50 research outputs found
Wave packet propagation by the Faber polynomial approximation in electrodynamics of passive media
Maxwell's equations for propagation of electromagnetic waves in dispersive
and absorptive (passive) media are represented in the form of the Schr\"odinger
equation , where is a linear
differential operator (Hamiltonian) acting on a multi-dimensional vector
composed of the electromagnetic fields and auxiliary matter fields describing
the medium response. In this representation, the initial value problem is
solved by applying the fundamental solution to the initial field
configuration. The Faber polynomial approximation of the fundamental solution
is used to develop a numerical algorithm for propagation of broad band wave
packets in passive media. The action of the Hamiltonian on the wave function
is approximated by the Fourier grid pseudospectral method. The algorithm
is global in time, meaning that the entire propagation can be carried out in
just a few time steps. A typical time step is much larger than that in finite
differencing schemes, . The accuracy and stability
of the algorithm is analyzed. The Faber propagation method is compared with the
Lanczos-Arnoldi propagation method with an example of scattering of broad band
laser pulses on a periodic grating made of a dielectric whose dispersive
properties are described by the Rocard-Powels-Debye model. The Faber algorithm
is shown to be more efficient. The Courant limit for time stepping, , is exceeded at least in 3000 times in the Faber propagation
scheme.Comment: Latex, 17 pages, 4 figures (separate png files); to appear in J.
Comput. Phy
Investigation on polynomial integrators for time-domain electromagnetics using a high-order discontinuous Galerkin method
International audienceIn this work, we investigate the application of polynomial integrators in a high-order discontinuous Galerkin method for solving the time-domain Maxwell equations. After the spatial discretization, we obtain a time-continuous system of ordinary differential equations of the form, ∂tY(t)=HY(t), where Y(t) is the electromagnetic field, H is a matrix containing the spatial derivatives, and t is the time variable. The formal solution is written as the exponential evolution operator, exp(tH), acting on a vector representing the initial condition of the electromagnetic field. The polynomial integrators are based on the approximation of exp(tH) by an expansion of the form ∑ _m=0^\infinity gm(t) Pm(H), where gm(t) is a function of time and Pm(H) is a polynomial of order m satisfying a short recursion. We introduce a general family of expansions of exp(tH) based on Faber polynomials. This family of expansions is suitable for non-Hermitian matrices, and consequently the proposed integrators can handle absorbing media and conductive materials. We discuss the efficient implementation of this technique, and based on some test problems, we compare the virtues and shortcomings of the algorithm. We also demonstrate how this scheme provides an efficient alternative to standard explicit integrators
Compact support wavelet representations for solution of quantum and electromagnetic equations: Eigenvalues and dynamics
Wavelet-based algorithms are developed for solution of quantum and electromagnetic differential equations. Wavelets offer orthonormal localized bases with built-in multiscale properties for the representation of functions, differential operators, and multiplicative operators. The work described here is part of a series of tools for use in the ultimate goal of general, efficient, accurate and automated wavelet-based algorithms for solution of differential equations.
The most recent work, and the focus here, is the elimination of operator matrices in wavelet bases. For molecular quantum eigenvalue and dynamics calculations in multiple dimensions, it is the coupled potential energy matrices that generally dominate storage requirements. A Coefficient Product Approximation (CPA) for the potential operator and wave function wavelet expansions dispenses with the matrix, reducing storage and coding complexity. New developments are required, however. It is determined that the CPA is most accurate for specific choices of wavelet families, and these are given here. They have relatively low approximation order (number of vanishing wavelet function moments), which would ordinarily be thought to compromise both wavelet reconstruction and differentiation accuracy. Higher-order convolutional coefficient filters are determined that overcome both apparent problems. The result is a practical wavelet method where the effect of applying the Hamiltonian matrix to a coefficient vector can be calculated accurately without constructing the matrix.
The long-familiar Lanczos propagation algorithm, wherein one constructs and diagonalizes a symmetric tridiagonal matrix, uses both eigenvalues and eigenvectors. We show here that time-reversal-invariance for Hermitian Hamiltonians allows a new algorithm that avoids the usual need to keep a number Lanczos vectors around. The resulting Conjugate Symmetric Lanczos (CSL) method, which will apply for wavelets or other choices of basis or grid discretization, is simultaneously low-operation-count and low-storage. A modified CSL algorithm is used for solution of Maxwell's time-domain equations in Hamiltonian form for non-lossy media. The matrix-free algorithm is expected to complement previous work and to decrease both storage and computational overhead. It is expected- that near-field electromagnetic solutions around nanoparticles will benefit from these wavelet-based tools. Such systems are of importance in plasmon-enhanced spectroscopies
SPIG2018
This Special Issue covers a wide range of topics from fundamental studies to applications of ionized gases. It is dedicated to four topics of interest: 1. ATOMIC COLLISION PROCESSES (electron and photon interactions with atomic particles, heavy particle collisions, swarms, and transport phenomena); 2. PARTICLE AND LASER BEAM INTERACTION WITH SOLIDS (atomic collisions in solids, sputtering and deposition, and laser and plasma interactions with surfaces); 3. LOW TEMPERATURE PLASMAS (plasma spectroscopy and other diagnostic methods, gas discharges, and plasma applications and devices); 4. GENERAL PLASMAS (fusion plasmas, astrophysical plasmas, and collective phenomena). This Special Issue of Atoms will highlight the need for continued research on ionized gas physics in different topics ranging from fundamental studies to applications, and will review current investigations
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity
Framework for media oriented transport systems
Dissertação de mestrado integrado em Engenharia Electrónica Industrial e ComputadoresThe natural evolution of embedded systems resulted in a faster execution of tasks,
increased possibility for including additional features, allied to lower power consumption
and benefiting from ever-growing rates of integration as far as silicon is
concerned. The automotive industry is not an exception with regards to the integration
of technology for a vast arrays of applications in systems which vary from
entertainment of infotainment to systems related to vehicle safety and stability
such as driver assists. The existence of diverse independent systems in modern
cars, combined with the necessity of centralizing the user interface, simplifying the
operation of the system and minimizing the user’s intervention, help to promote
the comfort and reduce the likelihood of distractions taking place while driving.
Modern communication oriented network standards, e.g. MOST or FlexRay, enable
information compatibility when exchanged between systems communicating
over different protocols. Moreover, the coexistence of packet, control and timesensitive
information are ensured within timing requirements, providing a reliable
QoS (Quality of Service) and by making use of a single physical transmission mean.
Synchronized multimedia data (e.g. synchronized video and audio transmission)
are example of this kind of (time-sensitive) information.
This dissertation proposes a framework for design and development of network
distributed applications in the field of automotive infotainment, compliant with
the industry standards and using FPGA technology in order to ensure the system
requirements satisfaction and promote IP Core re-utilization.A evolução natural dos sistemas embebidos traduziu-se numa maior rapidez na execução
de tarefas, a possibilidade de incluir mais funcionalidades, aliado a menores
consumos energéticos e beneficiando de crescentes e elevadas taxas de integração
ao nível de silício. A indústria automóvel não é excepção no que diz respeito à
integração de tecnologia para as mais variadas aplicações, com ou sem tolerância
à falha, em sistemas que vão desde entretenimento ou infotainment a sistemas
relacionados com a estabilidade e segurança do veículo, como é exemplo
as driver assists. Existem de vários sistemas independentes nos modernos veículos
automóveis. Estes, combinados com a necessidade de centralização ao nível de
interface com o utilizador, tornam imperativa a simplicidade da operação. Para
tal, requerem a minimizaccão da intervenção do utilizador, promovendo o conforto
e diminuindo a probabilidade de desconcentração durante o exercício de condução.
Os mais modernos standards de redes de comunicação como é exemplo o MOST
ou o FlexRay, permitem a compatibilidade de informação trocada entre sistemas
que comunicam através de distintos protocolos de comunicação. Para além disso,
ainda garantem a coexistência de informação de controlo, informação do entretenimento
e informação do tipo time-sensitive, onde os requisitos de temporização
devem ser assegurados, mantendo uma qualidade de serviço fiàvel e fazendo uso
de um único meio físico de transmissão. São exemplos deste tipo de informação,
dados síncronos do tipo multimédia (e.g. streaming de àudio e vídeo de forma
sincronizada). Pretende-se desenvolver uma framework para desenvolvimento de
aplicações de rede distribuídas, do tipo infotainment e que beneficia a aplicação de
tecnologias como FPGA, no offloading de computação para este dispositivo, como
meio de garantir a satisfação dos requisitos, e promover a reutilização deste tipo
de sistemas, mantendo o elevado desempenho na troca de dados e promovendo a
portabilidade e a modularidade
The Fifteenth Marcel Grossmann Meeting
The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity