1,721,033 research outputs found
Polynomial Spline Collocation Method For Nonlinear Two--Dimensional Weakly Singular Integral Equations
No full textINTRODUCTION The solution of a second kind Fredholm integral equation with weakly singular kernel is typically nonsmooth near the boundary of the domain of integration (its derivatives are unbounded, see, for example, [1-3, 5, 7-8, 10-14]). If one wants to obtain a high order convergence of a numerical method for these equations one has to take into account, in some way, the singular behavior of the exact solution. The purpose of the present paper is to discuss how it can be done using polynomial splines on special graded grids in the numerical solution of a sufficiently wide class of nonlinear two-dimensional weakly singular integral equations. 2. INTEGRAL EQUATION We consider the nonlinear equation u(x) \Gamma Z G K(x; y; u(y))dy = f(x) ; x 2 G ; (1) where G j<
Field-induced anisotropy in the quasi-two-dimensional weakly anisotropic antiferromagnet [CuCl(pyz)2]BF4
Get PDFWe measured NMR and magnetic susceptibility for the quasi-two-dimensional, weakly XY -like, spin-1/2 square-lattice Heisenberg antiferromagnet [CuCl(pyz)2]BF4 (pyz = pyrazine = N2C4H4) near the critical temperature. The Néel temperature TN and the order-parameter critical exponent β were obtained from the NMR line broadening as a function of temperature. As the applied field strength (H || c) was increased, TN increased and β decreased. This behavior indicates that the field effectively enhanced XY anisotropy. The susceptibility as a function of temperature did not show a clear feature for TN, but showed field-dependent minima below TN for both H || c and H || ab, where minimum features disappeared for μ0H > 2 T
Lie symmetry analysis of two dimensional weakly singular integral equations
No full textIn this paper, symmetry groups of a two-dimensional weakly singular integral equation are discussed. A new method is proposed for the prolongation formula of the given equations. Using the introduced prolongation formula, we derive the symmetry groups and invariant solutions of the above-mentioned weakly singular integral equation wherever possible. In order to solve the extracted determining equation, a special approach is proposed. The symmetry groups for different types of the free terms are presented
Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations
Get PDF„Polynomial spline collocation method for nonlinear two‐dimensional weakly singular integral equations" Mathematical Modelling Analysis, 2(1), p. 122-129
First Published Online: 14 Oct 201
A comparison of transformation methods for evaluating two-dimensional weakly singular integrals
No full textAccurate numerical evaluation of integrals arising in the boundary element method is fundamental to achieving useful results via this solution technique. In this paper, a number of techniques are considered to evaluate the weakly singular integrals which arise in the solution of Laplace's equation in three dimensions and Poisson's equation in two dimensions. Both are two-dimensional weakly singular integrals and are evaluated using (in a product fashion) methods which have recently been used for evaluating one-dimensional weakly singular integrals arising in the boundary element method. The methods used are based on various polynomial transformations of conventional Gaussian quadrature points where the transformation polynomial has zero Jacobian at the singular point. Methods which split the region of integration into sub-regions are considered as well as non-splitting methods. In particular, the newly introduced and highly accurate generalized composite subtraction of singularity and non-linear transformation approach (GSSNT) is applied to various two-dimensional weakly singular integrals. A study of the different methods reveals complex relationships between transformation orders, position of the singular point, integration kernel and basis function. It is concluded that the GSSNT method gives the best overall results for the two-dimensional weakly singular integrals studied.Griffith Sciences, School of Natural SciencesNo Full Tex
Dynamical conductivity of a two-dimensional weakly doped Holstein system
No full textThe generalized Drude formula is used to study conductivity properties of the two-dimensional weakly doped Holstein model with a free-electron-like dispersion. The relaxation processes associated with the scattering of conduction electrons by optical phonons are described in terms of a frequency- and temperature-dependent memory function. The imaginary and real parts of the memory function are analyzed in detail in the regime when characteristic energy scales of the problem, i.e., electron Fermi energy and optical phonon energy, are comparable in size. Results obtained at zero temperature and at finite temperatures are used to determine temperature effects in the real part of the dynamical conductivity as well as the frequency dependence of the optical electron mass and the electron relaxation rate. Finally, the characteristic fingerprints of a Holstein system with multiple phonon branches are identified in the dynamical electron conductivity
Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory
No full text4 pages, 1 figure, published in Phys. Rev. LettInternational audienceWe consider the grand potential of a two-dimensional weakly interacting homogeneous Bose gas at zero temperature. Building on a number-conserving Bogoliubov method for a lattice model in the grand canonical ensemble, we calculate the next order term as compared to the Bogoliubov prediction, in a systematic expansion of in powers of the parameter measuring the weakness of the interaction. Our prediction is in very good agreement with recent Monte Carlo calculations
Interface fluctuations in the two-dimensional weakly asymmetric simple exclusion process
No full textAbstractWe consider the two-dimensional weakly asymmetric simple exclusion process, where the asymmetry is along the X-axis. The generator for such a process can be written as ε—2L0+ε—1Lα, ε>0, where L0 and Lα are the generators for the nearest neighbor symmetric simple exclusion and totally asymmetric simple exclusion, respectively. We prove propagation of chaos and convergence to Burgers equation with viscosity in the limit as ε goes to zero. The density fluctuation field converges to a generalized Ornstein–Uhlenbeck process. The covariance kernel for a class of travelling wave solutions is consistent with a phase boundary which fluctuates according to a linear stochastic partial differential equation
Long-range ordering of turbulent stresses in 2D turbulence
No full textWe use filter-space techniques to study the geometric alignment of turbulent stresses and strain rates in an experimental quasi-two-dimensional weakly turbulent flow. When these stresses and strains are misaligned, the usual turbulent energy cascade can be suppressed; and more generally, the relative alignment of these two tensors determines the direction of the cascade. We show that as a function of length scale, the turbulent stress undergoes a transition to system-spanning order. However, by exploring analogously defined quantities in a field built from random Fourier modes, we see qualitatively similar behavior, suggesting that at least some of this ordering is purely kinematic. By comparing our results from the experiment and the random field, we highlight the role played by the orientation of the rate of strain tensor in the energy transfer process; additionally, our results allow us to pose several intriguing conjectures
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