Related papers: Trapped surfaces in vacuum arising dynamically fro…
We study properties of stable, strictly stable and locally outermost marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes possessing certain symmetries such as isometries, homotheties and conformal Killings. We first…
In this paper, we examine the formation of small capillary waves (parasitic ripples) on the surface of steep steadily-travelling gravity waves. Previously, authors have developed ad-hoc analytical procedures for describing the formation of…
We prove that "first singularities" in the non-trapped region of the maximal development of spherically symmetric asymptotically flat data for the Einstein-Vlasov system must necessarily emanate from the center. The notion of "first"…
We consider a pair of three - level atoms interacting with a common vacuum and analyze the process of entanglement production due to spontaneous emission. We show that in the case of closely separated atoms, collective damping can generate…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which…
Mesoscopic theory for self-assembling systems near a planar confining surface is developed. Euler- Lagrange (EL) equations and the boundary conditions (BC) for the local volume fraction and the correlation function are derived from the DFT…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable…
Photophoretic forces, several orders of magnitude stronger than radiation pressure, enable particle trapping at remarkably low optical intensities and have opened pathways to applications in aerosol science, free-space 3D volumetric…
We investigate the critical threshold phenomena in a large class of one dimensional pressureless Euler--Poisson (EP) equations, with non-vanishing background states. First, we establish local-in-time well-posedness in proper regularity…
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy $W=\int H^2$ under compactly supported infinitesimal conformal variations. Examples include all constant mean…
We study hypersurfaces with prescribed null expansion in an initial data set. We propose a notion of stability and prove a topology theorem. Eichmair's Perron approach toward the existence of marginally outer trapped surface adapts to the…
A scenario for gravitational particle creation in a stiff matter dominated flat Friedmann-Robertson-Walker universe is presented. The primary creation of scalar particles is calculated using quantum field theory in curved spacetime and it…
A method for creating metasurfaces using a standing wave, formed in a dielectric, is proposed. Such metasurfaces are formed from metal suspensions, deposited on a dielectric plate, placed in a metal frame-screen. A series of parameters for…
We study ion condensation onto a patterned surface of alternating charges. The competition between self-energy and ion-surface interactions leads to the formation of ionic crystalline structures at low temperatures. We consider different…
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence,…
The creation of a quantum Universe is described by a {\em density matrix} which yields an ensemble of universes with the cosmological constant limited to a bounded range $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain…
We introduce on any smooth oriented minimal surface in Euclidean $3$-space a meromorphic quadratic differential, $P$, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of…
This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4\pi must be smoothly embedded. Related results are proved for varifolds and for soap film surfaces.