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In this paper, we establish the existence of transition density for geometric $\alpha$-stable processes by using the property of self-decomposability--a fundamental concept in the theory of L\'evy processes. In contrast to traditional and…

We show that the vibrational response of a glassy liquid at finite frequencies can be described by continuum mechanics despite the vast degeneracy of the vibrational ground state; standard continuum elasticity assumes a unique ground state.…

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…

The notions of noise sensitivity and stability were recently extended for the voter model. In this model, the vertices of a graph have opinions that are updated by uniformly selecting edges. We further extend stability results to different…

We show that the classical stochastic motion of an open bosonic string leads to the same results as the standard first quantization of this system. For this, the diffusion constant governing the process has to be proportional to \alpha ',…

We continue our investigation of finite deformation linear viscoelastodynamics by focusing on constructing accurate and reliable numerical schemes. The concrete thermomechanical foundation developed in the previous study paves the way for…

I provide a proof of the existence of absolutely continuous invariant measures (and study their statistical properties) for multidimensional piecewise expanding systems with not necessarily bounded derivative or distortion. The proof uses…

We define a class of flows with exponential kinematics termed Periodic Exponential Shear (PES) flow which involve periodic exponential stretching of fluid elements along with their rotation. We exhibit analytical and numerical results for…

A function f is continuous iff the PRE-image f^{-1}[V] of any open set V is open again. Dual to this topological property, f is called OPEN iff the IMAGE f[U] of any open set U is open again. Several classical Open Mapping Theorems in…

We establish an exponential stabilization result for linear port-Hamiltonian systems of first order with quite general, not necessarily continuous, energy densities. In fact, we have only to require the energy density of the system to be of…

Control problems not admitting the dynamic programming principle are known as time-inconsistent. The game-theoretic approach is to interpret such problems as intrapersonal dynamic games and look for subgame perfect Nash equilibria. A…

We investigate the long time behavior of a system of viscoelastic particles modeled with the homogeneous Boltzmann equation. We prove the existence of a universal Maxwellian intermediate asymptotic state and explicit the rate of convergence…

We consider smooth random dynamical systems defined by a distribution with a finite moment of the norm of the differential, and prove that under suitable non-degeneracy conditions any stationary measure must be H\"older continuous. The…

The SBV regularity of weak entropy solutions to the Burgers-Poisson equation is considered. We show that the derivative of a solution consists of only the absolutely continuous part and the jump part.

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

We introduce and study the mechanical system which describes the dynamics and statics of rigid bodies of constant density floating in a calm incompressible fluid. Since much of the standard equilibrium theory, starting with Archimedes,…

A convex surface contracting by a strictly monotone, homogeneous degree one function of curvature remains smooth until it contracts to a point in finite time, and is asymptotically spherical in shape. No assumptions are made on the…

We deal with finite dimensional linear and nonlinear control systems. If the system is linear and autonomous and satisfies the classical normality assumption, we improve the well known result on the strict convexity of the reachable set…

It is well known that for a standard Brownian motion (BM) $ \{B(t), \;t \geq 0\}$ with values in $\mathbb{R}^d$, its convex hull $ V(t)=\conv \{\{\,B(s),\;s \leq t \}$ with probability $1$ for each $t > 0$ contains $0$ as an interior point…

This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by…