Local Simulation Algorithms for Coulomb Interaction

Long ranged electrostatic interactions are time consuming to calculate in molecular dynamics and Monte-Carlo simulations. We introduce an algorithmic framework for simulating charged particles which modifies the dynamics so as to allow equilibration using a local Hamiltonian. The method introduces an auxiliary field with constrained dynamics so that the equilibrium distribution is determined by the Coulomb interaction. We demonstrate the efficiency of the method by simulating a simple, charged lattice gas.Comment: Last figure changed to improve demonstration of numerical efficienc

Poincaré on the Foundation of Geometry in the Understanding

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them

DFFR: A New Method for High-Throughput Recalibration of Automatic Force-Fields for Drugs

We present drug force-field recalibration (DFFR), a new method for refining of automatic force-fields used to represent small drugs in docking and molecular dynamics simulations. The method is based on fine-tuning of torsional terms to obtain ensembles that reproduce observables derived from reference data. DFFR is fast and flexible and can be easily automatized for a high-throughput regime, making it useful in drug-design projects. We tested the performance of the method in a few model systems and also in a variety of druglike molecules using reference data derived from: (i) density functional theory coupled to a self-consistent reaction field (DFT/SCRF) calculations on highly populated conformers and (ii) enhanced sampling quantum mechanical/molecular mechanics (QM/MM) where the drug is reproduced at the QM level, while the solvent is represented by classical force-fields. Extension of the method to include other sources of reference data is discussed