相关论文: Shape optimization of light structures and the van…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
We consider the mass conserving Allen-Cahn equation proposed in \cite{Bra-Bre}: the Lagrange multiplier which ensures the conservation of the mass contains not only nonlocal but also local effects (in contrast with \cite{Che-Hil-Log}). As a…
Following the recent work of V. Moncrief, A. Marini, R. Maitra and P. Mondal on the geometry of field theoretic configuration spaces, this account examines how the regularized Ricci curvature of the $SU(2)_L \times U(1)_Y$ Yang-Mills orbit…
We review the limit shape problem for the Plancherel measure and its generalizations found in supersymmetric gauge theory instanton count. We focus on the measure, interpolating between the Plancherel measure and uniform measure, a U(1)…
The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
The accuracy of mass estimates by gravitational lensing using the thin-lens approximation applied to Navarro-Frenk-White mass models with a soft truncation mechanism recently proposed by Baltz, Marshall and Oguri is studied. The…
We define new natural variants of the notions of weighted covering and separation numbers and discuss them in detail. We prove a strong duality relation between weighted covering and separation numbers and prove a few relations between the…
One of the theoretical motivations behind the belief that black holes as described by general relativity exist in nature is that it is hard to find matter configurations that mimic their properties, especially their compactness. One of the…
Non-spherical dynamical approximations and models for the gravitational collapse are used to extend the well-known Press \& Schechter (PS) approach, in order to determine analytical expressions for the mass function of cosmic structures.…
We revisit the problem of the structure and physical properties of electrically charged static spherically symmetric solutions of the Einstein-Maxwell system of equations where the matter model is a polytropic gas. We consider a…
We develop the theory of Diophantine approximation for systems of simultaneously small linear forms, which coefficients are drawn from any given analytic non-degenerate manifolds. This setup originates from a problem of Sprind\v{z}uk from…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
We prove a compactness principle for the anisotropic formulation of the Plateau problem in codimension one, along the same lines of previous works of the authors [DGM14, DPDRG15]. In particular, we perform a new strategy for proving the…
We investigate the vanishing elasticity limit for minimizers of the Landau-de Gennes model with finite energy. By adopting a refined blow-up and covering analysis, we establish the optimal $ L^p $ ($ 1<p<+\infty $) convergence of minimizers…
First we review Veltman's suggestion to attack the naturalness problem in the Standard model by requiring absence of quadratic divergences and the resulting mass formula. Then we emphasise the influence of Veltman's suggestion in…
The paper outlines novel variational technique for finding microstructures of optimal multimaterial composites, bounds of composites properties, and multimaterial optimal designs. The translation method that is used for the exact…
An exact solution to the vacuum Einstein equations is presented, whose structure is based on the Hopf fibration. The solution employs a geodesic null vector field that defines a twisting congruence and appears in the metric in Kerr-Schild…
We derive a new formulation of the compressible Euler equations exhibiting remarkable structures, including surprisingly good null structures. The new formulation comprises covariant wave equations for the Cartesian components of the…
One of the stiffest equations of state for matter in a compact star is constant energy density and this generates the interior Schwarzschild radius to mass relation and the Misner maximum mass for relativistic compact stars. If dark matter…