In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by one-dimensional diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data....

We study a process of anomalous diffusion, based on intermittent velocity fluctuations , and we show that its scaling depends on whether we observe the motion of many independent trajectories or that of a Liouville-like equation driven density. The reason for this discrepancy seems to be that the Liouville-like equation is unable to reproduce the multi-scaling properties emerging from trajector...

We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuousstate branching theory. In particular, this equation governs the evolution of the Lévy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) alm...

We determine the stationary two-point correlation function of the onedimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann-Hilbert problem related to the Painlevé...

A stochastic partial differential equation along the lines of the Kardar-Parisi-Zhang equation is introduced for the evolution of a growing interface in a radial geometry. Regular polygon solutions as well as radially symmetric solutions are identified in the de-terministic limit. The polygon solutions, of relevance to on-lattice Eden growth from a seed in the zero-noise limit, are unstable in ...

In this paper rst we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four signi cant conic problems in nite dimensional spaces, de ned as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let be a homogeneous function of degree p > 0, K a p...

In this paper first we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four significant conic problems in finite dimensional spaces, defined as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let φ be a homogeneous function of degree p > ...

In this paper first we prove four fundamental theorems of the alternative, called scaling dualities, characterizing exact and approximate solvability of four significant conic problems in finite dimensional spaces, defined as: homogeneous programming (HP), scaling problem (SP), homogeneous scaling problem (HSP), and algebraic scaling problem (ASP). Let φ be a homogeneous function of degree p > ...

We discuss a stochastic closure for the equation of motion satisfied by multiscale correlation functions in the framework of shell models of turbulence. We present a plausible closure scheme to calculate the anomalous scaling exponents of structure functions by using the exact constraints imposed by the equation of motion. We present an explicit calculation for fifth-order scaling exponent by v...

A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law of a Feller branching diffusion, which generalizes the work of Dawson and Li [3]. As an application of the stochastic equation, it is proved that the superpro...