Related papers: Singularity theory and heat equation
Quantum gravity computations suggest the existence of an ultraviolet and an infrared fixed point where quantum scale invariance emerges as an exact symmetry. We discuss a particular variable gravity model for the crossover between these…
In this work we analyze the viability of use a particular models of scalar fields in the context of the galactic dark matter problem. These models are based on a single scalar field, minimally coupled to the gravity in a asymptotically flat…
New mathematical and numerical results are given for the coupling of the temperature equation of a fluid with Radiative Transfer: existence and uniqueness and a convergent monotone numerical scheme. The technique is shown to be feasible for…
In this paper, we revisit the proof of the existence of a solution to the semilinear heat equation in one space dimension with a at blowup profile, already proved by Bricmont and Kupainen together with Herrero and Vel\'{a}zquez. Though our…
In previous publications, we have started investigating some possible applications to the retraction theory in gravitational physics and showed that it can be very useful in providing proofs and explaining the topological bases. In the…
The Unified Transform provides a novel method for analyzing boundary value problems for linear and for integrable nonlinear PDEs. The numerical implementation of this method to linear elliptic PDEs formulated in the {\it interior} of a…
Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M=M_0 x M_1 x ... M_n are investigated under dimensional reduction to tensor-multi-scalar theories. In the Einstein conformal frame, these…
Reducing a 3-dimensional Chern-Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an…
The trace of the heat kernel in a (D+1)-dimensional Euclidean spacetime (integer D > 1) is used to derive the free energy in finite temperature field theory. The spacetime presents a D-dimensional compact space (domain) with a…
In diffraction catastrophes such as the rainbow the wave nature of light resolves ray singularities and draws delicate interference patterns. In quantum catastrophes such as the black hole the quantum nature of light resolves wave…
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular…
The long-time solutions of the Galerkin-truncated three-dimensional, incompressible Euler equation relax to an absolute equilibrium as a consequence of phase space and kinetic energy conservation in such a finite-dimensional system. These…
In this paper, for compressible Euler equations in multiple space dimensions, we prove the break-down of classical solutions with a large class of initial data by tracking the propagation of radially symmetric expanding wave including…
We utilize the deformation theory of algebraic singularities to study charged matter in compactifications of M-theory, F-theory, and type IIa string theory on elliptically fibered Calabi-Yau manifolds. In F-theory, this description is more…
We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean free path is of order of the system size. Within the accuracy of the single-scattering approximation to the radiative transport equation,…
The goal of this numerical study is to get insight into singular solutions of the two-dimensional (2D) Euler equations for non-smooth initial data, in particular for vortex sheets. To this end high resolution computations of vortex layers…
According to de Broglie, temperature plays a basic role in quantum Hamilton-Jacobi theory. Here we show that a possible dependence on the temperature of the integration constants of the relativistic quantum Hamilton-Jacobi may lead to…
We show that matrix models in Chern-Simons theory admit an interpretation as 1D exactly solvable models, paralleling the relationship between the Gaussian matrix model and the Calogero model. We compute the corresponding Hamiltonians,…
Pseudospherical surfaces determined by Cauchy problems involving the Camassa-Holm equation are considered herein. We study how global solutions influence the corresponding surface, as well as we investigate two sorts of singularities of the…
BRAHMS has the ability to study relativistic heavy ion collisions over a wide range of pT and rapidity. This allows us to test whether thermal models can be generalized to describe the rapidity dependence of particle ratios. This appears to…