Related papers: A Conjecture about Molecular Dynamics
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
A general theory of nucleation for colloids and macromolecules in solution is formulated within the context of fluctuating hydrodynamics. A formalism for the determination of nucleation pathways is developed and stochastic differential…
To understand the foundations of quantum mechanics, we have to think carefully about how theoretical concepts are rooted in -- and limited by -- the nature of experience, as Bohr attempted to show. Geometrical pictures of physical phenomena…
Molecular clouds are the principle stellar nurseries of our universe, keeping them in the focus of both observational and theoretical studies. From observations, some of the key properties of molecular clouds are well known but many…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
Quantum dynamics is linear. How do we know? From theory or experiment? The history of this question is reviewed. Nonlinear generalizations of quantum mechanics have been proposed. They predict small but clear nonlinear effects, which very…
In order to understand the physics phenomea on the fundamental aspects, the software simulations are a good exercise to succed in this way. Some work of heat transport and molecular physics laboratory are studied in a comparative mode…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
The dynamics of dissipative soft-sphere gases obeys Newton's equation of motion which are commonly solved numerically by (force-based) Molecular Dynamics schemes. With the assumption of instantaneous, pairwise collisions, the simulation can…
Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…
Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in…
Quantifying convergence and sufficient sampling of macromolecular molecular dynamics simulations is more often than not a source of controversy (and of various ad hoc solutions) in the field. Clearly, the only reasonable, consistent and…
Molecular dynamics (MD) simulations have become popular in materials science, biochemistry, biophysics and several other fields. Improvements in computational resources, in quality of force field parameters and algorithms have yielded…
Development of several alternative mathematical models for the biological system in question and discrimination between such models using experimental data is the best way to robust conclusions. Models which challenge existing theories are…
Experiments that look for nonlinear quantum dynamics test the fundamental premise of physics that one of two separate systems can influence the physical behavior of the other only if there is a force between them, an interaction that…
Tracking the behaviour of stochastic systems is a crucial task in the statistical sciences. It has recently been shown that quantum models can faithfully simulate such processes whilst retaining less information about the past behaviour of…
We show that all existing methods quantifying rotational motion in molecular fluids eventually fail in systems undergoing complex rotational motion characterised by slow, heterogeneous, or intermittent dynamics. This impacts in particular…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…