T. Elperin

Estimation of network reliability using graph evolution models

Monte Carlo techniques for estimating various network reliability characteristics, including terminal connectivity, are developed by assuming that edges are subject to failures with arbitrary probabilities and nodes are absolutely reliable. The core of the approach is introducing network time-evolution processes and using certain graph-theoretic machinery, resulting in a considerable increase in accuracy for Monte Carlo estimates, especially for highly reliable networks. Simulation strategies and numerical results are presented and discussed. >

Turbulence energetics in stably stratified geophysical flows: Strong and weak mixing regimes

Traditionally, turbulence energetics is characterised by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterised by the ratio of the buoyancy gradient to squared shear, called the Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE, and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no ‘energetics Ric’, in contrast to the hydrodynamic-instability threshold, Ric−instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25 < Ri < 1, separates two different turbulent regimes: strong mixing and weak mixing rather than the turbulent and the laminar regimes, as the classical concept states. This explains persistent occurrence of turbulence in the free atmosphere and deep ocean at Ri ≫ 1, clarifies the principal difference between turbulent boundary layers and free flows, and provides the basis for improving operational turbulence closure models. Copyright

Ballistic Impact: Recent Advances in Analytical Modeling of Plate Penetration Dynamics–A Review

This review covers studies dealing with simplified analytical models for ballistic penetration of an impactor into different solid media, namely, metals, soil, concrete, and composites at high speeds, but not at hypervelocities. The overview covers mainly papers that were published in the last decade, but not analyzed in previous reviews on impact dynamics. Both mathematical models and their engineering applications are considered. The review covers 280 citations. DOI: 10.1115/1.2048626

On the ballistic resistance of multi-layered targets with air gaps

Abstract High velocity penetration of a 3-D rigid sharp impactor into a ductile layered target with air gaps between the plates is studied using the assumption about the localized projectile-target interaction. The special property of the penetration phenomenon for conical-nosed impactors is established, namely, that the ballistic performance of the target is independent on the air gap widths and on the sequence of the plates in the target. Similar results are also obtained for 3-D non-conical impactors on the basis of some class of models. These findings are in good agreement with available experimental results.

Hysteresis processes in the regular reflection↔Mach reflection transition in steady flows

Abstract Ernst Mach recorded experimentally, in the late 1870s, two different shock-wave reflection configurations and laid the foundations for one of the most exciting and active research field in an area that is generally known as Shock Wave Reflection Phenomena . The first wave reflection, a two-shock wave configuration, is known nowadays as regular reflection , RR, and the second wave reflection, a three-shock wave configuration, was named after Ernst Mach and is called nowadays Mach reflection , MR. A monograph entitled Shock Wave Reflection Phenomena , which was published by Ben-Dor in 1990, summarized the state-of-the-art of the reflection phenomena of shock waves in steady, pseudo-steady and unsteady flows. Intensive analytical, experimental and numerical investigations in the last decade, which were led mainly by Ben-Dors research group and his collaboration with Chpouns, Zeitouns and Ivanovs research groups, shattered the state-of-the-knowledge, as it was presented in Ben-Dor (Shock Wave Reflection Phenomena, Springer, New York, 1991), for the case of steady flows. Skewss and Hornungs research groups joined in later and also contributed to the establishment of the new state-of-the-knowledge of the reflection of shock waves in steady flows. The new state-of-the-knowledge will be presented in this review. Specifically, the hysteresis phenomenon in the RR↔MR transition process, which until the early 1990s was believed not to exist, will be presented and described in detail, in a variety of experimental set-ups and geometries. Analytical, experimental and numerical investigations of the various hysteresis processes will be presented.

Clustering instability of the spatial distribution of inertial particles in turbulent flows

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is a size of the particles. The critical size is estimated for a strong clustering (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence-free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for clusters formation is more than

Melting dynamics in current‐carrying conductors and its effect on electrodynamic characteristics

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Evaporation of liquid droplets containing small solid particles

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Monte Carlo simulation of gas−solids suspension flows in impinging streams reactors

This work studies the dynamics of melting in current‐carrying conductors. Formulae are derived which describe the dependence of temperature at the front of phase transition upon the distance from the axis of the conductor. The thermodynamic stability of a phase transition front is investigated. It is shown that due to strong variations of conductivity during melting the rate of change of conductivity is of the same order as an active resistance of a conductor. Clearly the magnitude of this effect depends upon the ratio of electric conductivities in liquid and solid phases. The effect is stronger when this ratio is lower.

The reflection of asymmetric shock waves in steady flows: a numerical investigation

Abstract Evaporation of a liquid droplet containing small solid particles (slurry droplets) is analyzed in a quasi-steady approximation. The developed model takes into account effects of compressibility and filtration of a gas-vapor mixture within the porous shell. It is shown that in the case of small temperature differences in the neighborhood of a slurry droplet at the second stage of drying (evaporation through a porous shell), the regime of slow evaporation and saturation (negligibly small drying rate) occurs. In the case of high temperature differences in the neighborhood of a slurry droplet at the second stage of drying, the pressure of the gas-vapor mixture within the porous shell significantly increases leading to the fragmentation of a porous shell. The comparison of the proposed model with the diffusion model, which neglects the Stefans flux shows that the diffusion model incorrectly describes evaporation of a slurry droplet at the final stage of drying.