Independent Diffusion Processes Research Articles

On the expectations of the present values of the time of ruin perturbed by diffusion

In this paper, we consider the surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. A compound geometric distribution and the expectations of the present values of the time of ruin due to oscillation and a claim, respectively, are studied. Recursive formulas and explicit expressions for the moments of, and the asymptotic formulas and the Tijms-type approximations for, the compound geometric distribution and the expectations of the present values of the time of ruin are derived. In addition, explicit analytical solutions to the compound geometric distribution and to these expectations can be obtained if the claim size distribution is a combination of exponentials or a mixture of Erlangs. Finally, a lower bound and an upper bound on the compound geometric distribution are proposed, provided the associated claim size distribution is in some of the reliability-based classes.

Use of Nonlinear Frequency Response for Discriminating Adsorption Kinetics Mechanisms Resulting with Bimodal Characteristic Functions

One of the characteristic examples of the inability of the classical linear frequency response (FR) method to identify the correct kinetic mechanism is adsorption of some substances (p-xylene, 2-butane, propane or n-hexane) on silicalite-1. The linear FR resulted with bimodal FR characteristic functions, which fitted equally well to three different kinetic models: nonisothermal micropore diffusion, two independent isothermal diffusion processes, and an isothermal diffusion-rearrangement process. We show that the second order frequency response functions (FRFs), obtained from the nonlinear FR, can be used for discrimination among these three mechanisms. Starting from the nonlinear models, we derive the theoretical expressions for the first and second order FRFs corresponding to these three mechanisms and show that different shapes of the second order FRFs are obtained for each mechanism. This would enable identification of the real mechanism from nonlinear FR data.

Moisture diffusion and hygrothermal aging in bismaleimide matrix carbon fiber composites: part II—woven and hybrid composites

Moisture absorption and hygrothermal aging in a woven and woven/uni-weave composites are studied. Different from the neat resin and uni-weave composite, the short term diffusion in the woven composite is non-Fickian, in that the uptake initially increases rather rapidly but quickly slows down. A dual-diffusivity model that can successfully describe the observed weight gain curves has been developed. This model is composed of two independent diffusion processes with very different diffusivities. The fast process is associated with diffusion in cure-induced voids and cracks, while the slow process is the intrinsic diffusion in the matrix. Two different hybrids, namely, uni-weave/woven/uni-weave (U-W-U) and woven/uni-weave/woven (W-U-W), are also investigated. The short term absorption curves of the U-W-U and W-U-W composites can be described by Fickian diffusion and the dual-difftisivity model, respectively. The resemblance between the U-W-U and uni-weave composites, as well as that between the W-U-W and woven composites suggest that the diffusion properties of a composite are controlled by the outer plies. During prolonged moisture absorption, the swelling stresses eventually cause the formation of interfacial cracks in the composite.

A generalized defective renewal equation for the surplus process perturbed by diffusion

In this paper, we consider the surplus process of the classical continuous time risk model containing an independent diffusion (Wiener) process. We generalize the defective renewal equation for the expected discounted function of a penalty at the time of ruin in Garber and Landry [Insurance: Math. Econ. 22 (1998) 263]. Then an asymptotic formula for the expected discounted penalty function is proposed. In addition, the associated claim size distribution is studied, and reliability-based class implications for the distribution are given.

On the discounted distribution functions of the surplus process perturbed by diffusion

In this paper, we derive explicit expressions for the discounted joint and marginal distribution functions of the surplus immediately prior to the time of ruin and the deficit at the time of ruin, and for the discounted distribution function of the amount of the claim causing ruin, based on the surplus process of ruin theory with an independent diffusion process. Furthermore, we show that these distribution functions satisfy defective renewal equations.

Colour segmentation based on separate anisotropic diffusion of chromatic and achromatic channels

The paper presents a new technique for segmenting images only on the basis of colour information. It is shown how segmentation can benefit from splitting colour signals into chromatic and achromatic channels and separately smoothing them through anisotropic diffusion. Operatively, this is accomplished through two independent diffusion processes: one involves only the chromatic information, conveniently embedded in a complex function, while the other affects the lightness information. The results of the two diffusions are separately segmented by k-means clustering techniques and their combination yields the final image partition into homogeneous regions. Some experimental results are reported which verify the effectiveness of the proposed technique.

The Stationary Arrival Process of Independent Diffusers from a Continuum to an Absorbing Boundary Is Poissonian

We consider the arrival process of infinitely many identical independent diffusion processes from an infinite bath to an absorbing boundary. Previous results on this problem were confined to independent Brownian particles arriving at an absorbing sphere. The present paper extends these results to general diffusion processes, without any symmetries and without resorting to explicit expressions for solutions to the relevant equations. It is shown that for general absorbing boundaries and force fields, the steady stream of arrivals is Poissonian with rate equal to the total flux on the absorbing boundary, as calculated from the continuum theory of diffusion with transport. The considered arrival problem arises in the theory of Langevin simulations of ions in electrolytic solutions. In a Langevin simulation ions enter and exit the simulation region, and it is necessary to compute the probability laws for their entrance times into the simulation. While the simulated ions inside the small simulation region interact with each other and with the far field of the surrounding bath and the applied voltage, the physical chemistry continuum description of the surrounding bath implies independent diffusion in a mean field. Under these conditions the result of this paper applies to the stream of new ions that arrive from the continuum bath into the discrete simulation region. The recirculation problem, of ions that have already visited and exited the simulation region, as well as the integration of these results into a simulation of interacting ions will be studied in separate papers.

Many-body diffusion algorithm for interacting harmonic fermions

A new quantum Monte Carlo algorithm is presented to numerically implement the recently developed many-body diffusion approach for identical particles. For fermions, the procedure avoids the sign problem by defining a set of independent stochastic diffusion processes. Based on a symmetry analysis of both the free density matrix and the potential, the total random process is restricted to a well-defined state space with absorbing or reflecting boundary conditions. The absorption rate of the walkers at absorbing boundaries contributes substantially to the ground-state energy. The feasibility of the many-body diffusion algorithm is illustrated by its application to interacting harmonic fermions.

Atomic Scale Simulation of Point Defects Diffusion and Reactions Using Transputers

The diffusion and agglomeration of point defects under high energy electron irradiation have been examined by the means of parallel computing. The whole process is divided into independent diffusion processes running in parallel and communications between these processes to represent the reactions. We have calculated the concentration of point defects and extended defects and the size of the latter, and compared them to the results of the chemical reaction rate theory and to experimental data. Furthemore, we have shown that under high irradiation rates, small deviations due to the random nature of the process may, in some circumstances, lead to catastrophic situations as the result of enhancement of the reactions due to local interactions.

Adsorption and transport of n-hexane in silicalite-1 by the frequency response technique

L. Song and L. V. C. Rees, J. Chem. Soc., Faraday Trans., 1997, 93, 649 DOI: 10.1039/A606468J

Frequency response diffusion of propane in silicalite-1

The frequency response spectra of propane in silicalite-1 were measured at equilibrium pressures of 0.5–8.0 Torr and temperatures of 303–363 K and analysed by non-isothermal diffusion, two independent diffusion processes, and single-diffusion models. The first model is physically feasible for the explanation of the bimodal FR behaviour of this system, but the heat effect can be eliminated by reducing the coverage in the zeolite. Compared with propane, the bimodal form of the frequency response curves of p-xylene in silicalite-1 is attributed to two diffusion processes occurring separately in the sinusoidal and straight channels of the sorbent. The intracrystalline self-diffusion coefficient of propane in silicalite-1 determined in the present work is of the order of 10 −9 m 2 s −1 and decreases with increasing concentration of the adsorbate in the zeolite. This result is consistent with PFG NMR and previous FR studies.

Analysis of bimodal frequency-response behaviour of p-xylene diffusion in silicalite-1

The bimodal frequency-response spectra of p-xylene diffusion in silicalite-1 at 373 K have been analysed using the two independent diffusion processes, diffusion–rearrangement and non-isothermal diffusion models. The FR parameters and equilibrium constants derived from these three models have been compared. It was found that the two independent diffusion and diffusion–rearrangement models can well represent the experimental data and give similar equilibrium constants and diffusion time constants. It may be due to the similar principles used in these two models that the molecules in the straight channels are mobile, while those absorbed in the sinusoidal channels are ‘immobile’. On the other hand, the non-isothermal diffusion model gives a poor fit of the experimental data. The non-isothermality parameter γ obtained from data fitting is not consistent with the value calculated from the K constant obtained from the same fit. The frequency-response spectra obtained within the hysteresis loop region of the p-xylene isotherm at 348 K are also discussed.

Phase Diffusion and Quantum Noise in the Optical Parametric Oscillator: A Semiclassical Approach

Abstract We calculate by the semiclassical method the noise spectra of a non-degenerate optical parametric oscillator operating above threshold when taking into account two independent diffusion processes on the pump phase and on the signal-idler phase difference. We also show that the phase diffusion processes are important when calculating the quantum noise in an optical parametric oscillator for noise frequencies close to the beat frequency between the signal and idler modes.

On an Optimal Stopping Problem for Multi-Parameter Diffusion Processes

Abstract This paper deals with the case without terminal rewards in the optimal stopping problem for a d-parameter Markov process which is constructed by the product of mutually independent one-parameter diffusion processes. We call one-parameter diffusion processes reward processes. This paper shows the existence of an optimal tactic which is expressed as the dynamic allocation indices for reward processes. While this paper also shows that the optimal stopping point for the original problem is expressed as the smallest optimal stopping times of the one-parameter optimal stopping problems for reward processes. On the basis of this fact we give a necessary and sufficient condition concerning the finiteness of the smallest optimal stopping point to the original problem. By deriving that the optimal stopping region of the original problem is equal to the Cartesian product of the optimal stopping regions for reward processes, we reduce the Bellman’s equation, which is written as a free boundary problem, to a fixed boundary problem when a solution of the optimal stopping problem for each reward process is known.

On the reliability of stochastic systems: a comment

Basu and Ebrahimi (1983) describe a reliability model based on the first crossing time of two independent Wiener diffusion processes that represent strength and stress processes of a component. This comment gives an explicit form for their reliability function and discusses some practical aspects and extensions of their reliability model.

On the nearly nonstationary seasonal time series

AbstractA time series is said to be nearly nonstationary if some of its characteristic roots are close to the unit circle. For a seasonal time series, such a notion of near‐nonstationarity is studied in a double‐array setting. This approach not only furnishes a natural transition between stationarity and nonstationarity, but also unifies the corresponding asymptotic theories in a seasonal‐time‐series context. The general theory is expressed in terms of functionals of independent diffusion processes. The asymptotic results have applications to estimation and testing in a nearly nonstationary situation and serve as a useful alternative to the common practice of seasonal adjustment.

Diffusion of ion-implanted In and Tl in SiO2

The diffusion of In and Tl implanted into SiO2 has been investigated by means of Rutherford backscattering spectrometry. The diffusion of these elements is shown to be strongly dependent on their chemical state in SiO2. By combining these results with previous results for Ga, a general model has been formulated which describes the incorporation and diffusion of Group III elements in SiO2. The most important parameter of this model is the valence state of these elements in SiO2. In their trivalent state these elements are incorporated on Si sites of the SiO2 network, where they are virtually immobile. On the other hand, interstitial monovalent Group III ions are observed to show rapid diffusion. In addition to this, there is a second independent diffusion process, which is attributed to interstitial migration of InOH or TlOH molecules. After high-temperature annealing of SiO2 covered with Si3N4, the In and Tl diffusion profiles exhibit a peak at the SiO2-Si interface. This segregation is tentatively explained by stress relief at the SiO2-Si interface.

Structure and polymorphism of bipolar isopranyl ether lipids from archaebacteria.

We describe in this work the structure and polymorphism of a variety of lipids extracted from Sulfolobus solfataricus, an extreme thermoacidophilic archaebacterium growing at about 85 degrees C and pH 2. These lipids are quite different from the usual fatty acid lipids of eukaryotes and prokaryotes: each molecule consists of two C40 omega-omega' biphytanyl residues (with 0 to 4 cyclopentane groups per residue), ether linked at both ends to two (variably substituted) glycerol or nonitol groups. Four lipid preparations were studied; the total and the polar lipid extracts, and two hydrolytic fractions, the symmetric glycerol dialkyl glycerol tetraether and the asymmetric glycerol dialkyl nonitol tetraether, as a function of water content and temperature, using X-ray scattering techniques. The main conclusions from the study of the four lipid preparations can be summarized as follows. (1) As with other lipids, a remarkable number and variety of phases are observed over a temperature-concentration range close to "physiological" conditions. The possibility is discussed that this polymorphism reflects a fundamental property of lipids, closely related to their physiological rôle. (2) As in other lipids, two types of chain conformations are observed: a disordered one (type alpha) at high temperature; at lower temperature, a more ordered packing of stiff chains, all parallel to each other (type beta'). At temperatures and degrees of hydration approaching the conditions prevailing in the living cell, the conformation is of type alpha. (3) In all the phases with chains in the alpha conformation, the unsubstituted glycerol headgroups, whose concentration is high in these lipids, segregate in the hydrocarbon matrix, away from the other polar groups. This property may have interesting biological consequences: for example, the chains of a fraction of the bipolar lipid molecules can span hydrocarbon gaps as wide as 75 A. (4) Two cubic phases are observed in the total and the polar lipid extracts, which display a remarkable degree of metastability, most unusual in lipid phase transitions involving structures with chains in the alpha conformation. This phenomenon can be explained by the interplay of the physical structure of the cubic phases (the two contain two intertwined and unconnected three-dimensional networks of rods) and the chemical structure of the lipid molecules: the two headgroups of most molecules being anchored on each of the two networks of rods, the migration of the lipid molecules is hindered by the two independent diffusion processes and by the entanglement of the chains.(ABSTRACT TRUNCATED AT 400 WORDS)

Optimal control of an M/G/1 queuing system with removable server via diffusion approximation

In this paper, applying the technique of diffusion approximation to an M/G/1 queuing system with removable server, we provide a robust approximation model for determining an optimal operating policy of the system. The following costs are incurred to the system: costs per hour for keeping the server on or off, fixed costs for turning the server on or off, and a holding cost per customer per hour. The expected discounted cost is used as a criterion for optimality. Using a couple of independent diffusion processes approximating the number of customers in the system, we derive approximation formulae of the expected discounted cost that do not depend on the service time distribution but its first two moments. Some new results on the characterization of the optimal operating policy are provided from these results. Moreover, in order to examine the accuracy of the approximation, they are numerically compared with the exact results.

Scattering of light and neutrons in a model for superionic conductors

We discuss the cross sections for neutron scattering and light scattering from a superionic conductor. The motion of the mobile ions is treated as an independent continuous diffusion process through a periodic potential. While this determines the neutron scattering intensity completely, the light scattering is, in addition, strongly influenced by the spatial variation of the polarizability. This leads to selection rules and to differences between the two kinds of spectra. We present a rather complete study of a one-dimensional model which displays the general features of the problem. The results are based on a numerically accurate solution of the corresponding Fokker-Planck equation.