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We study a nonlocal thermistor problem for fractional derivatives in the conformable sense. Classical Schauder's fixed point theorem is used to derive the existence of a tube solution.
The Bochner-Riesz multipliers $ B_{\delta }$ on $ \mathbb R ^{n}$ are shown to satisfy a range of sparse bounds, for all $0< \delta < \frac {n-1}2 $. The range of sparse bounds increases to the optimal range, as $ \delta $ increases to the critical value, $ \delta =\frac {n-1}2$, even assuming only partial infor...
We study singularly perturbed linear systems of rank two of ordinary differential equations of the form $\hbar x\partial_x \psi (x, \hbar) + A (x, \hbar) \psi (x, \hbar) = 0$, with a regular singularity at $x = 0$, and with a fixed asymptotic regularity in the perturbation parameter $\hbar$ of Gevrey type in a fixed se...
The classical Stolarsky invariance principle connects the spherical cap $L^2$ discrepancy of a finite point set on the sphere to the pairwise sum of Euclidean distances between the points. In this paper we further explore and extend this phenomenon.
We introduce and study the unconstrained polarization (or Chebyshev) problem which requires to find an $N$-point configuration that maximizes the minimum value of its potential over a set $A$ in $p$-dimensional Euclidean space. This problem is compared to the constrained problem in which the points are required to bel...
We prove a two weight theorem for fractional singular integrals in higher dimensions assuming energy side conditions on the weights. The testing conditions are taken over quasicubes, namely globally biLipschitz images of cubes.
We perform the analytic continuation of solutions to the hypergeometric differential equation of order $n$ to the third regular singularity, usually denoted $z=1$, with the help of recurrences of their Mellin--Barnes integral representations. In the resonant case, there are necessarily logarithmic solutions.
We consider the quasi-Ablowitz-Segur and quasi-Hastings-McLeod solutions of the inhomogeneous Painlevé II equation $$ u"(x)=2u^3(x)+xu(x)-\alpha \qquad \textrm{for } \alpha \in \mathbb{R} \textrm{ and } \|\alpha\| > \frac{1}{2}. $$ These solutions are obtained from the classical Ablowitz-Segur and Hastings-McLeod...
A new ether-drift experiment in Düsseldorf is currently measuring the relative frequency shift of two cryogenic optical resonators upon active rotations of the apparatus. I point out that the observed fractional amplitude of the sidereal variations of the signal in February, C_sid \sim (11 \pm 2) 10^{-16}, is entirely...
Many have dedicated their time trying to determine the ideal conditions for a cylinder to have equal probabilities of falling with one of its faces facing upwards or on its side. However, to this day, there is no concrete analysis of what these conditions should be.
In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subjected to uniform magnetic field and inner-pressurized loads are studied. Rather than directly assuming the material constants into some certain function forms as displayed in previous researches, we firstly give the volum...
In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The model is derived from a variational principle by choosing an appropriate shallow wa...
Conservation principles establish the primacy of potentials over fields in electrodynamics, both classical and quantum. The contrary conclusion that fields are primary is based on the Newtonian concept that forces completely determine dynamics, and electromagnetic forces depend directly on fields.
In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by nonlinear differential equation which demonstrates chaotic behavior and bifurcat...
Although many papers have appeared on the theory of photographing relativistically moving objects, pioneered by the classic work of Penrose and Terrell, three problems remain outstanding. (1) There does not seem to exist a general formula which gives the projection of a relativistically moving object, applicable to an...
We investigate the minimal conditions to store coherently a RF pulse in a material medium. We choose a commercial quartz as memory support because it is a widely available component with a high Q-factor.
Which non-local hidden variables could complement the description of physical reality? The present model of extended Newtonian dynamics (MEND) is generalize but not alternative to Newtonian Dynamics because its extended Newtonian Dynamics to arbitrary reference frames.
This paper addresses the problem of the separation of rotational and internal motion. It introduces the concept of average angular velocity as the moment of inertia weighted average of particle angular velocities.
The mechanical properties of the human lip between relaxed and fully contracted are not enough to explain the full range of professional brass players. Brass players manipulate their mouth cavity and vocal tract which act as Helmholtz resonators driving the lips.
Present work deals with the dynamics of vehicles which intentionally operate in the ground proximity. The dynamics in ground effect is influenced by the vehicle orientation with respect to the ground, since the aerodynamic force and moment coefficients, which in turn depend on height and angle of attack, also vary wit...
The concept of nonlinear modes is applied in order to analyze the behavior of a model of woodwind reed instruments. Using a modal expansion of the impedance of the instrument, and by projecting the equation for the acoustic pressure on the normal modes of the air column, a system of second order ordinary differential ...
In this paper, we discuss the problem of determination of light radiation pressure force upon an anisotropic surface. The optical parameters of such a surface are considered to have major and minor axes, so the model is called an orthotropic model.
A 2-D micropolar equivalent single-layer (ESL), first-order shear deformation (FSDT) plate model for 3-D web-core sandwich panels is developed. First, a 3-D web-core unit cell is modeled by classical shell finite elements.
Nonlocal strain gradient continuum mechanics is a methodology widely employed in literature to assess size effects in nanostructures. Notwithstanding this, improper higher-order boundary conditions (HOBC) are prescribed to close the corresponding elastostatic problems.
In a recent paper titled "Coherent electromagnetic wavelets and their twisting null congruences," I defined the local inertia density (I), reactive energy density (R), and energy flow velocity (v) of an electromagnetic field. These are the field equivalents of the mass, rest energy, and velocity of a relativis...
The charging of insulating samples degrades the quality and complicates the interpretation of images in scanning electron microscopy and is important in other applications, such as particle detectors. In this paper we analyze this nontrivial phenomenon on different time scales employing the drift-diffusion-reaction ap...
Energy harvesting (EH) is a multidisciplinary research area, involving physics, materials science and engineering, with the objective of providing renewable sources of sufficient power to operate targeted low-power applications. Piezoelectric transducers are often used for vibrational, inertial and direct movement EH....
In this letter we study the classical motion of an electric dipole in the presence of a uniform magnetic field in the approximation of small oscillations. The normal modes of oscillations are obtained and propose a criterion of applicability of the method of small oscillations.
Methods of enhanced laser cooling of particle beams in storage rings and Robinson's damping criterion are discussed. The dynamics of amplitudes of betatron oscillations and instantaneous orbits of electrons interacting with laser beams being displaced in the radial direction is investigated.
A phenomenological method is developed to consider elastic guided wave propagation in complex curved waveguides. The theory on guided wave propagation in hollow circular cylinders is used in order to verify the method.
Three contradictory but state-of-the-art concepts for defining and evaluating stored electromagnetic energy are treated in this communication, and are collated with the widely accepted definition of stored energy, which is the total energy minus the radiated energy. All three concepts are compared, and the results are...
Recently, large-scale trapped ion systems have been realized in experiments for quantum simulation and quantum computation. They are the simplest systems for dynamical stability and parametric resonance.
We discuss a general definition of directional derivative of any tensor flow field and its practical applications in physics. It is shown that both Lagrangian and Eulerian descriptions as complementary types of flow field specifications adopted in modern theoretical hydrodynamics, imply two complementary types of dire...
In this paper, we consider two space variables of nonlinear telegraph equation in terms of voltage and current. The numerical algorithm based on the Laplace transform method (LDM) is applied to obtain analytic and approximate solutions of the space-time nonlinear telegraph equations.
This paper is concerned with the approximation of the radiative transfer equation for a grey medium in the slab geometry by the moment method. We develop a novel moment model inspired by the classical $P_N$ model and $M_N$ model.
The Gaussian formula and spherical aberrations of the static and relativistic curved mirrors are analyzed using the optical path length (OPL) and Fermat's principle. The geometrical figures generated by the rotation of conic sections about their symmetry axes are considered for the shapes of the mirrors.
It is well known that two permanent magnets of fixed orientation will either always repel or attract one another regardless of the distance between them. However, if one magnet is rotated at sufficient speed, a stable position at a given equilibrium distance can exist for a second free magnet.
Scattering of refracting Huygens' metasurfaces is revisited. A new analytical closed-form solution is obtained for the two-dimensional problem under transverse electric (TE) plane-wave incidence -- a solution which gives the scattering for any (in-plane) angle of incidence and frequency.
In part 1, we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into accou...
Huygens' principle (HP), extinction theorem (ET), and Franz's / Franz-Harrington formulation (FHF, which is a mathematical expression of surface equivalence principle) are the important components of electromagnetic (EM) theory, and they are generalized from the following aspects. <br>1) Traditional HP, ET, an...
The analysis of site effects is very important since the amplification of seismic motion in some specific areas can be very strong. In this paper, the site considered is located in the centre of Nice on the French Riviera.
We have recently (Heras et al. in Eur. Phys. J. Plus 136:847, 2021) argued that classical electrodynamics can predict nonlocal effects by showing an example of a topological and nonlocal electromagnetic angular momentum. In this paper we discuss the dual of this angular momentum which is also topological and nonlocal....
Despite its simplicity, it seems to my best of knowledge that the possibly simplest approach towards deriving equations governing irreversible thermodynamics from gas-kinetic considerations within the framework of classical mechanics has never been pursued. In this paper we address this omission and derive the equatio...
Plane waves are regarded as the general solution of the wave equation. However the plane wave expansion of standing waves by means of complex phasors leads to a theory in which the time coordinate does not receive the same treatment as the three space coordinates.
The formula for dipole radiation reaction torque acting on a system of charges, and the Larmor-like formula for the angular momentum loss by this system, differ in the time derivative term which is the analogue of the Schott term in the energy loss problem. In the well-known textbooks this discrepancy is commonly avoi...
We develop a compact perturbative series for accoustic wave propagation in a medium with a non Gaussian stochastic speed of sound. We use Martin - Siggia and Rose auxiliary field techniques to render the classical wave propagation problem into a "quantum" field theory one, and then frame this problem within so...
Poisson ratio is an important mechanical property that reveals the deformation patterns of materials. A positive Poisson ratio is a feature of the majority of materials.
We focus on the study of the processes undergone by a perfect gas when the external pressure is suddenly modified. The analysis shows that, from the second law perspective, there is a non-evident asymmetry between the processes of compression and expansion between the same pressures, which is manifested through differ...
Gauss' law and the equation of continuity must be satisfied in all materials be they solids, liquids or gases. Most materials are classified as simple materials; i.e., their electrical properties are linear, isotropic and homogeneous.
A proof is given of the vector identity proposed by Gubarev, Stodolsky and Zakarov that relates the volume integral of the square of a 3-vector field to non-local integrals of the curl and divergence of the field. The identity is applied to the case of the magnetic vector potential and magnetic field of a rotating cha...
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane.
The novel concept of spectral diffusivity is introduced to analyse the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts.
For partial wetting, motion of the triple liquid-gas-solid contact line is influenced by heterogeneities of the solid surface. This influence can be strong in the case of inertial (e.g. oscillation) flows where the line can be pinned or move intermittently.
The classical dam break problem has become the de facto standard in validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used for flooding simulations.
The purpose of this note is to see to what extent ideal gas laws can be obtained from simple Newtonian mechanics, specifically elastic collisions. We present simple one-dimensional situations that seem to validate the laws.
This chapter focuses on vibration energy harvesting using electrostatic converters. It synthesizes the various works carried out on electrostatic devices, from concepts, models and up to prototypes, and covers both standard (electret-free) and electret-based electrostatic vibration energy harvesters (VEH).
We consider a lumped circuit model of an augmented electromagnetic railgun that consists of a gun circuit and an augmentation circuit that is inductively coupled to the gun circuit. The gun circuit is driven by a d.c. voltage generator, and the augmentation circuit is driven by an a.c. voltage generator.
In this paper, we construct a parallel image of the conventional Maxwell theory by replacing the observer-time by the proper-time of the source. This formulation is mathematically, but not physically, equivalent to the conventional form.
An easy-to-implement scheme to split self-collimated acoustic beams in sonic crystals (SCs) is proposed by introducing line-defects into SCs, by which an incoming self-collimated beam can be split into a 90 degree-bended one and a transmitted one with an arbitrary power ratio by adjusting the value of defect size. An ...
Conformal mapping is an important mathematical tool in many physical and engineering fields, especially in electrostatics, fluid mechanics, classical mechanics, and transformation optics. However in the existing textbooks and literatures, it is only adopted to solve the problems which have only two terminals.
In this paper, Newton's law of cooling is considered from a different perspective with newly defined fractional conformable. Obtained results are compared with experimental results and found optimal fractional orders which fit better with real data.
We present the theory, the design and the discussion of an experiment which allows to choose between the local formulation of Riemann-Lorenz and the non-local formulation of Heaviside-Hertz in order to describe Classical Electromagnetism.
An extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe power-law type of non-locality is discussed. Two phenomenological possibilities are explored.
The paper analyses the ground antenna echo using microwave frequency detector and high speed sampling technology and a new method detecting buried object in time domain near-field is presented. The method detecting particular reflection echo frequency of microwave pulse via digital signal processing is to reduce the f...
The equation derived by <a href="http://F.Rohrlich" rel="external noopener nofollow" class="link-external link-http">this http URL</a> (Phys.Rev.E 77, 046609 (2008)) reproduces Eq. (76.3) from the Landau and Lifshitz book (The Classical Theory of Fields).
It is shown that Aharonov-Bohm effect may be derived from Hamilton-Jacobi equation. It might have been predicted well before the quantum mechanics creation by Heisenberg and Schroedinger.
We report the experimental observation of an elastic bound mode in the continuum (BIC) in a compact region of an architected beam. We consider a long slender beam with rigid masses attached at periodic intervals, with a compact segment bounded by four protruding side beams.
In sight of fundamental thermal limits on further substantial performance improvements of modern digital computational processing units, wave-based analog computation is becoming an enticing alternative. A wave, as it propagates through a carefully tailored medium, performs the desired computational operation.
A logical error in the usual derivation of the energy conservation law is analyzed, and a way to avoid the error is presented.
Light transport in graded index media follows a curved trajectory determined by the Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse.
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways.
Saturation effects affecting absorption and fluorescence spectra of an atomic vapor confined in an Extremely Thin Cell (cell thickness $L < 1 \mu m$) are investigated experimentally and theoretically. The study is performed on the $D_{2}$ line ($\lambda ~= ~852 nm)$ of $Cs$ and concentrates on the two situations $L...
Exact radiative wave solutions to the classical homogeneous Maxwell equations in the vacuum have been found that are not transverse, exhibit both torsion and spin, and for which the second Poincare invariant, E.B, is not zero. Two four component rank 3 tensors of spin current and torsion are constructed on topological...
The experiment is described which shows that Coulomb interaction spreads with a limit velocity and thus this kind of interaction cannot be considered as so called "instantaneous action at a distance".
The motion of a handle spinning in space has an odd behavior. It seems to unexpectedly flip back and forth in a periodic manner as seen in a popular YouTube video.
An unexpected prediction of classical electrodynamics is that a charge can accelerate before a force is applied. We would expect that a preaccelerated charge would radiate so that there would be spontaneous preradiation, an acausal phenomenon.
In this paper we show how to get the Lorentz transformations from E=mc^2, the laws of conservation of energy and momentum, and the special relativity principle. To this end we first deduce the law of addition of relativistic velocities
A simple method of calculating the Wannier-Stark resonances in 2D lattices is suggested. Using this method we calculate the complex Wannier-Stark spectrum for a non-separable 2D potential realized in optical lattices and analyze its general structure.
Using superposition and numerical approximations of a published analytical expression for the magnetic field generated by a finite solenoid, we show that the magnetic field external to parallel identical solenoids can be nearly uniform and substantial, even when the solenoids have lengths that are large compared to the...
It is shown that a pair of identical emitters (e.g. wire dipole antennas) in the focal points of a disc, made of left-handed metamaterial (a "perfect" lens), form a non-radiating electromagnetic configuration. The emitters are fed with voltages of equal magnitude and pi-out-of-phase.
Dispersion characteristics of magnetostatic waves in tangentially magnetized to saturation ferrite film with a "magnetic wall" condition (tangential component of microwave magnetic field is equal to zero) on the one of the film surface were calculated. It is found, that unidirectional magnetostatic waves appea...
Three-dimensional thermoelastic analysis in presence of electro magnetic field is investigated of a rectangular plate. In the context of Green-Naghdi model-II, fractional order energy equation is adopted for a rotating anisotropic rectangular plate which is subjected to simply supported and isothermal on its four late...
We show that the Hamiltonian mean field (HMF) model describes the equilibrium behavior of a system of long pendula with flat bobs that are coupled through long-range interactions (charged or self gravitating). We solve for the canonical partition function in the coordinate frame of the pendula angles.
Negative-index materials (NIMs) are shown to support optical anti-parity-time (anti-PT) symmetry even when they are lossless. Here we prove the feasibility in achieving higher-order exceptional points (EPs) in loss-free waveguide arrays by utilizing the anti-$\mathcal{PT}$ symmetry induced by NIM.
This research investigates the simultaneous effect of in-plane and transverse loads in reinforced concrete shells. The infinitesimal shell element is divided into layers (with triaxial behavior) that are analyzed according to the smeared rotating crack approach.
Data from spacecrafts tracking exhibit many anomalies that suggest the dependence of the speed of electromagnetic radiation with the motion of its source. This dependence is different from that predicted from emission theories that long ago have been demonstrated to be wrong.
It is shown that a newly derived "exact expression" for radiation of an accelerated charge in the recent literature is simply incorrect, having arisen because of a wrong relativistic transformation of the distance parameter. The ensuing claim that the newly derived expression alone that satisfies the energy co...
Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing the occurrence of poorly conditioned numerical systems.
A photon source is located in a rotating waveguide. An absorber with a sharp absorbing frequency absorbs some of the emitted photons.
We develop a method for systematically constructing Lagrangian functions for dissipative mechanical, electrical and, mechatronic systems. We derive the equations of motion for some typical mechatronic systems using deterministic principles that are strictly variational.
Simplified description of an experiment of the Michelson-Morley type being completed at the University of Western Australia with a discussion of the possible meanings of its outcome.
It is proven, without using the microscopic reversibility argument of Onsager, that lossy reciprocal systems have a hidden time-reversal symmetry. The key idea is that the dissipation channels of lossy dielectrics can be mimicked by a distributed network of lossless transmission lines.
An interesting phenomenon that occurs in projectile motion, the "coming and going", is analyzed considering linear air resistance force. By performing both approximate and numerical analysis, it is showed how a determined critical angle and an interesting geometrical property of projectiles can change due to v...
A new description of the endochronic and the Mroz model is discussed. It is based on the definition of a suitable pseudo-potential and the use of the generalized normality assumption.
The definition and properties of the Euler-Lagrange cohomology groups $H^{2k-1}$, $1 \leqslant k \leqslant n$, on a symplectic manifold $({\cal M}^{2n},\omega)$ are given and studied. For $k = 1$ and $k = n$, they are isomorphic to the corresponding de Rham cohomology groups $H_{dR}^1({\cal M}^{2n})$ and $H_{dR}^{2n-1...
We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.
The current language for CNC programming is G-code which dates from the beginning of the eighties with the norm ISO 6983. With the new technologies, G-code becomes obsolete.
This second part of a two-part essay discusses recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their similarity transformation approach (see Part I), but the contemporary approach utilizes rigged Hilbert space (whereas the older approach used Hilbert sp...
We present the first experimental demonstration of focusing ultrasound waves through a flat acoustic metamaterial lens composed of a planar network of subwavelength Helmholtz resonators. We observed a tight focus of half-wavelength in width at 60.5 KHz by imaging a point source.
We demonstrate that the acoustic spin of a first-order Bessel beam can be transferred to a subwavelength (prolate) spheroidal particle at the beam axis in a viscous fluid. The induced radiation torque is proportional to the acoustic spin, which scales with the beam energy density.

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