Towards deterministic equations for Levy walks: the fractional material derivative

Levy walks are random processes with an underlying spatiotemporal coupling. This coupling penalizes long jumps, and therefore Levy walks give a proper stochastic description for a particle's motion with broad jump length distribution. We derive a generalized dynamical formulation for Levy walks in which the fractional equivalent of the material derivative occurs. Our approach will be useful for the dynamical formulation of Levy walks in an external force field or in phase space for which the description in terms of the continuous time random walk or its corresponding generalized master equation are less well suited

Black-body furnace Patent

Development of black-body source calibration furnac

Antipollution system to remove nitrogen dioxide gas

Gas phase reaction system using anhydrous ammonia removes nitrogen dioxide. System consists of ammonia injection and mixing section, reaction section /reactor/, and scrubber section. All sections are contained in system ducting

Jamming transitions and avalanches in the game of Dots-and-Boxes

We study the game of Dots-and-Boxes from a statistical point of view. The early game can be treated as a case of Random Sequential Adsorption, with a jamming transition that marks the beginning of the end-game. We derive set of differential equations to make predictions about the state of the lattice at the transition, and thus about the distribution of avalanches in the end-game.Comment: 7 pages, 8 figures, revtex

A hot gas generator for large scale supersonic combustor testing

Exhaust gas of hydrazine-nitrogen tetroxide rocket for simulating combustor inlet requirements of scramjet engine

Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion

Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is $\langle x^2(t)\rangle\simeq\mathscr{K}(t)t$ with $\mathscr{K}(t)\simeq t^{\alpha-1}$ for $0<\alpha<2$. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.Comment: 7 pages, 5 figure

High-response on-line gas analysis system for hydrogen-reaction combustion products

The results of testing an on-line quadrupole gas analyzer system are reported. Gas samples were drawn from the exhaust of a hydrogen-oxygen-nitrogen rocket which simulated the flow composition and dynamics at the combustor exit of a supersonic combustion ramjet engine. System response time of less than 50 milliseconds was demonstrated, with analytical accuracy estimated to be + or - 5 percent. For more complex chemical systems with interfering atom patterns, analysis would be more difficult. A cooled-gas pyrometer probe was evaluated as a total temperature indicator and as the primary mass flow measuring element for the total sample flow rate

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density $\sigma_c$-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of $\sigma_c$ for the concave interfaces versus the Debye screening length $1/\kappa$ and the extent of confinement $a$ for these three interfaces for small $\kappa a$ values. For large $\kappa a$ the critical adsorption condition approaches the planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness $a$ is of the order of $1/\kappa$. We also rationalize how $\sigma_c(\kappa)$ gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length onto critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities.Comment: 12 pages, 10 figures, RevTe

An Empirical Analysis of the Canadian Term Structure of Zero-Coupon Interest Rates

Zero-coupon interest rates are the fundamental building block of fixed-income mathematics, and as such have an extensive number of applications in both finance and economics. The risk-free government zero-coupon term structure is, however, not directly observable and needs to be generated from the prices of marketable, coupon-bearing bonds. The authors introduce the first public-domain database of constant-maturity zero-coupon yield curves for the Government of Canada bond market. They first outline the mechanics of the curve-fitting algorithm that underlie the model, and then perform some preliminary statistical analysis on the resulting yield curves. The full sample period extends from January 1986 to May 2003; it is broken down into two subsamples, reflecting the structural and macroeconomic changes that impacted the Canadian fixed-income markets over that time. The authors examine the evolution of a number of key interest rates and yield-curve measures over the period, perform a principal-components analysis of the common factors that have influenced yield changes over time, and compare holding-period returns over the sample for assets of various maturities.Financial markets; Interest rates; Econometric and statistical methods

Critical adsorption of polyelectrolytes onto charged Janus nanospheres

Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations and the binding energy distributions close to the adsorption-desorption transition for Janus nanoparticles to those for simple spherical particles. Finally, we discuss experimentally relevant physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.Comment: 13 pages, 11 figures, RevTeX