Publications

Stochastically drifted Brownian motion for self-propelled particles

Brownian Motion, with some persistence in the direction of motion, typically known as active Brownian Motion, has been observed in many significant chemical and biological transport processes. Here, we present a model of drifted Brownian Motion that …

Hierarchical Symmetry-Breaking Model for Stem Cell Differentiation

Waddington envisioned stem cell differentiation as a marble rolling down a hill, passing through hierarchically branched valleys representing the cell’s temporal state. The terminal valleys at the bottom of the hill indicate the possible committed …

Multilayered noise model for transport in complex environments

Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the …

Self-Regulated Symmetry Breaking Model for Stem Cell Differentiation

In conventional disorder–order phase transitions, a system shifts from a highly symmetric state, where all states are equally accessible (disorder) to a less symmetric state with a limited number of available states (order). This transition may occur …

Emergent Criticality in Coupled Boolean Networks

Early embryonic development involves forming all specialized cells from a fluid-like mass of identical stem cells. The differentiation process consists of a series of symmetry-breaking events, starting from a high-symmetry state (stem cells) to a …

Stochastic pursuit-evasion curves for foraging dynamics

A hybrid fluctuating hydrodynamics and kinetic Monte Carlo method for modeling chemically-powered nanoscale motion

© 2017, Springer International Publishing AG. We present a stochastic multiscale method for modeling heterogeneous catalysis at the nanoscale. The system is decomposed into the fluid domain and the catalyst-fluid interface. We implemented the …

A stochastic reaction-diffusion model for protein aggregation on DNA

© 2017 World Scientific Publishing Company. Vital functions of DNA, such as transcription and packaging, depend on the proper clustering of proteins on the double strand. The present study investigates how the interplay between DNA allostery and …

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

© 2016 Elsevier B.V. In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by …

Fluctuating hydrodynamics for ionic liquids

© 2017 Elsevier B.V. We present a mean-field fluctuating hydrodynamics (FHD) method for studying the structural and transport properties of ionic liquids in bulk and near electrified surfaces. The free energy of the system consists of two competing …