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.
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.
Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt found...
详细信息
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...
详细信息
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.
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use...
The theory of the focusing NLS equation under periodic boundary conditions, together with the Floquet spectral theory of its associated Zakharov-Shabat liner operator L, is developed in sufficient detail for later use in studies of perturbations of the NLS equation. ''Counting lemmas'' for the non-selfadjoint operator L, are established which control its spectrum and show that all of its eccentricities are finite in number and must reside within a finite disc D in the complex eigenvalue plane. The radius of the disc D is controlled by the H-1 norm of the potential q. For this integrable NLS Hamiltonian system, unstable tori are identified, and Backlund transformations are then used to construct global representations of their stable and unstable manifolds - ''whiskered tori'' for the NLS pde. The Floquet discriminant DELTA(lambda;q) used to introduce a natural sequence of NLS constants of motion, [F(j)(q) = DELTA(lambda = lambda(j)c(q);q), where lambda(j)c denotes the j(th) critical point of the Floquet discriminant DELTA(lambda)]. A Taylor series expansion of the constants F(j)(q), with explicit representations of the first and second variations, is then used to study neighborhoods of the whiskered tori. In particular, critical tori with hyperbolic structure are identified through the first and second variations of F(j)(q), which themselves are expressed in terms of quadratic products of eigenfunctions of L. The second variation permits identification, within the disc D, of important bifurcations m the spectral configurations of the operator L. The constant F(j)(q), as the height of the Floquet discriminant over the critical point lambda(j)c, admits a natural interpretation as a Morse function for NLS isospectral level sets. This Morse interpretation is studied in some detail. It is valid globally for the infinite tail, {F(j)(q)}\j\>N, which is associated with critical points outside the disc D. Within this disc, the interpretation is only valid locally, with the s
In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Single-cell data can have high dimensionalit...
详细信息
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...
详细信息
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.
Surface area of a macromolecule, accessible to a solvent, is defined and calculated, taking into account the probabilistic character of atomic positions due to the high frequency atomic vibrations. For a given a space...
Surface area of a macromolecule, accessible to a solvent, is defined and calculated, taking into account the probabilistic character of atomic positions due to the high frequency atomic vibrations. For a given a space point, we consider a probability of the event, that this point is covered by a macromolecule. A volume is defined as a space integral of this probability field. The envelope, accessible to a solvent molecule center, becomes fuzzy, existing only in a probabilistic sense. The accessible area is defined as a derivative of the envelope volume with respect to the probe size. The accessible area thus defined has the advantage of being an analytic function of atomic coordinates and allows for an arbitrary (not necessarily spherical) probe geometry. Space integration is performed on a rectangular grid, using a third order Runge-Kutta integration scheme and the analytical subgrid averaging.
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.
暂无评论