Evolution of perturbations of a charged interface between immiscible inviscid fluids in the interelectrode gap

Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the “shallow” and “deep” upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation. In the cases of the “shallow” and “deep” upper fluid examples of the development of an initial perturbation of the “step” type are given. The development of an initial perturbation of the “step” type are also considered in the near-critical electric fields and in the case of degeneration of cubic dispersion.     

Heat transfer mechanisms during short-pulse laser heating of two-layer composite thin films

 Using a simple perturbation technique, an analytical investigation is presented for the heat transfer mechanisms during ultrafast laser heating of two-layer composite thin slabs from a microscopic point of view. The composite slab consists of two thin metal films which are in perfect thermal contact. The microscopic parabolic two-step model is adopted to describe the behavior of the composite slab. In the microscopic two-step model, the heating process is modeled by the deposition of radiation energy on electrons, the transport of energy by electrons, and the heating of the material lattice through electron–phonon interactions. The proposed perturbation technique is used when the normalized temperature difference between the solid lattice and the electron gas is relatively a small perturbed quantity. Received on 20 September 2000 / Published online: 29 November 2001     

Soft Neutral Elastic Inhomogeneities with Membrane-type Interface Conditions

A foreign body, called an “inhomogeneity,” when introduced in a host solid disturbs the stress field which is present in it. One can explore the possibility of modifying the contact mechanism between the inhomogeneity and the host body so as to leave the stress field in the host solid undisturbed. If such a procedure succeeds, then the inhomogeneity is called “neutral.” Modification of the contact mechanism between the inhomogeneity and the host solid can be achieved, for example, by a suitably designed thick or thin interphase between them. When the interphase is thin, it can be represented by an “imperfect interface” model. In the present study we consider “soft” inhomogeneities which are more compliant than the host body. A “membrane-type interface” which models a thin and stiff interphase is used in rendering such inhomogeneities neutral. Illustrative examples are constructed for cylindrical neutral inhomogeneities of elliptical cross section under a triaxial loading, and for spheroidal inhomogeneities subjected to an axisymmetric loading.      

Initial Conditions and Near-Field Dynamics in Turbulent Liquid Sheets

High-speed liquid “curtains” have been proposed to protect solid structures in fusion energy applications. Minimizing free-surface waves and spray formation in such flows is important for effective protection in this application. In this work, free-surface waves and turbulent breakup were studied experimentally in jets of water issuing from a rectangular nozzle into ambient air at a Reynolds number of 1.2 × 10⁵. Laser-Doppler anemometry was used to characterize the streamwise and transverse velocity components in the nozzle for two different flow calming section designs. Planar laser-induced fluorescence was used to measure the free-stream position in the near-field of the sheet. The results suggest that transverse velocity fluctuations in the nozzle are the primary factor in determining the amplitudes of free-surface waves. Removing a small amount of low-speed fluid immediately downstream of the nozzle exit (“boundary-layer cutting”) is shown to both significantly reduce free-surface waves and the amount of spray due to turbulent breakup. Overall, boundary-layer cutting appears to have the greatest benefit when used on a “well-conditioned” turbulent liquid sheet.     

Free convection from a vertical permeable circular cone with non-uniform surface heat flux

 In this paper, the problem of laminar free convection from a vertical permeable circular cone maintained with non-uniform surface heat flux is considered. The governing boundary layer equations are reduced non-similar boundary layer equations with surface heat flux proportional to x ⁿ (where x is the distance measured from the leading edge). The solutions of the reduced equations are obtained by using three distinct solution methodologies; namely, (i) perturbation solution for small transpiration parameter, ξ, (ii) asymptotic solution for large ξ, and (iii) the finite difference solutions for all ξ. The solutions are presented in terms of local skin-friction and local Nusselt number for smaller values of Prandtl number and heat flux gradient and are displayed in tabular form as well as graphically. Effects of pertinent parameters on velocity and temperature profiles are also shown graphically. Solutions obtained by finite difference method are also compared with the perturbation solutions for small and large ξ and found to be in excellent agreement. Received on 1 October 1999     

THE PROBLEMS OF THE NONLINEAR UNSYMMETRICAL BENDING FOR CYLINDRICALLY ORTHOTROPIC CIRCULAR PLATE（II）

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Regarding some thermoelastic models of “coating-substrate” system deformation

In present research, we investigate dynamic coupled thermoelasticity problem for a “coating-substrate” system. We present a number of models of thermoelastic deformation of the “coating-substrate” system with thermomechanical characteristics which may vary both continuously and discontinuously. To solve these problems, we use the variational principle of coupled thermoelasticity in the Laplace transforms space and hypotheses on a distribution of temperature and displacements transforms. The transforms inversion is realized according to the Durbin method. The calculations were carried out based on both proposed simplified models and FEM.     

A dual-porosity model for gas reservoir flow incorporating adsorption behaviour—part I. Theoretical development and asymptotic analyses

In this paper a rigorous dual-porosity model is formulated, which accurately represents the coupling between large-scale fractures and the micropores within dual porosity media. The overall structure of the porous medium is conceptualized as being blocks of diffusion dominated micropores separated by natural fractures (e.g. cleats for coal) through which Darcy’s flow occurs. In the developed model, diffusion in the matrix blocks is fully coupled to the pressure distribution within the fracture system. Specific assumptions on the pressure behaviour at the matrix boundary, such as step-time function employed in some earlier studies, are not invoked. The model involves introducing an analytical solution for diffusion within a matrix block, and the resultant combined flow equation is a nonlinear integro-(partial) differential equation. Analyses to the equation in this text, in addition to the theoretical development of the proposed model, include: (1) discussion on the “fading memory” of the model; (2); one-dimensional perturbation solution subject to a specific condition; and (3) asymptotic analyses of the “long-time” and “short-time” responses of the flow. Two previous models, the Warren-Root and the modified Vermeulen models, are compared with the proposed model. The advantages of the new model are demonstrated, particularly for early time prediction where the approximations of these other models can lead to significant error.     

Amorphous and crystalline states of ultrasoft colloids: a molecular dynamics study

In this work, we study the temperature-induced development of “dynamically arrested” states in dense suspensions of “soft colloids” (multi-arm star polymers and/or block-copolymers micelles) by means of molecular dynamics (MD) simulations. Temperature increase in marginal solvents results in “soft sphere” swelling, dynamical arrest, and eventually crystallization. However, two distinct “dynamically arrested” states were found, one almost amorphous (“glassy”) and one with a considerable degree of crystallinity, yet lower than that of the fully equilibrated crystal. It is remarkable that even that latter state permitted self-diffusion in the timescale of the simulations, an effect that underlies the importance of the “ultra-soft” nature of inter-particle potential. The “number of connections” criterion for crystallinity proved to be very successful in identifying the ultimate thermodynamic trend from the very early stages of the α-relaxation. This paper was presented at the Third Annual Rheology Conference, AERC 2006, April 27–29, 2006, Crete, Greece.     

A systematic derivation of a consistent set of “Boussinesq equations”

The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ?, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit $\varepsilon\rightarrow0The often used “Boussinesq equations” for the determination of the coupled flow and temperature field in natural convection are systematically deduced by an asymptotic approach. With the nondimensional temperature difference that drives the flow, ɛ, as a perturbation parameter the leading order equations are identified as the appropriate equations, named “asymptotic Boussinesq equations”. These equations appear as the distinguished limit e?0\varepsilon\rightarrow0 and Ec? 0{Ec}\rightarrow 0 with Ec/e = const.{Ec}/\varepsilon =const. The equations are compared to “Boussinesq equations” of other studies and used to calculate Nusselt numbers in laminar and turbulent flows in infinite vertical channels as an example and for the justification of the asymptotic approach.     

A rheological approach to drill-in fluids optimization

The aim of this work is to propose design criteria, based on rheological characterisation for improving drill-in fluids performance. In particular, it reports an example in which rheological approaches helped improve drill-in fluids resistance to temperature. As a starting system a commercial drill-in fluid containing xanthan gum and calcium carbonate was chosen and evaluated. Different samples were then prepared by changing the initial formulation in order to increase the system's stability to temperature. Drill-in fluids' performance have been compared by considering their “damaging potential”, filtration properties and, “cakes”. All drill-in fluids have been tested before and after aging at a given temperature with “hot rolling tests”. The systems' gel structure was characterized by measuring dynamic moduli (G′ and G′′) in the linear viscoelastic range and all samples were compared by evaluating their “melting” temperature and gel network strength during time cure tests. The results obtained from this work suggest that the rheological tests carried out on the whole drill-in fluid can provide insights into fluids' damaging potential and “cake” structure. In particular, rheology proved to be able to provide quantitative information about gel strength and temperature stability that permitted one to improve drill-in fluids' formulation in order to preclude formation damage and to meet industrial requirements. Received: 6 February 2000 Accepted: 15 November 2000     

Numerical analysis of an asymptotic model for the collapse of a vapor bubble

In this work, we analyze the thermal collapse of a vapor bubble immersed in a unbounded and subcooled liquid. In this thermal regime, controlled basically by Jakob number (Ja), we present an asymptotic limit of the governing equations by identifying the appropriate temporary and spatial scales to solve numerically the mathematical model. In the limit of Ja ≫ 1, the governing equations describe the spatial and temporal evolution of the adjacent thermal boundary layer to the radius of the bubble. In particular, we prove that the influence of curvature effects due to conductive and convective heat terms of the energy equation for the liquid are responsible to characterize the thermal collapse regime. The numerical results for the evolution of the nondimensional radius of the bubble, a, and the corresponding nondimensional temperature profiles, θ, for different values of the Ja, show that the ending collapse state has a singular behavior, which we have denoted as a “thermal runaway”.     

Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Numerical study of vortex reconnection for two anti-parallel vortex tubes

By direct numerical simulation of the Navier-Stokes equations we investigate the reconnection of two antiparallel vortex tubes. A new type of perturbation of the initial vorticity field is given which is different from that presented in Refs. [8] and [9]. The formation and the evolution of the “curved vortex belts”, their mutual action with the “bridges” are found. These are important phenomena not studied by others. The project supported by the LNM of Institute of Mechanics, Academia Sinica and The National Natural Science Foundation of China     

Decentralized adaptive neural control of nonlinear systems with unknown time delays

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, and three problems of “computational explosion,” “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Influence of wall proximity on the equilibrium temperature of curved interfaces

Equilibrium conditions of a single-component two-phase-system having a plane or a concave interface interacting with a solid wall are the major focus of the paper. The concave interface is termed “closed”, if it forms a vapour bubble, and “opened”, in the case of a common liquid meniscus. The equations derived describe the equilibrium temperature in dependence of the wall distance and the interfacial curvature. They show that an attraction between the vapour-liquid interface and the wall rises the equilibrium temperature. At comparable conditions, the equilibrium temperature is higher for the closed than for the opened interface. Received on 18 December 1997     

Nonlinearly Elastic Shell Models: A Formal Asymptotic Approach II. The Flexural Model

This paper is the sequel of Part I, in which the limiting displacement field of a thin shell when its thickness approaches zero is identified as the solution of a two‐dimensional nonlinear membrane shell model. When the geometry of the middle surface of the shell and the boundary conditions allow non‐zero “inextensional displacements”, the previous membrane limit model is not relevant. In this case, we show how to “update” the assumptions on the applied forces acting on the shell so that a limiting model can be derived by an asymptotic analysis. Furthermore, we identify this limit as the two‐dimensional nonlinear flexural shell model. (Accepted January 13, 1997)     

Concentration distribution in the wake of a sphere buried in a granular bed through which fluid flows

The concentration distribution in the wake of a soluble sphere immersed in a granular bed of inert particles, through which fluid flows with “uniform velocity”, has been obtained numerically, for solute transport by both advection and diffusion/dispersion. Fluid flow in the granular bed around the sphere was assumed to follow Darcy’s law and, at each point, dispersion of solute was considered in both the cross-stream and streamwise directions. The elliptic PDE equation, resulting from a differential material balance on the solute, was solved numerically over a wide range of values of the relevant parameters (Peclet number and Schmidt number). The solution gives the concentration contour plots and, for each concentration level, the width and downstream length of the corresponding contour surface were determined. General expressions are presented to predict contaminant “plume” size downstream of the polluting source.     

Spectral Stability of Small-Amplitude Viscous Shock Waves in Several Space Dimensions

A planar viscous shock profile of a hyperbolic–parabolic system of conservation laws is a steady solution in a moving coordinate frame. The asymptotic stability of viscous profiles and the related vanishing-viscosity limit are delicate questions already in the well understood case of one space dimension and even more so in the case of several space dimensions. It is a natural idea to study the stability of viscous profiles by analyzing the spectrum of the linearization about the profile. The Evans function method provides a geometric dynamical-systems framework to study the eigenvalue problem. In this approach eigenvalues correspond to zeros of an essentially analytic function E(rl,rw){\mathcal{E}(\rho\lambda,\rho\omega)} which detects nontrivial intersections of the so-called stable and unstable spaces, that is, spaces of solutions that decay on one (“−∞”) or the other side (“ + ∞”) of the shock wave, respectively. In a series of pioneering papers, Kevin Zumbrun and collaborators have established in various contexts that spectral stability, that is, the non-vanishing of E(rl,rw){\mathcal{E}(\rho\lambda,\rho\omega)} and the non-vanishing of the Lopatinski–Kreiss–Majda function Δ(λ,ω), imply nonlinear stability of viscous shock profiles in several space dimensions. In this paper we show that these conditions hold true for small amplitude extreme shocks under natural assumptions. This is done by exploiting the slow-fast nature of the small-amplitude limit, which was used in a previous paper by the authors to prove spectral stability of small-amplitude shock waves in one space dimension. Geometric singular perturbation methods are applied to decompose the stable and unstable spaces into subbundles with good control over their limiting behavior. Three qualitatively different regimes are distinguished that relate the small strength e{\epsilon} of the shock wave to appropriate ranges of values of the spectral parameters (ρλ, ρ ω). Various rescalings are used to overcome apparent degeneracies in the problem caused by loss of hyperbolicity or lack of transversality.     

Validation of the thermal equilibrium assumption in the transient conjugated forced convection channel flow

 The validity of the local thermal equilibrium assumption in the transient conjugated forced convection channel flow is investigated analytically. Closed form expressions are presented for the temperatures of the fluid and solid domains and for the criterion which insure the validity of the local thermal equilibrium assumption. It is found that three dimensionless parameters control the local thermal equilibrium assumption. These parameters are the Biot number Bi, the dimensionless channel length ξ_max and the solid to fluid total thermal capacity ratio C _R. The qualitative and quantitative aspects of the effects of these three parameters on the channel thermalization time are investigated. Received on 9 August 2000