Related papers: To logconcavity and beyond
From the paper "Formality Conjecture" (Ascona 1996): "I am aware of only one such a class, it corresponds to simplest good graph, the complete graph with $4$ vertices $($and $6$ edges$)$. This class gives a remarkable vector field on the…
We consider smooth flows preserving a smooth invariant measure, or, equivalently, locally Hamiltonian flows on compact orientable surfaces and show that almost every such locally Hamiltonian flow with only simple saddles has singular…
The phenomenon of convection is found in a wide variety of settings on different scales -- from applications in the cooling technology of laptops to heating water on a stove, and from the movement of ocean currents to describing…
We establish effective existence and uniqueness for the heat flow on time-dependent Riemannian manifolds, under minimal assumptions tailored towards the study of Ricci flow through singularities. The main point is that our estimates only…
The understanding of the underlying dynamical mechanisms which determine the macroscopic laws of heat conduction is a long standing task of non-equilibrium statistical mechanics. A better understanding of the mechanism of heat conduction…
Superconductivity has continued to be a fascinating phenomenon ever since its discovery in 1911. The magnitude of the transition temperature, Tc, provides valuable insight into the underlying physics. Here we provide select examples of the…
We study the heat equation on time-dependent metric measure spaces (as well as the dual and the adjoint heat equation) and prove existence, uniqueness and regularity. Of particular interest are properties which characterize the underlying…
A 2D numerical hydrodynamics approach is considered for modelling recent experimental results on the oscillation and collective behavior of convective flows. Our simulations consider the rising dynamics of heated fluid columns in a…
We show an energy convexity along any harmonic map heat flow with small initial energy and fixed boundary data on the unit 2-disk. In particular, this gives an affirmative answer to a question raised by W. Minicozzi asking whether such…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
We consider the dynamic property of the volume preserving mean curvature flow. This flow was introduced by Huisken who also proved it converges to a round sphere of the same enclosed volume if the initial hypersurface is strictly convex in…
The gas flow characteristics in lid-driven cavities are influenced by several factors, such as cavity geometry, gas properties, and boundary conditions. In this study, the physics of heat and gas flow in cylindrical lid-driven cavities with…
Seminal work by Cortadella, Kondratyev, Lavagno, and Sotiriou includes a hand-written proof that a particular handshaking protocol preserves flow equivalence, a notion of equivalence between synchronous latch-based specifications and their…
The striking anomalies in physical properties of supercooled water that were discovered in the 1960-70s, remain incompletely understood and so provide both a source of controversy amongst theoreticians, and a stimulus to experimentalists…
Link invariants of long pieces of orbits of a volume-preserving flow can be used to define diffeomorphism invariants of the flow. In this paper, we extend the notions of wrapping number and trunk and define invariants of links with respect…
We establish global existence of smooth solutions to heat flow for Yang-Mills-Higgs functional on Kahler fibrations. As an application, we give a new proof of the key inequality for Mundet's Hitchin-Kobayashi correspondence theorem using…
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms…
We show that the porous medium equation does not in general preserve $\alpha$-concavity of the pressure for $0\le\alpha<1/2$ or $1/2<\alpha\le 1$. In particular, this resolves an open problem of V\'azquez on whether concavity of pressure is…
We consider the volume preserving flow of smooth, closed and convex hypersurfaces in the hyperbolic space $\mathbb{H}^{n+1}$ with speed given by a general nonhomogeneous function of the Gauss curvature. For a large class of speed functions,…
We construct a smooth, strictly positive, Gaussian-decaying density on $\mathbb{R}^2$ for which Fisher information along the heat flow is not log-convex. This disproves the Cheng--Geng log-convexity conjecture in dimension two and, by…