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.
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...
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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 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.
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.
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.
Risk-driven behaviour provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of het...
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We prove that the gradient descent training of a two-layer neural network on empirical or population risk may not decrease population risk at an order faster than t−4/(d−2) under mean field scaling. The loss functiona...
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