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Register a new userAdvancements in Milestoning I: Accelerated Milestoning via Wind Assisted Re-weighted Milestoning (WARM)
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The Milestoning algorithm created by Ron Elber et al. is a method for determining the time scale of processes too complex to be studied using brute force simulation methods. The fundamental objects implemented in the Milestoning algorithm are the first passage time distributions between adjacent protein configuration milestones. The method proposed herein aims to further enhance Milestoning by employing an artificial applied force, akin to wind, which pushes the trajectories from their initial states to their final states, and subsequently re-weights the trajectories to yield the true first passage time distributions in a fraction of the computation time required for unassisted calculations. The re-weighting method, rooted in Itos stochastic calculus, was adapted from previous work by Andricioaei et al. The theoretical basis for this technique and numerical examples are presented.
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The Milestoning method has achieved great success in the calculation of equilibrium kinetic properties such as rate constants from molecular dynamics simulations. The goal of this work is to advance Milestoning into the realm of non-equilibrium statistical mechanics, in particular, the calculation of time correlation functions. In order to accomplish this, we introduce a novel methodology for obtaining flux through a given milestone configuration as a function of both time and initial configuration, and build upon it with a novel formalism describing autocorrelation for Brownian motion in a discrete configuration space. The method is then applied to three different test systems: a harmonic oscillator, which we solve analytically, a two well potential, which is solved numerically, and an atomistic molecular dynamics simulation of alanine dipeptide.
The concepts of weighted reciprocal of temperature and weighted thermal flux are proposed for a heat engine operating between two heat baths and outputting mechanical work. With the aid of these two concepts, the generalized thermodynamic fluxes and forces can be expressed in a consistent way within the framework of irreversible thermodynamics. Then the efficiency at maximum power output for a heat engine, one of key topics in finite-time thermodynamics, is investigated on the basis of a generic model under the tight-coupling condition. The corresponding results have the same forms as those of low-dissipation heat engines [M. Esposito, R. Kawai, K. Lindenberg, and C. Van den Broeck, {Phys. Rev. Lett.} textbf{105}, 150603 (2010)]. The mappings from two kinds of typical heat engines, such as the low-dissipation heat engine and the Feynman ratchet, into the present generic model are constructed. The universal efficiency at maximum power output up to the quadratic order is found to be valid for a heat engine coupled symmetrically and tightly with two baths. The concepts of weighted reciprocal of temperature and weighted thermal flux are also transplanted to the optimization of refrigerators.
We consider natural inflation in a warm inflation framework with a temperature-dependent dissipative coefficient $Gamma propto T^3$. Natural inflation can be compatible with the Planck 2018 results with such warm assistance. With no a priori assumptions on the dissipative effects magnitude, we find that the Planck results prefer a weak dissipative regime for our benchmark scale $f=5 M_{rm pl}$, which lies outside the $2sigma$ region in the cold case. The inflation starts in the cold regime and evolves with a growing thermal fluctuation that dominates over quantum fluctuation before the end of the inflation. The observed spectral tilt puts stringent constraints on the models parameter space. We find that $f< 1 M_{rm pl}$ is excluded. A possible origin of such dissipative coefficient from axion-like coupling to gauge fields and tests of the model are also discussed.
We introduce an assisted exchange model (AEM) on a one dimensional periodic lattice with (K+1) different species of hard core particles, where the exchange rate depends on the pair of particles which undergo exchange and their immediate left neighbor. We show that this stochastic process has a pair factorized steady state for a broad class of exchange dynamics. We calculate exactly the particle current and spatial correlations (K+1)-species AEM using a transfer matrix formalism. Interestingly the current in AEM exhibits density dependent current reversal and negative differential mobility- both of which have been discussed elaborately by using a two species exchange model which resembles the partially asymmetric conserved lattice gas model in one dimension. Moreover, multi-species version of AEM exhibits additional features like multiple points of current reversal, and unusual response of particle current.
Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such as capacity and delay. Here we introduce a general random diffusion (GRD) model to investigate the traffic fluctuation in weighted networks, where a random walks choice of route is affected not only by the number of links a node has, but also by the weight of individual links. We obtain analytical solutions that characterise the relation between the average traffic and the fluctuation through nodes and links. Our analysis is supported by the results of numerical simulations. We observe that the value ranges of the average traffic and the fluctuation, through nodes or links, increase dramatically with the level of heterogeneity in link weight. This highlights the key role that link weight plays in traffic fluctuation and the necessity to study traffic fluctuation on weighted networks.
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