Search results for "Mathematical analysis"
showing 10 items of 2409 documents
On the Path and Area J<sub>x1</sub>-Integral Components and their Relationship to the Out-of-Plane Constraint in Elastic Cracked Plates
2009
In this paper, the path and area components of the Jx1-integral, JP and JA, in three dimensional elastic cracked plates under mode-I loading are investigated aiming at relating them to the out-of-plane constraint conditions resulting from different specimen thicknesses. It is concluded that the JP and JA components of the Jx1-integral vary in the region where the out-of-plane constraint extends. Sufficiently far from the crack front, these integrals tend to stabilize, indicating that the thickness constraint vanishes and that a 2D-like stress and strain fields have been reached. A pure plane strain condition is only attained when the specimen thickness is very large when compared to the in-…
Solving the Cut-Off Wave Numbers in Partially filled Rectangular Waveguides with Ferrite by the Cauchy Integral Method
2005
The modal analysis of the off-centered rectangular waveguide loaded with a vertical slab of ferrite material, biased in the y-direction by a DC magnetic field, leads to the resolution of a transcendent equation whose infinite solutions are the TE/sub m0/ cutoff wave numbers in the guide. The method based on the Cauchy integral (Delvest L.M. and Lyness, J.N., 1967) is becoming very popular for solving such equations. This powerful method is described for solving the propagation constant in a partially ferrite filled waveguide. The method is used to calculate the propagation constant of the fundamental TE mode for some configurations used in the literature about ferrites. Results obtained in …
A lumped model for a seismic source
1993
A lumped mechanical model is proposed and solved. This model is dynamically equivalent, in the mean field approximation, to a faulted lithosphere. The transition from the continuous system (modelled according to W. H. Prescott and A. Nur) to the lumped one, has been made by preserving all the relevant features exhibited by the continuous system. In particular the coupling between different components of the stress and strain tensors is suitably taken into account. The dynamics of the lumped system depends on six control parameters fixed by the physical properties of the continuous system. Three of the control parameters are dimensionless and describe: the seismic wave quality factor of the…
Inverse photonic-crystal-fiber design through geometrical and material scalings
2020
Geometrical and material - i.e., external and internal - scaling symmetries are exploited to obtain approximated analytical expressions for the mode effective index, group index, and chromatic dispersion of a scaled fiber. Our results include material refractive index scaling that changes the numerical aperture. First, the analytical expressions are successfully tested with a conventional step index fiber in a broadband range of wavelengths, from 1 to 2 mu m. Then, we establish a procedure to adapt the analytical expressions to photonic crystal fibers (PCFs) and illustrate its application in a triangular PCF with circular holes. These adapted analytical expressions show good agreement with …
The Numerical Simulation of Relativistic Fluid Flow with Strong Shocks
2001
In this review we present and analyze the performance of a Go-dunov type method applied to relativistic fluid flow. Our model equations are the corresponding Euler equations for special relativistic hydrodynamics. By choosing an appropriate vector of unknowns, the equations of special relativistic fluid dynamics (RFD) can be written as a hyperbolic system of conservation laws. We give a complete description of the spectral decomposition of the Jacobian matrices associated to the fluxes in each spatial direction, (see (Donat et al., 1998), for details), which is the essential ingredient of the Godunov-type numerical method we propose in this paper. We also review a numerical flux formula tha…
A Second Order Accurate Kinetic Relaxation Scheme for Inviscid Compressible Flows
2013
In this paper we present a kinetic relaxation scheme for the Euler equations of gas dynamics in one space dimension. The method is easily applicable to solve any complex system of conservation laws. The numerical scheme is based on a relaxation approximation for conservation laws viewed as a discrete velocity model of the Boltzmann equation of kinetic theory. The discrete kinetic equation is solved by a splitting method consisting of a convection phase and a collision phase. The convection phase involves only the solution of linear transport equations and the collision phase instantaneously relaxes the distribution function to an equilibrium distribution. We prove that the first order accur…
Forces Between Thin Coils With Parallel Axes Using Bessel Functions
2013
A method based on Bessel functions is presented for calculating the forces between combinations of thin coils with parallel axes. The coaxial case is solved in closed form in terms of elliptic integrals, whereas for the noncoaxial case the force components are expressed both as integrals of Bessel functions and as integrals of complete elliptic integrals. The results for the coaxial case have been compared with calculations in the literature with excellent agreement. The numerical results presented for the noncoaxial have been cross-checked by comparing the two methods. These methods can also be applied to current loops, disk coils, thick noncoaxial cylindrical coils, and various combinatio…
Heat Conduction Problem for Double-Layered Ball
2014
Heat conduction models for double layered spherical sample are developed. Parabolic (classic, based on Fourier’s Law) and hyperbolic (based on Modified Fourier’s Law) heat conduction equations are used to describe processes in the sample during Intensive Quenching. Solution and numerical results are obtained for 1D model using Conservative Averaging method and transforming the original problem for a sphere to a new problem for a slab, with non classic boundary condition. Models include boundary conditions of third kind and non-linear BC case. Numerical results are presented for several relaxation time and initial heat flux values.
General measurement technique of the ratio between chromatic dispersion and the nonlinear coefficient
2021
Measuring the nonlinear coefficient γ of any guiding medium, regardless of the sign and magnitude of its group-velocity dispersion parameter β 2 , is challenging because of the lack of general solutions of the nonlinear Schrodinger equation (NLSE). Indeed, existing approaches typically need to disregard chromatic-dispersion effects to determine γ [1] . Here we propose an all-encompassing approach to measure the ratio β 2 /γ and prove our method in polarization-maintaining (PM) and single-mode (SM) fibers with positive and negative β 2 .
Systems of Linear Equations
2016
A linear equation in \(\mathbb {R}\) in the variables \(x_1,x_2,\ldots ,x_n\) is an equation of the kind: