An asymptotic analysis for one dimensional stress wave propagation in damaged viscoelastic media

A regular perturbation technique is suggested to deal with the problem of one dimensional stress wave propagation in viscoelastic media with damage. Based upon the first order asymptotic solution obtained, the characteristics of wave attenuation are studied. In fact, there exist three different time-dependent phenomena featuring the dynamic response of the materials, the first expressing the characteristics of wave propagation, the second indicating the innate effect of visco-elastic matrix and the third coming from the time dependent damage. The comparision of first order asymptotic solution with the numerical results calculated by a finite difference procedure shows that the perturbation expansion technique may offer a useful approach to the problem concerned.

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

The motion and the core structure of a geostrophic vortex - one-time scale inner solution and the motion of the vortex

By means of the matched asymptotic expansion method with one-time scale analysis we have shown that the inviscid geostrophic vortex solution represents our leading solution away from the vortex. Near the vortex there is a viscous core structure, with the length scale O(a). In the core the viscous stresses (or turbulent stresses) are important, the variations of the velocity and the equivalent height are finite and dependent of time. It also has been shown that the leading inner solutions of the core structure are the same for two different time scales of S/(ghoo)1/2 and S/a (ghoo)1/2. Within the accuracy of O(a) the velocity of a geostrophic vortex center is equal to the velocity of the local background flow, where the vortex is located, in the absence of the vortex. Some numerical examples demonstrate the contributions of these results.

Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat-plate

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions : the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a seriesexpansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Plane strain problem of growing crack for a perfectly plastic solid

In this paper, fundamental equations of the plane strain problem based on the 3-dimensional plastic flow theory are presented for a perfectly-plastic solid The complete governing equations for the growing crack problem are developed. The formulae for determining the velocity field are derived.The asymptotic equation consists of the premise equation and the zero-order governing equation. It is proved that the Prandtl centered-fan sector satisfies asymptotic equation but does not meet the needs of hlgher-order governing equations.

The asymptotic near-tip solution for mode-iii crack in steady growth in power hardening media

Two local solutions, one perpendicular and one parallel to the direction of solar gravitational field, are discussed. The influence of gravity on the gas-dynamical process driven by the piston is discussed in terms of characteristic theory, and the flow field is given quantitatively. For a typical piston trajectory similar to the one for an eruptive prominence, the velocity of the shock front which locates ahead the transient front is nearly constant or slightly accelerated, and the width of the compressed flow region may be kept nearly constant or increased linearly, depending on the velocity distribution of the piston. Based on these results, the major features of the transient may be explained. Some of the fine structure of the transient is also shown, which may be compared in detail with observations.

Measures of Plant Surface-areas for Eurasian Watermilfoil and Water Stargrass

Plant surface areas were measured from samples of two common submersed aquatics with widely diverging morphologies: Eurasian watermilfoil ( Myriophyllum spicatum L.) and water stargrass ( Heteranthera dubia (Jacq.) MacM.). Measures for the highly dissected leaves of Eurasian watermilfoil involved development of a regression equation relating leaf length to direct measures of a subsample of leaf parts. Measures for the simple leaves of the stargrass were sums of measured triangles. Stem surfaces for both species were calculated as measured cylinders. Though the means of the stem length and leaf length were larger for stargrass samples, their mean surface area was 95 cm 2 which was less than the 108 cm 2 recorded for Eurasian watermilfoil samples. Relating surface area to dry weight for the stargrass was straightforward, with 1 mg of dry weight yielding an average 0.678 cm 2 of surface area. Biomass measures for the water milfoil were confounded by the additional weight of epiphytic algae persisting on cleaned samples. The results suggest that a lesstime consuming method for surface area measures of plants with highly dissected leaves and a caveat for using biomass measures to estimate surface area in such plants.

A Finite Element Analysis of a Crack Penetrating or Deflecting into an Interface in a Thin Laminate

The crack tip driving force of a crack growing from a pre-crack that is perpendicular to and terminating at an interface between two materials is investigated using a linear fracture mechanics theory. The analysis is performed both for a crack penetrating the interface, growing straight ahead, and for a crack deflecting into the interface. The results from finite element calculations are compared with asymptotic solutions for infinitesimally small crack extensions. The solution is found to be accurate even for fairly large amounts of crack growth. Further, by comparing the crack tip driving force of the deflected crack with that of the penetrating crack, it is shown how to control the path of the crack by choosing the adhesion of the interface relative to the material toughness.

Stability of Switched Feedback Time-Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

The stabilization of dynamic switched control systems is focused on and based on an operator-based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L, C) on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input-output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input-output relations in switched feedback control systems so as to guarantee the closed-loop stabilization.

Subdiffusion of nonlinear waves in quasiperiodic potentials

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Growth, mortality, and exploitation of the Engraulidae, with special reference to the anchoveta, Cetengraulis mysticetus, and the colorado, Anchoa naso, in the Eastern Pacific Ocean

ENGLISH: Growth and mortality data for Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ring ens, E. anchoita, E. encraslcbolus, E. japonicus, and E. australis were assembled and compared. Estimates of the coefficients of natural mortality, M, of E. anchoita and Ancboa naso were made from the maximum age of the former and from data for the other species. The relative yields per recruit at different fishing mortality rates and lengths at entry into the fishery were calculated for each species, using what are considered to be the best estimates and other likely values of K, a constant of growth, and M. The maximum yields per recruit are theoretically obtainable at very high fishing mortality rates, except when the length at entry is low relative to the asymptotic length. K and M may be positively related to the temperature and to each other, and if such is the case at higher temperatures greater fishing effort would be needed to attain the maximum yield per recruit. The applicability of the yield-per-recruit approach to the data is discussed, and suggestions for further research are made. SPANISH: Se reunieron y compararon los datos sobre el crecimiento y mortalidad correspondientes a Cetengraulis mysticetus, Anchoa naso, Engraulis mordax, E. ringens, E. anchoíta, E. encrasicbolus, E. japonicus y E. australls. Los estimativos de los coeficientes de la mortalidad natural, M, de E. anchoita y Anchoa naso se obtuvieron según la edad máxima de E. anchoita y según los datos de las otras especies. Se calculó para cada especie el rendimiento relativo por recluta a diferentes tasas de mortalidad por la pesca y a diferentes longitudes de entrada a la pesquería, empleándose lo que se considera que son los mejores estimativos y otros valores probables de K, una constante de crecímíento, y M. El rendimiento máximo por recluta se obtiene teóricamente a tasas muy altas de la mortalidad por la pesca con excepción de cuando la longitud a la entrada es baja en relación a la longitud asintótica. K y M pueden estar relacionadas positivamente a la temperatura y mutuamente, y si este es el caso a temperaturas más altas se necesitará un esfuerzo superior de pesca para obtener el rendimiento máximo por recluta. La aplicabilidad del enfoque a los datos rendimiento-por-recluta es discutido y se hacen sugerencias para otras investigaciones. (PDF contains 66 pages.)

Age and growth of Mugil cephalus (Linnaeus, 1758) (Perciformes: Mugilidae) in Bonny Estuary

The age and growth of Mugil cephalus was investigated in Bonny Estuary, Nigeria, from January, 1995 to December, 1996. Length-weight relationships were isometric with length exponents of 2.84 (males), 2.90 (females) and 2.88 (overall). Modal length at age were 12.0cm, 20.9cm, 25.0cm, 28.4cm and 30.2cm TL for ages 0+, 1+, 2+, 3+ and 4+ respectively. Corresponding total weights were 20.01g, 78.93g, 173.12g, 217.61g and 247.50g, respectively. Asymptotic length (Lo) was estimated 33.2cm TL, asymptotic weight (W sub(o)) was 484g, growth coefficient K=0.55847 super(-1) and hypothetical age at zero length To = 0.152yr. Longevity, Tmax, was 5.0yr, length and weight growth performance indices were Q super(1)=2.79 and Q = 1.44, respectively. Total mortality, natural mortality and fishing mortality were z = 1.02yr super(-1), M=0.607yr super(-1) and F=O. 3129yr super(-1), respectively. The exploitation ratio E was 0.4048 and exploitation rate U = 0.2302yr super(-1)

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.