We investigate the relationship between the mixing times of the Glauber dynamics of a statistical mechanical system with its thermodynamic equilibrium structure. For this we consider the mean-field Blume-Capel model, one of the simplest statistical mechanical models that exhibits the following intricate phase transition structure: within a two dimensional parameter space there exists a curve at...

For many fundamental sampling problems, the best, and often the only known, approach to solving them is to take a long enough random walk on a certain Markov chain and then return the current state of the chain. Techniques to prove how long “long enough” is, i.e., the number of steps in the chain one needs to take in order to be sufficiently close to the stationary distribution of the chain, ar...

For many fundamental sampling problems, the best, and often the only known, approach to solving them is to take a long enough random walk on a certain Markov chain and then return the current state of the chain. Techniques to prove how long “long enough” is, i.e., the number of steps in the chain one needs to take in order to be sufficiently close to the stationary distribution of the chain, ar...

Rapid mixing is important in biomedical analysis. In this study, rapid mixing is obtained through two-phase hydraulic focusing in microchannels. Two mixing streams are focused by two sheath streams. Assuming a laminar flow in the channel, the spreading behavior of the two immiscible fluids is modeled and solved analytically. The results show that both viscosity ratio and flow rate ratio between...

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient condi...

We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient condi...

We analyse the characteristics of two-fluid mixing in T-shaped microchannels on rotating platforms (Lab-on-a-Compact-Disk framework). Three regimes of mixing were identified based on the distinct flow behaviour in each of these regimes. A diffusion-based mixing regime was obtained for low rotation speeds. A Coriolis force based mixing regime was observed for intermediate rotation speeds, which ...