Killed Random Processes and Heat Kernels [Erratum]

In J. Villarroel “Killed random processes and heat kernels” (Vol. 144, No. 2, August, 2005) on page 1238, the sentence before (2) should be: “We suppose that given that ( took a value x and hence has not yet been killed), the probability of being killed at any time t + h > t is O(h) ....” On page 1239, the expression for ζ(t; p|x′) after Eq. (6) should be:

Deactivation of a fixed bed Cr2O3/Al2O3 catalyst during butene-1 dehydrogenation, I. Simulated and experimental results

A model has been tested to predict the carbon concentration profiles in a fixed bed reactor during butene-1-dehydrogenation on a Cr₂O₃/Al₂O₃ catalyst. Simulated and experimental results show an important influence of the temperature on the profiles obtained. The model predicts well the average carbon level in the catalytic bed and gives a slightly higher maximum carbon concentration.     

Photorefractive response and optical damage of LiNbO<Subscript>3</Subscript> optical waveguides produced by swift heavy ion irradiation

The photorefractive behaviour of a novel type of optical waveguides fabricated in LiNbO₃ by swift heavy ion irradiation is investigated. First, the electro-optic coefficient r ₃₃ of these guides that is crucial in the photorefractive effect is measured. Second, two complementary aspects of the photorefractive response are studied: (i) recording and light-induced and dark erasure of holographic gratings; (ii) optical beam degradation in single-beam configuration. The main photorefractive parameters, recording and erasing time constants, maximum refractive-index change and optical damage thresholds are determined.     

Anthocyanins from Aristotelia chilensis Prevent Olanzapine-Induced Hepatic-Lipid Accumulation but Not Insulin Resistance in Skeletal Muscle Cells

Type 2 diabetes and obesity are major problems worldwide and dietary polyphenols have shown efficacy to ameliorate signs of these diseases. Anthocyanins from berries display potent antioxidants and protect against weight gain and insulin resistance in different models of diet-induced metabolic syndrome. Olanzapine is known to induce an accelerated form of metabolic syndrome. Due to the aforementioned, we evaluated whether delphinidin-3,5-O-diglucoside (DG) and delphinidin-3-O-sambubioside-5-O-glucoside (DS), two potent antidiabetic anthocyanins isolated from Aristotelia chilensis fruit, could prevent olanzapine-induced steatosis and insulin resistance in liver and skeletal muscle cells, respectively. HepG2 liver cells and L6 skeletal muscle cells were co-incubated with DG 50 μg/mL or DS 50 μg/mL plus olanzapine 50 μg/mL. Lipid accumulation was determined in HepG2 cells while the expression of p-Akt as a key regulator of the insulin-activated signaling pathways, mitochondrial function, and glucose uptake was assessed in L6 cells. DS and DG prevented olanzapine-induced lipid accumulation in liver cells. However, insulin signaling impairment induced by olanzapine in L6 cells was not rescued by DS and DG. Thus, anthocyanins modulate lipid metabolism, which is a relevant factor in hepatic tissue, but do not significantly influence skeletal muscle, where a potent antioxidant effect of olanzapine was found.     

On the Integrability of the Poisson Driven Stochastic Nonlinear Schrödinger Equations

We consider the Cauchy problem for the dissipative nonlinear Schrödinger equations driven by a Poisson noise, namely (1) where γ_n > 0 and 0 < t₁ < ? < t_n < ? are certain sequences of random numbers and is the deterministic loss coefficient. This perturbation incorporates the possibility of sudden changes in the field that occur randomly. If Γ= 0, we prove that the resulting equation can be piece‐wise related to the unperturbed NLS equation and show how to solve the initial value problem. We also determine a complete set of conserved quantities. When Γ≠ 0 the equation is nonintegrable. Nevertheless, we determine the random evolution of physically relevant quantities like the field’s Energy E(t) ≡∫dx|u|²(t, x) and momentum. By considering a joint z‐Laplace transform we obtain the mean Energy decay. A naturally related quantity is the “half‐life”, or the time before the Energy degrades below a given value E₁. We show that the mean of this random quantity satisfies an integral equation and solve it by Laplace transformation. In particular cases we also determine the complete probability distribution of Energy and half life.     

The Stochastic Burger's Equation in Ito's Sense

We consider the solution to Burger's equation coupled to a stochastic noise in Ito's sense. The main random properties of the wave are determined. The solution is related to a deterministic problem with a rescaled diffusion coefficient. Depending on the value of a parameter, the initial value problem may be ill posed, well posed up to an explosion time, or well posed for all time. Traveling waves are destroyed asymptotically by white noise. However, the only effect of colored noise is to render the wave position random.     

Stochastic Perturbations of Line Solitons of KP

We consider the properties of localized solutions of the KP equation coupled to a stochastic noise. Corresponding to white noise, we find that the traveling waves are destroyed asymptotically, and we determine the distribution of the wave position and the arrival time. For generalized Ornstein–Uhlenbeck processes, we show that the only effect of noise is to render the asymptotic position random; in particular, when the noise has a sufficiently strong attenuation mechanism, the random wave coincides asymptotically with the unperturbed one. We also consider linearization of the corresponding Cauchy problem in the plane corresponding to this kind of initial data.     

The Inverse Problem for Ward's System

We study the direct and inverse problems for a 2 + 1-dimensional model recently formulated by Richard Ward. We recover the instanton solutions, and we also obtain new ones.     

Continuous-time random walks with reset events

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant drift: the process moves in a fixed direction between the reset events, either by the effect of the random jumps, or by the action of a deterministic bias. However, the orientation of its motion is randomly determined after each restart. As a result of these alternating dynamics, interesting properties do emerge. General formulas for the propagator as well as for two extreme statistics, the survival probability and the mean first-passage time, are also derived. The rigor of these analytical results is verified by numerical estimations, for particular but illuminating examples.