We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias potential is "nonlocal", and its gradient ad...

Weconstructmolli cation operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are Lp stable for any real number p ∈ [1,∞], and commutewith thedi erential operators∇,∇×, and ∇⋅. We also constructmolli cation operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector elds. We use the ...

Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.

This paper develops some mollification formulas involving convolutions between popular radial basis function (RBF) basic functions Φ, and suitable mollifiers. Polyharmonic splines, scaled Bessel kernels (Matern functions) and compactly supported basic functions are considered. A typical result is that in Rd the convolution of | • |β and (•2 + c2)−(β+2d)/2 is the generalized multiquadric (•2 + c...

Non-associative elasto-plasticity is the working model of plasticity for soil and rock mechanics. Yet, it is usually viewed as non-variational. In this work, we prove a contrario the existence of a variational evolution for such a model under a natural capping assumption on the hydrostatic stresses and a less natural mollification of the stress admissibility constraint. The obtained elasto-plas...

1. Introduction Various authors have explored the role of molliication in the solution of improperly posed problems such as numerical diierentiation and the numerical solution of rst kind integral equations. For example, Murio 13], exploiting earlier suggestions of Manselli and Miller 11] as well as Vasin 16], has shown how molliied numerical diierentiators can be constructed for the diierentia...

The solution of a nonlinear parabolic SPDE on the circle, with multiplicative Gaussian noise that is white-noise in time and a bonafide function in space, is approximated by a system of branching and interacting particles. Convergence of the system is established in the space of continuous-function-valued càdlàg processes via a mollification procedure.