Anomalous 1D fluctuations of a simple 2D random walk in a large deviation regime

The following question is the subject of our work: could a two-dimensional random path pushed by some constraints to an improbable "large deviation regime", possess extreme statistics with one-dimensional Kardar-Parisi-Zhang (KPZ) fluctuations? The answer is positive, though non-universal, since the fluctuations depend on the underlying geometry. We consider in details two examples of 2D systems for which imposed external constraints force the underlying stationary stochastic process to stay in an atypical regime with anomalous statistics. The first example deals with the fluctuations of a stretched 2D random walk above a semicircle or a triangle. In the second example we consider a 2D biased random walk along a channel with forbidden voids of circular and triangular shapes. In both cases we are interested in the dependence of a typical span \left \sim t^{\gamma} of the trajectory of $t$ steps above the top of the semicircle or the triangle. We show that $\gamma = \frac{1}{3}$, i.e. \left shares the KPZ statistics for the semicircle, while $\gamma=0$ for the triangle. We propose heuristic derivations of scaling exponents $\gamma$ for different geometries, justify them by explicit analytic computations and compare with numeric simulations. For practical purposes, our results demonstrate that the geometry of voids in a channel might have a crucial impact on the width of the boundary layer and, thus, on the heat transfer in the channel.Comment: 17 pages, 8 figures, some parts of the paper are rewritte

Dynamic Speckle Interferometry of Technical and Biological Objects

The theory of speckle dynamics in the image plane of a reflecting and thin transparent object is considered. It was assumed that the optical paths of the reflected and probing transparent object waves vary due to (1) translational motion, (2) oscillations with a period T, and (3) random relative displacements of pairs of scattering centers Δ u (reflecting object) and random changes in the refractive index Δ n (transparent object). The formulas relating the mean value, dispersion, and relaxation time of Δ u and Δ n values with the time-averaged radiation intensity at the observation point and the time autocorrelation function of this intensity are obtained. It is shown that at the averaging time multiple of T, the technique in real time allows to determine plastic deformations of the order of 10−3 on bases of the order of 10 microns, which is suitable for the control of elastic deformations on bases of the order of 100 microns. The possibilities of the method of averaged speckle images for the study of (1) features of the nucleation, start, and movement of the fatigue crack, and (2) the activity of living cells infected and not infected with the virus are demonstrated

Using FoxNet for TCP/IP networking in ML/OS

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1998.Includes bibliographical references (leaves 42-43).by Alexander Vladimirov.M.Eng

Duality principle for discrete linear inclusions

Two properties of finite sets {Aj} of n x n-matrices are introduced: P-stability and BV-stability. These properties can be interpreted as two kinds of robustness of orbits of the form xi+1 = Ajixi + ui with respect to disturbances {ui}. Duality between these properties is established, which proves that they are equivalent, respectively, to the right convergent product (RCP) property and the left convergent product (LCP) property of finite sets of matrices. The results can be applied, in particular, in the theory of polyhedral Skorokhod problems and sweeping processes with oblique reflection

Dynamics of an inhomogeneously broadened passively mode-locked laser

We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model

Lipschitz continuity of polyhedral Skorokhod maps

We show that a special stability condition of the associated system of oblique projections (the so-called ℓ-paracontractivity) guarantees that the corresponding polyhedral Skorokhod problem in a Hilbert space X is solvable in the space of absolutely continuous functions with values in X. If moreover the oblique projections are transversal, the solution exists and is unique for each continuous input and the Skorokhod map is Lipschitz continuous in both C([0,T]; X) and W1,1(0,T; X). An explicit upper bound for the Lipschitz constant is derived

Dynamics of an inhomogeneously broadened passively mode-locked laser

We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model