Related papers: Time dependent singularities in incompressible pot…
The distribution of scattering delay times is analyzed for classical electrons which are transmitted through a finite waveguide. For non-zero magnetic field the distribution shows a regular pattern of maxima (logarithmic singularities).…
An analogue of the Oppenheimer-Synder collapsing model is treated analytically, where the matter source is a scalar field with an exponential potential. An exact solution is derived followed by matching to a suitable exterior geometry, and…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
Under mean curvature flow, a closed, embedded hypersurface $M(t)$ becomes singular in finite time. For certain classes of mean-convex mean curvature flows, we show the continuity of the first singular time $T$ and the limit set "$M(T)$",…
To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance…
The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it…
For ideal fluid flow with zero surface tension and gravity, it remains unknown whether local singularities on the free surface can develop in well-posed initial value problems with smooth initial data. This is so despite great advances over…
A theoretical technique which allows to include contributions from non-orthogonality of the electron states in the leads connected to a tunneling junction is derived. The theory is applied to a single barrier tunneling structure and a…
For the first time a statistical analysis of oil spill beaching is applied to the whole Mediterranean Sea. A series of probability maps of beaching in case of an oil spill incident are proposed as a complementary tool to vulnerability…
We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to…
Turbulence is one of the most frequently encountered non-equilibrium phenomena in nature yet characterising the transition that gives rise to it has remained an elusive task. Although in recent studies critical points marking the onset of…
The search of finite-time singularity solutions of Euler equations is considered for the case of an incompressible and inviscid fluid. Under the assumption that a finite-time blow-up solution may be spatially anisotropic as time goes by…
The Liouville theorem states that classical time evolution is an incompressible flow in phase space. We investigate two formulations of classical mechanics in which this property is manifested. First, the traditional Hamilton-Jacobi theory…
Failure times of a machinery cannot always be assumed independent and identically distributed, e.g. if after reparations the machinery is not restored to a same-as-new condition. Framed within the renewal processes approach, a…
Short term unpredictability is discovered numerically for high Reynolds number fluid flows under periodic boundary conditions. Furthermore, the abundance of the short term unpredictability is also discovered. These discoveries support our…
I survey some of the developments in the theory of Ricci flow and its applications from the past decade. I focus mainly on the understanding of Ricci flows that are permitted to have unbounded curvature in the sense that the curvature can…
We present a model appropriate to the initial motion (2-3 chords of travel) of a flat-plate airfoil accelerating in an inviscid fluid. The separated flow structures are represented as vortex sheets in the conventional manner and similarity…
This paper discusses the time-dependence of the threshold function in the perfect plasticity model. In physical terms, it is natural that the threshold function depends on some unknown variable. Therefore, it is meaningful to discuss the…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…