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Girsanov reweighting for metadynamics simulations
No full textABSTRACT
Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques—metadynamics/Girsanov-reweighting—the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a β-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation
WavePacket: A Matlab package for numerical quantum dynamics. II: Open quantum systems, optimal control, and model reduction
No full textWavePacket is an open-source program package for numeric simulations in quantum dynamics. It can solve time-independent or time-dependent linear Schrödinger and Liouville-von Neumann-equations in one or more dimensions. Also coupled equations can be treated, which allows, e.g., to simulate molecular quantum dynamics beyond the Born-Oppenheimer approximation. Optionally accounting for the interaction with external electric fields within the semi-classical dipole approximation, WavePacket can be used to simulate experiments involving tailored light pulses in photo-induced physics or chemistry. Being highly versatile and offering visualization of quantum dynamics 'on the fly', WavePacket is well suited for teaching or research projects in atomic, molecular and optical physics as well as in physical or theoretical chemistry. Building on the previous Part I which dealt with closed quantum systems and discrete variable representations, the present Part II focuses on the dynamics of open quantum systems, with Lindblad operators modeling dissipation and dephasing. This part also describes the WavePacket function for optimal control of quantum dynamics, building on rapid monotonically convergent iteration methods. Furthermore, two different approaches to dimension reduction implemented in WavePacket are documented here. In the first one, a balancing transformation based on the concepts of controllability and observability Gramians is used to identify states that are neither well controllable nor well observable. Those states are either truncated or averaged out. In the other approach, the H2-error for a given reduced dimensionality is minimized by H2 optimal model reduction techniques, utilizing a bilinear iterative rational Krylov algorithm.
The present work describes the MATLAB version of WavePacket 5.3.0 which is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics can be found
Cyclization dynamics of finite-length collapsed self-avoiding polymers
Get PDFWe study the end-point cyclization of ideal and interacting polymers as a function of chain length N. For the cyclization time �cyc of ideal chains we recover the known scaling �cyc � N2 for different backbone models, for a self-avoiding slightly collapsed chain we obtain from Langevin simulations and scaling theory a modified scaling �cyc � N5=3. By extracting the memory kernel
that governs the non-Markovian end-point kinetics, we demonstrate that the dynamics of a finite-length collapsed chain is dominated by the crossover between swollen and collapsed behavior
Interactions between Meso- and Sub-Mesoscale Gravity Waves and their Efficient Representation in Mesoscale-Resolving Models
No full textAs present weather-forecast codes and increasingly many atmospheric climate models resolve at least part of the mesoscale flow, and hence also internal gravity waves (GWs), it is natural to ask whether even in such configurations sub-gridscale GWs might impact the resolved flow, and how their effect could be taken into account. This motivates a theoretical and numerical investigation of the interaction between unresolved sub-mesoscale and resolved mesoscale GWs, using Boussinesq dynamics for simplicity. By scaling arguments, first a subset of sub-mesoscale GWs that can indeed influence the dynamics of mesoscale GWs is identified. Therein, hydrostatic GWs with wavelengths corresponding to the largest unresolved scales of present-day limited-area weather forecast models are an interesting example. A large-amplitude WKB theory, allowing for a mesoscale unbalanced flow, is then
formulated, based on multi-scale asymptotic analysis utilizing a proper scale-separation parameter. Purely vertical propagation of sub-mesoscale GWs is found to be most important, implying inter alia that the resolved flow is only affected by the vertical flux convergence of sub-mesoscale horizontal momentum at leading order. In turn, sub-mesoscale GWs are refracted by mesoscale vertical wind shear while conserving their wave-action density. An efficient numerical implementation of the theory uses a phase-space ray tracer, thus handling the frequent appearance of caustics. The WKB approach and its numerical implementation are validated successfully against sub-mesoscale resolving simulations of the resonant radiation of mesoscale inertia GWs by a horizontally as well as vertically confined sub-mesoscale GW packet
Formula Feeding Predisposes Neonatal Piglets to Clostridium difficile Gut Infection
No full textSpontaneous outbreaks of Clostridium difficile infection (CDI) occur in neonatal piglets, but the predisposing factors are largely not known. To study the conditions for C. difficile colonization and CDI development, 48 neonatal piglets were moved into isolators, fed bovine milk–based formula, and infected with C. difficile 078. Analyses included clinical scoring; measurement of the fecal C. difficile burden, toxin B level, and calprotectin level; and postmortem histopathological analysis of colon specimens. Controls were noninfected suckling piglets. Fecal specimens from suckling piglets, formula-fed piglets, and formula-fed, C. difficile–infected piglets were used for metagenomics analysis. High background levels of C. difficile and toxin were detected in formula-fed piglets prior to infection, while suckling piglets carried about 3-fold less C. difficile, and toxin was not detected. Toxin level in C. difficile–challenged animals correlated positively with C. difficile and calprotectin levels. Postmortem signs of CDI were absent in suckling piglets, whereas mesocolonic edema and gas-filled distal small intestines and ceca, cellular damage, and reduced expression of claudins were associated with animals from the challenge trials. Microbiota in formula-fed piglets was enriched with Escherichia, Shigella, Streptococcus, Enterococcus, and Ruminococcus species. Formula-fed piglets were predisposed to C. difficile colonization earlier as compared to suckling piglets. Infection with a hypervirulent C. difficile ribotype did not aggravate the symptoms of infection. Sow-offspring association and consumption of porcine milk during early life may be crucial for the control of C. difficile expansion in piglets
Variational Selection of Features for Molecular Kinetics
Get PDFThe modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long-time kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of twelve fast-folding protein simulations, and show that our procedure leads to more efficient model selection
Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach
No full textHuman mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution
Electrons to Reactors Multiscale Modeling: Catalytic CO Oxidation over RuO2
No full textFirst-principles kinetic Monte Carlo (1p-kMC) simulations for CO oxidation on two RuO2 facets, RuO2(110) and RuO2(111), were coupled to the computational fluid dynamics (CFD) simulations package MFIX, and reactor-scale simulations were then performed. 1p-kMC coupled with CFD has recently been shown as a feasible method for translating molecular scale mechanistic knowledge to the reactor scale, enabling comparisons to in situ and online experimental measurements. Only a few studies with such coupling have been published. This work incorporates multiple catalytic surface facets into the scale-coupled simulation, and three possibilities were investigated: the two possibilities of each facet individually being the dominant phase in the reactor, and also the possibility that both facets were present on the catalyst particles in the ratio predicted by an ab initio thermodynamics-based Wulff construction. When lateral interactions between adsorbates were included in the 1p-kMC simulations, the two surfaces, RuO2(110) and RuO2(111), were found to be of similar order-of-magnitude in activity for the pressure range of 1 × 10–4 bar to 1 bar, with the RuO2(110) surface-termination showing more simulated activity than the RuO2(111) surface-termination. Coupling between the 1p-kMC and CFD was achieved with a lookup table generated by the error-based modified Shepard interpolation scheme. Isothermal reactor scale simulations were performed and compared to two separate experimental studies, conducted with reactant partial pressures of ≤0.1 bar. Simulations without an isothermality restriction were also conducted and showed that the simulated temperature gradient across the catalytic reactor bed is <0.5 K, which validated the use of the isothermality restriction for investigating the reactor-scale phenomenological temperature dependences. The approach with the Wulff construction based reactor simulations reproduced a trend similar to one experimental data set relatively well, with the (110) surface being more active at higher temperaures; in contrast, for the other experimental data set, our reactor simulations achieve surprisingly and perhaps fortuitously good agreement with the activity and phenomenological pressure dependence when it is assumed that the (111) facet is the only active facet present. The active phase of catalytic CO oxidation over RuO2 remains unsettled, but the present study presents proof of principle (and progress) toward more accurate multiscale modeling from electrons to reactors and new simulation results
A multiscale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics
No full textWe investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one
Large deviation principle for a stochastic Allen--Cahn equation
Get PDFAbstract. In this paper we consider the Allen–Cahn equation perturbed by a stochastic flux
term and prove a large deviation principle. Using an associated stochastic flow of diffeomorphisms
the equation can be transformed to a parabolic partial differential equation with random
coefficients. We use this structure and first provide a large deviation principle for stochastic
flows in function spaces with Hölder-continuity in time. Second, we use a continuity argument
and deduce a large deviation principle for the stochastic Allen–Cahn equation