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Open Access Publications from the University of California

Scholarly Works (9 results)

  • Article
  • Peer Reviewed
UC Merced Previously Published Works (2023)
We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. We devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.
    Cover page: Learning stochastic dynamics with statistics-informed neural networkCreative Commons 'BY' version 4.0 license
    • Article
    • Peer Reviewed
    UC Merced Previously Published Works (2016)
    We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.
      Cover page: 111 years of Brownian motion
      • Article
      • Peer Reviewed
      UC Merced Previously Published Works (2018)
      We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and dissociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as reaction-diffusion master equation algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction-limited and diffusion-limited irreversible association in three dimensions and compare to existing theoretical predictions at low and moderate densities. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium and compare to recent theoretical predictions. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. Our studies reinforce the common finding that microscopic mechanisms and correlations matter for diffusion-limited systems, making continuum and even mesoscopic modeling of such systems difficult or impossible. We also find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.
        Cover page: Efficient reactive Brownian dynamics
        • Thesis
        • Peer Reviewed
        UC Merced Electronic Theses and Dissertations (2024)

        This thesis aims to characterize the behavior of reactive gas mixtures and aggregate dynamics at small scales. Since at scales ranging from nanometers to micrometers fluids are discrete systems made of individual particles, the full characterization of their dynamics requires modeling approaches capable of capturing both the mean behavior of the fluid and the impacts of thermal fluctuations due to random molecular motion. Here I present three different approaches to model fluid systems at small scales in a physically-accurate, mathematically-sound and computationally-efficient manner.

        First, I discuss how to model the dynamics of reactive gas mixtures at the mesoscopic scale in a thermodynamically consistent manner. To this end, I incorporate a chemical Langevin equation approach into the framework of fluctuating hydrodynamics (continuum stochastic approach). I find that in order to obtain physically accurate results, one needs to fully characterize the temperature dependence of the rate constants of a chemical reaction. I validate this formulation by simulating a reversible dimerization reaction and characterize the spectrum of fluctuations at thermodynamic equilibrium.

        Secondly, I discuss a Brownian dynamics formulation (particle-based approach) to model the formation of aggregates. I incorporate rotational effects, size-dependent diffusivities and settling under gravity into the well-established framework of Diffusion-Limited Cluster Aggregation. I characterize how the inclusion of rotational effects and settling lowers the fractal dimension typically found in aggregates, while size-dependent diffusivities slow down their growth rate.

        Finally, I discuss a boundary integral formulation to solve the Stokes Equations (continuum deterministic approach) to characterize the internal and external stresses felt by different types of marine aggregates settling under gravity or exposed to some laminar shear flow. I find that the internal stresses induced by gravity distribute differently in aggregates compared to those induced by a shear flow, leading to different breakup distributions. Furthermore, I find that the largest stress felt by aggregates exposed to a shear background flow shows a quadratic dependence on the aggregate's radius, indicating that the contribution of extensional effects on the stresses is dominant over rotational effects.

          Cover page: Mathematical and physical modeling of reactive gas dynamics and aggregation dynamics at small scales
          • Article
          • Peer Reviewed
          LBL Publications (2018)
          In the present study, quantitative feasibility tests of the hydrodynamic description of a two-dimensional fluid at the molecular level are performed, both with respect to length and time scales. Using high-resolution fluid velocity data obtained from extensive molecular dynamics simulations, we computed the transverse and longitudinal components of the velocity field by the Helmholtz decomposition and compared them with those obtained from the linearized Navier-Stokes (LNS) equations with time-dependent transport coefficients. By investigating the vortex dynamics and the sound wave propagation in terms of these field components, we confirm the validity of the LNS description for times comparable to or larger than several mean collision times. The LNS description still reproduces the transverse velocity field accurately at smaller times, but it fails to predict characteristic patterns of molecular origin visible in the longitudinal velocity field. Based on these observations, we validate the main assumptions of the mode-coupling approach. The assumption that the velocity autocorrelation function can be expressed in terms of the fluid velocity field and the tagged particle distribution is found to be remarkably accurate even for times comparable to or smaller than the mean collision time. This suggests that the hydrodynamic-mode description remains valid down to the molecular scale.
            Cover page: Molecular hydrodynamics: Vortex formation and sound wave propagation.
            • Article
            • Peer Reviewed
            LBL Publications (2017)
            We develop numerical methods for stochastic reaction-diffusion systems based on approaches used for fluctuatinghydrodynamics (FHD). For hydrodynamicsystems, the FHD formulation is formally described by stochastic partial differential equations (SPDEs). In the reaction-diffusion systems we consider, our model becomes similar to the reaction-diffusion master equation (RDME) description when our SPDEs are spatially discretized and reactions are modeled as a source term having Poissonfluctuations. However, unlike the RDME, which becomes prohibitively expensive for an increasing number of molecules, our FHD-based description naturally extends from the regime where fluctuations are strong, i.e., each mesoscopic cell has few (reactive) molecules, to regimes with moderate or weak fluctuations, and ultimately to the deterministic limit. By treating diffusion implicitly, we avoid the severe restriction on time step size that limits all methods based on explicit treatments of diffusion and construct numerical methods that are more efficient than RDME methods, without compromising accuracy. Guided by an analysis of the accuracy of the distribution of steady-state fluctuations for the linearized reaction-diffusion model, we construct several two-stage (predictor-corrector) schemes, where diffusion is treated using a stochastic Crank-Nicolson method, and reactions are handled by the stochastic simulation algorithm of Gillespie or a weakly second-order tau leaping method. We find that an implicit midpoint tau leaping scheme attains second-order weak accuracy in the linearized setting and gives an accurate and stable structure factor for a time step size of an order of magnitude larger than the hopping time scale of diffusing molecules. We study the numerical accuracy of our methods for the Schlögl reaction-diffusion model both in and out of thermodynamic equilibrium. We demonstrate and quantify the importance of thermodynamicfluctuations to the formation of a two-dimensional Turing-like pattern and examine the effect of fluctuations on three-dimensional chemical front propagation. By comparing stochastic simulations to deterministic reaction-diffusion simulations, we show that fluctuations accelerate pattern formation in spatially homogeneous systems and lead to a qualitatively different disordered pattern behind a traveling wave.
              Cover page: Stochastic simulation of reaction-diffusion systems: A fluctuating-hydrodynamics approach
              • Article
              • Peer Reviewed
              UC Merced Previously Published Works (2018)
              Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive incompressible liquid mixtures with stochastic chemistry. Fluctuating multispecies mass diffusion is formulated using a Maxwell-Stefan description without assuming a dilute solution, and momentum dynamics is described by a stochastic Navier-Stokes equation for the fluid velocity. We consider a thermodynamically consistent generalization for the law of mass action for non-dilute mixtures and use it in the chemical master equation (CME) to model reactions as a Poisson process. The FHD approach provides remarkable computational efficiency over traditional reaction-diffusion master equation methods when the number of reactive molecules is large, while also retaining accuracy even when there are as few as ten reactive molecules per hydrodynamic cell. We present a numerical algorithm to solve the coupled FHD and CME equations and validate it on both equilibrium and nonequilibrium problems. We simulate a diffusively driven gravitational instability in the presence of an acid-base neutralization reaction, starting from a perfectly flat interface. We demonstrate that the coupling between velocity and concentration fluctuations dominates the initial growth of the instability.
                Cover page: Fluctuating hydrodynamics of reactive liquid mixtures
                • Article
                • Peer Reviewed
                UC Merced Previously Published Works (2019)
                At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. Péraud, Phys. Rev. Fluids 1, 074103 (2016)2469-990X10.1103/PhysRevFluids.1.074103]. However, at length and time scales larger than the Debye scales, electrolytes are effectively electroneutral and the charged-fluid PNP equations become too stiff to solve numerically. Here we formulate the isothermal incompressible equations of fluctuating hydrodynamics for reactive multispecies mixtures involving charged species in the electroneutral limit and design a numerical algorithm to solve these equations. Our model does not assume a dilute electrolyte solution but rather treats all species on an equal footing, accounting for cross diffusion and nonideality using Maxwell-Stefan theory. By enforcing local electroneutrality as a constraint, we obtain an elliptic equation for the electric potential that replaces the Poisson equation in the fluctuating PNP equations. We develop a second-order midpoint predictor-corrector algorithm to solve either the charged-fluid or electroneutral equations with only a change of the elliptic solver. We use the electroneutral algorithm to study a gravitational fingering instability, triggered by thermal fluctuations, at an interface where an acid and base react to neutralize each other. Our results demonstrate that, because the four ions diffuse with very different coefficients, one must treat each ion as an individual species and cannot treat the acid, base, and salt as neutral species. This emphasizes the differences between electrodiffusion and classical Fickian diffusion, even at electroneutral scales.
                  Cover page: Fluctuating hydrodynamics of electrolytes at electroneutral scales
                  • Article
                  • Peer Reviewed
                  LBL Publications (2023)
                  Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N's, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.
                    Cover page: Surface coverage dynamics for reversible dissociative adsorption on finite linear latticesCreative Commons 'BY' version 4.0 license
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