Добірка наукової літератури з теми "Telegrapher's models"

<abstract><p>This work deals with wave propagation into a coaxial cable, which can be modelled by the 3D Maxwell equations or 1D simplified models. The usual model, called the telegrapher's model, is a 1D wave equation of the electrical voltage and current. We derived a more accurate model from the Maxwell equations that takes into account dispersive effects. These two models aim to be a good approximation of the 3D electromagnetic fields in the case where the thickness of the cable is small. We perform some numerical simulations of the 3D Maxwell equations and of the 1D simplified models in order to validate the usual model and the new one. Moreover, we show that, while the usual telegrapher model is of order one with respect to the thickness of the cable, the dispersive 1D model is of order two.</p></abstract>

AbstractThe Cattaneo or telegrapher’s equation describes the crossover from initial ballistic to normal diffusion. Here we study and survey time-fractional generalisations of this equation that are shown to produce the crossover of the mean squared displacement from superdiffusion to subdiffusion. Conditional solutions are derived in terms of Fox H-functions and the δth-order moments as well as the diffusive flux of the different models are derived. Moreover, the concept of the distribution-like is proposed as an alternative to the probability density function.

We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.

A family of consistent thin-wire representation models blended with a 3-D optimized vector finite-element time-domain/finite-difference time-domain method is developed in this paper for nanomaterial and graphene devices. Based on a tailored set of telegrapher’s equations, the novel technique approximates traveling waves along the radial direction of the wire and minimizes artificial instabilities. Also, through a non-overlapping grid discretization algorithm, the hyperbolic character of Maxwell’s laws is physically preserved. In this way, tilted or circular-loop structures of arbitrary orientation are accurately coupled with the curvilinear algorithm. These attributes are successfully verified via various nanoscale components and finite-sized graphene arrangements.

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher-dimensional stochastic media (d > 1) where the particle can move along 2d directions. We derive the equations for probability density function using the "formulae of differentiation" of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media for it results in a true diffusion at constant speed in the limit of large dimensions.

A new approach, the propagating-source method, is introduced to solve the time-dependent Boltzmann equation. The method relies on the decomposition of the particle distribution function into scattered and unscattered particles. It is assumed in this paper that the particles are transported in a constant-velocity spherically expanding supersonic flow (such as the solar wind) in the presence of a radial magnetic field. Attention too has been restricted to very fast particles. The present paper addresses only large-angle scattering, which is modelled as a BGK relaxation time operator. A subsequent paper (Part 2) will apply the propagating-source method to a small-angle quasilinear scattering operator. Initially, we consider the simplest form of the BGK Boltzmann equation, which omits both adiabatic deceleration and focusing, to re-derive the well-known telegrapher equation for particle transport. However, the derivation based on the propagating-source method yields an inhomogeneous form of the telegrapher equation; a form for which the well-known problem of coherent pulse solutions is absent. Furthermore, the inhomogeneous telegrapher equation is valid for times t much smaller than the ‘scattering time’ τ, i.e. for times t [Lt ] τ, as well as for t > τ. More complicated forms of the BGK Boltzmann equation that now include focusing and adiabatic deceleration are solved. The basic results to emerge from this new approach to solving the BGK Boltzmann equation are the following. (i) Low-order polynomial expansions can be used to investigate particle propagation and transport at arbitrarily small times in a scattering medium. (ii) The theory of characteristics for linear hyperbolic equations illuminates the role of causality in the expanded integro-differential Fokker–Planck equation. (iii) The propagating-source approach is not restricted to isotropic initial data, but instead arbitrarily anisotropic initial data can be investigated. Examples using different ring-beam distributions are presented. (iv) Finally, the numerical scheme can include both small-angle and large-angle particle scattering operators (Part 2). A detailed discussion of the results for the various Boltzmann-equation models is given. In general, it is found that particle beams that experience scattering by, for example, interplanetary fluctuations are likely to remain highly anisotropic for many scattering times. This makes the use of the diffusion approximation for charged-particle transport particularly dangerous under many reasonable solar-wind conditions, especially in the inner heliosphere.

We develop a systematic procedure to quantise canonically Hamiltonians of light-matter models of transmission lines coupled through lumped linear lossless ideal nonreciprocal elements, that break time-reversal symmetry, in a circuit QED set-up. This is achieved through a description of the distributed subsystems in terms of both flux and charge fields. We prove that this apparent redundancy is required for the general derivation of the Hamiltonian for a wider class of networks. By making use of the electromagnetic duality symmetry in transmission lines (waveguides), we provide unambiguous identification of the physical degrees of freedom, separating out the nondynamical parts. This doubled description can also treat the case of other extended lumped interactions in a regular manner that presents no spurious divergences, as we show explicitly in the example of a circulator connected to a Josephson junction through a transmission line. This theory enhances the quantum engineering toolbox to design complex networks with nonreciprocal elements.

Abstract In this work, we construct an efficient numerical method to solve 3D Maxwell’s equations in coaxial cables. Our strategy is based upon a hybrid explicit-implicit time discretization combined with edge elements on prisms and numerical quadrature. One of the objectives is to validate numerically generalized telegrapher’s models that are used to simplify the 3D Maxwell equations into a 1D problem. This is the object of the second part of the article.

AbstractAnomalous diffusion is ubiquitous in nature and relevant for a wide range of applications, including energy transport, especially in bio- and nano-technologies. Numerous approaches have been developed to describe it from a microscopic point of view, and recently, it has been framed within universality classes, characterized by the behaviour of the moments and auto-correlation functions of the transported quantities. It is important to investigate whether such universality applies to macroscopic models. Here, the spectrum of the moments of the solutions of the transport equations is investigated for three continuous PDE models featuring anomalous diffusion. In particular, we consider the transport described by: (i) a generalized diffusion equation with time-dependent diffusion coefficient; (ii) the Porous Medium Equation and (iii) the Telegrapher Equation. For each model, the key features of the source-type solution as well as the analytical results for the moment analysis are revisited and extended via both analytical and numerical approaches. Equivalence of the asymptotic behaviour of the corresponding heat transport is confirmed within the realm of weak anomalous diffusion.

AbstractThe Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher’s equation. A detailed understanding of the large time behaviour of the solutions to these equations has been mostly achieved in the case where the relaxation function, measuring the intensity of the relaxation towards equally distributed velocity densities, is constant. The goal of the presented work is to provide a general method to tackle the question of convergence to equilibrium when the relaxation function is not constant, and to do so as quantitatively as possible. In contrast to the usual modal decomposition of the equations, which is natural when the relaxation function is constant, we define a new Lyapunov functional of pseudodifferential nature, one that is motivated by the modal analysis in the constant case, that is able to deal with full spatial dependency of the relaxation function. The approach we develop is robust enough that one can apply it to multi-velocity Goldstein-Taylor models, and achieve explicit rates of convergence. The convergence rate we find, however, is not optimal, as we show by comparing our result to those found in [8].

Dans cette thèse, nous nous intéressons à la propagation des ondes électromagnétiques dans un réseau de câbles coaxiaux minces (constitués d'un matériau diélectrique qui entoure un fil intérieur métallique) avec sections transverses hétérogènes. Le premier objectif, atteint dans la thèse de G. Beck, était de réduire les équations de Maxwell 3D à un graphe quantique dans lequel on se ramène au calcul du potentiel et du courant électriques en résolvant des modèles 1D simplifiés. Ainsi, l'objectif principal de cette thèse est la validation numérique de ces modèles 1D.Dans un premier temps, nous avons proposé, analysé et mis en œuvre des méthodes numériques efficaces pour résoudre les modèles simplifiés 1D. Afin de réaliser la comparaison 1D/3D, un défi majeur est de concevoir des méthodes numériques pour résoudre les équations de Maxwell 3D qui sont adaptées à la spécificité des câbles électriques fins. Une procédure de discrétisation naïve basée sur un schéma explicite saute-mouton peut être vraiment coûteuse en raison de la finesse du câble. Nous avons alors proposé une approche originale consistant à adapter les éléments d'arête "Nedelec" à des mailles prismatiques allongées et à proposer une procédure de discrétisation temporelle hybride, explicite dans les directions longitudinales et implicite dans les directions transversales. En particulier, la condition de stabilité de la CFL qui en résulte n'est pas affectée par l'épaisseur du câble.Cependant, la méthode ci-dessus n'est efficace que pour des câbles parfaitement cylindriques : son extension naïve aux câbles déformés génère un recouplage longitudinal-transversal qui détruit l'efficacité de la méthode. En présence de déformations, la méthode doit donc être modifiée. En conséquence, afin de préserver le découplage longitudinal-transversal, nous proposons une méthode hybride combinant une discrétisation conforme dans les variables longitudinales et une méthode Galerkin discontinue dans les variables transversales. Cette méthode coïncide avec la précédente dans les parties cylindriques du câble
In this thesis we are interested in the electromagnetic wave propagation in a network of thin coaxial cables (made of a dielectric material which surrounds a metallic inner wire) with heterogeneous cross sections. The first goal, achieved in the PhD thesis of G. Beck few years ago, was to reduce 3D Maxwell’s equations to a quantum graph in which we reduce ourselves to the calculation of the electric potential and current by solving simplified 1D models. Thus, the main objective of this thesis is the numerical validation of these 1D models.In a first step we have proposed, analysed and implemented efficient numerical methods for solving the 1D approximate problems. In order to achieve the 1D/3D comparison, a major challenge is to design numerical methods for solving 3D Maxwell’s equations dedicated to taking into account the specificity of thin electric cables. A naive discretization procedure based on a leap-frog explicit scheme can be really costly because of the thinness of the cable. In the case have then proposed an original approach consisting in adapting Nedelec’s edge elements to elongated prismatic meshes and proposing a hybrid time discretization procedure which is explicit in the longitudinal directions and implicit in the transverse ones. In particular, the resulting CFL stability condition is not affected by the small thickness of the cable. However the above is only effective for perfectly cylindrical cables : its naive extension do deformed cables generates longitudinal-transverse recoupling that destroys the efficiency of the method. In the presence of deformations, the method needs to be modified. In order to preserve the longitudinal/transverse decoupling, we propose a hybrid method combining a conforming discretization in the longitudinal variable and a Discontinuous Galerkin method in the transverse ones. This method coincides with the previous one in the cylindrical parts of the cable

PLC - power line communication is not new. It has been known for many years. But It never be used in massive scale. There were only sporadic applications, for example ripple control system HDO used in the Czechoslovakia. PLC currently experiencing a renaissance thanks to the advent of Smart Grid. PLC offering relatively low bit rates and relatively unreliable transmission, but these disadvantages compensates very low costs to build a communication infrastructure and it offers specific functionalities for Smart Grid. The question is whether the declared parameters will be met in the real world. This thesis tries to find an answer.

The male telegraphers whose voices originally predominated in disembodied speech forums sometimes suggested that women should be excluded from virtual speech forums, and often worried that women should interact in the virtual world in traditionally gendered ways. Such nineteenth-century women telegraphers as Ella Thayer and Lida Churchill nevertheless voluminously produced literature that provided a format for their own technologically enabled literary utopias of new gender forms in the telegraphic virtual realm. Telegraphy seems to have appealed to women writers exactly because it provided a freedom that authors otherwise achieved primarily through the creation of literature. The freedom women experienced virtually emboldened the inscription of newly gendered models for both virtual and physical-world selfhood through the creation of women telegraphers’ literature.