Related papers: Time dependent singularities in incompressible pot…
We show the existence of superprocesses in a random medium with location dependent branching. Technically, we make use of a duality relation to establish the uniqueness of the martingale problem and to obtain the moment formulas.
For the water waves equations, the existence of splat singularities has been shown in [3], i.e., the interface self-intersects along an arc in finite time. The aim of this paper is to show the absence of splat singularities for the…
We study the problem of determining uniquely a time-dependent singular potential $q$, appearing in the wave equation $\partial_t^2u-\Delta_x u+q(t,x)u=0$ in $Q=(0,T)\times\Omega$ with $T>0$ and $\Omega$ a $ \mathcal C^2$ bounded domain of…
Concept drift, i.e., the change of the data generating distribution, can render machine learning models inaccurate. Several works address the phenomenon of concept drift in the streaming context usually assuming that consecutive data points…
We consider the Sommerfeld problem of diffraction by an opaque half-plane with a real wavenumber interpreting it as the limiting case, as time tends to infinity, of the corresponding time-dependent diffraction problem. We prove that the…
We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist…
Sufficient conditions for the well-posedness of the initial value problem for the scalar wave equation are obtained in space-times with hypersurface singularities
We introduce a general framework for defining context-dependent time distributions in quantum systems using projective measurements. The time-of-flow (TF) distribution, derived from population transfer rates into a measurement subspace,…
We introduce a classical field theory based on a concept of extended causality that mimics the causality of a point-particle Classical Mechanics by imposing constraints that are equivalent to a particle initial position and velocity. It…
The key element in time-dependent density functional theory is the one-to-one correspondence between the one-particle density and the external potential. In most approaches this mapping is transformed into a certain type of Sturm-Liouville…
We describe how a convectively unstable active field in an open flow configuration becomes absolutely unstable due to local mixing. A representation of the mixing region as those with locally enhanced effective diffusion allows us to find…
The spread of the time arrows from the environment to an observed subsystem is followed within a harmonic model. A similarity is pointed out between irreversibility and a phase with spontaneously broken symmetry. The causal structure of…
A quantum spin system is discussed, where a heat flow between infinite reservoirs takes place in a finite region. A time dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time…
The singularities of the electromagnetic field are derived to include all the point-like multipoles representing an electric charge and current distribution. Firstly derived in the static case, the result is generalized to the dynamic one.…
The Schr\"{o}dinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. This blowup is generally ascribed to the intrinsic dispersive character of the associated time…
Considering the evolution of a perfect fluid with self-similarity of the second kind, we have found that an initial naked singularity can be trapped by an event horizon due to collapsing matter. The fluid moves along time-like geodesics…
We develop a theory describing how a convectively unstable active field in an open flow is transformed into absolutely unstable by local mixing. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to…
In this paper we consider the Cauchy problem for the 3D Navier-Stokes equations for incompressible flows. The initial data are assumed to be smooth and rapidly decaying at infinity. A famous open problem is whether classical solutions can…
Differential transfer relations of flux density, general physics quantities' and its corresponding energy's, between time domains of source and observer are derived from conservative rule of various physical quantities and time function…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…