General References, Diffusion Processes, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion Processes, Electromigration, Point Defects, Linear Defects, Planar Defects, Irradiation Effects and Ionic Conduction

General References, Diffusion, Electromigration, Point Defects, Dislocations, Planar Defects, Irradiation Effects and Ionic Conduction

When potassium dihydrogen phosphate crystals (KH(2)PO(4) or KDP) are illuminated by multi-gigawatt nanosecond pulses, damages may appear in the crystal bulk. One can increase damage resistance through a conditioning that consists in carrying out a laser pre-exposure of the crystal. The present paper addresses the modeling of laser-induced damage and conditioning of KDP crystals. The method is based on heating a distribution of defects, the cooperation of which may lead to a dramatic temperature rise. In a previous investigation [Opt. Express 15, 4557-4576 (2007)], calculations were performed for cases where the heat diffusion was permitted in one and three spatial dimensions, corresponding respectively to planar and point defects. For the sake of completeness, the present study involves the 2D heat diffusion that is associated with linear defects. A comparison to experimental data leads to the conclusion that 1D calculations are the most appropriate for describing the laser-induced damage in KDP. Within this framework, the evolution of the damage density is given as a function of the laser energy density and an in-depth analysis of the results is provided based on simple analytical expressions that can be used for experimental design. Regarding the conditioning, assuming that it is due to a decrease in the defect absorption efficiency, two scenarios associated with various defect natures are proposed and these account for certain of the observed experimental facts. For instance, in order to improve the crystal resistance to damage, one needs to use a conditioning pulse duration shorter than the testing pulse. Also, a conditioning scenario based on the migration of point (atomic-size) defects allows the reproduction of a logarithmic-like evolution of the conditioning gain with respect to the number of laser pre-exposures. Moreover, this study aims at refining the knowledge regarding the precursor defects responsible for the laser-induced damage in KDP crystals. Within the presented modeling, the best candidate permitting the reproduction of major experimental facts is comprised of a collection of one-hundred-nanometer structural defects associated with point defects as for instance cracks and couples of oxygen interstitials and vacancies.

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson in J Financ Quant Anal 18(1):141–148 (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same efficiency as the quadratic approximation of Barone-Adesi and Whaley in J Financ 42:301–320 (1987), with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston’s stochastic volatility model, our method is shown to be extremely efficient and fairly accurate.

Since diffusion processes arise in so many different fields, efficient technics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations of the first-passage times as a by-product. For efficiency reasons, it is particularly challenging to simulate directly this hitting time by avoiding to construct the whole paths. In the Brownian case, the distribution of the first-passage time is explicitly known and can be easily used for simulation purposes. The authors introduce a new rejection sampling algorithm which permits to perform an exact simulation of the first-passage time for general one-dimensional diffusion processes. The efficiency of the method, which is essentially based on Girsanov’s transformation, is described through theoretical results and numerical examples.

Interplay between bulk and intrinsic pinning and commensurability effects in high- Tc superconductors

A Closed-Form Solution to American Options under General Diffusions

The inductance of vortices {ital L}{sub {ital V}}({ital T},{ital B}) in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} films is studied for temperature 8{lt}{ital T}{lt}85 K, and magnetic field 0{lt}{ital B}{lt}6 T with the goal of identifying the morphology of the vortex pinning sites and the type of the glass phase below the vortex lattice melting transition {ital B}{sub {ital g}}({ital T}). The key feature that distinguishes point, linear, and planar pinning sites is how rapidly {ital L}{sub {ital V}} increases when thresholds in {ital T} and {ital B} are crossed. We find that, below a threshold field {ital B}{sub {ital p}}({ital T}){lt}{ital B}{sub {ital g}}({ital T}), the effective pinning force on each vortex is independent of {ital B}. At {ital B}{sub {ital p}}{lt}{ital B}{lt}{ital B}{sub {ital g}}, {ital L}{sub {ital V}} increases as {ital B}{sup 2}, whereas at {ital B}{approx_equal}{ital B}{sub {ital g}}, {ital L}{sub {ital V}} diverges faster than {ital B}{sup 2} following a scaling law on {ital f}, consistent with a phase transition between a glass and a liquid vortex state. Although the value of the threshold field, {ital B}{sub {ital p}}{approx_equal}8(1{minus}{ital T}/{ital T}{sub {ital C}}) T, is consistent with any type of pinning defect, the increase of {italmore » L}{sub {ital V}}{proportional_to}{ital B}{sup 2} for {ital B}{approx_gt}{ital B}{sub {ital p}} is much less rapid than predicted for collective pinning of vortices by point defects. Linear and planar defects are possible explanations, but the necessary theoretical calculations are currently absent. {copyright} {ital 1996 The American Physical Society.}« less

Ethylenediamine tetraacetate (EDTA)-mediated calcite dissolution occurs via a different process than water-promoted dissolution. Near-atomic-scale observations in EDTA solutions demonstrate that, after penetration through a critical pit depth barrier, step velocity increases linearly with pit depth for EDTA-promoted dissolution. The parallel processes of water-dominated dissolution at point defects and ligand-dominated dissolution at linear defects are clearly observable in real-time atomic force micrographs. EDTA and water initiate and propagate dissolution steps with pit-depth-dependent and -independent step velocities, respectively. The linear defects are susceptible to continuously increasing step velocities, but the point defects are not. The findings update the conceptual framework of the microscopic mechanism of mineral dissolution.

A physical and mathematical model of the transition from a discrete model of linear and flat defects nuclei to continuum models of defects such as dislocations and disclinations and their combinations is presented, where the tensors of energy-momentum and angular momentum of an alternating field are considered, for which the type and structure of the Maxwell stress tensor σif αβ are given and the corresponding angular momentum tensor, using the dynamic equation for the evolution of internal stresses and the correlation between the stresses σif αβ in the defect core and the elastic stresses σelik in its environment, obtains elastic displacement and deformation fields identical to these fields from Burgers and Frank vectors of continuous models. The spectral density of the autocorrelation functions of the velocity of photoelectrons Ψβ⊥(β) and cations , which transforms into linear spectra as T → 0, is considered reflecting the existence of threshold values of oscillation and rotations currents of photoelectrons and cations at all stages of plastic deformation and fracture. The features of the process of sliding linear defects in metals are disclosed.

Automated identification and characterization of clustered weld defects, which comprise a plural of closely distributed individual member defects, is challenging. In this paper, time, Cartesian and Polar domain features in phased array ultrasonic sectorial scanning data are studied to segment clustered weld defect echoes by density based and K-means clustering. Through multiple domain segmentation, all individual member defect echoes are successfully identified. Then size and depth estimation is performed on each individual member defect to describe its patterns and to locate its depth. The developed technique is applied to experimental data collected from scanning on a tubular T weld test sample and is shown to discriminate, locate, and measure all the individual defects inside clustered defects. Based on the geometrical features of each individual member defect, they are classified as either point, linear or planar defects.

Spiral depinning from linear and planar defects

The theory of the local optical oscillations near the defects of different types (point, linear, and plane) in semiconductors (SC) with a ionic crystal lattice is built. In the optical frequency range the transverse local oscillations (LO) exist in the crystal with a light defect and the longitudinal LO exist in the crystal with a heavy defect. The conduction electrons don't take part in forming of the frequencies of the LO, but influence their field structure essentially owing to the Coulomb interactions of the electrons with the lattice ions and the defect. Because of the Coulomb's screening of the defect by conduction electrons, the space about the defect divides into two regions: the near zone (r &lt;&lt; r<SUB>D</SUB>, r<SUB>D</SUB> is the Debye's radius of screening) and the distant zone (r &gt;&gt; r<SUB>D</SUB>). In the near zone the coordinate dependencies of the LO amplitudes have the same form as in the ionic dielectrical crystals. In the distant zone the LO amplitudes decrease exponentially at the macroscopic distances which have scales of the Debye's radius r<SUB>D</SUB> or the length of the transverse electromagnetic waves in the SC media.

The theory of the local optical oscillations near the defects of different types (point, linear and plain) is built for semiconductors (SC) with ionic cristal lattice. This phenomenon is that the oscillations with the discrete frequency and the amplitude, decreasing at large distances appear near the defects (same as the Lifshitz's local oscillations in an atomic crystal ).