Search results for "Boundary value problem"
showing 10 items of 551 documents
A study on spectral optimisation in partial response CPM signals
1995
An optimisation technique for the minimisation of the effective bandwidth in partial response CPM signals is described. The minimum Euclidean distance is used as optimisation constraint because the bit error probability is a function of this parameter for high values of signal to noise ratio. The procedure has been implemented for a correlation length corresponding to two signalling intervals. The optimisation problem leads to a system of two nonlinear differential equations for the pulse shape, together with some boundary conditions. Numerical solution of the differential equations has been performed; initial conditions have been adjusted, to satisfy the boundary conditions using an iterat…
Universal natural shapes: From unifying shape description to simple methods for shape analysis and boundary value problems
2012
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three …
Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model
2021
Topological physics strongly relies on prototypical lattice model with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that is directly mapped to the one-dimensional Su-Schrieffer-Heeger chiral model. Starting from the continuous two dimensional wave equation we use a combination of monomadal approximation and the condition of equal length tube segments to arrive at the wanted discrete equations. It is shown that open or closed boundary conditions topological leads automatically to the existence of edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conserv…
Diffusion front capturing schemes for a class of Fokker–Planck equations: Application to the relativistic heat equation
2010
In this research work we introduce and analyze an explicit conservative finite difference scheme to approximate the solution of initial-boundary value problems for a class of limited diffusion Fokker-Planck equations under homogeneous Neumann boundary conditions. We show stability and positivity preserving property under a Courant-Friedrichs-Lewy parabolic time step restriction. We focus on the relativistic heat equation as a model problem of the mentioned limited diffusion Fokker-Planck equations. We analyze its dynamics and observe the presence of a singular flux and an implicit combination of nonlinear effects that include anisotropic diffusion and hyperbolic transport. We present numeri…
A second-order sparse factorization method for Poisson's equation with mixed boundary conditions
1992
Abstract We propose an algorithm for solving Poisson's equation on general two-dimensional regions with an arbitrary distribution of Dirichlet and Neumann boundary conditions. The algebraic system, generated by the five-point star discretization of the Laplacian, is solved iteratively by repeated direct sparse inversion of an approximating system whose coefficient matrix — the preconditioner — is second-order both in the interior and on the boundary. The present algorithm for mixed boundary value problems generalizes a solver for pure Dirichlet problems (proposed earlier by one of the authors in this journal (1989)) which was found to converge very fast for problems with smooth solutions. T…
Coherent Control of Stimulated Emission inside one dimensional Photonic Crystals:Strong Coupling regime
2006
The present paper discusses the stimulated emission, in strong coupling regime, of an atom embedded inside a one dimensional (1D) Photonic Band Gap (PBG) cavity which is pumped by two counter-propagating laser beams. Quantum electrodynamics is applied to model the atom-field interaction, by considering the atom as a two level system, the e.m. field as a superposition of normal modes, the coupling in dipole approximation, and the equations of motion in Wigner-Weisskopf and rotating wave approximations. In addition, the Quasi Normal Mode (QNM) approach for an open cavity is adopted, interpreting the local density of states (LDOS) as the local density of probability to excite one QNM of the ca…
Seismically induced, non-stationary hydrodynamic pressure in a dam-reservoir system
2003
Stochastic seismic analysis of hydrodynamic pressure in a dam-reservoir system is presented in this paper. The analysis is conducted assuming infinite reservoir compressible fluid and modeling seismic acceleration as a normal zero-mean stochastic process obtained by Penzien filter. The non-homogeneous boundary conditions associated to the problem have been incorporated into the equation of pressure wave scattering in the form of a forcing function turning the non-homogeneous boundary value problem into an homogeneous one. Solution obtained via modal analysis in time-domain is coupled with the use of classical Ito stochastic differential calculus to characterize the stochastic hydrodynamic p…
PANORMUS-SPH. A new Smoothed Particle Hydrodynamics solver for incompressible flows
2015
Abstract A new Smoothed Particle Hydrodynamics (SPH) solver is presented, fully integrated within the PANORMUS package [7] , originally developed as a Finite Volume Method (FVM) solver. The proposed model employs the fully Incompressible SPH approach, where a Fractional Step Method is used to make the numerical solution march in time. The main novelty of the proposed model is the use of a general and highly flexible procedure to account for different boundary conditions, based on the discretization of the boundary surfaces with a set of triangles and the introduction of mirror particles with suitable hydrodynamic properties. Both laminar and turbulent flows can be solved (the latter using t…
Electromagnetic Scattering by a Strip Grating with Plane-Wave Three-Dimensional Oblique Incidence by Means of Decomposition into E-Type and H-Type Mo…
1993
A numerical algorithm to analyze the plane-wave three-dimensional oblique incidence on a strip grating is presented. Electromagnetic field is decomposed into vector Floquet harmonics of the E-type and H-type modes. To impose boundary conditions on the incident, reflected and transmitted waves, two integral equations of Fredholm of first kind are obtained. These equations are solved numerically with the standard Galerkin procedure, and the convergence of the algorithm is examined numerically. Since the superficial current near the edges of a conducting strip have been taken into account, the computational algorithm shows a fast convergence. Results are compared with other numerical results a…
Efficient finite-difference scheme for solving some heat transfer problems with convection in multilayer media
2000
Abstract An efficient finite-difference method for solving the heat transfer equation with piecewise discontinuous coefficients in a multilayer domain is developed. The method may be considered as a generalization of the finite-volumes method for the layered systems. We apply this method with the aim to reduce the 3D or 2D problem to the corresponding series of 2D or 1D problems. In the case of constant piecewise coefficients, we obtain the exact discrete approximation of the steady-state 1D boundary-value problem.