Zobrazeno 1 - 10
of 271
pro vyhledávání: '"Mattingly, P. C."'
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential equation associated with the governing drift-diffusion equation. We co
Externí odkaz:
http://arxiv.org/abs/2410.05657
When studying out-of-equilibrium systems, one often excites the dynamics in some degrees of freedom while removing the excitation in others through damping. In order for the system to converge to a statistical steady state, the dynamics must transfer
Externí odkaz:
http://arxiv.org/abs/2404.06465
When auditing a redistricting plan, a persuasive method is to compare the plan with an ensemble of neutrally drawn redistricting plans. Ensembles are generated via algorithms that sample distributions on balanced graph partitions. To audit the partis
Externí odkaz:
http://arxiv.org/abs/2401.17455
Fr\'echet means of samples from a probability measure $\mu$ on any smoothly stratified metric space M with curvature bounded above are shown to satisfy a central limit theorem (CLT). The methods and results proceed by introducing and proving analytic
Externí odkaz:
http://arxiv.org/abs/2311.09455
Variation of empirical Fr\'echet means on a metric space with curvature bounded above is encoded via random fields indexed by unit tangent vectors. A central limit theorem shows these random tangent fields converge to a Gaussian such field and lays t
Externí odkaz:
http://arxiv.org/abs/2311.09454
Any measure $\mu$ on a CAT(k) space M that is stratified as a finite union of manifolds and has local exponential maps near the Fr\'echet mean $\bar\mu$ yields a continuous "tangential collapse" from the tangent cone of M at $\bar\mu$ to a vector spa
Externí odkaz:
http://arxiv.org/abs/2311.09453
In any CAT(k) space M, the "shadow" of a tangent vector Z at a point p is the set vectors that form an angle of \pi or more with Z. Taking logarithm maps at points approaching p along a fixed geodesic ray from p with tangent Z collapses the shadow to
Externí odkaz:
http://arxiv.org/abs/2311.09451
We consider the advection-diffusion equation on $\mathbb{T}^2$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale $|\log \nu|$, where $\nu$ is the
Externí odkaz:
http://arxiv.org/abs/2304.05374
In this paper we give sufficient conditions for random splitting systems to have a positive top Lyapunov exponent. We verify these conditions for random splittings of two fluid models: the conservative Lorenz-96 equations and Galerkin approximations
Externí odkaz:
http://arxiv.org/abs/2210.02958
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector fields preservi
Externí odkaz:
http://arxiv.org/abs/2201.06643