The exponential stability for stochastic delay partial differential equations

AbstractIn this paper we consider by the energy equality the exponential stability of energy solutions to a non-linear stochastic functional partial differential equation with finite delay r>0 in separable Hilbert spaces. Our method is very simple and is powerful for concrete stochastic delay partial differential equations

Stability theorems of stochastic difference equations

AbstractIn this paper we prove the general comparison theorem for the difference inequalities and several stochastic stability theorems of the nonlinear difference equations using this theorem.Our theorems generalize Ma and Caughey's theorems

Formation of intermediate-mass black holes in circumnuclear regions of galaxies

Recent high-resolution X-ray imaging studies have discovered possible candidates of intermediate-mass black holes with masses of M_\bullet \sim 10^{2-4} \MO in circumnuclear regions of many (disk) galaxies. It is known that a large number of massive stars are formed in a circumnuclear giant H {\sc ii} region. Therefore, we propose that continual merger of compact remnants left from these massive stars is responsible for the formation of such an intermediate-mass black hole within a timescale of $\sim 10^9$ years. A necessary condition is that several hundreds of massive stars are formed in a compact region with a radius of a few pc.Comment: 11 pages, PASJ in pres

Vertical Sounding by Central Induction Method

The apparent resistivity methods are widely used to determine the structure of horizontally stratified earth. But with these methods, some material difficulties are unavoided in cases where there are four or more layers. On the other hand, the central induction methods which have been studied by Koenigsberger, Nunier and Stefanescu seem to have a distinct advantage over the resistivity methods in resolving structures involving four or more layers. In this paper the authors discuss the theory of C. I. M. The numerical tables for interpreting the C. I. M. data are presented, and a new procedure in which the phase angle of the resultant magnetic field is measured is proposed

Pullback attractors for differential equations with multiple variable delays in Lipschitz nonlinearities

We establish the results on the existence of pullback attractors for nonautonomous functional differential equations with multiple delays appearing within nonlinear Lipschitz terms. The results are complementary to recently presented findings in [Caraballo & Kiss, 2013a, 2013b], and they extend the class of nonlinearities to which existence results can be established by improving on a condition presented in [Caraballo & Kiss, 2013b]

The Exponential Stability of Neutral Stochastic Delay Partial Differential Equations

In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of neutral stochastic semilinear partial delay differential equations. This kind of equations arises in problems related to coupled oscillators in a noisy environment, or in viscoeslastic materials under random or stochastic influences

On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier-Stokes equations

We prove existence and uniqueness of solutions for a stochastic version of the 3DLagrangian averaged Navier-Stokes (LANS-®) equation in a bounded domain. To this end, we previously prove some existence and uniqueness results for an abstract stochastic equation and justify that our model falls within this framework

Learning the constitutive relation of polymeric flows with memory

We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian Process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full Multi-Scale Simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other Soft Matter systems, which possess a similar hierarchy of length- and time-scales.Comment: 19 pages, 9 figure