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At least 883 records · Page 49
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DOE OSTI2014

Periodic and stochastic thermal modulation of protein folding kinetics

Chemical reactions are usually observed either by relaxation of a bulk sample after applying a sudden external perturbation, or by intrinsic fluctuations of a few molecules. Here we show that the two ideas can be combined to measure protein folding kinetics, either by periodic thermal modulation, or by creating artificial thermal noise that greatly exceeds natural thermal fluctuations. We study the folding reaction of the enzyme phosphoglycerate kinase driven by periodic temperature waveforms. As the temperature waveform unfolds and refolds the protein, its fluorescence color changes due to FRET (Förster resonant Energy Transfer) of two donor/acceptor fluorophores labeling the protein. We adapt a simple model of periodically driven kinetics that nicely fits the data at all temperatures and driving frequencies: The phase shifts of the periodic donor and acceptor fluorescence signals as a function of driving frequency reveal reaction rates. We also drive the reaction with stochastic temperature waveforms that produce thermal fluctuations much greater than natural fluctuations in the bulk. Such artificial thermal noise allows the recovery of weak underlying signals due to protein folding kinetics. This opens up the possibility for future detection of a stochastic resonance for protein folding subject to noise with controllable amplitude.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Stochastic many-body perturbation theory for anharmonic molecular vibrations

A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Mixed quantal-semiquantal dynamics with stochastic particles for backreaction

A mixed quantal-semiquantal theory is presented in which the semiquantal squeezed-state wave packet describes the heavy degrees of freedom. Starting from the mean-field equations of motion that are naturally derived from the time-dependent variational principle, we introduce the stochastic particle description for both the quantal and semiquantal parts in an aim to take into account the interparticle correlation, in particular the “quantum backreaction” beyond the mean-field approximation. A numerical application on a model of O{sub 2} scattering from a Pt surface demonstrates that the proposed scheme gives correct asymptotic behavior of the scattering probability, with improvement over the mixed quantum-classical scheme with Bohmian particles, which is comprehended by comparing the Bohmian and the stochastic trajectories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Estimation of stochastic volatility with long memory for index prices of FTSE Bursa Malaysia KLCI

In recent years, modeling in long memory properties or fractionally integrated processes in stochastic volatility has been applied in the financial time series. A time series with structural breaks can generate a strong persistence in the autocorrelation function, which is an observed behaviour of a long memory process. This paper considers the structural break of data in order to determine true long memory time series data. Unlike usual short memory models for log volatility, the fractional Ornstein-Uhlenbeck process is neither a Markovian process nor can it be easily transformed into a Markovian process. This makes the likelihood evaluation and parameter estimation for the long memory stochastic volatility (LMSV) model challenging tasks. The drift and volatility parameters of the fractional Ornstein-Unlenbeck model are estimated separately using the least square estimator (lse) and quadratic generalized variations (qgv) method respectively. Finally, the empirical distribution of unobserved volatility is estimated using the particle filtering with sequential important sampling-resampling (SIR) method. The mean square error (MSE) between the estimated and empirical volatility indicates that the performance of the model towards the index prices of FTSE Bursa Malaysia KLCI is fairly well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Constant-complexity stochastic simulation algorithm with optimal binning

At the molecular level, biochemical processes are governed by random interactions between reactant molecules, and the dynamics of such systems are inherently stochastic. When the copy numbers of reactants are large, a deterministic description is adequate, but when they are small, such systems are often modeled as continuous-time Markov jump processes that can be described by the chemical master equation. Gillespie’s Stochastic Simulation Algorithm (SSA) generates exact trajectories of these systems, but the amount of computational work required for each step of the original SSA is proportional to the number of reaction channels, leading to computational complexity that scales linearly with the problem size. The original SSA is therefore inefficient for large problems, which has prompted the development of several alternative formulations with improved scaling properties. We describe an exact SSA that uses a table data structure with event time binning to achieve constant computational complexity with respect to the number of reaction channels for weakly coupled reaction networks. We present a novel adaptive binning strategy and discuss optimal algorithm parameters. We compare the computational efficiency of the algorithm to existing methods and demonstrate excellent scaling for large problems. This method is well suited for generating exact trajectories of large weakly coupled models, including those that can be described by the reaction-diffusion master equation that arises from spatially discretized reaction-diffusion processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Entropy production of doubly stochastic quantum channels

We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A moment-convergence method for stochastic analysis of biochemical reaction networks

Traditional moment-closure methods need to assume that high-order cumulants of a probability distribution approximate to zero. However, this strong assumption is not satisfied for many biochemical reaction networks. Here, we introduce convergent moments (defined in mathematics as the coefficients in the Taylor expansion of the probability-generating function at some point) to overcome this drawback of the moment-closure methods. As such, we develop a new analysis method for stochastic chemical kinetics. This method provides an accurate approximation for the master probability equation (MPE). In particular, the connection between low-order convergent moments and rate constants can be more easily derived in terms of explicit and analytical forms, allowing insights that would be difficult to obtain through direct simulation or manipulation of the MPE. In addition, it provides an accurate and efficient way to compute steady-state or transient probability distribution, avoiding the algorithmic difficulty associated with stiffness of the MPE due to large differences in sizes of rate constants. Applications of the method to several systems reveal nontrivial stochastic mechanisms of gene expression dynamics, e.g., intrinsic fluctuations can induce transient bimodality and amplify transient signals, and slow switching between promoter states can increase fluctuations in spatially heterogeneous signals. The overall approach has broad applications in modeling, analysis, and computation of complex biochemical networks with intrinsic noise.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Diffusive flux in a model of stochastically gated oxygen transport in insect respiration

Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

An alternative realization of the exact non-Markovian stochastic Schrödinger equation

Based on the path integral approach, we derive a new realization of the exact non-Markovian stochastic Schrödinger equation (SSE). The main difference from the previous non-Markovian quantum state diffusion (NMQSD) method is that the complex Gaussian stochastic process used for the forward propagation of the wave function is correlated, which may be used to reduce the amplitude of the non-Markovian memory term at high temperatures. The new SSE is then written into the recently developed hierarchy of pure states scheme, in a form that is more closely related to the hierarchical equation of motion approach. Numerical simulations are then performed to demonstrate the efficiency of the new method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Hierarchy of forward-backward stochastic Schrödinger equation

Driven by the impetus to simulate quantum dynamics in photosynthetic complexes or even larger molecular aggregates, we have established a hierarchy of forward-backward stochastic Schrödinger equation in the light of stochastic unravelling of the symmetric part of the influence functional in the path-integral formalism of reduced density operator. The method is numerically exact and is suited for Debye-Drude spectral density, Ohmic spectral density with an algebraic or exponential cutoff, as well as discrete vibrational modes. The power of this method is verified by performing the calculations of time-dependent population differences in the valuable spin-boson model from zero to high temperatures. By simulating excitation energy transfer dynamics of the realistic full FMO trimer, some important features are revealed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Stochastic level-set variational implicit-solvent approach to solute-solvent interfacial fluctuations

Recent years have seen the initial success of a variational implicit-solvent model (VISM), implemented with a robust level-set method, in capturing efficiently different hydration states and providing quantitatively good estimation of solvation free energies of biomolecules. The level-set minimization of the VISM solvation free-energy functional of all possible solute-solvent interfaces or dielectric boundaries predicts an equilibrium biomolecular conformation that is often close to an initial guess. In this work, we develop a theory in the form of Langevin geometrical flow to incorporate solute-solvent interfacial fluctuations into the VISM. Such fluctuations are crucial to biomolecular conformational changes and binding process. We also develop a stochastic level-set method to numerically implement such a theory. We describe the interfacial fluctuation through the “normal velocity” that is the solute-solvent interfacial force, derive the corresponding stochastic level-set equation in the sense of Stratonovich so that the surface representation is independent of the choice of implicit function, and develop numerical techniques for solving such an equation and processing the numerical data. We apply our computational method to study the dewetting transition in the system of two hydrophobic plates and a hydrophobic cavity of a synthetic host molecule cucurbit[7]uril. Numerical simulations demonstrate that our approach can describe an underlying system jumping out of a local minimum of the free-energy functional and can capture dewetting transitions of hydrophobic systems. In the case of two hydrophobic plates, we find that the wavelength of interfacial fluctuations has a strong influence to the dewetting transition. In addition, we find that the estimated energy barrier of the dewetting transition scales quadratically with the inter-plate distance, agreeing well with existing studies of molecular dynamics simulations. Our work is a first step toward the inclusion of fluctuations into the VISM and understanding the impact of interfacial fluctuations on biomolecular solvation with an implicit-solvent approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Electron thermal confinement in a partially stochastic magnetic structure

Using a high-repetition-rate Thomson scattering diagnostic, we observe a peak in electron temperature $T_e$ coinciding with the location of a large magnetic island in the Madison Symmetric Torus. Magnetohydrodynamic modeling of this quasi-single helicity plasma indicates that smaller adjacent islands overlap with and destroy the large island flux surfaces. The estimated stochastic electron thermal conductivity (≈30 m 2 /s) is consistent with the conductivity inferred from the observed $T_e$ gradient and ohmic heating power. Island-shaped $T_e$ peaks can result from partially stochastic magnetic islands.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-time scale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to stochastic MD time steps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action with respect to time and by initializing the path configurations from a nonequilibrium distribution, the algorithm enables significant speedups in terms of the length of MD trajectories that can be integrated in a given amount of wall-clock time. The method is demonstrated for Brownian dynamics, although it is generalizable to other stochastic equations of motion including open systems. We apply the method to two simple systems, a harmonic oscillator and a Lennard-Jones liquid, and we show that in comparison to the conventional Euler integration scheme for Brownian dynamics, the new method can reduce the wall-clock time for integrating trajectories of a given length by more than three orders of magnitude in the former system and more than two in the latter. This new method for parallelizing MD in the dimension of time can be trivially combined with algorithms for parallelizing the MD force evaluation to achieve further speedup.

Rosa-Raíces, Jorge L.↗
DOE OSTI2021

Comparing (stochastic-selection) ab initio multiple spawning with trajectory surface hopping for the photodynamics of cyclopropanone, fulvene, and dithiane

Ab Initio Multiple Spawning (AIMS) simulates the excited-state dynamics of molecular systems by representing nuclear wavepackets in a basis of coupled traveling Gaussian functions, called trajectory basis functions (TBFs). New TBFs are spawned when nuclear wavepackets enter regions of strong nonadiabaticity, permitting the description of non-Born–Oppenheimer processes. The spawning algorithm is simultaneously the blessing and the curse of the AIMS method: it allows for an accurate description of the transfer of nuclear amplitude between different electronic states, but it also dramatically increases the computational cost of the AIMS dynamics as all TBFs are coupled. Recently, a strategy coined stochastic-selection AIMS (SSAIMS) was devised to limit the ever-growing number of TBFs and tested on simple molecules. In this work, we use the photodynamics of three different molecules—cyclopropanone, fulvene, and 1,2-dithiane—to investigate (i) the potential of SSAIMS to reproduce reference AIMS results for challenging nonadiabatic dynamics, (ii) the compromise achieved by SSAIMS in obtaining accurate results while using the smallest average number of TBFs as possible, and (iii) the performance of SSAIMS in comparison to the mixed quantum/classical method trajectory surface hopping (TSH)—both in terms of its accuracy and computational cost. We show that SSAIMS can accurately reproduce the AIMS results for the three molecules considered at a much cheaper computational cost, often close to that of TSH. We deduce from these tests that an overlap-based criterion for the stochastic-selection process leads to the best agreement with the reference AIMS dynamics for the smallest average number of TBFs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

The 3D magnetic topology and plasma dynamics in open stochastic magnetic field lines

We report the thermal quench triggered by locked modes is known to be mainly due to open stochastic magnetic field lines connected to the wall boundary. It is essential to understand the 3D structure of open stochastic field lines since it determines the overall plasma dynamics in the system. In this study, we analyze the 3D magnetic topology for two key concepts, the connection length L c and the effective magnetic mirror ratio M eff , and present a comprehensive picture of electron and ion dynamics related to the magnetic topology. The connection length determines the 3D structure of the ambipolar potential, and a sharp potential drop across distinct L c regions induces the E × B transport and mixing across the field line. The confinement of electrons and ions along the field line is determined by the ambipolar potential and [Formula: see text] configuration. Electron and ion temperatures in magnetic hills (M eff < 1) are lower than in magnetic wells (M eff > 1) because particles in magnetic hills are more likely to escape toward the wall boundary along the field line. The mixing between the magnetic wells and hills by E × B and magnetic drift motions results in collisionless detrapping of electrons and ions, which reduces their temperature efficiently. Numerical simulations of two different magnetic configurations demonstrate the importance of the collisionless detrapping mechanism, which could be the main cause of plasma temperature drop during the thermal quench.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Inherent stochasticity during insulator–metal transition in VO 2

Vanadium dioxide (VO 2 ), which exhibits a near-room-temperature insulator–metal transition, has great potential in applications of neuromorphic computing devices. Although its volatile switching property, which could emulate neuron spiking, has been studied widely, nanoscale studies of the structural stochasticity across the phase transition are still lacking. In this study, using in situ transmission electron microscopy and ex situ resistive switching measurement, we successfully characterized the structural phase transition between monoclinic and rutile VO 2 at local areas in planar VO 2 /TiO 2 device configuration under external biasing. After each resistive switching, different VO 2 monoclinic crystal orientations are observed, forming different equilibrium states. We have evaluated a statistical cycle-to-cycle variation, demonstrated a stochastic nature of the volatile resistive switching, and presented an approach to study in-plane structural anisotropy. Furthermore, our microscopic studies move a big step forward toward understanding the volatile switching mechanisms and the related applications of VO 2 as the key material of neuromorphic computing.

36 MATERIALS SCIENCE↗