Boundary Layer Stability¶in Real Vanishing Viscosity Limit

In the previous paper [20], an Evans function machinery for the study of boundary layer stability was developed. There, the analysis was restricted to strongly parabolic perturbations, that is to an approximation of the form u _t +(F(u)) _x =ν(B(u)u _x ) _x $ (ν≪1) with an “elliptic” matrix B. However, real models, like the Navier–Stokes approximation of the Euler equations for a gas flow, involve incompletely parabolic perturbations: B is not invertible in general. We first adapt the Evans function to this realistic framework, assuming that the boundary is not characteristic, neither for the hyperbolic first order system u _t +(F(u)) _x = 0, nor for the perturbed system. We then apply it to the various kinds of boundary layers for a gas flow. We exhibit some examples of unstable boundary layers for a perfect gas, when the viscosity dominates heat conductivity. Received: 27 November 2000/ Accepted: 16 March 2001     

Linear stability of shock profiles for systems of conservation laws with semi-linear relaxation

The Evans function theory, which has recently been applied to the study of linear stability of viscous shock profiles, is developed below for semi-linear relaxation. We study the linear stability of shock profiles in the Lax, undercompressive and overcompressive cases. The results we obtain are similar to those found for viscous approximations by Gardner and Zumbrun [Commun. Pure Appl. Math. 51 (7) (1998) 797].     

The refined inviscid stability condition and cellular instability of viscous shock waves

Combining the work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and Texier and Zumbrun, we propose as a mechanism for the onset of cellular instability of viscous shock and detonation waves in a finite-cross-section duct, the violation of the refined planar stability condition of Zumbrun-Serre, a viscous correction of the inviscid planar stability condition of Majda. More precisely, we show for a model problem involving flow in a rectangular duct with artificial periodic boundary conditions that transition to multidimensional instability through violation of the refined stability condition of planar viscous shock waves on the whole space generically implies for a duct of sufficiently large cross-section, a cascade of Hopf bifurcations involving more and more complicated cellular instabilities. The refined condition is numerically calculable as described by Benzoni-Gavage-Serre-Zumbrun.     

Asymptotic Behavior Near Transition Fronts for Equations of Generalized Cahn–Hilliard Form

We consider the asymptotic behavior of perturbations of standing wave solutions arising in evolutionary PDE of generalized Cahn–Hilliard form in one space dimension. Such equations are well known to arise in the study of spinodal decomposition, a phenomenon in which the rapid cooling of a homogeneously mixed binary alloy causes separation to occur, resolving the mixture into its two components with their concentrations separated by sharp transition layers. Motivated by work of Bricmont, Kupiainen, and Taskinen [5], we regard the study of standing waves as an interesting step toward understanding the dynamics of these transitions. A critical feature of the Cahn–Hilliard equation is that the linear operator that arises upon linearization of the equation about a standing wave solution has essential spectrum extending onto the imaginary axis, a feature that is known to complicate the step from spectral to nonlinear stability. Under the assumption of spectral stability, described in terms of an appropriate Evans function, we develop detailed asymptotics for perturbations from standing wave solutions, establishing phase-asymptotic orbital stability for initial perturbations decaying with appropriate algebraic rate.     

Transition to Longitudinal Instability of Detonation Waves is Generically Associated with Hopf Bifurcation to Time-Periodic Galloping Solutions

We show that transition to longitudinal instability of strong detonation solutions of reactive compressible Navier–Stokes equations is generically associated with Hopf bifurcation to nearby time-periodic “galloping”, or “pulsating”, solutions, in agreement with physical and numerical observation. In the process, we determine readily numerically verifiable stability and bifurcation conditions in terms of an associated Evans function, and obtain the first complete nonlinear stability result for strong detonations of the reacting Navier–Stokes equations, in the limit as amplitude (hence also heat release) goes to zero. The analysis is by pointwise semigroup techniques introduced by the authors and collaborators in previous works.     

Interaction of Magnetization Centers of Different Signs as the Cause of the Nonmonotonic Field Dependence of the Domain Wall Velocity in Synthetic Pt/Co/Ir/Co/Pt Ferrimagnets

The purpose of the work is to find the dependence of growth rate of magnetization centers of various types on their surrounding by other nucleation centers in a synthetic Pt/Co/Ir/Co/Pt ferrimagnet with perpendicular magnetic anisotropy. The following four types of nucleation centers exist in a sample with two ferromagnetic layers of different thicknesses: P+ centers correspond to the regions where the magnetizations of the thick and thin Co layers are directed along an applied field (↑↑); P– centers are the regions where the magnetizations of the layers are opposite to an applied field (↓↓); and AP+ and AP– centers correspond to the regions where the magnetizations of the thick and thin Co layers are opposite to each other and the total magnetic moment is along (↑↓) or opposite to (↓↑) an applied field, respectively. P– nucleation centers are found to be surrounded by AP+ regions in any field and exhibit a monotonic field dependence of their boundary. The field dependence of the growth rate of AP– nucleation centers is nonmonotonic since, as the field increases, they are surrounded by AP+ nucleation centers, AP+ and P– regions, and only P– nucleation centers in strong fields.     

Electrophysical properties of epitaxial layers of solid solutions of lead and tin tellurides doped with cadmium

Epitaxial layers of Pb_1−xSn_xTe (x≈0.2), undoped and doped with cadmium, are grown in a quasi-closed volume using the hot-wall method on BaF₂ fragments. The doping impurity is introduced directly into the material of the vapor source before synthesis in an equi-atom ratio with additional tellurium. The boundary of the limit of homogeneity from the side of the metallic components and in the region of the stoichiometric composition of the epitaxial layers doped with cadmium and the undoped epitaxial layers is established. The electrical conductivity and the Hall effect are investigated in the 77–450 K temperature range, and the temperature dependences of the intrinsic concentrations and of the ratio of the electron and hole mobilities are established. The temperature dependence of the Hall mobility is also investigated. The stability of the electrical parameters of the epitaxial layers are studied. It is shown that doping with cadmium enables highly stable n-type epitaxial layers to be obtained. Chernovits Branch, Institute of Problems of the Study of Materials, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–64, July, 1996.     

On the baroclinic instability of nonplanar flows

Summary Different ocean models with one or two layers having constant static stability and supporting constant-shear flows, whose directions are allowed to change with depth, are examined in the frame-work of the linear nonzonal baroclinic stability theory and in the absence of the β-effect. The analysis is reduced to solving a simple Sturm-Liouville boundary value problem in one dimension. A fairly general dispersion relation is found which correctly reproduces several special cases analysed by other authors. This relation shows a fair variety of possible behaviours for stability curves of two-layer models. The results show that the presence of a nonplanar shear-flow may have profound consequences on the stability character of the stationary geostrophic flow. In fact, it appears that the stability properties are strongly dependent on the propagation angle of the disturbance so that wave numbers which appear stable in the usual zonal theory may result unstable on such a nonzonal flow andvice versa. Paper presented at the 1^o Congresso del Gruppo Nazionale per la Fisica dell'Atmosfera e dell'Oceano, June 19–22, 1984, Rome.     

Phase diagram of multilayer ferromagnet-layered-antiferromagnet structures

This paper discusses the thickness-roughness phase diagram of a three-layer system consisting of two ferromagnetic layers separated by an antiferromagnetic interlayer. It is shown that the stability region of single-domain ferromagnetic layers is determined by the ratio between the width of the atomic steps that appear at the interfaces of the layers during their growth and the thicknesses of the layers, and also by the values of the interlayer and intralayer exchange interactions. A basis is provided for the phenomenological “magnetic closeness” model proposed by Slonczewski, and an expression is obtained for the constants of this model. Fiz. Tverd. Tela (St. Petersburg) 41, 1240–1247 (July 1999)     

Waveguides with Combined Dirichlet and Robin Boundary Conditions

We consider the Laplacian in a curved two-dimensional strip of constant width squeezed between two curves, subject to Dirichlet boundary conditions on one of the curves and variable Robin boundary conditions on the other. We prove that, for certain types of Robin boundary conditions, the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Laplacian in a Dirichlet-Robin annulus determined by the geometry of the strip. Moreover, we show that an appropriate combination of the geometric setting and boundary conditions leads to a Hardy-type inequality in infinite strips. As an application, we derive certain stability of the spectrum for the Laplacian in Dirichlet–Neumann strips along a class of curves of sign-changing curvature, improving in this way an initial result of Dittrich and Kříž (J. Phys. A, 35:L269–275, 2002).      

Causes of phase variations in the air–ice boundary reflection coefficient in the microwave range

We study phase variations in the coefficient of reflection from a flat air–ice boundary at the ice melting point. The measurements were performed by different methods at frequencies 3.3, 6, 13, and 32 GHz. The experimental data were compared with simple theoretical models. It was found that ice wettening in thin layers leads to a phase variation in the reflection coefficient by up to a few ten degrees with satisfactory agreement between the experiment and the theory. However, anomalies of the transmission properties of the samples unexplainable in terms of the model of effective dielectric permittivity of the melting layers were observed in a narrow temperature range before the ice destruction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 52, No. 3, pp. 260–266, March 2009.     

Reactive diffusion in Sc/Si multilayer X-ray mirrors with CrB2 barrier layers

Processes undergoing in Sc/Si multilayer X-ray mirrors (MXMs) with periods of ∼27 nm and barrier layers of CrB₂0.3- and 0.7-nm thick within the temperature range of 420–780 K were studied by methods of small-angle X-ray reflectivity (λ=0.154 nm) and cross-sectional transmission electron microscopy. All layers with the exception of Sc ones are amorphous. Barrier layers are stable at least up to a temperature of 625 K and double the activation energy of diffusional intermixing at moderate temperatures. Introduction of barriers improves the thermal stability of Sc/Si MXMs at least by 80 degrees. Diffusion of Si atoms through barrier layers into Sc layers with formation of silicides was shown to be the main degradation mechanism of MXMs. A comparison of the stability for Sc/Si MXMs with different barriers published in the literature is conducted. The ways of further improvement of barrier properties are discussed.     

Filtration of IR radiation by three-component polymer-crystalline systems

We have investigated the regularities in forming the spectral characteristic of three-component polymeric-crystalline polytetrafluorethylene-Ge-LiF interference systems in the wide IR spectral region 0.8–160 μm. The efficiency of suppressing short-wave radiation by structurally asymmetric imerference systems consisting of polytetrafluorethylene and quasihomogeneous layers with a high refractive index is shown. Two of this kind of three-layer systems are sufficient for suppressing background radiation within the wavelength interval from the visible range to ∼35 μm owing to multiple reflection at the boundaries of elementary Ge and LiF layers that form quasihomogeneous layers (λ ∼ 1.7–17.0 μm) and also due to absorption in the Ge (λ<1.7 μm) and Lif (λ ∼ 17–35 μm) layers. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No_ 3, pp. 379–381, May–June, 2000.     

Length scale dependence of chiral symmetry breaking in free-standing films of achiral smectic C

The textures of a smectic C phase in free-standing films of the Schiff base 5O.6 are studied as a function of the number of layers and temperature. Periodic stripes with alternating contrast are observed in SmA boundary layers. On further cooling a transition to the splay stripes occurs in the smectic A temperature interval. In the smectic C phase all the periodic textures disappear, whereas in films with one free boundary a periodic arrangement of splay stripes is found. Mechanisms of symmetry breaking are discussed. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 29–32 (10 July 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Modification of the spin-wave dispersion law in multilayer films by changes in the symmetry of the boundary conditions

The present paper is the first attempt to study the transformation of spin-wave resonance spectra when symmetric boundary conditions are smoothly replaced by asymmetric. The transition is done by gradually reducing the thickness of one of the layers in a three-layer film. Spin deexcitation is caused by a dissipation mechanism. We find that in the transition region between symmetric and asymmetric boundary conditions the dispersion curve experiences a break, whose position depends on the degree of deexcitation (the thickness of the upper layer). The break is caused by the appearance of asymmetric transitional spin-wave modes, which cannot be excited under symmetric boundary conditions. Zh. éksp. Teor. Fiz. 111, 1667–1673 (May 1997)     

Nonlinearities in the reflection and transmission spectra of the photonic bandgap heterostructures with n–i–p–i crystals

Nonlinear optical properties of photonic crystal heterostructures with embedded n–i–p–i superlattices are investigated. Self-consistent calculations of the transmission and reflection spectra near the defect mode are performed using the transfer-matrix method and taking into account the gain saturation. Analysis of features and output characteristics is carried out for one-dimensional photonic crystal heterostructure amplifiers in the GaAs–GaInP system having at the central part an active “defect” from doubled GaAs n–i–p–i crystal layers. The gain saturation in the active layers in the vicinity of the defect changes the index contrast of the photonic structure and makes worse the emission at the defect mode. Spectral bistability effect, which can be exhibited in photonic crystal heterostructure amplifiers, is predicted and the hysteresis loop and other attending phenomena are described. The bistability behavior and modulation response efficiency demonstrate the potential possibilities of the photonic crystal heterostructures with n–i–p–i layers as high-speed optical amplifiers and switches.      

Flexible ceramic–polymer composite films with temperature-insensitive and tunable dielectric permittivity

BaTiO₃–polymer composite layers have been produced by the spin-on technique (thickness 3–10 μm). The dielectric permittivity of the layers at room temperature can be tuned from 2.8 to approximately 33 by varying the ceramic filling from 0 to 60% by volume. The dielectric properties of the films are almost insensitive to temperature variations in the range 20–180 °C. Free-standing composite layers with ceramic content ≤50% are flexible without noticeable change of permittivity after repeated mechanical bending. Received: 22 November 2001 / Accepted: 24 November 2001 / Published online: 23 January 2002     

Structural and electrical characteristics of zirconium oxide layers derived by photo-assisted sol–gel processing

This paper reports the photo-assisted formation of ZrO₂ layers derived by sol–gel processing at low temperatures using intense radiation from ultraviolet (UV) excimer lamps. Excellent layer properties can be readily obtained for these sol–gel layers after 5-min exposure to the UV irradiation at around 300 °C. Analyses of the as-deposited sol–gel layers by UV/VIS spectrophotometry show that the organic species contained in the layers have been removed to a large extent after 5-min irradiation. This is further confirmed by X-ray photoelectron spectroscopy analyses of the same irradiated layers, which indicate the formation of ZrO₂ with little carbon contamination contributed by the organic species and less oxidation of Si at the interface. Electrical measurements of these layers are also reported. Received: 31 July 2001 / Accepted: 6 September 2001 / Published online: 17 October 2001     

Pointwise Convergence to Knudsen Layers of the Boltzmann Equation

In this paper Green’s functions for the Boltzmann equation around a global Maxwellian are used to construct the non-characteristic nonlinear Knudsen layers as well as their time-asymptotic stability. Furthermore, the detailed pointwise structures, nonlinear wave couplings, and wave interactions with boundary are studied.     

Low-temperature STM/STS investigation of nanostructures created by an STM tip on Au(111) surfaces

The structural stability of rapidly solidified (about 10⁴ K/s) Sn–3.7Ag–0.9Zn eutectic solder was explored by high-temperature annealing. For the as-cast solders, the applied fast cooling rate had a significant influence on the microstructure of the solders. The faster the applied cooling rates, the smaller the β-Sn dendrites. After annealing at 473 K for 20 and 50 h, β-Sn dendrites congregated together into bulk ones for minimizing the interfacial energy, and Ag₃Sn intermetallic compounds (IMCs) as well as ternary Ag–Zn–Sn IMCs segregated on the grain boundary of the β-Sn dendrites. It seems that the coarsening of the β-Sn dendrites in the rapidly solidified specimen brought a significant softening during annealing of the explored Sn–Ag–Zn alloy. Finally, the β-Sn dendrites vanished gradually with increase of the annealing period, which leads to a kind of softening.