The image segmentation problem in computer vision is considered. Given a two-dimensional domain D and a function defined on it (the original image), the problem is to obtain a ‘cartoon’ associated with this function...
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We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or -1) and these block spin values are kept fixed. We then impo...
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We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or -1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that beta(c) is close to 1, which, compared to the original nearest neighbor Ising beta(c) = 0.44..., shows that the critical temperature has been reduced by more than one half For none of the other 11 block-spin configurations that ive have considered is there any indication of a phase transition in the constrained system of original spins.
In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonhar...
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In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see (3]). In the case of an orthonormal basis, our estimate reduces to Kadec' optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4] for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases.
For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is prim...
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For a volume-preserving map, we show that the exit time averaged over the entry set of a region is given by the ratio of the measure of the accessible subset of the region to that of the entry set. This result is primarily of interest to show two things: First, it gives a simple bound on the algebraic decay exponent of the survival probability. Second, it gives a tool for computing the measure of the accessible set. We use this to compute the measure of the bounded orbits for the Henon quadratic map. (C) 1997 American Institute of Physics.
This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u(t) = Lu + Nf(u), where L and N are linear differential operators and f(u) is a nonlinear f...
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This work develops fast and adaptive algorithms for numerically solving nonlinear partial differential equations of the form u(t) = Lu + Nf(u), where L and N are linear differential operators and f(u) is a nonlinear function. These equations are adaptively solved by projecting the solution u and the operators L and N into a wavelet basis. Vanishing moments of the basis functions permit a sparse representation of the solution and operators. Using these sparse representations fast and adaptive algorithms that apply operators to functions and evaluate nonlinear functions, are developed for solving evolution equations. For a wavelet representation of the solution u that contains N-s significant coefficients, the algorithms update the solution using O(N-s) operations. The approach is applied to a number of examples and numerical results are given. (C) 1997 Academic Press.
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyp...
We work with symplectic diffeomorphisms of the n-annulus A(n) = T*(R-n/Z(n)). Using the variational approach of Aubry and Mather, we are able to give a local description of the stable (and unstable) manifold for a hyperbolic fixed point. We use this in order to get a Melnikov-like formula for exact symplectic twist maps. This formula involves an infinite series that could be computed in some specific cases. We apply our formula to prove the existence of heteroclinic orbits for a family of twist maps in R-4.
The linear stability analysis of the full time-dependent Kirchhoff equations for elastic filaments gives precise information about possible dynamical instabilities. The associated dispersion relations derived in the p...
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The linear stability analysis of the full time-dependent Kirchhoff equations for elastic filaments gives precise information about possible dynamical instabilities. The associated dispersion relations derived in the preceding paper provides the selection mechanism for the shapes selected by highly unstable filaments. Here we perform a nonlinear analysis and derive new amplitude equations which describe the dynamics above the instability threshold. The straight filament is studied in detail and the motion is shown to be described by a pair of nonlinear Klein-Gordon equations which couple the local deformation amplitude to the twist density. Of particular interest is the effect of boundary conditions on the instability threshold. It is shown that with suitable choice of boundary conditions the threshold of instability is delayed. We also show the existence of pulse-like and front-like traveling wave solutions.
A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower f...
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A formulation for selecting operator and control inputs to a high fidelity dynamics model, governed by differential-algebraic equations, is presented to minimize deviation in its response relative to that of a lower fidelity model that is also governed by differential-algebraic equations of motion. An adjoint variable method for computing sensitivity of the error measure defined is derived and implemented in a nonlinear programming formulation that is suitable for iterative minimization of the error functional. A numerical example using a multibody mechanism is presented to demonstrate effectiveness of the method and provide insights into means for effectively formulating problems of model correlation and strategies for their solution.
The detection and unfolding of degenerate local bifurcations provides one of very few generally applicable analytical tools for studying complex dynamics in systems of arbitrarily high dimension. Using the Brusselator...
The detection and unfolding of degenerate local bifurcations provides one of very few generally applicable analytical tools for studying complex dynamics in systems of arbitrarily high dimension. Using the Brusselator partial differential equations (PDEs) (Prigogine and Lefever, 1968) as motivation and main example, we critically review this method. We extend and correct previous calculations, presenting explicit formulae from which normal forms accurate to third order may be computed, and for the first time we carefully compare bifurcations and dynamics of these normal forms with those of the untransformed systems restricted to a center manifold, and with Galerkin and finite difference approximations of the original PDE. While judicious use of symbolic manipulations makes feasible such high-order center manifold and normal form calculations, we show that the conclusions drawn from them are of limited use in understanding spatio-temporal complexity and chaos. As Guckenheimer (1981) argued, the method permits proof of existence of quasi-periodic motions and, under mild genericity assumptions, Sil'nikov chaos (sub-shifts of finite type), but the parameter and phase space ranges in which these results may be applied are extremely small.
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