Instability of the Motion of a Drop in Filtration Flows

The behavior of an inclusion (drop) of foreign fluid in a porous medium saturated with another fluid is considered. A steady-state regime of gravity-induced drop settlement is found and the instability of this regime is demonstrated. The horizontal motion of a liquid inclusion under the action of a stationary reservoir pressure gradient is also studied.     

Turbulence Energy Distribution in the Stokes Layer

Using the method of matched asymptotic expansions, an analytical solution of the balance equation for turbulence energy is constructed for a shallow basin (sea) in which the fluid depth does not exceed the Stokes layer thickness. In this case, a gradient-viscous balance is established with the turbulent viscosity being balanced mainly by the pressure gradient. It is shown that nonlinear boundary layers attributable to turbulence energy diffusion are formed near the bottom and the free surface (or ice). In the neighborhood of the point of maximum flow velocity (if this maximum is attained inside the flow), a nonlinear internal boundary layer also develops. Outside these layers, the turbulence energy generation is in the first approximation balanced by the energy dissipation. Asymptotic solutions for the boundary layers are constructed.     

Global Existence of the Equilibrium Diffusion Model in Radiative Hydrodynamics

This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the well-posedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.     

Flow regime transition criteria for two-phase flow in a vertical annulus

In this work, a new flow regime transition model is proposed for two-phase flows in a vertical annulus. Following previous works, the flow regimes considered are bubbly (B), slug (S) or cap-slug (CS), churn (C) and annular (A). The B to CS transition is modeled using the maximum bubble package criteria of small bubbles. The S to C transition takes place for small annulus perimeter flow channels and it is assumed to occur when the mean void fraction over the entire region exceeds that over the slug–bubble section. If the annulus perimeter is larger that the distorted bubble limit the cap-slug flow regime will be considered since in these conditions it is not possible to distinguish between cap and partial-slug bubbles. The CS to C transition is modeled using the maximum bubble package criteria. However, this transition considers the coalescence of cap and spherical bubbles in order to take into account the flow channel geometry. Finally, the C to A transition is modeled assuming two different mechanisms, (a) flow reversal in the liquid film section along large bubbles; (b) destruction on liquid slugs or large waves by entrainment or deformation. In the S to C and C to A flow regime transitions the annulus flow channel is considered as a rectangular flow channel with no side walls. In all the modeled transitions the drift-flux model is used to obtain the final correlations. The final equations for every flow regime transition are easy to be implemented in computational codes and not experimental input is needed. The prediction accuracy of the newly developed model has been checked against air–water as well as boiling flow regime maps. In all the cases, the new developed model shows better predicting capabilities than the existing correlations most used in literature.     

Mathematical analysis of plasmonic resonance for 2-D photonic crystal

In this article, we study the plasmonic resonance of infinite photonic crystal mounted by the double negative nanoparticles in two dimensions. The corresponding physical model is described by the Helmholz equation with so called Bloch wave condition in a periodic domain. By using the quasi-periodic layer potential techniques and the spectral theorem of quasi-periodic Neumann–Poincaré operator, the quasi-static expansion of the near field in the presence of nanoparticles is derived. Furthermore, when the magnetic permeability of nanoparticles satisfies the Drude model, we give the conditions under which the plasmonic resonance occurs, and the rate of blow up of near field energy with respect to nanoparticle's bulk electron relaxation rate and filling factor are also obtained. It indicates that one can appropriately control the bulk electron relaxation rate or filling factor of nanoparticle in photonic crystal structure such that the near field energy attains its maximum, and enhancing the efficiency of energy utilization.     

基于Lorenz映射的混沌系统分支变换预报规律研究

尽管Lorenz系统具有混沌和非周期性质, 但其分支变换是可预报的.本文以强迫Lorenz系统为数学模型, 基于Lorenz映射, 研究了混沌系统分支变换的预报规律, 将原有关于分支开始变换条件和新分支持续时间的两条一般规律扩展到了3条, 并首次分析了系统当前状态达到变换条件所需时间的预报规律, 从而为预报混沌系统非周期演变提供了另一途径.结果表明: 映射尖点位置为分支变换的临界值, 当变量z超过相应临界值时, 系统在当前分支的运动即将结束, 下一循环将跳跃到另一分支运动; 系统在同一分支循环的次数随极值z_max单调减小, z_max 越小, 达到变换条件需循环的次数越多; 系统在新分支持续的时间是先前分支最大极值z_M 的单调增加函数, z_M越大, 持续时间增加的幅度也越大.此外, 外强迫影响着混沌系统分支变换的预报规律, 其不但使正负分支的变换条件出现差异, 且与新分支持续时间的增加速率和达到变换条件所需时间的递减速率密切相关. 关键词： Lorenz映射 分支变换 外强迫 预报规律     

Stationary Analysis of a Fluid Queue Driven by Some Countable State Space Markov Chain

Motivated by queueing systems playing a key role in the performance evaluation of telecommunication networks, we analyze in this paper the stationary behavior of a fluid queue, when the instantaneous input rate is driven by a continuous-time Markov chain with finite or infinite state space. In the case of an infinite state space and for particular classes of Markov chains with a countable state space, such as quasi birth and death processes or Markov chains of the G/M/1 type, we develop an algorithm to compute the stationary probability distribution function of the buffer level in the fluid queue. This algorithm relies on simple recurrence relations satisfied by key characteristics of an auxiliary queueing system with normalized input rates.      

Photomagnetic effect in bilayer two-dimensional electron–hole systems

In tilted magnetic fields a bilayer electron–hole system is found to generate a photocurrent under terahertz radiation as the system is tuned to electron cyclotron resonance conditions. The photoinduced current amplitude oscillates with the magnetic field in correlation with Shubnikov–de Haas oscillations for electrons. The phenomenon is accounted for by a photomagnetic effect in electron–hole systems in the quantum Hall regime and has potentialities for terahertz detection and spectroscopy.     

Image enhancement and stress separation of thermoelastically measured data under random loading

Traditional thermoelastic stress analysis (TSA) presupposes that the structure being analyzed is cyclically loaded at a constant amplitude and frequency. This approach typically has been used to satisfy the adiabatic reversible assumptions. The authors employ an alternative signal analysis technique that enables one to evaluate the magnitude of the individual components of stress in a component subjected to a loading that is random in both frequency and magnitude. However, the nature of the measured information does not change; i.e., data are inherently noisy, and edge information is unreliable. The latter two aspects have caused many thermoelastic stress analyses to be more qualitative than quantitative. The present paper emphasizes developing the TSA technique into a practical, noncontacting quantitative method for stress analyzing actual engineering structures that are randomly loaded. In particular, ability to determine the individual stresses thermoelastically under random loading is demonstrated.     

The thermoelastic Aldo contact model with frictional heating

In the study of the essential features of thermoelastic contact, Comninou and Dundurs (J. Therm. Stresses 3 (1980) 427) devised a simplified model, the so-called “Aldo model”, where the full 3D body is replaced by a large number of thin rods normal to the interface and insulated between each other, and the system was further reduced to 2 rods by Barber's Conjecture (ASME J. Appl. Mech. 48 (1981) 555). They studied in particular the case of heat flux at the interface driven by temperature differences of the bodies, and opposed by a contact resistance, finding possible multiple and history dependent solutions, depending on the imposed temperature differences.The Aldo model is here extended to include the presence of frictional heating. It is found that the number of solutions of the problem is still always odd, and Barber's graphical construction and the stability analysis of the previous case with no frictional heating can be extended. For any given imposed temperature difference, a critical speed is found for which the uniform pressure solution becomes non-unique and/or unstable. For one direction of the temperature difference, the uniform pressure solution is non-unique before it becomes unstable. When multiple solutions occur, outermost solutions (those involving only one rod in contact) are always stable.A full numerical analysis has been performed to explore the transient behaviour of the system, in the case of two rods of different size. In the general case of N rods, Barber's conjecture is shown to hold since there can only be two stable states for all the rods, and the reduction to two rods is always possible, a posteriori.