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.
In this paper we rigorously show the existence and smoothness in epsilon of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values ...
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In this paper we rigorously show the existence and smoothness in epsilon of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameter epsilon. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.
We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understa...
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We present an efficient algorithm for calculating the minimum energy path(MEP)and energy barriers between local minima on a multidimensional potential energy surface(PES).Such paths play a central role in the understanding of transition pathways between metastable *** method relies on the original formulation of the string method[***.B,66,052301(2002)],*** evolve a smooth curve along a direction normal to the *** algorithm works by performing minimization steps on hyperplanes normal to the *** the problem of finding MEP on the PES is remodeled as a set of constrained minimization *** provides the flexibility of using minimization algorithms faster than the steepest descent method used in the simplified string method[***.,126(16),164103(2007)].At the same time,it provides a more direct analog of the finite temperature string *** applicability of the algorithm is demonstrated using various examples.
We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced ...
We study the motion of surfaces in an intrinsic formulation in which the surface is described by its metric and curvature tensors. The evolution equations for the six quantities contained in these tensors are reduced in number in two cases: (i) for arbitrary surfaces, we use principal coordinates to obtain two equations for the two principal curvatures, highlighting the similarity with the equations of motion of a plane curve;and (ii) for surfaces with spatially constant negative curvature, we use parameterization by Tchebyshev nets to reduce to a single evolution equation. We also obtain necessary and sufficient conditions for a surface to maintain spatially constant negative curvature as it moves. One choice for the surface's normal motion leads to the modified Korteweg-de Vries equation, the appearance of which is explained by connections to the AKNS hierarchy and the motion of space curves.
An inertial manifold is constructed for the scalar reaction-diffusion equation u t = vu xx +ƒ(u) with a cubic nonlinearity. Uniform bounds are obtained for the number of zeros along solutions to the variational equati...
An inertial manifold is constructed for the scalar reaction-diffusion equation u t = vu xx +ƒ(u) with a cubic nonlinearity. Uniform bounds are obtained for the number of zeros along solutions to the variational equations satisfied by the difference of two elements on the unstable manifolds of equilibria. This uniformity leads to the global parameterization of the attractor as a function defined in the linear unstable manifold of the least stable equilibrium. By the introduction of local techniques near each equilibrium, we succeed in constructing an inertial manifold of lowest possible dimension.
Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed...
In this letter, a nonlinear deviation from the Navier-Stokes equation is obtained from the recently proposed LBGK models, which are designed as an alternative to lattice gas or lattice Boltzmann equation. The classica...
In this letter, a nonlinear deviation from the Navier-Stokes equation is obtained from the recently proposed LBGK models, which are designed as an alternative to lattice gas or lattice Boltzmann equation. The classical Chapman-Enskog method is extended to derive the nonlinear-deviation term as well as its coefficient. Their analytical expression is derived for the first time, thanks to the simplicity of the LBGK models. A numerical simulation of a shock profile is presented. The influence of the correction on the kinetics of compressible flow is discussed. A complete analysis of the thermodynamics including the temperature will be presented elsewhere.
Multidimensional tunneling appears in many problems at nano *** high dimensionality of the potential energy surface(*** degrees of freedom)poses a great challenge in both theoretical and numerical description of *** s...
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Multidimensional tunneling appears in many problems at nano *** high dimensionality of the potential energy surface(*** degrees of freedom)poses a great challenge in both theoretical and numerical description of *** simulation based on Schrodinger equation is often prohibitively *** propose an accurate,efficient,robust and easy-to-implement numerical method to calculate the ground state tunneling splitting based on imaginary-time path integral(‘instanton’formulation).The method is genuinely multi-dimensional and free from any additional ad hoc assumptions on potential energy *** enables us to calculate the effects of all coupling modes on the tunneling degree of freedom without *** also review in this paper some theoretical background and survey some recent work from other groups in calculating multidimensional quantum tunneling effects in chemical reactions.
Computational phenotyping is essential for biomedical research but often requires significant time and resources, especially since traditional methods typically involve extensive manual data review. While machine lear...
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