相关论文: Average exit times in volume preserving maps
In this short paper, an older Efron's result is extended to obtain a cutting plane integral formula for the mean volume of a random simplex in any d dimensions.
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
Given a volume preserving dynamical system with non-compact phase space, one is sometimes interested in special subsets of its wandering set. One example from celestial mechanics is the set of initial values leading to collision. Another…
We derive bounds on the volume of an inclusion in a body in two or three dimensions when the conductivities of the inclusion and the surrounding body are complex and assumed to be known. The bounds are derived in terms of average values of…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
Many real phenomena may be modelled as locally finite unions of $d$-dimensional time dependent random closed sets in $\mathbb{R}^d$, described by birth-and-growth stochastic processes, so that their mean volume and surface densities, as…
In this work we make use of generalized inverses associated with quantum channels acting on finite-dimensional Hilbert spaces, so that one may calculate the mean hitting time for a particle to reach a chosen goal subspace. The questions…
Stochastic dynamical systems arise as models for fluid particle motion in geophysical flows with random velocity fields. Escape probability (from a fluid domain) and mean residence time (in a fluid domain) quantify fluid transport between…
Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…
The phase space of a typical Hamiltonian system contains both chaotic and regular orbits, mixed in a complex, fractal pattern. One oft-studied phenomenon is the algebraic decay of correlations and recurrence time distributions. For…
We study the properties of the dissipative accretion flow around rotating black holes in presence of mass loss. We obtain the complete set of global inflow-outflow solutions in the steady state by solving the underlying conservation…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
A quantitative Brenier decomposition shows that the deviation of a map from volume preserving is bounded by the deviation of the derivative from volume preserving. A study of the matrix nearness problem for $SL(n)$ and $Sp(2n)$ relates the…
Piecewise smooth maps are known to exhibit a wide range of dynamical features including numerous types of periodic orbits. Predicting regions in parameter space where such periodic orbits might occur and determining their stability is…
The survival probability measures the probability that a system taken out of equilibrium has not yet moved out from its initial state. Inspired by the generalized entropies used to analyze nonergodic states, we introduce a generalized…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
An average pedestrian flow through an exit is one of the most important index in evaluating pedestrian dynamics. In order to study the flow in detail, the floor field model, which is a crowd model by using cellular automaton, is extended by…
Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…