Relativistic theory for localized electrostatic excitations in degenerate electron-ion plasmas

A self-consistent relativistic two-fluid model is proposed for electron-ion plasma dynamics. A one-dimensional geometry is adopted. Electrons are treated as a relativistically degenerate fluid, governed by an appropriate equation of state. The ion fluid is also allowed to be relativistic, but is cold, nondegenerate, and subject only to an electrostatic potential. Exact stationary-profile solutions are sought, at the ionic scale, via the Sagdeev pseudopotential method. The analysis provides the pulse existence region, in terms of characteristic relativistic parameters, associated with the (ultrahigh) particle density.

Metal speciation dynamics in colloidal ligand dispersions. Part 2: electrochemical lability

We investigate the dynamic nature of metal speciation in colloidal dispersions using a recently proposed theory [J.P. Pinheiro, M. Minor, H.P. Van Leeuwen, Langmuir, 21 (2005) 8635] for complexing ligands that are situated on the surface of the particles. The new approach effectively modifies the finite rates of association/dissociation of the colloidal metal complexes, thus invoking consideration of the two basic dynamic criteria: the association/dissociation kinetics of the volume complexation reaction (the ‘‘dynamic’’ criterion), and the interfacial flux of free metal to a macroscopic surface due to dissociation of complex species (the ‘‘lability’’ criterion). We demonstrate that the conventional approach for homogeneous systems that assume a smeared-out ligand distribution, overestimates both the dynamics and the lability of metal complexes when applied to colloidal ligands. It is also shown that the increase of lability with increasing particle radius, as expected for a homogeneous solution, is moderated for spherical microelectrodes and practically eliminated for planar electrodes.

Ruin problems under IBNR Dynamics

In this paper, we consider a discrete-time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg-type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non-delayed risk model, and numerical simulations are carried out with Belgian market data.

Latent Variable Models for Stochastic Discount Factors.

Latent variable models in finance originate both from asset pricing theory and time series analysis. These two strands of literature appeal to two different concepts of latent structures, which are both useful to reduce the dimension of a statistical model specified for a multivariate time series of asset prices. In the CAPM or APT beta pricing models, the dimension reduction is cross-sectional in nature, while in time-series state-space models, dimension is reduced longitudinally by assuming conditional independence between consecutive returns, given a small number of state variables. In this paper, we use the concept of Stochastic Discount Factor (SDF) or pricing kernel as a unifying principle to integrate these two concepts of latent variables. Beta pricing relations amount to characterize the factors as a basis of a vectorial space for the SDF. The coefficients of the SDF with respect to the factors are specified as deterministic functions of some state variables which summarize their dynamics. In beta pricing models, it is often said that only the factorial risk is compensated since the remaining idiosyncratic risk is diversifiable. Implicitly, this argument can be interpreted as a conditional cross-sectional factor structure, that is, a conditional independence between contemporaneous returns of a large number of assets, given a small number of factors, like in standard Factor Analysis. We provide this unifying analysis in the context of conditional equilibrium beta pricing as well as asset pricing with stochastic volatility, stochastic interest rates and other state variables. We address the general issue of econometric specifications of dynamic asset pricing models, which cover the modern literature on conditionally heteroskedastic factor models as well as equilibrium-based asset pricing models with an intertemporal specification of preferences and market fundamentals. We interpret various instantaneous causality relationships between state variables and market fundamentals as leverage effects and discuss their central role relative to the validity of standard CAPM-like stock pricing and preference-free option pricing.

Stochastic processes and their applications semi-markov analysis of some inventory and queuing problems

This thesis analyses certain problems in Inventories and Queues. There are many situations in real-life where we encounter models as described in this thesis. It analyses in depth various models which can be applied to production, storag¢, telephone traffic, road traffic, economics, business administration, serving of customers, operations of particle counters and others. Certain models described here is not a complete representation of the true situation in all its complexity, but a simplified version amenable to analysis. While discussing the models, we show how a dependence structure can be suitably introduced in some problems of Inventories and Queues. Continuous review, single commodity inventory systems with Markov dependence structure introduced in the demand quantities, replenishment quantities and reordering levels are considered separately. Lead time is assumed to be zero in these models. An inventory model involving random lead time is also considered (Chapter-4). Further finite capacity single server queueing systems with single/bulk arrival, single/bulk services are also discussed. In some models the server is assumed to go on vacation (Chapters 7 and 8). In chapters 5 and 6 a sort of dependence is introduced in the service pattern in some queuing models.

Queueing Theory And Other Applications Of Stochastic Processes Queueing And Inventory Models With Rest Periods

In this thesis we study the effect of rest periods in queueing systems without exhaustive service and inventory systems with rest to the server. Most of the works in the vacation models deal with exhaustive service. Recently some results have appeared for the systems without exhaustive service.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

Dynamics of convectively driven banded jets in the laboratory

The banded organization of clouds and zonal winds in the atmospheres of the outer planets has long fascinated observers. Several recent studies in the theory and idealized modeling of geostrophic turbulence have suggested possible explanations for the emergence of such organized patterns, typically involving highly anisotropic exchanges of kinetic energy and vorticity within the dissipationless inertial ranges of turbulent flows dominated (at least at large scales) by ensembles of propagating Rossby waves. The results from an attempt to reproduce such conditions in the laboratory are presented here. Achievement of a distinct inertial range turns out to require an experiment on the largest feasible scale. Deep, rotating convection on small horizontal scales was induced by gently and continuously spraying dense, salty water onto the free surface of the 13-m-diameter cylindrical tank on the Coriolis platform in Grenoble, France. A “planetary vorticity gradient” or “β effect” was obtained by use of a conically sloping bottom and the whole tank rotated at angular speeds up to 0.15 rad s−1. Over a period of several hours, a highly barotropic, zonally banded large-scale flow pattern was seen to emerge with up to 5–6 narrow, alternating, zonally aligned jets across the tank, indicating the development of an anisotropic field of geostrophic turbulence. Using particle image velocimetry (PIV) techniques, zonal jets are shown to have arisen from nonlinear interactions between barotropic eddies on a scale comparable to either a Rhines or “frictional” wavelength, which scales roughly as (β/Urms)−1/2. This resulted in an anisotropic kinetic energy spectrum with a significantly steeper slope with wavenumber k for the zonal flow than for the nonzonal eddies, which largely follows the classical Kolmogorov k−5/3 inertial range. Potential vorticity fields show evidence of Rossby wave breaking and the presence of a “hyperstaircase” with radius, indicating instantaneous flows that are supercritical with respect to the Rayleigh–Kuo instability criterion and in a state of “barotropic adjustment.” The implications of these results are discussed in light of zonal jets observed in planetary atmospheres and, most recently, in the terrestrial oceans.

Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

Stochastic volatility jump-diffusions for European equity index dynamics

Major research on equity index dynamics has investigated only US indices (usually the S&P 500) and has provided contradictory results. In this paper a clarification and extension of that previous research is given. We find that European equity indices have quite different dynamics from the S&P 500. Each of the European indices considered may be satisfactorily modelled using either an affine model with price and volatility jumps or a GARCH volatility process without jumps. The S&P 500 dynamics are much more difficult to capture in a jump-diffusion framework.