Finite Speed Of Signal Propagation Research Articles

Lorentz Symmetry Group, Retardation and Energy Transformations in a Relativistic Engine

In a previous paper, we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents, the above analysis led to suggestion of a relativistic engine. Since the system is effected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how can we accommodate the law of momentum and energy conservation. The subject of momentum conservation was discussed in a pervious paper, while preliminary results regarding energy conservation where discussed in some additional papers. Here we give a complete analysis of the exchange of energy between the mechanical part of the relativistic engine and the field part, the energy radiated from the relativistic engine is also discussed. We show that the relativistic engine effect on the energy is 4th-order in 1c and no lower order relativistic engine effect on the energy exists.

Material Engineering and Design of a Relativistic Engine: How to Avoid Radiation Losses

In a previous paper [1] we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light at vacuum, causing the total force in the system to not add up to zero. This was demonstrated in a specific example of two current loops with time dependent currents in at least one of the loops [1], or in one-time dependent loop current and a permanent magnet assembly [2, 3]. A relativistic engine was thus suggested. Since the system is affected by a total force for a finite period of time this means that the system acquires mechanical momentum and energy, the question then arises how to accommodate the law of momentum and energy conservation. The subject of momentum conversation was discussed in [4], while a preliminary discussion of the subject of electric energy conservation is given in [5, 6]. Here we discuss some of the radiation losses associated with the engine and their implications on the energy balance.

Time-delay polaritonics

Non-linearity and finite signal propagation speeds are omnipresent in nature, technologies, and real-world problems, where efficient ways of describing and predicting the effects of these elements are in high demand. Advances in engineering condensed matter systems, such as lattices of trapped condensates, have enabled studies on non-linear effects in many-body systems where exchange of particles between lattice nodes is effectively instantaneous. Here, we demonstrate a regime of macroscopic matter-wave systems, in which ballistically expanding condensates of microcavity exciton-polaritons act as picosecond, microscale non-linear oscillators subject to time-delayed interaction. The ease of optical control and readout of polariton condensates enables us to explore the phase space of two interacting condensates up to macroscopic distances highlighting its potential in extended configurations. We demonstrate deterministic tuning of the coupled-condensate system between fixed point and limit cycle regimes, which is fully reproduced by time-delayed coupled equations of motion similar to the Lang-Kobayashi equation.

Computational visualization of retardation effects on observed particle distributions

The retardation equation for straight line signal propagation is solved analytically for the two-dimensional case and used to plot the retarded positions graphically for a variety of particle distributions moving relatively to the observer. The results show that in case of a finite signal propagation speed the observed particle distribution must appear as expanded/compressed if it moves towards/away from the observer. The apparent change of scale of the distribution goes hereby along with an inverse change in particle density.

Telegraphic processes with stochastic resetting

We investigate the effects of resetting mechanisms on random processes that follow the telegrapher's equation instead of the usual diffusion equation. We thus study the consequences of a finite speed of signal propagation, the landmark of telegraphic processes. Likewise diffusion processes where signal propagation is instantaneous, we show that in telegraphic processes, where signal propagation is not instantaneous, random resettings also stabilize the random walk around the resetting position and optimize the mean first-arrival time. We also obtain the exact evolution equations for the probability density of the combined process and study the limiting cases.

Momentum conservation in a relativistic engine

In a previous paper we have shown that Newton’s third law cannot strictly hold in a distributed system of which the different parts are at a finite distance from each other. This is due to the finite speed of signal propagation which cannot exceed the speed of light in vacuum, which in turn means that when summing the total force in the system the force does not add up to zero. This was demonstrated in a specific example of two current loops with time-dependent currents, the above analysis led to the suggestion of a relativistic engine. Since the system is affected by a total force for a finite period of time this means that the system acquires momentum, the question then arises if we need to abandon the law of momentum conservation. In this paper we make a detailed calculation and show that any momentum gained by the material part of the system is equal in magnitude and opposite in direction to the momentum gained by the electromagnetic field. Hence the total momentum of the system is conserved.

Synchronization in phase-coupled Kuramoto oscillator networks with axonal delay and synaptic plasticity.

We explore both analytically and numerically an ensemble of coupled phase oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time delay and learning effects combine, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.

The telegraph equation for cosmic-ray transport with weak adiabatic focusing

Time-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model.

Single-shot 35 fs temporal resolution electron shadowgraphy

We obtain single-shot time-resolved shadowgraph images of the electromagnetic fields resulting from the interaction of a high intensity ultrashort laser pulse with a metal surface. Using a high brightness relativistic electron beam and a high streaking speed radiofrequency deflector, we report <35 fs temporal resolution enabling a direct visualization of the retarded-time dominated field evolution which follows the laser-induced charge emission. A model including the finite signal propagation speed well reproduces the data and yields measurements of fundamental parameters in short pulse laser-matter interaction such as the amount of emitted charge and the emission time scale.

Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations

Neural field equations describe the activity of neural populations at a mesoscopic level. Although the early derivation of these equations introduced space dependent delays coming from the finite speed of signal propagation along axons, there have been few studies concerning their role in shaping the (nonlinear) dynamics of neural activity. This is mainly due to the lack of analytical tractable models. On the other hand, constant delays have been introduced to model the synaptic transmission and the spike initiation dynamics. By incorporating the two kinds of delays into the neural field equations, we are able to find the Hopf bifurcation curves analytically, which produces many Hopf--Hopf interactions. We use normal theory to study two different types of connectivity that reveal a surprisingly rich dynamical portrait. In particular, the shape of the connectivity strongly influences the spatiotemporal dynamics.

Systems of conservation laws with rotation and Galilean symmetry

We show that the structure of multidimensional systems of conservation laws, equipped with a single, convex entropy, and with both rotation and Galilean symmetries, is perhaps surprisingly limited. The following are established.The simplest examples of such systems, with only one vector field, are at most simple extensions of the familiar Euler systems.In such models of magnetohydrodynamic flow, including a solenoidal, Galilean invariant magnetic field, the property of finite signal propagation speeds is often lost.The only such system describing adiabatic multi-fluid flow, with the mass of each species conserved separately, corresponds to independent flow of each species. Whatever interaction between the different species occurs in an energy equation or through some other dependent variable, and not simply through expressions for the pressures in terms of the speciesʼ densities. A similar conclusion holds for incompressible flow.

BIFURCATIONS, STABILITY AND SYNCHRONIZATION IN DELAYED OSCILLATORY NETWORKS

Current studies in neurophysiology award a key role to collective behaviors in both neural information and image processing. This fact suggests to exploit phase locking and frequency entrainment in oscillatory neural networks for computational purposes. In the practical implementation of artificial neural networks delays are always present due to the non-null processing time and the finite signal propagation speed. This manuscript deals with networks composed by delayed oscillators, we show that either long delays or constant external inputs can elicit oscillatory behavior in the single neural oscillator. Using center manifold reduction and normal form theory, the equations governing the whole network dynamics are reduced to an amplitude-phase model (i.e. equations describing the evolution of both the amplitudes and the phases of the oscillators). The analysis of a network with a simple architecture reveals that different kind of phase locked oscillations are admissible, and the possible coexistence of in-phase and anti-phase locked solutions.

Global Exponential Stability and Global Convergence in Finite Time of Delayed Neural Networks With Infinite Gain

This paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity, while the delay accounts for the finite switching speed of the neuron amplifiers, or the finite signal propagation speed. It is known that the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability. The goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay. More precisely, conditions are given under which there is a unique equilibrium point of the neural network, which is globally exponentially stable for the states, with a known convergence rate. The conditions are easily testable and independent of the delay. Moreover, global convergence in finite time of the state and output is investigated. In doing so, new interesting dynamical phenomena are highlighted with respect to the case without delay, which make the study of convergence in finite time significantly more difficult. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations but without delays.

Synchronized chaos in extended systems and meteorological teleconnections

While synchronized chaos is familiar in low-order systems, the relevance of this paradigm to natural phenomena and spatially extended systems is questionable because of the time lags introduced by finite signal propagation speeds. A form of partially synchronized chaos is here demonstrated in a low-order numerical model of the coupled large-scale atmospheric circulation patterns in the northern and southern hemispheres. The model is constructed using a Green's function method to represent the time-lagged boundary forcing of the flow in each hemisphere by Rossby waves emanating from the opposite hemisphere. The two hemispheric subsystems are semiautonomous because Rossby waves cannot penetrate the tropics except in narrow longitudinal bands where the background winds are westerly. Each hemisphere has previously been described by a 10-variable model, derived from a spectral truncation of the barotropic vorticity equation. The model exhibits dynamical regimes corresponding to ``blocked'' and ``zonal'' atmospheric flow patterns in the hemisphere. Applying the same spectral truncation to the Green's functions that define the coupling, we construct a 28-variable model of the coupled flow on a planet with simplified geometry and background wind field. Partial synchronization is manifest in a significant tendency for the two hemispheric subsystems to occupy the same regime simultaneously. This tendency is observed in actual meteorological data. Partial synchronization of this form can be viewed as an extension of on-off intermittency in a system with a synchronization manifold, to a region of parameter space that is far from the bifurcation point at which this manifold loses stability.

Transport Equations in Chromatography with a Finite Speed of Signal Propagation

Abstract It is known that the diffusion equation used to model transport in a large variety of chromatographic techniques has an infinite speed of signal propagation, i.e., if c(x,t) is the concentration at time t, then c(x,t) > 0 for any t > 0. We generalize and solve the telegraph equation, which is known to have a finite speed of signal propagation, to allow for asymmetric convection, as is appropriate for the theory of chromatographic processes. We derive the telegraph equation from a continuous time random walk picture and examine two sources of convection, an asymmetry in sojourn times in states in which diffusing particles move in one direction or the other, and a corresponding asymmetry in the velocities.

Observations on fixed‐bed dispersion models: The role of the interstitial fluid

AbstractModels of the role of the interstitial fluid for dispersion in a fixed bed for very high Reynolds numbers are examined in detail to determine how well they fit the physical requirements of finite speed of signal propagation, no backmixing, conservation and correct asymptotic form. It is concluded that no linear continuous partial differential equation of finite order can satisfy all of these requirements as well as the cell model, although all models for sufficiently large axial space and time variables are very good approximations to the cell model. Some new hyperbolic models are presented and their solutions obtained and compared with the standard solutions. In present day design it appears that no model has an outstanding advantage over any other.