Stability analysis of stochastically parametered nonconservative columns

Nonconservatively loaded columns. which have stochastically distributed material property values and stochastic loadings in space are considered. Young's modulus and mass density are treated to constitute random fields. The support stiffness coefficient and tip follower load are considered to be random variables. The fluctuations of external and distributed loadings are considered to constitute a random field. The variational formulation is adopted to get the differential equation and boundary conditions. The non self-adjoint operators are used at the boundary of the regularity domain. The statistics of vibration frequencies and modes are obtained using the standard perturbation method, by treating the fluctuations to be stochastic perturbations. Linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed. Bounds for the statistics of vibration frequencies are obtained. The critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought. Then, the frequency equation is employed to transform the eigenvalue statistics to critical load statistics. Specialization of the general procedure to Beck, Leipholz and Pfluger columns is carried out. For Pfluger column, nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics.

Stability of stochastic Leipholz column with stochastic loading

The Leipholz column which is having the Young modulus and mass per unit length as stochastic processes and also the distributed tangential follower load behaving stochastically is considered. The non self-adjoint differential equation and boundary conditions are considered to have random field coefficients. The standard perturbation method is employed. The non self-adjoint operators are used within the regularity domain. Full covariance structure of the free vibration eigenvalues and critical loads is derived in terms of second order properties of input random fields characterizing the system parameter fluctuations. The mean value of critical load is calculated using the averaged problem and the corresponding eigenvalue statistics are sought. Through the frequency equation a transformation is done to yield load parameter statistics. A numerical study incorporating commonly observed correlation models is reported which illustrates the full potentials of the derived expressions.

Tunable Brownian vortex at the interface

A general kind of Brownian vortices is demonstrated by applying an external nonconservative force field to a colloidal particle bound by a conservative optical trapping force at a liquid-air interface. As the liquid medium is translated at a constant velocity with the bead trapped at the interface, the drag force near the surface provides enough rotational component to bias the particle's thermal fluctuations in a circulatory motion. The interplay between the thermal fluctuations and the advection of the bead in constituting the vortex motions is studied, and we infer that the angular velocity of the circulatory motion offers a comparative measure of the interface fluctuations.

Persistent currents in a one-dimensional ring for a disordered Hubbard model

We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.

Simulation of ENSO-Related Surface Winds in the Tropical Pacific by an Atmospheric General Circulation Model Forced by Observed Sea Surface Temperatures

The authors present the simulation of the tropical Pacific surface wind variability by a low-resolution (R15 horizontal resolution and 18 vertical levels) version of the Center for Ocean-Land-Atmosphere Interactions, Maryland, general circulation model (GCM) when forced by observed global sea surface temperature. The authors have examined the monthly mean surface winds acid precipitation simulated by the model that was integrated from January 1979 to March 1992. Analyses of the climatological annual cycle and interannual variability over the Pacific are presented. The annual means of the simulated zonal and meridional winds agree well with observations. The only appreciable difference is in the region of strong trade winds where the simulated zonal winds are about 15%-20% weaker than observed, The amplitude of the annual harmonics are weaker than observed over the intertropical convergence zone and the South Pacific convergence zone regions. The amplitudes of the interannual variation of the simulated zonal and meridional winds are close to those of the observed variation. The first few dominant empirical orthogonal functions (EOF) of the simulated, as well as the observed, monthly mean winds are found to contain a targe amount of high-frequency intraseasonal variations, While the statistical properties of the high-frequency modes, such as their amplitude and geographical locations, agree with observations, their detailed time evolution does not. When the data are subjected to a 5-month running-mean filter, the first two dominant EOFs of the simulated winds representing the low-frequency EI Nino-Southern Oscillation fluctuations compare quite well with observations. However, the location of the center of the westerly anomalies associated with the warm episodes is simulated about 15 degrees west of the observed locations. The model simulates well the progress of the westerly anomalies toward the eastern Pacific during the evolution of a warm event. The simulated equatorial wind anomalies are comparable in magnitude to the observed anomalies. An intercomparison of the simulation of the interannual variability by a few other GCMs with comparable resolution is also presented. The success in simulation of the large-scale low-frequency part of the tropical surface winds by the atmospheric GCM seems to be related to the model's ability to simulate the large-scale low-frequency part of the precipitation. Good correspondence between the simulated precipitation and the highly reflective cloud anomalies is seen in the first two EOFs of the 5-month running means. Moreover, the strong correlation found between the simulated precipitation and the simulated winds in the first two principal components indicates the primary role of model precipitation in driving the surface winds. The surface winds simulated by a linear model forced by the GCM-simulated precipitation show good resemblance to the GCM-simulated winds in the equatorial region. This result supports the recent findings that the large-scale part of the tropical surface winds is primarily linear.

Stability of the viscous flow of a fluid through a flexible tube

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 = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (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 s((0)), 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 fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) 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 Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) 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 proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 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

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Variability of sif and cod of stochastic structural systems

Stochastic structural systems having a stochastic distribution of material properties and stochastic external loadings in space are analysed when a crack of deterministic size is present. The material properties and external loadings are considered to constitute independent, two-dimensional, univariate, real, homogeneous stochastic fields. The stochastic fields are characterized by their means, variances, autocorrelation functions or the equivalent power spectral density functions, and scale fluctuations. The Young's modulus and Poisson's ratio are treated to be stochastic quantities. The external loading is treated to be a stochastic field in space. The energy release rate is derived using the method of virtual crack extension. The deterministic relationship is derived to represent the sensitivities of energy release rate with respect to both virtual crack extension and real system parameter fluctuations. Taylor series expansion is used and truncation is made to the first order. This leads to the determination of second-order properties of the output quantities to the first order. Using the linear perturbations about the mean values of the output quantities, the statistical information about the energy release rates, SIF and crack opening displacements are obtained. Both plane stress and plane strain cases are considered. The general expressions for the SIF in all the three fracture modes are derived and a more detailed analysis is conducted for a mode I situation. A numerical example is given.

Vortex sheet simulation of a plane �canonical� mixing layer

Discrete vortex simulations of the mixing layer carried out in the past have usually involved large induced velocity fluctuations, and thus demanded rather long time-averaging to obtain satisfactory values of Reynolds stresses and third-order moments. This difficulty has been traced here, in part, to the use of discrete vortices to model what in actuality are continuous vortex sheets. We propose here a novel two-dimensional vortex sheet technique for computing mixing layer flow in the limit of infinite Reynolds number. The method divides the vortex sheet into constant-strength linear elements, whose motions are computed using the Biot-Savart law. The downstream far-field is modelled by a steady vorticity distribution derived by application of conical similarity from the solution obtained in a finite computational domain. The boundary condition on the splitter plate is satisfied rigorously using a doublet sheet. The computed large-scale roll-up of the vortex sheet is qualitatively similar to experimentally obtained shadow-graphs of the plane turbulent mixing layer. The mean streamwise velocity profile and the growth rate agree well with experimental data. The presently computed Reynolds stresses and third-order moments are comparable with experimental and previous vortex-dynamical results, without using any external parameter (such as the vortex core-size) of the kind often used in the latter. The computed autocorrelations are qualitatively similar to experimental results along the top and bottom edges of the mixing layer, and show a well-defined periodicity along the centreline. The accuracy of the present computation is independently established by demonstrating negligibly small changes in the five invariants (including the Hamiltonian) in vortex dynamics.

Interannual variations of Indian summer monsoon in a GCM: External conditions versus internal feedbacks

The potential predictability of the Indian summer monsoon due to slowly varying sea surface temperature (SST) forcing is examined. Factors responsible for limiting the predictability are also investigated. Three multiyear simulations with the R30 version of the Geophysical Fluid Dynamics Laboratory's climate model are carried out for this purpose, The mean monsoon simulated by this model is realistic including the mean summer precipitation over the Indian continent. The interannual variability of the large-scale component of the monsoon such as the "monsoon shear index" and its teleconnection with Pacific SST is well simulated by the model in a 15-yr integration with observed SST as boundary condition. On regional scales, the skill in simulating the interannual variability of precipitation over the Indian continent by the model is rather modest and its simultaneous correlation with eastern Pacific SST is negative but poor as observed. The poor predictability of precipitation over the Indian region in the model is related to the fact that contribution to the interannual variability over this region due to slow SST variations [El Nino-Southern Oscillation (ENSO) related] is comparable to those due to regional-scale fluctuations unrelated to ENSO SST. The physical mechanism through which ENSO SST tend to produce reduction in precipitation over the Indian continent is also elucidated. A measure of internal variability of the model summer monsoon is obtained from a 20-yr integration of the same model with fixed annual cycle SST as boundary conditions but with predicted soil moisture and snow cover. A comparison of summer monsoon indexes between this run and the observed SST run shows that the internal oscillations can account for a large fraction of the simulated monsoon variability. The regional-scale oscillations in the observed SST run seems to arise from these internal oscillations. It is discovered that most of the interannual internal variability is due to an internal quasi-biennial oscillation (QBO) of the model atmosphere. Such a QBO is also found in the author's third 18-yr simulation in which fixed annual cycle of SST as well as soil moisture and snow cover are prescribed. This shows that the model QBO is not due to land-surface-atmosphere interaction. It is proposed that the model QBO arises due to an interaction between nonlinear intraseasonal oscillations and the annual cycle. Spatial structure of the QBO and its role in limiting the predictability of the Indian summer monsoon is discussed.

Vibration and Stability of Fluid Conveying Pipes with Stochastic Parameters

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is-first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

Lopsidedness in WHISP galaxies II. Morphological lopsidedness

The distribution of stars and gas in many galaxies is asymmetric. This so-called lopsidedness is expected to significantly affect the dynamics and evolution of the disc, including the star formation activity. Here, we measure the degree of lopsidedness for the gas distribution in a selected sample of 70 galaxies from the Westerbork Hi Survey of Spiral and Irregular Galaxies. This complements our earlier work (Paper I) where the kinematic lopsidedness was derived for the same galaxies. The morphological lopsidedness is measured by performing a harmonic decomposition of the surface density maps. The amplitude of lopsidedness A(1), the fractional value of the first Fourier component, is typically quite high (about 0.1) within the optical disc and has a constant phase. Thus, lopsidedness is a common feature in galaxies and indicates a global mode. We measure A(1) out to typically one to four optical radii, sometimes even further. This is, on average, four times larger than the distance to which lopsidedness was measured in the past using near-IR as a tracer of the old stellar component, and therefore provides a new, more stringent constraint on the mechanism for the origin of lopsidedness. Interestingly, the value of A(1) saturates beyond the optical radius. Furthermore, the plot of A(1) versus radius shows fluctuations that we argue are due to local spiral features. We also try to explain the physical origin of this observed disc lopsidedness. No clear trend is found when the degree of lopsidedness is compared to a measure of the isolation or interaction probability of the sample galaxies. However, this does not rule out a tidal origin if the lopsidedness is long-lived. In addition, we find that the early-type galaxies tend to be more morphologically lopsided than the late-type galaxies. Both results together indicate that lopsidedness has a tidal origin.

Instability, intermittency, and multiscaling in discrete growth models of kinetic roughening

We show by numerical simulations that discretized versions of commonly studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhangequation and the Lai-Das Sarma-Villain equation) and related atomistic models of epitaxial growth have a generic instability in which isolated pillars (or grooves) on an otherwise flat interface grow in time when their height (or depth) exceeds a critical value. Depending on the details of the model, the instability found in the discretized version may or may not be present in the truly continuum growth equation, indicating that the behavior of discretized nonlinear growth equations may be very different from that of their continuum counterparts. This instability can be controlled either by the introduction of higher-order nonlinear terms with appropriate coefficients or by restricting the growth of pillars (or grooves) by other means. A number of such ''controlled instability'' models are studied by simulation. For appropriate choice of the parameters used for controlling the instability, these models exhibit intermittent behavior, characterized by multiexponent scaling of height fluctuations, over the time interval during which the instability is active. The behavior found in this regime is very similar to the ''turbulent'' behavior observed in recent simulations of several one- and two-dimensional atomistic models of epitaxial growth.

On the large-scale diffuse magnetic field of the sun - II. The contribution of active regions

Dikpati and Choudhuri (1993, 1995) developed a model for the poleward migration of the weak diffuse magnetic field on the Sun's surface. This field was identified with the poloidal component produced by the solar dynamo operating at the base of the convection zone, and its evolution was studied by considering the effects of meridional circulation and turbulent diffusion. The earlier model is extended in this paper by incorporating the flux from, the decay of tilted active regions near the solar surface as an additional source of the poloidal field. This extended model can now explain various low-latitude features in the time-latitude diagram of the weak diffuse fields. These low-latitude features could not be accounted for in the earlier model, which was very successful in modeling the behavior at high latitudes. The time-latitude diagrams show that regions of a particular polarity often have 'tongues' of opposite polarity. Such tongues can be produced in the theoretical model by incorporating fluctuations in the source term arising out of the decaying active regions.

Polymer collapse in supercritical solvents

We show analytically that in dilute solutions of high molecular weight polymers, a collapse transition of the chain can be induced by proximity to the critical point of the solvent. The transition is driven by the fluctuations in the medium, which lead to an effective attractive interaction of long range between different parts of the polymer. At the critical point itself, however, the chain adopts the same average conformations that characterize its size in the off-critical limit. In other words, on approach to the critical point, the polymer is found first to contract and collapse, and then subsequently to return to its original dimensions. This behavior has recently been observed in simulations of polymer-solvent mixtures near the lower critical solution temperature of the system, and it is also known to be characteristic of solutions of polymers in bicomponent solvent mixtures near the critical consolute point of the two solvents. (C) 1999 American Institute of Physics. [S0021-9606(99)50431-5].