Related papers: Incidence Estimates for Tubes in Complex Space
Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…
The statistical effects of different conditions in physical vapor deposition, such as sputter deposition, have on thin film morphology has long been the subject of interest. One notable effect is that of column development due to…
The Enskog-like kinetic approach, recently introduced by us to study strongly inhomogeneous flu- ids, is reconsidered in order to improve the description of the transport coefficients. The approach is based on a separation of the…
We describe a barrier argument for compact minimal submanifolds in the multi-Eguchi-Hanson and in the multi-Taub-NUT spaces, which are hyperkaehler 4-manifolds given by the Gibbons-Hawking ansatz. This approach is used to obtain results…
We study the Stokes problem over convex polyhedral domains on weighted Sobolev spaces. The weight is assumed to belong to the Muckenhoupt class $A_q$ for $q \in (1,\infty)$. We show that the Stokes problem is well-posed for all $q$. In…
Refining Yau's and Kolodziej's techniques, we establish very precise uniform a priori estimates for degenerate complex Monge-Amp\`ere equations on compact K\"ahler manifolds, that allow us to control the blow up of the solutions as the…
A new intrinsic volume metric is introduced for the class of convex bodies in $\mathbb{R}^n$. As an application, an inequality is proved for the asymptotic best approximation of the Euclidean unit ball by arbitrarily positioned polytopes…
Let $A$ and $B$ be sets in a finite vector space. In this paper, we study the magnitude of the set $A\cap f(B)$, where $f$ runs through a set of transformations. More precisely, we will focus on the cases that the set of transformations is…
This work extends the high-resolution isogeometric analysis approach established for scalar transport equations to the equations of gas dynamics. The group finite element formulation is adopted to obtain an efficient assembly procedure for…
We study the influence of the boundary conditions at the solid liquid interface on diffusion in a confined fluid. Using an hydrodynamic approach, we compute numerical estimates for the diffusion of a particle confined between two planes.…
In a recent paper [cond-mat/0303185], Wu and Yip presented calculations that they interpreted as indicating an instability of the interior gap phase -- a new, hybrid superfluid-normal state of matter that we proposed in [PRL 90, 047002…
Lattice Boltzmann simulations of liquid-gas systems are believed to be restricted to modest density ratios of less than 10. In this article we show that reducing the speed of sound and, just as importantly, the interfacial contributions to…
In this note, we point out that infinite-volume Gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a Hilbert space. This simple observation follows from a result of…
We study a wide spectrum of incidence problems involving points and curves or points and surfaces in $\mathbb R^3$. The current (and in fact the only viable) approach to such problems, pioneered by Guth and Katz [2010,2015], requires a…
In this paper we consider the semi-discretization in space of a first order scalar transport equation. For the space discretization we use standard continuous finite elements. To obtain stability we add a penalty on the jump of the gradient…
Upper bounds for the $L_p$-discrepancies of point distributions in compact metric measure spaces for $0<p\le\infty$ have been established in the paper [6] by Brandolini, Chen, Colzani, Gigante and Travaglini. In the present paper we show…
It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value $c$.…
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…
The problem of capacity achieving (optimal) input probability measures has been widely investigated for several channel models with constrained inputs. So far, no outstanding generalizations have been derived. This paper does a forward step…
Rayleigh-Benard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof, Lucas and Mullin [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single…