Search results for "singular"
showing 10 items of 589 documents
Local behaviour of singular solutions for nonlinear elliptic equations in divergence form
2012
We consider the following class of nonlinear elliptic equations $$\begin{array}{ll}{-}{\rm div}(\mathcal{A}(|x|)\nabla u) +u^q=0\quad {\rm in}\; B_1(0)\setminus\{0\}, \end{array}$$ where q > 1 and $${\mathcal{A}}$$ is a positive C 1(0,1] function which is regularly varying at zero with index $${\vartheta}$$ in (2−N,2). We prove that all isolated singularities at zero for the positive solutions are removable if and only if $${\Phi\not\in L^q(B_1(0))}$$ , where $${\Phi}$$ denotes the fundamental solution of $${-{\rm div}(\mathcal{A}(|x|)\nabla u)=\delta_0}$$ in $${\mathcal D'(B_1(0))}$$ and δ0 is the Dirac mass at 0. Moreover, we give a complete classification of the behaviour near zero of al…
Evaporation of Near-Extremal Reissner-Nordström Black Holes
2000
The formation of near-extremal Reissner-Nordstrom black holes in the S-wave approximation can be described, near the event horizon, by an effective solvable model. The corresponding one-loop quantum theory remains solvable and allows to follow analytically the evaporation process which is shown to require an infinite amount of time.
Regularization of spherical and axisymmetric evolution codes in numerical relativity
2007
Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne…
A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary
2016
We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\varepsilon}$ obtained by making a small hole of size $\varepsilon_1 \varepsilon_2 $ in an open regular subset $\Omega$ of $\mathbb{R}^n$ at distance $\varepsilon_1$ from the boundary $\partial\Omega$. As $\varepsilon_1 \to 0$, the perforation shrinks to a point and, at the same time, approaches the boundary. When $\boldsymbol\varepsilon \to (0,0)$, the size of the hole shrinks at a faster rate than its approach to the boundary. We denote by $u_{\bolds…
Sea-surface temperature co-variability in the Southern Atlantic and Indian Oceans and its connections with the atmospheric circulation in the Souther…
2003
The relationship between sea-surface temperature (SST) inter-annual variability at the subtropical and midlatitudes of the southern Atlantic and Indian Oceans and its links with the atmospheric circulation in the Southern Hemisphere are investigated over the 1950–1999 period. Exploratory analysis using singular value decomposition and further investigations based on simple indices show that a large part of regional SST variability is common between the southwestern parts of both basins at subtropical and midlatitudes during the austral summer. Interestingly, these areas are also significantly associated with the far southwestern Pacific (Tasman Sea area). The patterns and time series of co-…
Beneficia imperiali e 'logica del sistema'. Spunti di metodo tra le righe di Alberto Burdese.
2016
The contribution deals with some hermeneutical positions of classical Jurists concerning the beneficia imperialia from the point of view of their deviating from the ‘ratio iuris’. The Author – by recalling the metodological warning of Alberto Burdese about paying vigilant and cautious attention for the textual data – examines some sources which regard the relationship between beneficia and regulae iuris and between beneficia, aequitas, utilitas and the attribution of the interpretation of beneficia directly to the Emperor.
MR3090050 Reviewed Belabbas, Mohamed Ali On global stability of planar formations. IEEE Trans. Automat. Control 58 (2013), no. 8, 2148–2153. (Reviewe…
2014
The focus of the paper is planar formation control, i.e. the design of control laws to stabilize agents at given distances from each other, under the constraint that the dynamics of each agent only depends on a subset of the other agents. The main contribution of the paper is the following: It is shown that a simple four-agent formation cannot be globally stabilized using twice differentiable control laws (this is not the case for three-agent formations), even up to sets of measure zero of initial conditions. This suggests that for four-agent formations one needs to look for control laws that are either not differentiable (or even not continuous) or of higher order in the dynamics. The appr…
Critical end point behaviour in a binary fluid mixture
1997
We consider the liquid-gas phase boundary in a binary fluid mixture near its critical end point. Using general scaling arguments we show that the diameter of the liquid-gas coexistence curve exhibits singular behaviour as the critical end point is approached. This prediction is tested by means of extensive Monte-Carlo simulations of a symmetrical Lennard-Jones binary mixture within the grand canonical ensemble. The simulation results show clear evidence for the proposed singularity, as well as confirming a previously predicted singularity in the coexistence chemical potential [Fisher and Upton, Phys. Rev. Lett. 65, 2402 (1990)]. The results suggest that the observed singularities, particula…
NONSINGULAR BLACK HOLES IN PALATINI EXTENSIONS OF GENERAL RELATIVITY
2015
An introduction to extended theories of gravity formulated in metric-affine (or Palatini) spaces is presented. Focusing on spherically symmetric configurations with electric fields, we will see that in these theories the central singularity present in General Relativity is generically replaced by a wormhole structure. The resulting space-time becomes geodesically complete and, therefore, can be regarded as non-singular. We illustrate these properties considering two different models, namely, a quadratic f(R) theory and a Born-Infeld like gravity theory.
Stress fields by the symmetric Galerkin boundary element method
2004
The paper examines the stress state of a body with the discretized boundary embedded in the infinite domain subjected to layered or double-layered actions, such as forces and displacement discontinuities on the boundary, and to internal actions, such as body forces and thermic variations, in the ambit of the symmetric Galerkin boundary element method (SGBEM). The stress distributions due to internal actions (body forces and thermic variations) were computed by transforming the volume integrals into boundary integrals. The aim of the paper is to show the tension state in Ω∞ as a response to all the actions acting in Ω when this analysis concerns the crossing of the discretized boundary, thu…