Georgia Institute of Technology College of Sciences

TBA

It is well-known that a spacetime which expands sufficiently fast can stabilize the fluid for relativistic/Einstein-fluid systems. One may wonder whether the expansion of the fluid, instead of the background spacetime geometry, is also able to achieve a similar stabilizing effect. As an attempt to address this question, we consider the free boundary relativistic Euler equations in Minkowski background M1+3 equipped with a physical vacuum boundary, which models the motion of relativistic gas. For the class of isentropic, barotropic, and polytropic gas, we construct an open class of initial data which launch future-global solutions. Such solutions are spherically symmetric, have small initial density, and expand asymptotically linearly in time. In particular, the asymptotic rate of expansion is allowed to be arbitrarily close to the speed of light. Therefore, our main result is far from a perturbation of existing results concerning the classical Euler counterparts. This is joint work with Marcelo Disconzi and Chenyun Luo.

TBD

How is it that a diverse array of natural systems—such as tectonic plates, neurons, star surfaces, and financial markets—exhibit similar power-law signatures? I will discuss Bak, Tang, and Wiesenfeld's influential theory of self-organized criticality and then describe our solutions to long-standing conjectures about its sandpile model foundations.