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.
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.
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical app...
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Scaling properties of the field equation governing propagation of a thin flame front in a turbulent medium are discussed. It is shown that if the turbulent flame velocityuTcan be expressed through the turbulence inten...
Scaling properties of the field equation governing propagation of a thin flame front in a turbulent medium are discussed. It is shown that if the turbulent flame velocityuTcan be expressed through the turbulence intensityurmsand the laminar flame velocityu0asuT/u0∞ (urms/u0)x, then α → 1 in the scale invariant regime whenurms→ ∞.
The problem of propagation of turbulent premixed flame is analyzed using the field equation introduced recently by Kerstein, Ashurst and Williams (1987). The dynamic renormalization group method is applied to this equ...
The problem of propagation of turbulent premixed flame is analyzed using the field equation introduced recently by Kerstein, Ashurst and Williams (1987). The dynamic renormalization group method is applied to this equation and the formula for the turbulent flame velocity is derived in the lowest order in the ε-expansion. The formula, which does not include adjustable parameters, agrees well with experimental (Abdel-Gayed et al., 1984) and numerical (Ashurst & Barr 1983) results on flame propagation in high-Reynolds number turbulent media. Ways to design transport and large-eddy (sub-grid) models for simulation of combustion processes, based on the ideas developed in the present paper, are discussed.
The design of most consumer products can play a key role in their commercial success, and, therefore, the ability to protect new and innovative designs is an important part of a modern competitive marketplace. Since 1...
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The design of most consumer products can play a key role in their commercial success, and, therefore, the ability to protect new and innovative designs is an important part of a modern competitive marketplace. Since 1 April 2003, it has been possible to obtain European Union (EU)-wide design protection by means of a single registration made under the Community Design regulation (Council Regulation 6/2002 of 12 December 2001), usually referred to as a Registered Community Design (RCD). Before the advent of the RCD, a designer seeking protection across the EU was restricted to seeking registration at a national level. Now, with 28 member states in the EU, the ability to register a design with just a single filing is a major step forward in terms of protection of intellectual property rights in the EU.
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.
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