相关论文: Shape optimization of light structures and the van…
We establish an energy quantization for constrained Willmore surfaces, where the constraints are given by area, volume, and total mean curvature, assuming that the underlying conformal structures remain bounded. Furthermore, we show strong…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
The idea of reduction of couplings consists in searching for renormalization group invariant relations between parameters of a renormalizable theory that hold to all orders of perturbation theory. Based on the principle of the reduction of…
It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck…
We study a general convergence theory for the numerical solutions of compressible viscous and electrically conducting fluids with a focus on numerical schemes that preserve the divergence free property of magnetic field exactly. Our…
Cosmology's standard model posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the…
The hoop conjecture, introduced by Thorne almost five decades ago, asserts that black holes are characterized by the mass-to-circumference relation $4\pi {\cal M}/{\cal C}\geq1$, whereas horizonless compact objects are characterized by the…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
During the last stage of collapse of a compact object into the horizon of events, the potential energy of its surface layer decreases to a negative value below all limits. The energy-conservation law requires an appearance of a…
We consider the hypothesis of a limiting minimal curvature in gravity as a way to construct a class of theories exhibiting late-time cosmic acceleration. Guided by the minimal curvature conjecture (MCC) we are naturally lead to a set of…
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly…
We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the…
Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutions using a combination of a priori estimates for the…
In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…
The concept of convex compactness, weaker than the classical notion of compactness, is introduced and discussed. It is shown that a large class of convex subsets of topological vector spaces shares this property and that is can be used in…
We explore the well know mass deficit/surplus phenomenon in General Relativity to suggest that it could play a part in the dark matter conundrum. Specifically in collapses and condensations of matter associated with negative intrinsic…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
We interpret all Maurer-Cartan elements in the formal Hochschild complex of a small dg category which is cohomologically bounded above in terms of torsion Morita deformations. This solves the "curvature problem", i.e. the phenomenon that…
As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is…