Maria Colombo

Automated Parametrization of Biomolecular Force Fields from Quantum Mechanics/Molecular Mechanics (QM/MM) Simulations through Force Matching.

We introduce a novel procedure to parametrize biomolecular force fields. We perform finite-temperature quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, with the fragment or moiety that has to be parametrized being included in the QM region. By applying a force-matching algorithm, we derive a force field designed in order to reproduce the steric, electrostatic, and dynamic properties of the QM subsystem. The force field determined in this manner has an accuracy that is comparable to the one of the reference QM/MM calculation, but at a greatly reduced computational cost. This allows calculating quantities that would be prohibitive within a QM/MM approach, such as thermodynamic averages involving slow motions of a protein. The method is tested on three different systems in aqueous solution:  dihydrogenphosphate, glycyl-alanine dipeptide, and a nitrosyl-dicarbonyl complex of technetium(I). Molecular dynamics simulations with the optimized force field show overall excellent performance in reproducing properties such as structures and dipole moments of the solutes as well as their solvation pattern.

Hybrid QM/MM Car-Parrinello simulations of catalytic and enzymatic reactions

A review. First-principles mol. dynamics (Car-Parrinello) simulations based on d. functional theory have emerged as a powerful tool for the study of phys., chem. and biol. systems. At present, using parallel computers, systems of a few hundreds of atoms can be routinely investigated. By extending this method to a mixed quantum mech. - mol. mech. (QM/MM) hybrid scheme, the system size can be enlarged further. Such an approach is esp. attractive for the in situ investigation of chem. reactions that occur in a complex and heterogeneous environment. Here, we review some recent applications of hybrid Car-Parrinello simulations of chem. and biol. systems as illustrative examples of the current potential and limitations of this promising novel technique. [on SciFinder (R)]

Existence of Eulerian Solutions to the Semigeostrophic Equations in Physical Space: The 2-Dimensional Periodic Case

In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed.

Multimarginal Optimal Transport Maps for One-dimensional Repulsive Costs

Abstract. We study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.

On the Lagrangian structure of transport equations: The Vlasov–Poisson system

The Vlasov-Poisson system is a classical model in physics used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions

Existence and Uniqueness of Maximal Regular Flows for Non-smooth Vector Fields

d\leq 3

Rigidity of equality cases in Steiner's perimeter inequality

under strong assumptions on the initial data, while weak solutions are known to exist under milder conditions. However, in the setting of weak solutions it is unclear whether the Eulerian description provided by the equation physically corresponds to a Lagrangian evolution of the particles. In this paper we develop several general tools concerning the Lagrangian structure of transport equations with non-smooth vector fields and we apply these results: (1) to show that weak solutions of Vlasov-Poisson are Lagrangian; (2) to obtain global existence of weak solutions under minimal assumptions on the initial data.

Essential connectedness and the rigidity problem for Gaussian symmetrization

In this paper we provide a complete analogy between the Cauchy–Lipschitz and the DiPerna–Lions theories for ODE’s, by developing a local version of the DiPerna–Lions theory. More precisely, we prove the existence and uniqueness of a maximal regular flow for the DiPerna–Lions theory using only local regularity and summability assumptions on the vector field, in analogy with the classical theory, which uses only local regularity assumptions. We also study the behaviour of the ODE trajectories before the maximal existence time. Unlike the Cauchy–Lipschitz theory, this behaviour crucially depends on the nature of the bounds imposed on the spatial divergence of the vector field. In particular, a global assumption on the divergence is needed to obtain a proper blow-up of the trajectories.

Slow Time Behavior of the Semidiscrete Perona–Malik Scheme in One Dimension

Characterization results for equality cases and for rigidity of equality cases in Steiners perimeter inequality are presented. (By rigidity, we mean the situation when all equality cases are vertical translations of the Steiner symmetral under consideration.) We achieve this through the introduction of a suitable measure-theoretic notion of connectedness and a fine analysis of barycenter functions for sets of finite perimeter having segments as orthogonal sections with respect to a hyperplane.

Ill-Posedness of Leray Solutions for the Hypodissipative Navier–Stokes Equations

We provide a geometric characterization of rigidity of equality cases in Ehrhards symmetrization inequality for Gaussian perimeter. This condition is formulated in terms of a new measure-theoretic notion of connectedness for Borel sets, inspired by Federers definition of indecomposable current.