The fundamental problem on which Ilya Prigogine and the BrusselsAustin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an appa...

Kochukhov: The Doppler imaging problem is intrinsically ill-conditioned. It is not correct to characterize this problem by the number of unknowns. We are using regularization, and regularization effectively introduces a set of additional equations which smoothes the map in our case; in the case of the maximum entropy method, it selects an image with maximum entropy. So actually if I count equat...

The physical basis of the modern cosmological inflationary models with baryosynthesis and nonbaryonic dark matter and energy implies such predictions of particle theory, that, in turn, apply to cosmology for their test. It makes physics of early Universe ambiguous and particle model dependent. The study of modern cosmology is inevitably linked with the probe for the new physics, underlying it. ...

Abstract The occurrence of fingered preferential flow depends on both flow and porous media characteristics. The boundary condition of unsaturated infiltration has been investigated to assess whether it produces unstable wetting in homogeneous coarse sands. Laboratory tracer experiments were conducted in two coarse sand materials; for each sand material two initial conditions of air dry and fie...

We consider the dynamical properties of one kind of cyclically ordered orbits of the stadium billiard. We prove that the stadium billiard possesses infinitely many such orbits, that they are hyperbolic, and that their stable and unstable manifolds intersect transversely. Hence the stadium billiard contains a Smale horseshoe. We construct symbolic dynamics for these orbits and consider their sen...

Let X be a Banach space. Suppose that for all p ∈ (1,∞) a constant Cp,X depending only on X and p exists such that for any two Xvalued martingales f and g with tangent martingale difference sequences one has E‖f‖ ≤ Cp,XE‖g‖ p (∗). This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either f or g satisfy the so-ca...

The naming game has become an archetype for linguistic evolution and mathematical social behavioral analysis. In the model presented here, there are N individuals and K words. Our contribution is developing a robust method that handles the case when K=O(N). The initial condition plays a crucial role in the ordering of the system. We find that the system with high Shannon entropy has a higher co...

Kronecker product and tensor decompositions are used to construct approximations of severely ill-conditioned matrices that arise in three-dimensional image processing applications. Computa-tionally efficient methods to construct the approximations are developed by exploiting structure that is inherent in many image processing problems, such as those arising in microscopy and medical imaging. It...

Every solution of a linear elliptic equation on a bounded domain may be considered as an equilibrium of a free boundary problem. The free boundary problem consists of the corresponding parabolic equation on a variable unknown domain with free boundary conditions prescribing both Dirichlet and Neumann data. We establish a rigorous stability analysis of such equilibria, including the construction...

This paper contains rigorous results on nonequilibrium steady states for a class of particle systems coupled to unequal heat baths. These stochastic models are derived from the mechanical chains studied by Eckmann and Young by randomizing certain quantities while retaining other features of the model. Our results include the existence and uniqueness of nonequilibrium steady states, their relati...