A new derivation of the velocity correlations of a thermally fluctuating Brownian particle is shown by direct calculation from a stochastic hydrodynamic model in which the fluid-particle coupling is treated in a simple manner. The model significantly simplifies the calculation of statistics of a particle and has the virtue of being readily amenable to numerical simulation. To show that the mode...

We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models. ∗Proceedings contribution to the Corfu Summer Institute on Elementary Particle Physics and Gravity Workshop on Non C...

We present a new probabilistic model of compact commutative Lie groups that produces invariantequivariant and disentangled representations of data. To define the notion of disentangling, we borrow a fundamental principle from physics that is used to derive the elementary particles of a system from its symmetries. Our model employs a newfound Bayesian conjugacy relation that enables fully tracta...

Recently there has been a lot of interest in the transport properties of particle systems in random media [AHL, BE, F, GP, KPW, K, MA, R, Se]. A simple model for which the hydrodynamic scaling limit can be obtained is the Kawasaki dynamics for random Bernoulli measures [Q], [QY]. Such systems have been used to model electron transport in doped crystals. The hydrodynamic limit is a nonlinear dif...

The new method proposed in this work not only measures the particle size distribution and the average molar mass accurately using the static light scattering (SLS) technique when the Rayleigh-Gans-Debye approximation is valid for dilute poly-disperse homogenous spherical particles in dispersion, but also enables us to have insight into the theoretical analysis of the dimensionless shape paramet...

Deposition of colloidal- and nano-scale particles on surfaces is critical to numerous natural and engineered environmental, health, and industrial applications ranging from drinking water treatment to semi-conductor manufacturing. Nano-scale surface roughness-induced hydrodynamic impacts on particle deposition were evaluated in the absence of an energy barrier to deposition in a parallel plate ...

After a very brief review of twentieth century elementary particle physics, prospects for the next century are discussed. First and most important are technological limits of opportunities; next, the future experimental program, and finally the status of the theory, in particular its limitations as well as its opportunities. Invited talk given at the International Conference on Fundamental Scie...