Related papers: To logconcavity and beyond
We provide variants and improvements of the Brascamp-Lieb variance inequality which take into account the invariance properties of the underlying measure. This is applied to spectral gap estimates for log-concave measures with many…
We consider the evolution of a closed convex hypersurface under a volume preserving curvature flow. The speed is given by a power of the m-th mean curvature plus a volume preserving term, including the case of powers of the mean curvature…
The Sun's axisymmetric large-scale flows, differential rotation and meridional circulation, are thought to be maintained by the influence of rotation on the thermal-convective motions in the solar convection zone. These large-scale flows…
Israel-Stewart theory is a causal, stable formulation of relativistic dissipative fluid dynamics. This theory has been shown to give a decent description of the dynamical behavior of a relativistic fluid in cases where shear stress becomes…
We prove log-concavity of the lengths of the top rows of Young diagrams under Poissonized Plancherel measure. This is the first known positive result towards a 2008 conjecture of Chen that the length of the top row of a Young diagram under…
In addition to mass, energy, and momentum, classical dissipationless flows conserve helicity, a measure of the topology of the flow. Helicity has far-reaching consequences for classical flows from Newtonian fluids to plasmas. Since…
In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in…
We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of…
Thermal convection in an electrically conducting fluid (for example, a liquid metal) in the presence of a static magnetic field is considered in this chapter. The focus is on the extreme states of the flow, in which both buoyancy and…
We study a liquid-gas coexistence system in a container under gravity with heat flow in the direction opposite to gravity. By molecular dynamics simulation, we find that the liquid buoys up and continues to float steadily. The height at…
We prove that in a large collection of naturally defined sets of permutations of fixed length, the numbers of permutations at Ulam distance k from the identity form a log-concave sequence in k.
As a material property and as a metaphor, thermal conductivity occupies an important position in physical, biological and geological sciences. Yet, its precise measurement is dependent on using electricity as a proxy because flowing heat…
R. Pemantle conjectured, and T.M. Liggett proved in 1997, that the convolution of two ultra-logconcave is ultra-logconcave. Liggett's proof is elementary but long. We present here a short proof, based on the mixed volume of convex sets.
Motivated by a question of Tsai-Tsui-Wang, we consider the rigidity of map from manifolds with positive Ricci curvature to manifolds with positive sectional curvature. We show that if the Ricci curvature of the domain dominates that of the…
Superfluids and superconductors are ordinary matter that show a very surprising behavior at low temperatures. As their temperature is reduced, materials of both kinds can abruptly fall into a state in which they will support a persistent,…
Thermal conduction has been suggested as a possible mechanism by which sufficient extra heating is provided in radiation-dominated accretion flows. We consider the extreme case in which the generated energy due to the viscosity and the…
In case of the heat flow on the free loop space of a closed Riemannian manifold non-triviality of Morse homology for semi-flows is established by constructing a natural isomorphism to singular homology of the loop space. The construction is…
Magnetoconvection in a tall vertical box with vertical hot and cold walls, and an imposed steady uniform magnetic field perpendicular to the temperature gradient, is analyzed numerically. The geometry and the values of the non-dimensional…
Relativistic heat transport in electron-two-temperature plasmas with density gradients has been investigated. The Legendre expansion analysis of relativistically modified kinetic equations shows that strong inhibition of heat flux appears…
Laboratory experiments were conducted to study heat transport characteristics in a nonhomogeneously heated fluid annulus subjected to rotation along the vertical axis (z). The nonhomogeneous heating was obtained by imposing radial and…