A combination of analytic and numerical methods has yielded a clear understanding of the approach to the singularity in spatially inhomogeneous cosmologies. Strong support is found for the longstanding claim by Belinskii, Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or Mixmaster behavior. The Method of Consistent Potentials is used to establish the consistency of asy...

We introduce a simple finite difference scheme for the elliptic interface problem. The scheme is symmetric, definite and monotone with second order accuracy. It is also quite naturally adapted to corner singularities. A simple adaptive strategy yields competitive performance even in the severe case of intersecting interfaces.

The background-field method is adopted for studying the dynamics of coherent states within an interacting scalar field theory. Focusing on a state that corresponds to homogeneous condensate, quantum depletion expectation value operator demonstrated be due annihilation condensate constituents into relativistic quanta. Moreover, fact initial acceleration and energy nonsqueezed are determined in t...

We address the algebraic problem of analysing the local topology of each singularity of a plane complex algebraic curve defined by a squarefree polynomial with both exact (i.e. integers or rationals) and inexact data (i.e. numerical values). For the inexact data, we associate a positive real number that measures the noise in the coefficients. This problem is ill-posed in the sense that tiny cha...

We propose a method for the solution of non-Hermitian ill-conditioned nonlinear eigenvalue problems T (λ)x = 0, which is based on singularity theory of nonlinear equations. The singularity of T (λ) is characterized by a scalar condition μ(λ) = 0 where the singularity function μ is implicitly defined by a nonsingular linear system with the appropriately bordered matrix T (λ). One Newton step for...

Figure 4. Singularity formation when boundary conditions are such that the catenoid solution does not exist. 7 Figure 3. Limiting catenoid surface obtained from an initially cylindrical surface. is the minimal surface with the same xed boundary. Figure 3 shows the required catenoid. This surface was obtained as the limiting surface of a FEM evolution starting from a cylindrical initial surface ...

A Translation Invariance Denoising Algorithm with Wavelet Threshold and its Application on Signal Processing of Laser Interferometer Hydrophone is investigated. The obtained signal of Laser interferometer hydrophone exist a large number of singularity points, and the denoising algorithm of Donoho’s wavelet threshold may produce the Pseudo Gibbs phenomenon on the singularity points. To eliminate...

We propose a phase-space formulation for the nonlinear Schrödinger equation with a white-noise potential in order to shed light on two problems: the rate of dispersion and the singularity formation. Our main tools are the energy laws and the variance identity. The method is completely elementary. For the problem of dispersion, we show that in the absence of dissipation the ensemble-average disp...

Singularity is a fundamental problem with robotic manipulators. Various methods of singularity handling have been published in the past. In this paper, a singularity robust method is presented and its implementation issues discussed. It focuses on the discontinuity problem inherent in the singularity robust techniques with removal of degenerate components. Sources of the discontinuity are discu...