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In the absence of random mode mixing (RMM), linearization of the cross-mode modulation (XMM) under pump-probe configuration is in general complicated because the evolution of the pump light depends on the local mode decomposition of itself. In this work, general derivation of the Hamiltonian of the XMM system without RMM is carried out and discussed under two interesting scenarios where the pump evolution can be effectively linearized, leading to spatial dependent Hamiltonian of the probe light. Representative evolutions of pump and probe light over transmission are investigated with the assistance of Poincaré sphere based on the Hamiltonian approach. Our results are benchmarked against the results given by precession equations examined by Lin and Agrawal and numerical simulations using nonlinear coupled mode equations (CMEs). By highlighting the eigenstates as well as eigenvalues of the system, our approach provides an intuitive yet powerful approach to understand the XMM nonlinear problems and to dynamically manipulate the spatial profiles of the probe light.

This paper presents the first general framework to explain the magnetic force as a result of electric force interactions between current charges moving at any constant speed and combination. The explanation depends on analyzing the spreading electric field in the space and the movement of charges inside current elements. Previous work used special relativity to describe the magnetic force as an electric one, but this description contradicts the fact that electrically neutral wires stay neutral with or without current flowing through them, as well as, it does not facilitate the derivation of the infinitesimal laws of magnetism. In this paper, the provided explanation is proved by deriving the infinitesimal magnetic force law and Biot-Savart law using the basis of electric forces. This work lies at the intersection between Electrical Engineering and Physics, and it is important to understand what is magnetism and its origin. Such understanding may help engineers and scientists in making new advancements in magnetic materials and applied magnetic technologies.

Structured light such as beams carrying angular momentum attracted a flurry of interest in optics in recent years. In this work we present relevant results regarding the study of the so-called vector vortex beams, their propagation, manipulation, detection and their applications for several tasks in classical and quantum optics.

Line waves are recently discovered wave objects that are localized along two dimensions (i.e., in-plane and out-of-plane), thereby channeling the energy flow along a 1-D track, and can be supported by suitable planar discontinuities of the surface impedance in artificial (“metasurfaces”) and natural (e.g., graphene) low-dimensional materials. In a series of recent studies, we have explored non-Hermitian platforms supporting these exotic modes based on parity-time symmetry. Specifically, we have studied (analytically and numerically) the line-wave propagation in the presence of a uniform surface reactance (either capacitive or inductive) and a resistance discontinuity featuring a transition between gain and loss, illustrating the underlying physical mechanisms and their intriguing properties, and also addressing possible practical implementations based on photoexcited graphene. Here, we provide a compact overview of the salient results.

Acoustic and elastic metamaterials with space- and time-dependent material properties have received great attention recently as a means to realize systems that are not linear-time-invariant, usually with the goal to induce nonreciprocal wave propagation. However, for finite systems the set of modulation parameters that yield a strong mode-coupling response is not well characterized. In this work, we derive the Green’s function for finite elastic beams with spatiotemporally-modulated material properties. We show for the particular case of flexural wave modes in a thin finite beam that spatiotemporal modulation of the Young’s modulus can lead to the splitting and shifting of the resonances of the system.

We present a computational accommodation-invariant near-eye display, which relies on imaging with coherent light and utilizes static optics together with convolutional neural network-based preprocessing. The network and the display optics are co-optimized to obtain a depth-invariant display point spread function, and thus relieve the conflict between accommodation and ocular vergence cues that typically exists in conventional near-eye displays. We demonstrate through simulations that the computational near-eye display designed based on the proposed approach can deliver sharp images within a depth range of 3 diopters for an effective aperture (eyepiece) size of 10 mm. Thus, it provides a competitive alternative to the existing accommodation-invariant displays. acceptedVersion

This paper discusses the possible approaches to modeling the cognitive activity of the human brain using the mathematical apparatus of quantum field theory (primarily – potential wells) in terms of the theory of information representations. The article briefly describes the proposed theory of information representations, draws analogies, and identifies common features of information representations of the human mind and Feynman's virtual particles. The human mind is represented as a one-dimensional potential well with finite walls of different sizes and internal potential barrier simulating the boundary between consciousness and subconsciousness. This creates a foundation for a mathematical apparatus that can make it possible to forecast particular cognitive functions of the human brain.

In this work we present a general analysis of the extraordinary properties of surface Love waves and the unexpected wave phenomena that can occur in the Love wave waveguides. A brief history of the Love waves and their applications to Love wave sensors is given. The results of the author's recent research on Love wave sensors are presented. The analytical formula for the mass sensitivity of the Love wave sensor is shown. Extraordinary properties that reveal Love waves propagating in lossy media are introduced. Counterintuitive phenomena in Love wave waveguides such as: a) minimum of phase velocity as a function of liquid viscosity and b) maximum of attenuation as a function of liquid viscosity are reported. Moreover, the application of new mathematical tools in the analysis of Love wave sensors such as: Inverse Methods is discussed. New possible directions for research on Love wave sensors have been indicated.

As it is well-known, diabetic patients might to develop crisis in the renal apparatus either in the middle or long time [1]. This crisis is imminently attained to the high concentrations of glucose. In fact, under the theoretical assumption that the ions of glucose molecules push out giant molecules of albumin then one might to expect a direct dependence among them from classical electrodynamics basis. In this paper, this dependence and the physics-based relationships are derived. The theoretical result of this paper would be of interest in all those new applications of advanced sensors that might be able to measure status of both glucose and albuminuria. Thus, one can carry out a complete diagnostic of kidney status from glucose values. The paper presents theoretical predictions of glucose and albumin interactions while both of them are located along the renal glumerulus.

Nonlocal and non-Hermitian effects are becoming increasingly relevant in the modeling and engineering of metama-terials. Here, we review some strategies for extending the transformation-optics framework so as to enable the analysis and synthesis of these effects, while retaining the powerful and insight-providing geometrical interpretation that characterizes the conventional formulation.

The planar interface of two dissimilar partnering mediums, at least one of which is anisotropic, can guide an exceptional surface wave that propagates in an isolated direction. In order for this to be achieved, the constitutive parameters of the partnering mediums must satisfy certain constraints. Exceptional surface waves have localization characteristics that distinguish them from unexceptional surface waves: the decay of fields of an exceptional surface wave in an anisotropic partnering medium exhibits a combined linear-exponential dependency on distance from the interface, whereas the decay is purely exponential for an unexceptional surface wave. The notion of exceptional surface waves can be extended to compound waves that are guided by a pair of parallel planar interfaces.

We present a description of the spatial evolution of quantized discrete-mode operators along a lossy nonlinear transmission line. The nonlinearity is formed by hundereds or even thousands of Josephson junctions which are placed periodically along a microwave transmission line. Dissipation is added to the system Hamiltonian by coupling the nonlinear transmission line to an Ohmic bath. Using the Hamiltonian of the open quantum system, Heisenberg equations of motion for the discrete mode operators can be derived in terms of quantum Langevin equations. The temporal equations of motion are then translated to the spatial domain to investigate the performance of a nonlinear four-wave-mixing process, while signals propagate along the transmission line.

• Understand biomolecular systems through their motions •Numerical integration of Newton's laws of motion — Model atoms as point masses — Compute forces on every atom based on current positions — Update atom velocities and positions in discrete time steps of a few femtoseconds • Force computation described by a model: the force field

Rotary theory is a new electromagnetic theory, which appeared in 1998. It tries to explain the basic electromagnetic phenomena from another point of view and to answer to series of important questions connected with the fundamental electromagnetic laws. In rotary theory the method of moments is used in order to expand the vector of the magnetic field intensity and the vector of the magnetic flux density. These vectors are presented as moments of the vector of the current density of the tangential displacement current claiming in this way that the magnetic field is a form of a rotating electric field. All that gives the opportunity to present the Maxwell’s set of electromagnetic equations in fully electrical form, which can be expressed in relativistic form, too. In this way rotary theory became a part of the special theory of relativity of Einstein. The present paper is devoted to the extraction of the formulas of the effective radius-vector and the current density of the tangential displacement current for some inductors with different shapes. The paper is dedicated also to the solution of the direct and the inverse tasks for determination of the components of the vector of the magnetic field intensity, the effective radius-vector and the current density of the tangential displacement current at arbitrary point around a given inductor.

We present a generalization of the Haus master equation in which a dynamical boundary condition allows to describe complex pulse trains such as the Q-switched and harmonic transitions of passive mode-locking as well as the weak interactions between localized states. As an example, we investigate the influence of group velocity dispersion on the stability boundaries of the Q-switched regime. We compare our results with that of a time-delayed system., Comment: 4 pages, 5 figures

The behavior of electromagnetic waves in chirally twisted structures is a topic of enduring interest, dating back at least to the invention in the 1940s of the microwave travelling wave tube amplifier and culminating in contemporary studies of chiral metamaterials, metasurfaces, and photonic crystal fibers (PCFs). Optical fibers with chiral microstructures, drawn from a spinning preform, have many useful properties, exhibiting for example circular birefringence and circular dichroism. It has recently been shown that chiral fibers with N fold rotationally symmetric (symmetry group CN) transverse microstructures support families of helical Bloch modes (HBMs), each of which consists of a superposition of azimuthal Bloch harmonics (or optical vortices). An example is a fiber with N coupled cores arranged in a ring around its central axis (N core single ring fiber). Although this type of fiber can be readily modelled using scalar coupled mode theory, a full description of its optical properties requires a vectorial analysis that takes account of the polarization state of the light particularly important in studies of circular and vortical birefringence. In this paper we develop, using an orthogonal two dimensional helicoidal coordinate system embedded in a cylindrical surface at constant radius, a rigorous vector coupled mode description of the fields using local Frenet Serret frames that rotate and twist with each of the N cores. The analysis places on a firm theoretical footing a previous HBM theory in which a heuristic approach was taken, based on physical intuition of the properties of Bloch waves. We believe this study provides clarity in what can sometimes be a rather difficult field, and will facilitate further exploration of real-world applications of these fascinating waveguiding systems., Comment: 20 pages, 10 figures

Hertz-Heaviside Field Equations (HHFE) which describe radiation by arbitrary volumetric bodies in arbitrary motion are reviewed. The special case of HHFE for moving electric and magnetic Hertzian dipoles in arbitrary motion are investigated in the sense of Schwartz-Sobolev distributions. In presence of moving non-volumetric radiators HHFE decouple into wave equations expressed by D’Alembert wave operator of stationary media enhanced by convection currents with Diracdelta behavior. The electric and magnetic radiation fields of these dipole sources are discussed and their Doppler analyses are carried out for certain modes of motion.

Electron quantum optics offers fascinating insights into the dynamic electron evolution processes governed by quantum effects, attractive for novel electronic processing or sensing devices. A key requirement for these developments is to coherently and electromagnetically confine and control the electron evolution process and the ability to correctly describe the manifesting quantum effects related to the wave nature of the electron, e.g., interference. This work provides an overview of research conducted on using specifically shaped electric and magnetic fields to influence the electron evolution in nanostructures. The Wigner based quantum transport modeling approach is used to simulate the transport and to highlight quantum effects.

Eshelby tensors serve as the basis of micromechanics. It is a key component to construct the inclusion problems of composite materials. To deal with ellipsoidal inclusions problems merged into the domain of an infinite one-dimensional (1D) piezoelectric quasicrystal matrix, Eshelby tensors are extended from elastic isotropic inclusions to the piezoelectric quasicrystal materials inclusion problems in this paper. By introducing eigenstrain and Green’s function, a concise and uncomplicated explicit expression of Eshelby tensors for 1D piezoelectric quasicrystal are obtained by adopting the Cauchy’s residue theorem. As under the case of coupled electric field, the results of 1D piezoelectric Eshelby tensors are the functions about the inclusion’s shapes and surrounding quasicrystal matrix properties. And then, these obtained tensors can be separated into three scales. The first category includes the tensors owed to the elastic response, the second refers to those tensors attributed to the piezoelectric response, and the third category consists of the interactive terms of the elastic and electric field. Furthermore, the electroelastic Eshelby tensors for 1D piezoelectric quasicrystal are obtained in closed-form when the inclusion’s shapes are spheroid-like, elliptic cylinder like, rod-shaped-like, penny shaped-like, and ribbon-like, respectively.

The paper deals with computer simulation of soliton phenomena in fiber-optic communication lines. A mathematical model of soliton spread in a defective media is represented, a reasonable choice of numerical methods is discussed. Numerical simulation results of soliton-defect interactions are represented.

Analysis of the interaction of the electromagnetic field and matter is a topical area of research in modern physics. The goal of this paper is to move from mathematical postulates and formalisms of quantum mechanics to equations that include macroscopic variables. In this case, the macroscopic observables are determined by the mean values of the operator corresponding to the observable value, and the mean value is deter-mined by the density matrix. Then the equations are written only through the mean values, by substituting equivalent expressions for the density matrix. As a result, we come to a system of equations expressed in terms of such macroscopic variables as polarization and electromagnetic field. In the semi-classical approach, when the electromagnetic field is not quantized, it is necessary to add the Maxwell's equations of the electromagnetic field to the equations for the mean values. This forms a self-consistent system of equations.

Bessel-Gauss beams (BGBs) have been widely investigated in optics in the paraxial approximation, under the frame of a scalar wave theory. Such approximations no longer hold in the microwave/millimeter-wave range, where the vectorial nature of electromagnetic fields cannot be neglected, and experimental realizations of BGBs are still lacking. In this work, we discuss the generation of BGBs through a fully vectorial electromagnetic approach. The field derivation and the numerical evaluation of a BGB are first illustrated. A possible scheme for realizing such solutions is outlined, thus paving the way for the first experimental realization of BGBs at microwave frequencies.

The paper will consider the Bilimovich system, which can be considered as one of the examples with nonholonomic non-stationary inhomogeneous relation. We consider the case when there is no energy integral. The behavior of the system is quite complex, and strange attractors appear. Poincare maps and dynamic mode maps are constructed and studied.

Mean motion resonance (i.e., MMR) is a common phenomenon in our solar system and some exoplanetary systems. MMR refers to that the orbital frequencies or periods of two (or more) celestial bodies, such as satellites, comets, planets, represent a commensurability. MMRs play an important role in maintaining the stability of solar system and exoplanetary systems. MMRs also significantly affect the orbital characteristics and distribution of planets and asteroids in these systems. This paper focus on a 6:5 internal three body MMRs model formed by two massive bodies (i.e., planet and star) and one test massless particle. In order to understand the dynamical effect of eccentricity, initial semimajor axis and initial phase of the massless particle, a detailed analysis of the phase space structure by compute the Poincare surfaces of section in the planar circular restricted three body model is presented. The eccentricity, initial semimajor axis, and initial phase are found to be three important parameters affecting the topological structure and steady state of the resonant orbits. The stable and chaotic regime of the resonant orbits is observed. Some typical resonant orbits are obtained.

We consider the obstacle avoidance problem of formation vehicles in an obstacle laden environment. Two control forces, formation keeping force and generalized Lorentz force, are proposed to adaptively maintain the formation pattern while avoiding obstacles. The methods result in a flexible overall obstacle avoidance effect for formation systems demonstrated by numerical simulations.

In the dynamics of sinusoidally coupled Fitzhugh Nagumo neural oscillators, when new stable, steady states are induced on limit cycles, and the symmetry is broken, it leads to Oscillator death. Also, during this process, the interacting oscillators pull each other such that both fail to be on limit cycles and hence meet Oscillator death. The present work investigates the effect of the interplay between initial conditions and coupling gain in causing Oscillator death. Two regimes have been identified to explain whether Oscillator death would occur or not. In the first regime, the initial conditions are such that there exists a finite coupling gain after the arrival of synchronization, where the Oscillator death takes place. While in the second regime, the initial conditions are such that any amount of increase in coupling gain fails to give Oscillator death. The Samle's effect, which is known as inverse of Oscillator death activity, has also been explored. It was found that the oscillations get revived in response to the reduction in coupling gain below a threshold.

An object's shape may be deformed by a combination of gravitational, hydrostatic, mechanical, and electromagnetic forces. Therefore, to predict the deformation, it is necessary to know each force's distribution inside the object. Various expressions and methods, such as the Lorentz, Kelvin, generalized, and Korteweg-Helmholtz forces, can be used to calculate the electromagnetic force on a dielectric or magnetic material. However, the distributions of the aforementioned forces inside materials may differ significantly. We adopt the concepts of infinitesimal particles and external electromagnetic fields to address this issue. Adopting these concepts enables the electromagnetic force densities inside dielectric or magnetic materials to be uniquely determined. We refer to this type of density as the locally defined electromagnetic force density (F LEM ). This study primarily focuses on the derivation of F (LEM )• Subsequently, the distribution of F LEM is then demonstrated using simple numerical models.

Among the orientation systems of artificial satellites, the systems based on the use of gravitational torques acting on its rotational motion around the center of mass are widely used. The stability analysis and the stationary rotational motion stabilization of a satellite, the mass center of which moves in a circular orbit as well as the dynamics of these motions remain the subject of a number of studies although they have a classical character. In this paper, the stationary rotational motion stabilization problem of a satellite with measuring only the angular coordinates (without measuring their velocities) is solved. In this case, in contrast to the classical results, the motion stabilization is achieved in all angles by means of a bounded controller.

The dynamics of charged particles inside a Paul trap is a superposition of a slow secular motion and a fast micro-motion. The conventional methods, such as harmonic balance, approximate the particle trajectory with harmonic terms of the same order contributing equally to the motion. However, a careful analysis will show that in the analytically approximate solution, the harmonic terms have an unequal amplitude contribution to the particle dynamics given a set of operating conditions. In this paper we apply the modified Lindstedt Poincare method to highlight these unequal contributions. The harmonic terms surely become a significant factor in affecting the dynamics and hence in various applications inside Paul traps.

We study collision of soliton pair in model of nonlinear Schrodinger equation. The soliton collision is disturbed by the local perturbation of the fiber dispersion. The analysis of the eigenvalues of Zakharov–Shabat spectral problem is given. Reshaping of the eigenvalue sets occur in the form of bifurcations. Peculiar features include soliton fusion into a breather and conversion of solitons at rest into a pair with outward velocities.

This article shows that a rotation of an object can make antigravity, in which there is strong gravity that distorts time and space. At first, we derived the curvature tensors upon Einstein’s field equation, using spherical polar coordinates, and then calculated the coefficients of the curvature tensors, to simulate the strength of each component of the tensors, assuming that the stress-energy tensor reflects the strength of the gravity. As the result, we conclude that antigravity can be made by rotating the gravitational field, if the gravity is strong enough so that time and space can be distorted inside of the object.

Nonlinear model of single-walled nanotube geometrically nonlinear oscillations is derived. The Sanders-Koiter nonlinear shell theory accounting nonlocal elasticity is basis of this model. The system of the partially differential equations of the nanotube nonlinear oscillations is obtained. The system of nonlinear ordinary differential equations for the nanotube oscillations is derived using Galerkin technique. The backbone curves of free nonlinear oscillations are calculated.

Thermoelastic damping (TED) is a decisive component of the quality factor of Micro-electro-mechanical Systems (MEMS) and Nano-electro-mechanical Systems (NEMS) under vacuum. Nanobeam resonator is a key element of NEMS and the modeling of TED in nanobeams is a crucial task. With the miniaturization of resonators, the mechanical behavior of structures is influenced by size effects and the classical continuum mechanics is no longer precise. Eringen’s nonlocal elasticity theory is a popular size-dependent theory and there have been some TED researches based on it. However, the previous nonlocal models failed to explain the stiffness-enhancement mechanism observed in experiments. In this paper, we derive an analytical TED model for nanobeams based on Lim’s effective nonlocal stress model. Subsequently, the validity of the obtained model is proved and the effect of nonlocal elasticity on TED is discussed under different conditions.

In this paper a hybrid scheme given by diffusion equation in conjunction to classical electrodynamics to examine physics-based mechanisms behind the behavior of beta cells, is presented. Particular attention is paid on the scenario by which beta-cell is not able to segregate insulin granules. Thus, a mechanism that would explain anomalies as seen in the lost of functions to segregate granules of insulin, is proposed. In this manner, the main argument of this paper states that the processes previous to the segregation of insulin given by (i) entrance of insulin, (ii) exit of Potassium K+, (iii) entrance of Calcium 2+, and (iv) segregation of insulin belong in only one universal formulation. A pseudo code by which the diabetes disease might be seen as a bug of the biological software of beta cell is proposed. Therefore a scheme capable to fix that bug would constitute a path to alleviate the disease inside the framework of Nanomedicine.

Bacteria can transport a well defined electric charge so that one can expect electrical interactions with different biochemical compounds in order to optimize their colonization in healthy hosts. This paper focuses on the different manifestations of Keller-Segel equation from its reduced formulation and that is used to derive equations in a territory of classical electrodynamics. Therefore it was derived charge density and ionic current assumed to be created by the time variations while bacteria is carrying out inherent actions of chemotaxis. In addition, the correspondent Green’s equation is derived.