuracy.Indeed with d_(E)as the number of the components of the electric field,only a d_(E)×d_(E)nonlinear algebraic system needs to be solved at each interpolation node,and more importantly,all these small nonlinear systems are completely decoupled over one time step,rendering very high parallel efficiency.We evaluate the proposed schemes by comparing them with the methods in Bokil et al.(2017)and Lyu et al.(2021)(implemented in nodal form)regarding the accuracy,computational efficiency,and energy stability,by a parallel scalability study,and also through the simulations of the soliton-like wave propagation in one dimension,as well as the spatial-soliton propagation and two-beam interactions modeled by the two-dimensional transverse electric(TE)mode of the equations.

High-Order Spatial FDTD Solver of Maxwell’s Equations for Terahertz Radiation Production

We applied a spatial high-order finite-difference-time-domain (HO-FDTD) scheme to solve 2D Maxwell’s equations in order to develop a fluid model employed to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma. We examined the performance of the applied scheme, in this context, we implemented the developed model to study selected phenomena in terahertz radiation production, such as the excitation energy and conversion efficiency of the produced THz radiation, in addition to the influence of the pulse chirping on properties of the produced radiation. The obtained numerical results have clarified that the applied HO-FDTD scheme is precisely accurate to solve Maxwell’s equations and sufficiently valid to study the production of terahertz radiation by the filamentation of two femtosecond lasers in air plasma.

Physical interpretation of Planck's constant based on the Maxwell theory

The discovery of the Planck relation is generally regarded as the starting point of quantum physics.Planck＇s constant h is now regarded as one of the most important universal constants.The physical nature of h,however,has not been well understood.It was originally suggested as a fitting constant to explain the black-body radiation.Although Planck had proposed a theoretical justification of h,he was never satisfied with that.To solve this outstanding problem,we use the Maxwell theory to directly calculate the energy and momentum of a radiation wave packet.We find that the energy of the wave packet is indeed proportional to its oscillation frequency.This allows us to derive the value of Planck＇s constant.Furthermore,we show that the emission and transmission of a photon follows the all-or-none principle.The ＂strength＂ of the wave packet can be characterized by ζ,which represents the integrated strength of the vector potential along a transverse axis.We reason that ζ should have a fixed cut-off value for all photons.Our results suggest that a wave packet can behave like a particle.This offers a simple explanation to the recent satellite observations that the cosmic microwave background follows closely the black-body radiation as predicted by Planck＇s law.

Von Kármán rotating flow of Maxwell nanofluids featuring the Cattaneo-Christov theory with a Buongiorno model

This research paper analyzes the transport of thermal and solutal energy in the Maxwell nanofluid flow induced above the disk which is rotating with a constant angular velocity.The significant features of thermal and solutal relaxation times of fluids are studied with a Cattaneo-Christov double diffusion theory rather than the classical Fourier’s and Fick’s laws.A novel idea of a Buongiorno nanofluid model together with the Cattaneo-Christov theory is introduced for the first time for the Maxwell fluid flow over a rotating disk.Additionally,the thermal and solutal distributions are controlled with the impacts of heat source and chemical reaction.The classical von Karman similarities are used to acquire the non-linear system of ordinary differential equations(ODEs).The analytical series solution to the governing ODEs is obtained with the well-known homotopy analysis method(HAM).The validation of results is provided with the published results by the comparison tables.The graphically presented outcomes for the physical problem reveal that the higher values of the stretching strength parameter enhance the radial velocity and decline the circumferential velocity.The increasing trend is noted for the axial velocity profile in the downward direction with the higher values of the stretching strength parameter.The higher values of the relaxation time parameters in the Cattaneo-Christov theory decrease the thermal and solutal energy transport in the flow of Maxwell nanoliquids.The higher rate of the heat transport is observed in the case of a larger thermophoretic force.

Transient flow of magnetized Maxwell nanofluid: Buongiorno model perspective of Cattaneo-Christov theory

The present research article is devoted to studying the characteristics of Cattaneo-Christov heat and mass fluxes in the Maxwell nanofluid flow caused by a stretching sheet with the magnetic field properties.The Maxwell nanofluid is investigated with the impact of the Lorentz force to examine the consequence of a magnetic field on the flow characteristics and the transport of energy.The heat and mass transport mechanisms in the current physical model are analyzed with the modified versions of Fourier’s and Fick’s laws,respectively.Additionally,the well-known Buongiorno model for the nanofluids is first introduced together with the Cattaneo-Christov heat and mass fluxes during the transient motion of the Maxwell fluid.The governing partial differential equations(PDEs)for the flow and energy transport phenomena are obtained by using the Maxwell model and the Cattaneo-Christov theory in addition to the laws of conservation.Appropriate transformations are used to convert the PDEs into a system of nonlinear ordinary differential equations(ODEs).The homotopic solution methodology is applied to the nonlinear differential system for an analytic solution.The results for the time relaxation parameter in the flow,thermal energy,and mass transport equations are discussed graphically.It is noted that higher values of the thermal and solutal relaxation time parameters in the Cattaneo-Christov heat and mass fluxes decline the thermal and concentration fields of the nanofluid.Further,larger values of the thermophoretic force enhance the heat and mass transport in the nanoliquid.Moreover,the Brownian motion of the nanoparticles declines the concentration field and increases the temperature field.The validation of the results is assured with the help of numerical tabular data for the surface velocity gradient.

Derivation of Maxwell’s Equations via the Covariance Requirements of the Special Theory of Relativity, Starting with Newton’s Laws

The purpose of this paper is to establish a connection between Maxwell’s equations, Newton’s laws, and the special theory of relativity. This is done with a derivation that begins with Newton’s verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and Maxwell’s equations for free space emerge with the assumption that the tensor and its dual must both satisfy first-order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton’s third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that both can be assigned the same units. Requiring covariance under either spatial inversions or time reversals precludes magnetic charge being a source of electromagnetic fields that exert forces on electric charges.

Inverse scattering method and soliton solution family for the Einstein-Maxwell theory with multiple Abelian gauge fields

A Hauser-Ernst-type extended hyperbolic complex linear system given in our previous paper [Gao Y J 2004 Chin. Phys. 13 602] is slightly modified and used to develop a new inverse scattering method for the stationary axisymmetric Einstein-Maxwell theory with multiple Abelian gauge fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the inverse scattering method be fine and effective in practical application. As an example, a concrete family of soliton solutions for the considered theory is obtained.

Maxwell-Stefan理论模拟NaA沸石膜分离一氯甲烷中微量水的渗透特性

通过热浸渍晶种法制备了高质量的NaA沸石膜,并将其应用于蒸汽渗透脱除一氯甲烷中的微量水.实验结果表明,NaA膜对该体系显示了优异的分离性能,水对一氯甲烷的分离系数高达74831,产品中的水含量从0.2582%(ω)降低到0.005%(ω).将基于Maxwell-Stenfan理论和Langmuir理想吸附理论推导的吸附-扩散模型用于模拟水渗透流速与渗透侧真空度和进料温度的关系,预测趋势与实验值吻合很好,且拟合得到的参数与文献报道较接近,表明水蒸汽在NaA沸石膜中的传递为表面扩散机制,水蒸汽的吸附对渗透速率的贡献很大.水蒸汽的吸附热为-34.15kJ/mol.

Cattaneo-Christov heat and mass flux model for 3D hydrodynamic flow of chemically reactive Maxwell liquid

This research focuses on the Cattaneo-Christov theory of heat and mass flux for a three-dimensional Maxwell liquid towards a moving surface. An incompressible laminar flow with variable thermal conductivity is considered. The flow generation is due to the bidirectional stretching of sheet. The combined phenomenon of heat and mass transport is accounted. The Cattaneo-Christov model of heat and mass diffusion is used to develop the expressions of energy and mass species. The first-order chemical reaction term in the mass species equation is considered. The boundary layer assumptions lead to the governing mathematical model. The homotopic simulation is adopted to visualize the results of the dimensionless flow equations. The graphs of velocities, temperature, and concentration show the effects of different arising parameters. A numerical benchmark is presented to visualize the convergent values of the computed results. The results show that the concentration and temperature fields are decayed for the Cattaneo^Christov theory of heat and mass diffusion.

Adaptive Maxwell’s Equations Derived Optimization and Its Application in Antenna Array Synthesis

In this paper,a self-adaptive method for the Maxwell’s Equations Derived Optimization(MEDO)is proposed.It is implemented by applying the Sequential Model-Based Optimization(SMBO)algorithm to the iterations of the MEDO,and achieves the automatic adjustment of the parameters.The proposed method is named as adaptive Maxwell’s equations derived optimization(AMEDO).In order to evaluate the performance of AMEDO,eight benchmarks are used and the results are compared with the original MEDO method.The results show that AMEDO can greatly reduce the workload of manual adjustment of parameters,and at the same time can keep the accuracy and stability.Moreover,the convergence of the optimization can be accelerated due to the dynamical adjustment of the parameters.In the end,the proposed AMEDO is applied to the side lobe level suppression and array failure correction of a linear antenna array,and shows great potential in antenna array synthesis.

ANALYSIS OF FDTD TO UPML FOR MAXWELL EQUATIONS IN POLAR COORDINATES

An FDTD system associated with uniaxial perfectly matched layer（UPML） for an electromagnetic scattering problem in two-dimensional space in polar coordinates is considered.Particularly the FDTD system of an initial-boundary value problems of the transverse magnetic（TM） mode to Maxwell＇s equations is obtained by Yee＇s algorithm,and the open domain of the scattering problem is truncated by a circle with a UPML.Besides,an artificial boundary condition is imposed on the outer boundary of the UPML.Afterwards,stability of the FDTD system on the truncated domain is established through energy estimates by the Gronwall inequality.Numerical experiments are designed to approve the theoretical analysis.

Relating Maxwell's demon and quantitative analysis of information leakage for practical imperative programs

Shannon observed the relation between information entropy and Maxwell demon experiment to come up with information entropy formula. After that, Shannon＇s entropy formula is widely used to measure information leakage in imperative programs. But in the present work, our aim is to go in a reverse direction and try to find possible Maxwell＇s demon experimental setup for contemporary practical imperative programs in which variations of Shannon＇s entropy formula has been applied to measure the information leakage. To establish the relation between the second principle of thermodynamics and quantitative analysis of information leakage, present work models contemporary variations of imperative programs in terms of Maxwell＇s demon experimental setup. In the present work five contemporary variations of imperative program related to information quantification are identified. They are： （i） information leakage in imperative program, （ii） imperative multi- threaded program, （iii） point to point leakage in the imperative program, （iv） imperative program with infinite observation, and （v） imperative program in the SOA-based environment. For these variations, minimal work required by an attacker to gain the secret is also calculated using historical Maxwell＇s demon experiment. To model the experimental setup of Maxwell＇s demon, non-interference security policy is used. In the present work, imperative programs with one-bit secret information have been considered to avoid the complexity. The findings of the present work from the history of physics can be utilized in many areas related to information flow of physical computing, nano-computing, quantum computing, biological computing, energy dissipation in computing, and computing power analysis.

Supplemental Materials: Realization of Quantum Maxwell's Demon with Solid-State Spins

We report experimental realization of a quantum version of Maxwell＇s demon using solid state spins where the information acquiring and feedback operations by the demon are achieved through conditional quantum gates.A unique feature of this implementation is that the demon can start in a quantum superposition state or in an entangled state with an ancilla observer. Through quantum state tomography, we measure the entropy in the system, demon, and the ancilla, showing the influence of coherence and entanglement on the result. A quantum implementation of Maxwell＇s demon adds more controllability to this paradoxical thermal machine and may find applications in quantum thermodynamics involving microscopic systems.

New Reflection Principles for Maxwell's Equations and Their Applications

Some new reflection principles for Maxwell's equations are first established, which are then applied to derive two novel identifiability results in inverse electromagnetic obstacle scattering problems with polyhedral scatterers.

A New Formulation of Maxwell’s Equations in Clifford Algebra

A new unification of the Maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.

Analysis of Maxwell’s Equations. Cosmic Magnetism

According to Hypersphere World-Universe Model, dark matter particles DIRACs are magnetic dipoles consisting of two Dirac’s monopoles. We conclude that DIRACs are the subject of Maxwell’s equations. So-called “auxiliary” magnetic field intensity H is indeed current density of magnetic dipoles. The developed approach to magnetic field can explain a wealth of discovered phenomena in Cosmic Magnetism: a dark magnetic field, the large-scale structure of the Milky Way’s magnetic field, and other magnetic phenomena which are only partly related to objects visible in other spectral ranges.

Solving the Olbers’s Paradox, Explaining the “Red-Shift”, and Challenging the Relativities by “Sun Matters Theory” and “Sun Model of Universe”, an Evolution of the Einstein’s Static Universe Model

Olbers’s paradox, known as the dark night paradox, is an argument in astrophysics that the darkness of the night sky conflicts with the assumption of an infinite and eternal static universe. Big-Bang theory was used to partially explain this paradox, while introducing new problems. Hereby, we propose a better theory, named Sun Matters Theory, to explain this paradox. Moreover, this unique theory supports and extended the Einstein’s static universe model proposed by Albert Einstein in 1917. Further, we proposed our new universe model, “Sun Model of Universe”. Based on the new model and novel theory, we generated innovative field equation by upgrading Einstein’s Field Equation through adding back the cosmological constant, introducing a new variable and modifying the gravitationally-related concepts. According to the Sun Model of Universe, the dark matter and dark energy comprise the so-called “Sun Matters”. The observed phenomenon like the red shift is explained as due to the interaction of ordinary light with Sun Matters leading to its energy and frequency decrease. In Sun Model, our big universe consists of many universes with ordinary matter at the core mixed and surrounded with the Sun Matters. In those universes, the laws of physics may be completely or partially different from that of our ordinary universe with parallel civilizations. The darkness of night can be easily explained as resulting from the interaction of light with the Sun Matters leading to the sharp decrease in the light intensity. Sun Matters also scatter the light from a star, which makes it shining as observed by Hubble. Further, there is a kind of Sun Matters named “Sun Waters”, surrounding every starts. When lights pass by the sun, the Sun Waters deflect the lights to bend the light path. According to the Sun Model, it is the light bent not the space bent that was proposed in the theory of relativities.

The “Dead Universe” Theory: Natural Separation of Galaxies Driven by the Remnants of a Supermassive Dead Universe

This article explores the dead universe theory as a novel interpretation for the origin and evolution of the universe, suggesting that our cosmos may have originated from the remnants of a preceding universe. This perspective challenges the conventional Big Bang theory, particularly concerning dark matter, the expansion of the universe, and the interpretation of phenomena such as gravitational waves.

On Some Mathematical Connections between the Cyclic Universe, Inflationary Universe, p-Adic Inflation, p-Adic Cosmology and Various Sectors of Number Theory

This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.

The Role of Teachers’Apperception in Herbart’s Theory for Chinese Teaching in Shenzhen Primary Schools of China

This paper deeply analyzes the practical application of Herbart’s educational concept in contemporary education and teaching,especially its guiding significance to the primary school Chinese classroom in Shenzhen area.Herbart proposed that teachers should play a key role in students’cognitive process,that is,help students better understand and master new knowledge by combining it with existing knowledge.The survey results show that although teachers have some understanding of Herbart’s educational philosophy,it is not widely used in the concrete teaching process.However,the study also shows that there is a positive relationship between Herbart’s theory and students’academic performance,indicating that it plays an important role in improving students’interest and engagement in learning.The research also reveals the differences between educational concepts and practices,as well as the uneven distribution of educational resources,and puts forward measures to alleviate these contradictions,such as strengthening teacher training,improving teaching methods,and emphasizing moral education.At the same time,the study also highlights the critical role of teachers in promoting knowledge integration,arousing learning enthusiasm,shaping students’moral character,and promoting personal and professional growth.