Enhanced sampling of multidimensional free-energy landscapes using adaptive biasing forces

We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with molecular dynamics to handle in a more effective fashion multidimensional reaction coordinates. The proposed approach is anticipated to be particularly useful for reaction coordinates, the components of which are weakly coupled, as illuminated in a mathematical analysis of the long-time convergence of the algorithm. The strength as well as the intrinsic limitation of the method are discussed and illustrated in two realistic test cases

Correctors for some asymptotic problems

In the theory of anisotropic singular perturbation boundary value problems, the solution u ɛ does not converge, in the H 1-norm on the whole domain, towards some u 0. In this paper we construct correctors to have good approximations of u ɛ in the H 1-norm on the whole domain. Since the anisotropic singular perturbation problems can be connected to the study of the asymptotic behaviour of problems defined in cylindrical domains becoming unbounded in some directions, we transpose our results for such problems

Asymptotics of eigenstates of elliptic problems with mixed boundary data on domains tending to infinity

We analyze the asymptotic behavior of eigenvalues and eigenfunctions of an elliptic operator with mixed boundary conditions on cylindrical domains when the length of the cylinder goes to infinity. We identify the correct limiting problem and show in particular, that in general the limiting behavior is very different from the one for the Dirichlet boundary conditions.Comment: Asymptotic Analysis, 201

Reconciling alternate methods for the determination of charge distributions: A probabilistic approach to high-dimensional least-squares approximations

We propose extensions and improvements of the statistical analysis of distributed multipoles (SADM) algorithm put forth by Chipot et al. in [6] for the derivation of distributed atomic multipoles from the quantum-mechanical electrostatic potential. The method is mathematically extended to general least-squares problems and provides an alternative approximation method in cases where the original least-squares problem is computationally not tractable, either because of its ill-posedness or its high-dimensionality. The solution is approximated employing a Monte Carlo method that takes the average of a random variable defined as the solutions of random small least-squares problems drawn as subsystems of the original problem. The conditions that ensure convergence and consistency of the method are discussed, along with an analysis of the computational cost in specific instances

Correction to: Some results on the p(u)-Laplacian problem

Correction to: Mathematische Annalen https://doi.org/10.1007/s00208-019-01803-w In the Original Publication of the article, few errors have been identified in section 5 and acknowledgements section.Agência financiadora Ministry of Education and Science, Russian Federation 117198 Portuguese Foundation for Science and Technology (FCT), Portugal SFRH/BSAB/135242/2017info:eu-repo/semantics/publishedVersio

On global minimizers of repulsive-attractive power-law interaction energies

We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports independently of the number of Dirac Deltas in certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations.Comment: 14 pages, 2 figure

Escorted Free Energy Simulations: Improving Convergence by Reducing Dissipation

Nonequilibrium, ``fast switching'' estimates of equilibrium free energy differences, Delta F, are often plagued by poor convergence due to dissipation. We propose a method to improve these estimates by generating trajectories with reduced dissipation. Introducing an artificial flow field that couples the system coordinates to the external parameter driving the simulation, we derive an identity for Delta F in terms of the resulting trajectories. When the flow field effectively escorts the system along a near-equilibrium path, the free energy estimate converges efficiently and accurately. We illustrate our method on a model system, and discuss the general applicability of our approach.Comment: 4 pages, including 2 figures, accepted for publication in Phys Rev Let