Finite Speed Research Articles

Coulomb’s Law in Electrostatic, Gravitational and Inertial Forces and Emission of Radiation

Electric fields, from charges in bodies, in accordance with Coulomb’s law, occupying a vacuum, constitute an elastic medium called aether. Electrostatic, gravitational, and inertial forces are explained by considering the aether as an electric-field medium, supporting transmission of radiation at the speed of light. A partice of charge Q is supposed to be an impregnable hollow sphere, with radial force pulling the surface outwards, to maintain a stable structure of radius a and mass m, as the smallest quantities. Lines of force from stationary adjacent charges, are curled, in positive potential energy, for repulsion or negative for attraction. A charge Q, moving at constant velocity, carries its straight lines of radial fields, with increase forwards, to account for the kinetic energy. Force of gravity is by virtue of bodies displacing volumes of the aether, one in the shadow of another, to make for a pushings force of attraction, in accordance with Newton’s law. Due to finite speed of light, acceleration of charge Q moving at time t with velocity v, is not simultaneously passed to all the fields, resulting in curling of lateral field lines and creation of reactive field E and inertial force QE = -m(dv/dt), as inertia. Coulomb’s law is modified, with a velocity term, in view of aberration of electric field, for radiation from accelerated charges. Curving of space-time continuum is replaced with curling of electric field lines of force. Materials for teaching electromagnetic fields and radiation, in space, are well provided.

Rotating magnetic field configuration for controlled particle flux in material processing applications

Abstract Plasma technology has been an integral part of the semiconductor industries, especially to achieve the desired etch and selectivity of the outcome. These outcomes depend on various factors including the confinement of the charged particles of the plasma source. One of the widely employed confinement schemes is the multipole arrangement of magnetic fields, also known as a multicusp. Such arrangement provides minimum-B field value near the plasma axis and plays significant role in plasma-based ion sources for material processing and in plasma thrusters for spacecraft applications. In the present work, a novel rotating multicusp about its axis is studied to investigate its effect on the confinement of electrons present within it. The multicusp is allowed to rotate with a finite rotational speed, in the range of 0–107 rotation per second, thus inducing an axial electric field. It will lead to a directed axial flux of the electrons, determined by the rotational speed of the multicusp. The dynamics of the electrons enclosed within a rotating multicusp have been studied to explore its radial confinement. The results are of significance for semiconductor industries and others where downstream or afterglow plasmas are utilized for material applications.

Micromagnetic study of inertial spin waves in ferromagnetic nanodots

Here we report the possibility to excite ultra-short spin waves in ferromagnetic thin-films by using time-harmonic electromagnetic fields with terahertz frequency. Such ultra-fast excitation requires to include inertial effects in the description of magnetization dynamics. In this respect, we consider the inertial Landau-Lifshitz-Gilbert (iLLG) equation and develop analytical theory for exchange-dominated inertial spin waves. The theory predicts a finite limit for inertial spin wave propagation velocity, as well as spin wave spatial decay and lifetime as function of material parameters. Then, guided by the theory, we perform numerical micromagnetic simulations that demonstrate the excitation of ultra-short inertial spin waves (20 nm long) propagating at finite speed in a confined magnetic nanodot. The results are in agreement with the theory and provide the order of magnitude of quantities observable in realistic ultra-fast dynamics experiments.

Energy-Efficient Connected Cruise Control With Lean Penetration of Connected Vehicles

This paper focuses on energy-efficient longitudinal controller design for a connected automated truck that travels in mixed traffic consisting of connected and non-connected vehicles. The truck has access to information about connected vehicles beyond line of sight using vehicle-to-everything (V2X) communication. A novel connected cruise control design is proposed which incorporates additional delays into the control law when responding to distant connected vehicles to account for the finite propagation speed of traffic waves. The speeds of non-connected vehicles are modeled as stochastic processes. A fundamental theorem is proven which links the spectral properties of the motion signals to the average energy consumption. Controller synthesis for gain parameters is conducted over downstream traffic data and evaluated over a combination of synthetic and real cycles. It is demonstrated that even with lean penetration of connected vehicles, our controller can bring significant energy savings.

Numerical modelling of hyperbolic phase change problems: Application to continuous casting

Heat diffusion processes are generally modeled based on Fourier’s law to estimate how the temperature propagates inside a body. This type of modeling leads to a parabolic partial differential equation, which predicts an infinite thermal wave speed of propagation. However, experimental evidence shows that diffusive processes occur with a finite velocity of thermal propagation in many applications. In this paper, we develop a mathematical formulation to predict the finite speed of heat propagation in multidimensional phase change problems. The model generalizes the enthalpy formulation by adding a hyperbolic term. The governing equations are simulated by the finite element method. The proposed model is first verified by comparing numerical and experimental results illustrating the difference between the infinite and finite propagation velocity for heat inside biological tissues. Then, the results of the two and three-dimensional numerical solution of the continuous steel casting process are presented. We will illustrate that the effects of the initial conditions vanish faster when using the parabolic equation, while they persist in the hyperbolic modeling approach. The results demonstrate significant differences in the initial thermal dynamics and at the solid-liquid interface position when adding the hyperbolic term. The changes are more noticeable in the regions of the steel beam where rapid heat loss and, consequently, faster phase change occur.

Nonlinear Einstein paradigm of Brownian motion and localization property of solutions

We employ a generalization of Einstein's random walk paradigm for diffusion to derive a class of multidimensional degenerate nonlinear parabolic equations in nondivergence form. Specifically, in these equations, the diffusion coefficient can depend on both the dependent variable and its gradient, and it vanishes when either one of the latter does. It is known that solutions of such degenerate equations can exhibit finite speed of propagation (so‐called localization property of solutions). We give a proof of this property using a De Giorgi–Ladyzhenskaya iteration procedure for nondivergence form equations. A mapping theorem is then established to a divergence‐form version of the governing equation for the case of one spatial dimension. Numerical results via a finite‐difference scheme are used to illustrate the main mathematical results for this special case. For completeness, we also provide an explicit construction of the one‐dimensional self‐similar solution with finite speed of propagation function, in the sense of Kompaneets–Zel'dovich–Barenblatt. We thus show how the finite speed of propagation quantitatively depends on the model's parameters.

Light and Radio Radiations from a Moving Charged Particle

Two types of electromagnetic radiation are identified: light radiation and radio radiation. Light radiation is due to aberration of electric field in the motion of a charged particle in an external electric field, where energy radiated, proportional to the square of amplitude of velocity, is the difference between change in potential energy and change in kinetic energy. This is so with electrons revolving in the electric field of the nucleus of an atom. Radio radiation, due to finite speed of light, whereby an oscillating charged particle generates a magnetic field in phase with an electric field, at a point in space, resulting in generation of energy, proportional to the square of amplitude of acceleration, as from a radio antenna. The electric field in the Poynting vector is the sum of external accelerating field and internal induction field due to acceleration of a charged particle, in accordance with Faraday’s law. The induction field also acts on the same charge creating it, to produce the inertial force, equal and opposite to the accelerating force, thereby explaining the cause of inertia. Radio radiation explains the presence of Cosmic Microwave Background Radiation as a local phenomenon from within the atoms of a body

Aspects of Cattaneo-Christov heat flux in nonlinear radiative ternary, hybrid, and single mass diffusion past stretching surface; A comparative study

The main aim of this study is to analyze the convective heat transport in hydromagnetic TiO2 water nanofluid (NF), TiO2−SWCNT water hybrid nanofluid (HNF) and TiO2−SWCNT−MWCNT water ternary hybrid nanofluid flow (THNF) under the influence of Cattaneo-Christov (CC) heat flux and nonlinear thermal radiation over a stretching sheet. This study will help in environmental purification, to decompose harmful substances and other applications that require cooling. Furthermore, consideration of CC heat flux is important for a finite speed heat flow to reduce system disorder. The system of governing partial differential (PDEs) equations for the heat transport within THNF flow is transformed into the system of ordinary differential equations (ODEs) and solved numerically via the shooting technique with Runge-Kutta-4 method. The flow behaviors for Lorentz force and volume fraction of TiO2(φ1), SWCNT(φ2) and MWCNT(φ3) nanomaterials are portrayed for both no slip (α=0) and velocity slip (α=0.5) conditions. It is concluded that the velocity is more significant in the case of no slip condition when one, two and three different nanomaterials are dispersed in the base fluid water. It is further observed that the heat and momentum transport is more significant in the case when we consider TiO2−SWCNT−MWCNT water THNF flow as compared to TiO2 water NF, TiO2−SWCNT water HNF flow over a stretching surface. Our results show that the present analysis on heat transport in the THNF is more significant as compared to the THNF taken in the study given by Majunatha et al. [14].

Adaptive optics LEO uplink pre-compensation with finite spatial modes.

Adaptive optics pre-compensation of free-space optical communications uplink from ground to space is complicated by the "point ahead angle" due to spacecraft velocity and the finite speed of light, as well as anisoplanatism of the uplink beam and the wavefront beacon. This Letter explores how pre-compensation varies with the number of spatial modes applied and how it varies with a beacon at the point-ahead angle versus a downlink beacon. Using a w0 = 16cm Gaussian beam propagating through a modified Hufnagel-Valley model as an example, we find pre-compensation performance plateaus beyond ∼100 applied modes regardless of integrated turbulence strength, and that a point ahead beacon provides a 1-4 dB gain in median received power and an order-of-magnitude reduction in scintillation over a downlink beacon at wavelengths typical of optical communications. Modeling tailored to specific scenarios should be conducted to determine whether implementing a resource-intensive point ahead beacon is the optimum path to meeting link requirements.

Propagation phenomena of the solution for the relativistic BGK model

In this paper, we recognize the finite propagation speed of the solution for the relativistic Bhatnagar-Gross-Krook model of the Marle-type near equilibrium regime in the whole space Rx3. The global solutions vanish outside a modified line cone ⟨x⟩ = aMt with a, M > 1. Moreover, one can see that the slope of the modified line cone aM can be as close as to the maximum speed of the relativistic transport part. This means that the propagation speed is optimal.

Dynamics of Two Bodies with Trajectories on a Fixed Straight Line with Regard for the Finite Speed of Gravity

Dynamics of Two Bodies with Trajectories on a Fixed Straight Line with Regard for the Finite Speed of Gravity

Multipurpose Laser Instrument for Interplanetary Ranging, Time Transfer, and Wideband Communications

In this paper, we discuss the design and feasibility of a multifunctional laser instrument capable of precision ranging, time transfer, and wideband communications over interplanetary distances throughout our solar system. To simplify the communications discussion, On-Off Keying (OOK) is assumed for the high bandwidth (MHz to GHz) modulation format, and the required laser powers and transmit and receive apertures are determined for each Earth–planet link as a function of data rate. Optimization of the transmitter and receiver antenna gains is reviewed. It is further assumed that the spacecraft is in orbit about the planet of interest in order to justify the need for large data downloads rates and that single-photon sensitive detector arrays can be utilized to aid in the acquisition, detection, and tracking of the opposite terminal. Satellite acquisition and tracking is complicated by the long one-way propagation distances (up to 40 AU), the finite speed of light, the orbital and rotational velocities of the two planets, and, if applicable, the spacecraft orbital speed about the planet. Taking advantage of the highly circular and coplanar planetary orbits within our solar system, point ahead angles are estimated for all combinations of possible Earth–planet positions revealing solar orbital geometries where planetary motion does not introduce a need for point ahead angles. Finally, possible methods for simplifying the initial mutual acquisition of the planetary and Earth terminals and maintaining the coalignment of their respective optical systems is discussed.

Topological Speed Limit.

Any physical system evolves at a finite speed that is constrained not only by the energetic cost but also by the topological structure of the underlying dynamics. In this Letter, by considering such structural information, we derive a unified topological speed limit for the evolution of physical states using an optimal transport approach. We prove that the minimum time required for changing states is lower bounded by the discrete Wasserstein distance, which encodes the topological information of the system, and the time-averaged velocity. The bound obtained is tight and applicable to a wide range of dynamics, from deterministic to stochastic, and classical to quantum systems. In addition, the bound provides insight into the design principles of the optimal process that attains the maximum speed. We demonstrate the application of our results to chemical reaction networks and interacting many-body quantum systems.

Einstein's model of "the movement of small particles in a stationary liquid" revisited: finite propagation speed

The aforementioned celebrated model, though a breakthrough in Stochastic processes and a great step toward the construction of the Brownian motion, leads to a paradox: infinite propagation speed and violation of the 2nd law of thermodynamics. We adapt the model by assuming the diffusion matrix is dependent on the concentration of particles, rather than constant it was up to Einstein, and prove a finite propagation speed under the assumption of a qualified decrease of the diffusion for small concentrations. The method involves a nonlinear degenerated parabolic PDE in divergent form, a parabolic Sobolev-type inequality, and the Ladyzhenskaya-Ural'tseva iteration lemma.

A space-time nonlocal traffic flow model: Relaxation representation and local limit

We propose and study a nonlocal conservation law modelling traffic flow in the existence of inter-vehicle communication. It is assumed that the nonlocal information travels at a finite speed and the model involves a space-time nonlocal integral of weighted traffic density. The well-posedness of the model is established under suitable conditions on the model parameters and by a suitably-defined initial condition. In a special case where the weight kernel in the nonlocal integral is an exponential function, the nonlocal model can be reformulated as a $ 2\times2 $ hyperbolic system with relaxation. With the help of this relaxation representation, we show that the Lighthill-Whitham-Richards model is recovered in the equilibrium approximation limit.

Modelling the interaction of invasive-invaded species based on the general Bramson dynamics and with a density dependant diffusion and advection.

The main goal of the presented study is to introduce a model of a pairwise invasion interaction with a nonlinear diffusion and advection. The new equation is based on the further general works introduced by Bramson (1988) to describe the invasive-invaded dynamics. This type of model is made particular with a density dependent diffusion along with an advection term. The new resulting model is then analyzed to explore the regularity, existence and uniqueness of solutions. It is well known that density dependent diffusion operators induce a propagating front with finite speed for compactly supported functions. Based on this, we introduce an analytical approach to determine the evolution of such a propagating front in the invasion dynamics. Afterward, we study the problem with travelling wave profiles and a numerical assessment. As a main finding to remark: When both species propagate with significantly different travelling wave speeds, the interaction becomes unstable, while when the species propagate with similar low speeds, the interaction stabilizes.

The 𝒫(𝜑)₂ Model on de Sitter Space

In 1975 Figari, Høegh-Krohn and Nappi constructed theP(φ)2{\mathscr P}(\varphi )_2model on the de Sitter space. Here we complement their work with new results, which connect this model to various areas of mathematics. In particular, i.) we discuss the causal structure of de Sitter space and the induces representations of the Lorentz group. We show that the UIRs ofSO0(1,2)SO_0(1,2)for both the principal and the complementary series can be formulated on Hilbert spaces whose functions are supported on a Cauchy surface. We describe the free classical dynamical system in both its covariant and canonical form, and present the associated quantum one-particle KMS structures in the sense of Kay (1985). Furthermore, we discuss the localisation properties of one-particle wave functions and how these properties are inherited by the algebras of local observables.ii.) we describe the relations between the modular objects (in the sense of Tomita-Takesaki theory) associated to wedge algebras and the representations of the Lorentz group. We connect the representations of SO(1,2) to unitary representations ofSO(3)SO(3)on the Euclidean sphere, and discuss how theP(φ)2{\mathscr P}(\varphi )_2interaction can be represented by a rotation invariant vector in the Euclidean Fock space. We present a novel Osterwalder-Schrader reconstruction theorem, which shows that physicalinfrared problemsare absent on de Sitter space. As shown in Figari, Høegh-Krohn, and Nappi (1975), the ultraviolet problems are resolved just like on flat Minkowski space. We state the Haag–Kastler axioms for theP(φ)2{\mathscr P}(\varphi )_2model and we explain how thegeneratorsof the boosts and the rotations for the interacting quantum field theory arise from thestress-energy tensor. Finally, we show that the interacting quantum fields satisfy theequations of motionin their covariant form. In summary, we argue that the de SitterP(φ)2{\mathscr P}(\varphi )_2model is the simplest and most explicit relativistic quantum field theory, which satisfies basic expectations, like covariance, particle creation, stability and finite speed of propagation.

Cucker-Smale model with finite speed of information propagation: Well-posedness, flocking and mean-field limit

<p style='text-indent:20px;'>We study a variant of the Cucker-Smale model where information between agents propagates with a finite speed <inline-formula><tex-math id="M1">\begin{document}$ {{\mathfrak{c}}}>0 $\end{document}</tex-math></inline-formula>. This leads to a system of functional differential equations with state-dependent delay. We prove that, if initially the agents travel slower than <inline-formula><tex-math id="M2">\begin{document}$ {{\mathfrak{c}}} $\end{document}</tex-math></inline-formula>, then the discrete model admits unique global solutions. Moreover, under a generic assumption on the influence function, we show that there exists a critical information propagation speed <inline-formula><tex-math id="M3">\begin{document}$ {{{{\mathfrak{c}}}^\ast}}>0 $\end{document}</tex-math></inline-formula> such that if <inline-formula><tex-math id="M4">\begin{document}$ {{\mathfrak{c}}}\geq{{{{\mathfrak{c}}}^\ast}} $\end{document}</tex-math></inline-formula>, the system exhibits asymptotic flocking in the sense of the classical definition of Cucker and Smale. For constant initial datum the value of <inline-formula><tex-math id="M5">\begin{document}$ {{{{\mathfrak{c}}}^\ast}} $\end{document}</tex-math></inline-formula> is explicitly calculable. Finally, we derive a mean-field limit of the discrete system, which is formulated in terms of probability measures on the space of time-dependent trajectories. We show global well-posedness of the mean-field problem and argue that it does not admit a description in terms of the classical Fokker-Planck equation.</p>

An empirical comparison of various MSPE estimators and associated prediction intervals for small area means

Small area estimation is a method for prediction involving subpopulation of interest. A standard measure of uncertainty for the prediction is the mean squared prediction error (MSPE). Various predictors and MSPE estimators have been proposed based on different principles over past decades. Despite various existing studies on performance of individual MSPE estimators, a comprehensive comparison of different MSPE estimators in terms of finite sample performance, especially for several recently proposed MSPE estimators, has not been documented. To this end, we carry out a study that systematically compare the existing MSPE estimators regarding their finite sample performance and computational speed. Performance of prediction intervals is also considered, which involves both the predictor and the associated MSPE estimator. The study covers two main types of small area models, namely, the area-level (Fay-Herriot) model and the unit-level (nested-error regression) model. Illustrative examples are provided.

Stochastic dynamics with multiplicative dichotomic noise: Heterogeneous telegrapher’s equation, anomalous crossovers and resetting

We analyze diffusion processes with finite propagation speed in a non-homogeneous medium in terms of the heterogeneous telegrapher’s equation. In the diffusion limit of infinite-velocity propagation we recover the results for the heterogeneous diffusion process. The heterogeneous telegrapher’s process exhibits a rich variety of diffusion regimes including hyperdiffusion, ballistic motion, superdiffusion, normal diffusion and subdiffusion, and different crossover dynamics characteristic for complex systems in which anomalous diffusion is observed. The anomalous diffusion exponent in the short time limit is twice the exponent in the long time limit, in accordance to the crossover dynamics from ballistic diffusion to normal diffusion in the standard telegrapher’s process. We also analyze the finite-velocity heterogeneous diffusion process in presence of stochastic Poissonian resetting. We show that the system reaches a non-equilibrium stationary state. The transition to this non-equilibrium steady state is analyzed in terms of the large deviation function.