Simplicial Ricci Flow

We construct a discrete form of Hamilton's Ricci flow (RF) equations for a d-dimensional piecewise flat simplicial geometry, S. These new algebraic equations are derived using the discrete formulation of Einstein's theory of general relativity known as Regge calculus. A Regge-Ricci flow (RRF) equation is naturally associated to each edge, L, of a simplicial lattice. In defining this equation, we find it convenient to utilize both the simplicial lattice, S, and its circumcentric dual lattice, S*. In particular, the RRF equation associated to L is naturally defined on a d-dimensional hybrid block connecting $\ell$ with its (d-1)-dimensional circumcentric dual cell, L*. We show that this equation is expressed as the proportionality between (1) the simplicial Ricci tensor, Rc_L, associated with the edge L in S, and (2) a certain volume weighted average of the fractional rate of change of the edges, lambda in L*, of the circumcentric dual lattice, S*, that are in the dual of L. The inherent orthogonality between elements of S and their duals in S* provide a simple geometric representation of Hamilton's RF equations. In this paper we utilize the well established theories of Regge calculus, or equivalently discrete exterior calculus, to construct these equations. We solve these equations for a few illustrative examples.Comment: 34 pages, 10 figures, minor revisions, DOI included: Commun. Math. Phy

A thermal lattice Boltzmann model for micro/nano-flows

The dynamic behavior of charged micro and nanofluids plays a crucial role in a large variety of industrial and biological processes. Such dynamic behavior is characterized by the simultaneous occurrence of several competing mechanisms, such as electrostatic interactions, viscous dissipation and hydrodynamic effects, often taking place in complex geometries. This paper focuses on a thermal lattice Boltzmann model for micro/nano-flows

Baryon Destruction by Asymmetric Dark Matter

We investigate new and unusual signals that arise in theories where dark matter is asymmetric and carries a net antibaryon number, as may occur when the dark matter abundance is linked to the baryon abundance. Antibaryonic dark matter can cause {\it induced nucleon decay} by annihilating visible baryons through inelastic scattering. These processes lead to an effective nucleon lifetime of 10^{29}-10^{32} years in terrestrial nucleon decay experiments, if baryon number transfer between visible and dark sectors arises through new physics at the weak scale. The possibility of induced nucleon decay motivates a novel approach for direct detection of cosmic dark matter in nucleon decay experiments. Monojet searches (and related signatures) at hadron colliders also provide a complementary probe of weak-scale dark-matter--induced baryon number violation. Finally, we discuss the effects of baryon-destroying dark matter on stellar systems and show that it can be consistent with existing observations.Comment: 26 pages, 6 figure