Stability of degenerate diffusions with state-dependent switching

This paper deals with the ergodic properties of hybrid systems modelled by diffusion processes with state-dependent switching. We investigate the sufficient conditions expressed in terms of the parameters of the underlying process which would ensure the existence of a unique invariant probability and stability in distribution of the flow. It turns out that the conditions would depend on certain averaging mechanisms over the states of the discrete component of the hybrid system. (C) 1999 Academic Press.

Stability of non-parabolic flow in a flexible tube

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such 'non-parabolic' flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

Structure and stability of Li2F

The equilibrium geometries and fundamental vibration frequencies of the Li2F system were calculated by ab initio methods at the MP2 = full/6-311(+ +)G** and CCSD(T) levels. Two isomers were observed and are best described as salts of the Li-2(+) cation with F-. A linear isomer with an arrangement of atoms such as Li-Li-F and a bent C-2v structure are predicted. The stability of these structures are discussed in terms of charge resonance between Li and Li+. (C) 1999 Elsevier Science B.V. All rights reserved.

Weakly non-linear stability of a hydrodynamic accretion disc

When the cold accretion disc coupling between neutral gas and a magnetic field is so weak that the magnetorotational instability is less effective or even stops working, it is of prime interest to investigate the pure hydrodynamic origin of turbulence and transport phenomena. As the Reynolds number increases, the relative importance of the non-linear term in the hydrodynamic equation increases. In an accretion disc where the molecular viscosity is too small, the Reynolds number is large enough for the non-linear term to have new effects. We investigate the scenario of the `weakly non-linear' evolution of the amplitude of the linear mode when the flow is bounded by two parallel walls. The unperturbed flow is similar to the plane Couette flow, but with the Coriolis force included in the hydrodynamic equation. Although there is no exponentially growing eigenmode, because of the self-interaction, the least stable eigenmode will grow in an intermediate phase. Later, this will lead to higher-order non-linearity and plausible turbulence. Although the non-linear term in the hydrodynamic equation is energy-conserving, within the weakly non-linear analysis it is possible to define a lower bound of the energy (alpha A(c)(2), where A(c) is the threshold amplitude) needed for the flow to transform to the turbulent phase. Such an unstable phase is possible only if the Reynolds number >= 10(3-4). The numerical difficulties in obtaining such a large Reynolds number might be the reason for the negative result of numerical simulations on a pure hydrodynamic Keplerian accretion disc.

Stability of fluid flow past a membrane

The stability of fluid flow past a membrane of infinitesimal thickness is analysed in the limit of zero Reynolds number using linear and weakly nonlinear analyses. The system consists of two Newtonian fluids of thickness R* and H R*, separated by an infinitesimally thick membrane, which is flat in the unperturbed state. The dynamics of the membrane is described by its normal displacement from the flat state, as well as a surface displacement field which provides the displacement of material points from their steady-state positions due to the tangential stress exerted by the fluid flow. The surface stress in the membrane (force per unit length) contains an elastic component proportional to the strain along the surface of the membrane, and a viscous component proportional to the strain rate. The linear analysis reveals that the fluctuations become unstable in the long-wave (alpha --> 0) limit when the non-dimensional strain rate in the fluid exceeds a critical value Lambda(t), and this critical value increases proportional to alpha(2) in this limit. Here, alpha is the dimensionless wavenumber of the perturbations scaled by the inverse of the fluid thickness R*(-1), and the dimensionless strain rate is given by Lambda(t) = ((gamma) over dot* R*eta*/Gamma*), where eta* is the fluid viscosity, Gamma* is the tension of the membrane and (gamma) over dot* is the strain rate in the fluid. The weakly nonlinear stability analysis shows that perturbations are supercritically stable in the alpha --> 0 limit.

Reliability Based Design Optimization for Internal Stability of Reinforced Soil Structures Using Pseudo‐Static Method

Seismic design of reinforced soil structures involves many uncertainties that arise from the backfill soil properties and tensile strength of the reinforcement which is not addressed in current design guidelines. This paper highlights the significance of variability in the internal stability assessment of reinforced soil structures. Reliability analysis is applied to estimate probability of failure and pseudo‐static approach has been used for the calculation of the tensile strength and length of the reinforcement needed to maintain the internal stability against tension and pullout failures. Logarithmic spiral failure surface has been considered in conjunction with the limit equilibrium method. Two modes of failure namely, tension failure and pullout failure have been considered. The influence of variations of the backfill soil friction angle, the tensile strength of reinforcement, horizontal seismic acceleration on the reliability index against tension failure and pullout failure of reinforced earth structure have been discussed.

Stability of the flow of a fluid through a flexible tube at high Reynolds number

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (ρVR / η), the ratio of the viscosities of the wall and fluid ηr = (ηs/η), the ratio of radii H and the dimensionless velocity Γ = (ρV2/G)1/2. Here ρ is the density of the fluid, G is the coefficient of elasticity of the wall and Vis the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter ε = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate do), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctruations due to the Reynolds strees. There is an O(ε1/2) correction to the growth rate, s(1), due to the presence of a wall layer of thickness ε1/2R where the viscous stresses are O(ε1/2) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Γ and wavenumber k where s(l) = 0. At these points, the wail layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(ε) correction to the growth rate s(2) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s(2) increases [is proportional to] (H − 1)−2 for (H − 1) [double less-than sign] 1 (thickness of wall much less than the tube radius), and decreases [is proportional to] (H−4 for H [dbl greater-than sign] 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube.

Steady-State Stability of Current-Mode Active-Clamp ZVS DC-DC Converters

Active-clamp dc-dc converters are pulsewidth-modulated converters having two switches featuring zero-voltage switching at frequencies beyond 100 kHz. Generalized equivalent circuits valid for steady-state and dynamic performance have been proposed for the family of active-clamp converters. The active-clamp converter is analyzed for its dynamic behavior under current control in this paper. The steady-state stability analysis is presented. On account of the lossless damping inherent in the active-clamp converters, it appears that the stability region in the current-controlled active-clamp converters get extended for duty ratios, a little greater than 0.5 unlike in conventional hard-switched converters. The conventional graphical approach fails to assess the stability of current-controlled active-clamp converters, due to the coupling between the filter inductor current and resonant inductor current. An analysis that takes into account the presence of the resonant elements is presented to establish the condition for stability. This method correctly predicts the stability of the current-controlled active-clamp converters. A simple expression for the maximum duty cycle for subharmonic-free operation is obtained. The results are verified experimentally.

Stability of domain structures in multi-domain proteins

Multi-domain proteins have many advantages with respect to stability and folding inside cells. Here we attempt to understand the intricate relationship between the domain-domain interactions and the stability of domains in isolation. We provide quantitative treatment and proof for prevailing intuitive ideas on the strategies employed by nature to stabilize otherwise unstable domains. We find that domains incapable of independent stability are stabilized by favourable interactions with tethered domains in the multi-domain context. Stability of such folds to exist independently is optimized by evolution. Specific residue mutations in the sites equivalent to inter-domain interface enhance the overall solvation, thereby stabilizing these domain folds independently. A few naturally occurring variants at these sites alter communication between domains and affect stability leading to disease manifestation. Our analysis provides safe guidelines for mutagenesis which have attractive applications in obtaining stable fragments and domain constructs essential for structural studies by crystallography and NMR.