Thomas G. Fai

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We develop numerical schemes for solving the isothermal compressible and incom-pressible equations of fluctuating hydrodynamics on a grid with staggered momenta. We develop a second-order accurate spatial discretization of the diffusive, advective and stochastic fluxes that satisfies a discrete fluctuation-dissipation balance, and construct temporal(More)
Quantitative methods and approaches have been playing an increasingly important role in cell biology in recent years. They involve making accurate measurements to test a predefined hypothesis in order to compare experimental data with predictions generated by theoretical models, an approach that has benefited physicists for decades. Building quantitative(More)
We present a general variable viscosity and variable density immersed boundary method that is first-order accurate in the variable density case and, for problems possessing sufficient regularity, second-order accurate in the constant density case. The viscosity and density are considered material properties and are defined by a dynamically updated(More)
We formulate low Mach number fluctuating hydrodynamic equations appropriate for mod-eling diffusive mixing in isothermal mixtures of fluids with different density and transport coefficients. These equations represent a coarse-graining of the microscopic dynamics of the fluid molecules in both space and time, and eliminate the fluctuations in pressure(More)
semi-implicit numerical methods for solving low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with different densities and transport coefficients. We treat viscous dissipation implicitly using a recently-developed variable-coefficient Stokes solver [ increase the time step size(More)
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive stochastic drift term with diffusion coefficient obeying a Stokes-Einstein relation, in addition to the expected advection by a random velocity. The overdamped limit correctly(More)
We analyze the stability and convergence of first-order accurate and second-order accurate timestepping schemes for the Navier-Stokes equations with variable viscosity. These schemes are characterized by a mixed implicit/explicit treatment of the viscous term, in which a numerical parameter, λ, determines the degree of splitting between the implicit and(More)
We develop computational methods for the simulation of osmotic swelling phenomena relevant to microscopic vesicles containing transformable solute molecules. We introduce Stochastic Immersed Boundary Methods (SIBM) that can capture osmotically driven fluid transport through semi-permeable elastic membranes subject to thermal fluctuations. We also develop(More)
We show it is NP-hard to compute a minimum cover of point 2-transmitters, point k-transmitters and edge 2-transmitters in a simple polygon; the point 2-transmitter result extends to orthogonal polygons. Introduction. The traditional art gallery problem (AGP) considers placing guards in an art gallery—modeled by a polygon—such that every point in the room(More)
We consider a generalization of the classical Art Gallery Problem, where instead of a light source, the guards, called k-transmitters, model a wireless device with a signal that can pass through at most k walls. We show it is NP-hard to compute a minimum cover of point 2-transmitters, point k-transmitters, and edge 2-transmitters in a simple polygon. The(More)