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Minimum Action Method for Nonequilibrium Phase Transitions
Ruben Zakine, Eric Vanden-Eijnden
First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to an…
Sharp Asymptotic Estimates for Expectations, Probabilities, and Mean First Passage Times in Stochastic Systems with Small Noise
Tobias Grafke, Tobias Schäfer, Eric Vanden-Eijnden
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization pro…
Infinite Switch Simulated Tempering in Force (FISST)
Michael J. Hartmann, Yuvraj Singh, Eric Vanden-Eijnden +1
Many proteins in cells are capable of sensing and responding to piconewton scale forces, a regime in which conformational changes are small but significant for biological processes…
Numerical computation of rare events via large deviation theory
Tobias Grafke, Eric Vanden-Eijnden
An overview of rare events algorithms based on large deviation theory (LDT) is presented. It covers a range of numerical schemes to compute the large deviation minimizer in various…
Dynamical computation of the density of states and Bayes factors using nonequilibrium importance sampling
Grant M. Rotskoff, Eric Vanden-Eijnden
Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known…
Extreme event quantification in dynamical systems with random components
Giovanni Dematteis, Tobias Grafke, Eric Vanden-Eijnden
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question…
Non-equilibrium transitions in multiscale systems with a bifurcating slow manifold
Tobias Grafke, Eric Vanden-Eijnden
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slo…
Spatiotemporal Self-Organization of Fluctuating Bacterial Colonies
Tobias Grafke, Michael E. Cates, Eric Vanden-Eijnden
We model an enclosed system of bacteria, whose motility-induced phase separation is coupled to slow population dynamics. Without noise, the system shows both static phase separatio…
A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
Grant M. Rotskoff, Gavin E. Crooks, Eric Vanden-Eijnden
Optimal control of nanomagnets has become an urgent problem for the field of spintronics as technological tools approach thermodynamically determined limits of efficiency. In compl…
Optimized Markov State Models for Metastable Systems
Enrico Guarnera, Eric Vanden-Eijnden
A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones (or core sets) to build M…
Large Deviations in Fast-Slow Systems
Freddy Bouchet, Tobias Grafke, Tomás Tangarife +1
The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctua…
Multiscale temporal integrators for fluctuating hydrodynamics
S. Delong, Y. Sun, B. E. Griffith +2
Following on our previous work [S. Delong and B. E. Griffith and E. Vanden-Eijnden and A. Donev, Phys. Rev. E, 87(3):033302, 2013], we develop temporal integrators for solving Lang…
Exact dynamical coarse-graining without time-scale separation
Jianfeng Lu, Eric Vanden-Eijnden
A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variab…
Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
A. Donev, E. Vanden-Eijnden
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functio…
Flows in Complex Networks: Theory, Algorithms, and Application to Lennard-Jones Cluster Rearrangement
Maria Cameron, Eric Vanden-Eijnden
A set of analytical and computational tools based on transition path theory (TPT) is proposed to analyze flows in complex networks. Specifically, TPT is used to study the statistic…
A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law
A. Donev, T. G. Fai, E. Vanden-Eijnden
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusi…
Arclength parametrized Hamilton's equations for the calculation of instantons
Tobias Grafke, Rainer Grauer, Tobias Schäfer +1
A method is presented to compute minimizers (instantons) of action functionals using arclength parametrization of Hamilton's equations. This method can be interpreted as a local va…
Reversible Diffusion by Thermal Fluctuations
A. Donev, T. G. Fai, and E. Vanden-Eijnden
A model for diffusion in liquids that couples the dynamics of tracer particles to a fluctuating Stokes equation for the fluid is investigated in the limit of large Schmidt number.…
Infinite swapping replica exchange molecular dynamics leads to a simple simulation patch using mixture potentials
Jianfeng Lu, Eric Vanden-Eijnden
Replica exchange molecular dynamics (REMD) becomes more efficient as the frequency of swap between the temperatures is increased. Recently in [Plattner et al, J. Chem. Phys. 135, 1…
Solvent coarse-graining and the string method applied to the hydrophobic collapse of a hydrated chain
Thomas F. Miller, Eric Vanden-Eijnden, David Chandler
Using computer simulations of over 100,000 atoms, the mechanism for the hydrophobic collapse of an idealized hydrated chain is obtained. This is done by coarse-graining the atomist…