Computational Statistical Mechanics Seminar

Tuesday 10am, Room 1314, Warren Weaver Hall
Questions or comments? Please email Jianfeng Lu or Eric Vanden-Eijnden.

• Hans Christian Öttinger (ETH Zürich), Feb 7
• Local equilibrium of the Gibbs interface in two-phase systems


• [CANCELLED] Bruce Turkington (University of Massachusetts Amherst), Feb 14
• Rescheduled to Mar 20 due to flooding in Warren Weaver Hall


• Lin Lin (Lawrance Berkeley National Laboratory), Feb 21
• Correlated proton tunneling in ice
• As opposed to the common belief in molecular dynamics which treats nuclei as classical particles, quantum effects of nuclei can be non-negligible in many systems, including a cup of water at room temperature. The quantum effects of nuclei is reflected in the single particle density matrix of the nuclei, which can be computed via Feynman's path integral theory. In the first part of the talk, we will analyze the single particle density matrix of protons (nuclei of hydrogen atoms) in various phases of ice under high pressure, which reveals the correlated nature of proton tunneling. In the second part of the talk, we will introduce a new method for evaluating the off-diagonal elements of the single particle matrix, which reflects the quantum momentum distribution of nuclei, a quantity that can be measured directly in experiment. (Joint work with Roberto Car, Joseph A. Morrone, and Michele Parrinello)


• Tang-Qing Yu (Chemistry, New York University), Feb 28
• Exploring Crystal Polymorphism using isothermal-isobaric Molecular Dynamics
• Crystal polymorphism is the ability of a solid material to exist in more than one crystal form under certain conditions. It is of great interest to pharmaceuticals and high energy materials. One of the main challenges faced by computational approaches for this problem is to efficiently explore the thermodynamic landscape of crystalline poly-morphs and predict free energy associated with different crystal structures. Some MD-based enhanced sampling methods (AFED, TAMD) have been developed to efficiently map out the free energy surface along some collective variables in a complex system and successfully applied into the conformational study of proteins. The basic idea is to give a large time scale to collective variables so that they effectively evolve under the potential of mean force. At the same time, a high temperature is artificially assigned to accelerate the exploration of the free energy surface. In this talk, we present how to adapt these enhanced sampling strategies to the scheme of NPT molecular dynamics and how to apply the new scheme in the prediction of crystal poly-morphs.


• Enrico Guarnera (New York University), Mar 6
• Markov State Model construction from simulation data
• The last decade has seen an unprecedented development in both Molecular Dynamics (MD) technics and Computer power for the simulation of biomolecules. Massive amounts of simulation data are being accumulated in a variety of contexts: protein folding, protein dynamics, protein-ligand binding, etc. The configurational space of biomolecules, as MD simulations show, is a problematic example of a data complex object whose description is among the current challenges in theoretical biophysics. The adoption of Markov State Models (MSM) in the context of protein conformational dynamics is currently considered a powerful tool to describe these data structures. However, a still open problem of the current MSMs is how to choose the proper set of states such that the system metastable dynamics can be described in a reduced model. Ideally, an effective MSM should take into account only a subset of metastable states that correspond to the slowest modes of the system. In this work a method is proposed to select the correct subset of system states wherein most of the metastable dynamics takes place. The method is grounded on the concept of metastability index \rho_M as formerly introduced by Bovier et al., whose definition is based on committor probabilities and mean first passage times. Milestoning is employed as initial step to specify a collection S of configurational states observed along a trajectory. Subsequently, a biased Monte Carlo procedure is adopted to minimize the metastability index \rho_M and obtain a subset M of metastable states that eventually constitute the reduced state space of a Markov state model. The method is first applied on diffusion trajectories of 1D/2D simple models and then on MD trajectories of a solvated Glycine-Alanine-Glycine tri-peptide.


• No meeting on Mar 13 (NYU spring break)


• Bruce Turkington (University of Massachusetts Amherst), Mar 20
• A statistical optimization principle for coarse-graining deterministic dynamics
• Given a complex dynamical system having a separation of time scales between some slow variables and other fast variables, it is often desirable to derive a closed reduced model for the evolution of the slow variables, relegating the fast variables to a statistical description. In this talk we develop an optimization principle that produces the governing equations of the reduced model for a specified set of resolved variables. This principle applies to any microdynamics that is Hamiltonian, and it defines a macrodynamics that has the format of nonequilibrium thermodynamics. The idea is to consider a family of trial probability densities on phase space parametrized by the resolved variables, and to minimize a time-integrated cost function over paths of these trial densities. The cost function quantifies the information-theoretic lack-of-fit of the trial densities to the Liouville equation, and the irreversibility of the resulting macrodynamics arises as the cost of coarse-graining.


• No meeting on Mar 27


• Yuan Yao (Peking University), Apr 3
• Challenges of Data Analysis in Biomolecular Dynamics
• In this talk I'll describe some collaborative work with Folding@home team, in particular Dr. Xuhui Huang, on data analysis in molecular dynamics simulation. One major challenge we are facing is to fill in the time scale gap, i.e. prediction of long term behavior from a large collection of short term simulations. Our approach is roughly divided into 3 stages: 1) split the sampled region into a large set of small cells, namely microstates, based on geometric information of conformations; 2) establish a transition network for microstates based on kinetic information from short term simulations and lump into metastable macrostates those kinetically highly-connected microstates; 3) estimate the time scale where Markovian behavior is exhibited and build up a Markov State Model (MSM) for predictions of long term behavior. High dimensionality and massive amount of data impose us various challenges in this Odyssey and motivate some new mathematical methods for data analysis.


• Katie Newhall (New York University), Apr 10
• Thermally induced magnetization reversals
• There is considerable interest in understanding thermally induced magnetization reversals in thin film magnetic elements, with application to random access memory storage. This intriguing stochastic dynamical system is challenging because it does not show detailed balance in the presence of spin-torque-transfers. Thus, the reversals in magnetization are nonequilibrium transition events which cannot be described by standard reaction-rate theories. I will present a technique for determining the averaged stochastic differential equation for the evolution of the energy in the limit of small damping. From this equation, the mean first passage time and the location of a phase transition in the behavior of the system, providing an understanding of thermal switching, the existence of a stable precession state, and spin-torque-transfer induced switching.


• Jingchen Liu (Columbia University), Apr 17
• Rare-event Analysis and Simulations for Gaussian and Its Related Processes
• Gaussian processes are employed to model spatially varying errors in various stochastic systems. In this talk, we consider the analysis of the extreme behaviors and the rare-event simulation problems for such systems. In particular, the topic covers various nonlinear functionals of Gaussian processes including the supremum norm, integral of convex functions, and stochastic partial differential equations with random coefficients. We present the asymptotic results and the efficient simulation algorithms for the associated rare-event probabilities.
  
  
• Jonathan Goodman (New York University), Apr 24
• Informal talk: rare events without importance sampling
• This is an informal presentation of a simple idea.
  Most rare event simulation strategies use importance functions derived from large deviation theory. This means that you need much information about the mechanism of the rare event before you can simulate it effectively. I present a Monte Carlo strategy for some rare event simulations that does not use such importance functions. Suppose the rare event problem is Pr[ f(X) > b ], where X has some distribution. If you have an MCMC sampler for X conditional on f(X) > b, then you can use it to estimate H(b) so that Pr( f(X) > H(b) ) = Pr( f(X) > b )/2 --- just take the median in the histogram of f(X) conditional on f(X) > b. A sequence of such bifurcation steps allows you to estimate b_n with Pr( f(X) > b_n ) = 1/2^n. Surprisingly, there are effective b-samplers for some model problems.


• No meeting on May 1


• Xu Yang (New York University), May 8
• A large deviation framework to analyze metastable behavior in climate system
• We studied the dynamic transition phenomena between different metastable states in climate systems. We try to build a framework using large deviation theory, in which different climate regimes are represented by the most likely states of equilibrium distribution (invariant measure) and the transition is described by the most likelihood paths connecting them in the small noise limit. Specifically we considered an energy-constrained stochastic dynamics, the most likely states of whose invariant measure coincide with the selective decay states (corresponding to climate patterns). We compute the transition pathways using a constrained String method. Nonequilibrium statistical climate systems were also analyzed where the transition pathways were computed by the geometric minimum action method.


• Aleksandar Donev (New York University), May 15
• Multiscale Problems in Fluctuating Hydrodynamics
• Thermal fluctuations play an important role in fluid dynamics, especially at small scales. Fluctuations have been incorporated into the classical equations of fluid dynamics, however, the resulting systems of stochastic PDEs are very difficult to handle. They are a sort of extreme example of multiscale problems, in the sense that there is infinitely many scales in space and in time. New numerical and analytical methods are required to understand them. Here I will describe a few examples where there is separation of time scales between physical processes and the open questions about the limiting dynamics in the stochastic setting. These include diffusive mixing of fluids, the low Mach number limit, and Brownian motion of immersed particles in a fluid. I will provide some plausible answers, but this informal talk will be mostly about posing questions that are (I believe) interesting from both the mathematical and physical perspectives.



• [CANCELLED] Misha Neklyudov (University of Tübingen), Mar 6
• The role of noise in finite ensembles of nanomagnetic particles