共查询到20条相似文献,搜索用时 312 毫秒
1.
Leonid Brevdo 《European Journal of Mechanics - A/Solids》1998,17(6):979-999
The initial boundary-value linear stability problem for small localised axisymmetric disturbances in a homogeneous elastic wave guide, with the free upper surface and the lower surface being rigidly attached to a half-space, is formally solved by applying the Laplace transform in time and the Hankel transforms of zero and first orders in space. An asymptotic evaluation of the solution, expressed as a sum of inverse Laplace-Hankel integrals, is carried out by using the approach of the mathematical formalism of absolute and convective instabilities. It is shown that the dispersion-relation function of the problem D0 (κ, ω), where the Hankel parameter κ is substituted by a wave number (and the Fourier parameter) κ, coincides with the dispersion-relation function D0 (k, ω) for two-dimensional (2-D) disturbances in a homogeneous wave guide, where ω is the frequency (and the Laplace parameter) in both cases. An analysis for localised 2-D disturbances in a homogeneous wave guide is then applied. We obtain asymptotic expressions for wave packets, triggered by axisymmetric perturbations localised in space and finite in time, as well as for responses to axisymmetric sources localised in space, with the time dependence satisfying e−iω0t + O(e−εt) for t → ∞, where Im ω0 = 0, ε > 0, and t denotes time, i.e. for signalling with frequency ω0. We demonstrate that, for certain combinations of physical parameters, axisymmetric wave packets with an algebraic temporal decay and axisymmetric signalling with an algebraic temporal growth, as √t, i.e., axisymmetric temporal resonances, are present in a neutrally stable homogeneous wave guide. The set of physically relevant wave guides having axisymmetric resonances is shown to be fairly wide. Furthermore, since an axisymmetric part of any source is L2-orthogonal to its non-axisymmetric part, a 3-D signalling with a non-vanishing axisymmetric component at an axisymmetric resonant frequency will generally grow algebraically in time. These results support our hypothesis concerning a possible resonant triggering mechanism of certain earthquakes, see Brevdo, 1998, J. Elasticity, 49, 201–237. 相似文献
2.
Thomas G. Mason 《Rheologica Acta》2000,39(4):371-378
We obtain the linear viscoelastic shear moduli of complex fluids from the time-dependent mean square displacement, <Δr
2(t)>, of thermally-driven colloidal spheres suspended in the fluid using a generalized Stokes–Einstein (GSE) equation. Different
representations of the GSE equation can be used to obtain the viscoelastic spectrum, G˜(s), in the Laplace frequency domain, the complex shear modulus, G
*(ω), in the Fourier frequency domain, and the stress relaxation modulus, G
r
(t), in the time domain. Because trapezoid integration (s domain) or the Fast Fourier Transform (ω domain) of <Δr
2(t)> known only over a finite temporal interval can lead to errors which result in unphysical behavior of the moduli near the
frequency extremes, we estimate the transforms algebraically by describing <Δr
2(t)> as a local power law. If the logarithmic slope of <Δr
2(t)> can be accurately determined, these estimates generally perform well at the frequency extremes.
Received: 8 September 2000/Accepted: 9 March 2000 相似文献
3.
Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders 总被引:1,自引:0,他引:1
The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 + , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions. 相似文献
4.
The Laplace transform method (LTM) is introduced to solve Burgers' equation. Because of the nonlinear term in Burgers' equation, one cannot directly apply the LTM. Increment linearization technique is introduced to deal with the situation. This is a key idea in this paper. The increment linearization technique is the following: In time level t, we divide the solution u(x, t) into two parts: u(x, tk) and w(x, t), tk⩽t⩽tk+1, and obtain a time‐dependent linear partial differential equation (PDE) for w(x, t). For this PDE, the LTM is applied to eliminate time dependency. The subsequent boundary value problem is solved by rational collocation method on transformed Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that the present method is effective and competitive. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
5.
This paper presents the electromagnetic wave propagation characteristics in plasma and the attenuation coefficients of the microwave in terms of the parameters he, v, w, L, wb. The φ800 mm high temperature shock tube has been used to produce a uniform plasma. In order to get the attenuation of the electromagnetic wave through the plasma behind a shock wave, the microwave transmission has been used to measure the relative change of the wave power. The working frequency is f = (2-35)GHz (ω=2πf, wave length A =15cm-8mm). The electron density in the plasma is ne = (3×10^10-1×10^14) cm^-3. The collision frequency v = (1×10^8-6×10^10) Hz. The thickness of the plasma layer L = (2-80)cm. The electron circular frequency ωb=eBo/me, magnetic flux density B0 = (0-0.84)T. The experimental results show that when the plasma layer is thick (such as L/λ≥10), the correlation between the attenuation coefficients of the electromagnetic waves and the parameters ne,v,ω, L determined from the measurements are in good agreement with the theoretical predictions of electromagnetic wave propagations in the uniform infinite plasma. When the plasma layer is thin (such as when both L and A are of the same order), the theoretical results are only in a qualitative agreement with the experimental observations in the present parameter range, but the formula of the electromagnetic wave propagation theory in an uniform infinite plasma can not be used for quantitative computations of the correlation between the attenuation coefficients and the parameters ne,v,ω, L. In fact, if ω<ωp, v^2<<ω^2, the power attenuations K of the electromagnetic waves obtained from the measurements in the thin-layer plasma are much smaller than those of the theoretical predictions. On the other hand, if ω>ωp, v^2<<ω^2 (just v≈f), the measurements are much larger than the theoretical results. Also, we have measured the electromagnetic wave power attenuation value under the magnetic field and without a magnetic field. The result indicates that the value measured under the magnetic field shows a distinct improvement. 相似文献
6.
Elliptical flow is common in the near vertical fracture area and in anisotropic reservoirs. However, the classical radial
flow models cannot provide a complete analysis for elliptical flow. This article presents a new mathematic model for gas elliptical
flow in tri-porosity gas reservoirs. The differential equation of the new model is written in Mathieu equation, so that the
solution can also be expressed by Mathieu functions. The numerical solution of the corresponding Mathieu functions ce
2n
(ξ, −q), Ke
2n
(ξ, −q) and their derivatives are obtained to derive the dimensionless pseudo pressure drop in Laplace space. The sensitivities
of tri-porosity systems, including the parameters related to anisotropies C
De2S
and ξ
w, the storativity ratios ω
f and ω
m, and the interporosity flow coefficients λvf and λmf, are studied using Laplace numerical inversion. The new solution includes not only the factors considered in classic solutions
in previous articles, but also incorporates the effect of reservoir anisotropy. 相似文献
7.
B. Budiansky 《Wave Motion》1979,1(3):187-191
By use of a steady state (e−iωt) dynamic elastic representation theorem for fields created by relative motions ΔUk on the faces of a crack, we reduce the problem of steady state response of an isolated three-dimensional planar crack, loaded by tractions on its surfaces, to an integral equation for ΔUk. 相似文献
8.
A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent
moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) 01(t)=0
exp(−λt), (ii) 02(t) =0(t/t
*)exp(−λt), and 03(t)=0[1+a
cos(ωt)], where λ and ω are real parameters and t
* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized
representation of an incomplete gamma function Γ(α,x;b) and its decomposition C
Γ and S
Γ. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present
analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations.
Received on 13 June 1997 相似文献
9.
Oscillatory MHD Couette flow of electrically conducting fluid between two parallel plates in a rotating system in the presence
of an inclined magnetic field is considered when the upper plate is held at rest and the lower plate oscillates non-torsionally
. An exact solution of the governing equations has been obtained by using Laplace transform technique. Asymptotic behavior
of the solution is analyzed for M
2
≪1, K
2
≪1 and ω
≪1 and for large M
2, K
2 and ω. Numerical results of velocities are depicted graphically and the frictional shearing stresses are presented in tables. It
is found that a thin boundary layer is formed near the lower plate, for large values of rotation parameter K
2, Hartman number M
2 and frequency parameter ω. The thickness of this boundary layer increases with increase in inclination of the magnetic field with the axis of rotation. 相似文献
10.
Martin Fuchs 《Journal of Mathematical Fluid Mechanics》2012,14(1):43-54
We investigate the steady flow of a shear thickening generalized Newtonian fluid under homogeneous boundary conditions on
a domain in
\mathbbR2{\mathbb{R}^{2}}. We assume that the stress tensor is generated by a potential of the form H = h (|e(u)|){H = h (|\varepsilon (u)|)}, e(u){\varepsilon (u)} denoting the symmetric part of the velocity gradient. We prove the existence of strong solutions for a large class of functions
h having the property that h′ (t)/t increases (shear thickening case). 相似文献
11.
Relaxation patterns of long,linear, flexible,monodisperse polymers: BSW spectrum revisited 总被引:1,自引:1,他引:0
Theoretical predictions for the dynamic moduli of long, linear, flexible, monodisperse polymers are summarized and compared
with experimental observations. Surprisingly, the predicted 1/2 power scaling of the long-time modes of the relaxation spectrum
is not found in the experiments. Instead, scaling with a power of about 1/4 extends all the way up to the longest relaxation
times near τ/τ
max = 1. This is expressed in the empirical relaxation time spectrum of Baumgaertel-Schausberger-Winter, denoted as “BSW spectrum,”
and justifies a closer look at the properties of the BSW spectrum. Working with the BSW spectrum, however, is made difficult
by the fact that hypergeometric functions occur naturally in BSW-based rheological material functions. BSW provides no explicit
solutions for the dynamic moduli, G
′(ω), G
″(ω), or the relaxation modulus G(t). To overcome this problem, close approximations of simple analytical form are shown for these moduli. With these approximations,
analysis of linear viscoelastic data allows the direct determination of BSW parameters. 相似文献
12.
A. Salhi 《Theoretical and Computational Fluid Dynamics》2002,15(6):339-358
Linear theory is applied to examine rotation and buoyancy effects on homogeneous turbulent shear flows with given vertical
velocity shear, S=d/dx
3. In the rotating shear case (where the rotation vector is perpendicular to the plane of the mean flow, Ω
i
=Ωδ
i
2), general solutions for the Fourier components of the fluctuating velocity are proposed. These solutions are compared with
those proposed in the literature for the Fourier components of the fluctuating velocity and density in the case of a homogeneous
stratified shear flow with vertical density gradient, S
ρ=d/dx
3. It is shown that from the normal mode stability stand point the Bradshaw parameter B=2Ω/S(1+2Ω/S) (in the rotating shear case) and the Richardson number R
i
(in the statified shear case) play similar roles in identifying the stability for all the wave components except in the case
where Ω·k=0, for which rotation has no effects on the flow.
Analysis of the long-time behavior of the non-dimensional spectral density of energy, e
g
, is carried out. In the stable case, e
g
has decaying oscillations or undergoes a power law decay in time. Analytical solutions for the streamwise two-dimensional
energy ℰ
ii
1/2 (i.e. the limit at k
1=0 of the one-dimensional energy spectra) are proposed. At large time, ℰ
ii
1(t)/ℰ
ii
1(0) oscillates around the value (3R
i
+1)/(4R
i
) except at R
i
=1 it stays constant in time. Similar behavior for ℰ
ii
1(t)/ℰ
ii
1(0) is also observed in the rotating shear case (ℰ
ii
1(t)/ℰ
ii
1(0) oscillates around the value (1+4B)/(4B)).
Due to the behavior of the dimensionless spectral density of energy in both flow cases, the turbulent kinetic energy, /2, the production rate, ?, and the rate due to the buoyancy forces, ℬ, are split into two parts, , ?=?1+?2, ℬ=ℬ1+ℬ2 (in the stratified shear case, both ?1 and ℬ1 vanish when R
i
>?, while in the rotating shear case one has ℬ=0). It is shown that when rotation is “cyclonic” (i.e. Ω/S>0), part reaches maximum magnitudes at St
≈2, independent of the B value, and the first time to a zero crossing of ?2 occurs at this particular value. When rotation is “anticyclonic” (i.e. Ω/S<0) one finds St
≈1.6 instead of St
≈2. In the stratified shear case, both ?2 and ℬ2 cross zero at Nt=St
≈2, and part reaches maximum magnitudes at this particular value. These results and in particular those for the turbulent kinetic energy
are compared with previous direct numerical simulation (DNS) results in homogeneous stratified shear flows.
Received 30 July 2001 and accepted 19 February 2002 相似文献
13.
This paper investigates the conversion of a dispersive longitudinal oscillation into reflected and transmitted electromagnetic radiation fields in slowly varying unmagnetized warm fluid plasmas, using W.K.B. approximations. The expressions for the power of the transmitted and reflected electromagnetic radiations, generated by electron acoustic waves, have also been obtained. It is shown that this conversion process becomes most efficient under certain conditions.
Nomenclature
In § 2 H magnetic field - H 1 - u electron fluid velocity - k t wave number of the transverse wave - k 1 wave number of the longitudinal wave in electron fluid - m electronic mass - N 0 number density of electrons in the unperturbed state - N perturbation in the electron number density - p perturbation in the electron fluid pressure - v e adiabatic sound velocity of the electron fluid - K t 2 c 2 2–e2 - K 1 2 v e 2 2–e2 - wave frequency - e electron plasma frequency - 1– e 2 / 2 - c velocity of light in vacuum In § 3 K 0 wave number in the 0X direction - K 1 2 K 1 2 –K 0 2 - K 2 2 K t 2 –K 0 2 - K 3 K 1–K 2 - K 4 K 1+K 2 - K 5 (K 1 K 2)1/2 See Appendix A - A 1 pressure amplitude of the reflected part of the incident wave - B 1 pressure amplitude of the transmitted part of the incident wave - L characteristic length of variation ofN 0 - e x unit vector along 0X - e z unit vector along 0Z In § 4 S t Poynting flux of the transverse electromagnetic radiation - S tZ /t Average of the transmitted part of the poynting flux along 0Z over the time period 2/ - S tZ /r Average of the reflected part of the poynting flux along 0Z over the time period 2/ In § 5 S 1 Energy flux carried by the longitudinal pressure wave - S 1Z /t Average of the transmitted part ofS 1 along 0Z over the time period 2/ 相似文献14.
Chien-Cheng Chang Jeng-Yu Su Sheng-Yuan Lei 《Theoretical and Computational Fluid Dynamics》1998,10(1-4):71-90
The paper is aimed at reviewing and adding some new results to our recent work on a force theory for viscous compressible
flows around a finite body. It has been proposed to analyze aerodynamic forces directly in terms of fluid elements of nonzero
vorticity and density gradient. Let ρ denote the density, u the velocity, and ω the vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two
major source elements:
R
e(x) =−?u
2∇ρ·∇ϕ and V
e(x) =−u×ω·∇ϕ,
where ϕ is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force
considered. In particular, under mild conditions, the (unique) choice of ϕ enforces that the elements R
e(x) and V
e(x) decay rapidly away from the body. Four kinds of finite body are considered: a circular cylinder, a sphere, a hemi sphere-cylinder,
and a delta wing of elliptic section—all in transonic-to-supersonic regimes. From an extensive numerical study carried out
for these bodies, it is found that these two elements contribute to 95% or more of the total drag or lift for all the cases
under consideration. Moreover, R
e(x) due to density gradient becomes progressively important relative to V
e(x) due to vorticity as the Mach number increases. The present method of force analysis enables effective analysis and assessment
of relative importance of aerodynamics forces, contributed from individual flow structures. The analysis could therefore be
very much useful in view of the rapid growth in numerical fluid dynamics; detailed (either local or global) flow information
is often available. The paper is dedicated to Sir James Lighthill in honor of his great contributions to aeronautics on the
occasion of the publication of his collected works.
Received 3 January 1997 and accepted 11 April 1997 相似文献
15.
The stability problem for the Hill equation containing two parameters is analyzed using the Mathematica computer algebra system. The characteristic constant is found as a series expansion in powers of a small parameter e. It is shown that the domains of instability are located only between the curves a = a(e) on the a-e plane crossing the axis e = 0 at the points a = (2k – 1)2 / 4, k = 1, 2, 3, ....The corresponding curves are found as power series in e with accuracy O(e
6). 相似文献
16.
Hermano Frid 《Archive for Rational Mechanics and Analysis》2006,181(1):177-199
We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems
of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems
whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which
are hyperplanes. In particular, we obtain the uniqueness of the self-similar L∞ entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is
in the sense of the convergence as t→∞ in Lloc1 of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, tξ)→R(ξ) as t→∞, in Lloc1(ℝn), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem. 相似文献
17.
V. F. Shumsky I. Getmanchuk T. Ignatova Yu. Maslak P. Cassagnau G. Boiteux F. Melis 《Rheologica Acta》2010,49(8):827-836
The viscoelastic characteristics of the blends of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) (PMMA/SAN) were investigated at various temperatures below, near, and above the phase separation temperature.
The investigated polymer system is characterized by a lower critical solution temperature. Rheological behavior of the blends
in the region of a phase separation was compared with change of the light scattering intensity. The presence of nanofillers
in the blend results in that the phase separation occurs at a higher temperature. At the isothermal conditions, the phase
separation begins earlier and proceeds with a higher rate as compared with the same blend without filler. The results of the
study show the considerable change of the viscoelastic characteristics of PMMA/SAN when the polymer system passes from the
homogeneous state to the heterogeneous one. Such characteristics as the dependence of the storage modulus (G
′) on the loss modulus (G
″), the dependence of the loss viscosity (η
″) on the dynamic viscosity (η
′), the dependences of the complex viscosity (η*), and the free volume fraction (f) on the blend composition are the most sensitive to the phase separation. The phase separation affects the characteristics
G
′(ω), where ω is the frequency only in a low-frequency range. Temperatures of phase separation were estimated using dependence G
′(T) at ω, which is the constant in the range of low frequencies. 相似文献
18.
Claude-Michel Brauner Alessandra Lunardi 《Archive for Rational Mechanics and Analysis》2000,154(2):157-182
We prove instability of the planar travelling wave solution in a two-dimensional free boundary problem modelling the propagation
of near- equidiffusional premixed flames in the whole plane. We reduce the problem to a fixed boundary fully nonlinear parabolic
system. The spectrum of the linearized operator contains an interval [0,ω
c
], ω
c
> 0, so we cannot construct backward solutions. We use an argument about stability of dynamical systems in Banach spaces
in order to prove pointwise instability of the moving front.
(Accepted: January 31, 2000)?Published online August 21, 2000 相似文献
19.
Hyung Ju Hwang Alan D. Rendall Juan J. L. Velázquez 《Archive for Rational Mechanics and Analysis》2011,200(1):313-360
The Vlasov–Poisson system describes interacting systems of collisionless particles. For solutions with small initial data
in three dimensions it is known that the spatial density of particles decays as t
−3 at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to
an extra power of decay, so that in N dimensions for
N \geqq 3{N \geqq 3} the derivative of the density of order k decays as t
−N-k
. An asymptotic formula for the solution at late times is also obtained. 相似文献
20.
Lagrangian time-scales in homogeneous non-Gaussian turbulence were studied using a one-dimensional Lagrangian Stochastic Model.
The existence of two time-scales τ
L
and T
L
, one typical of the inertial subrange and the other which is an integral property, is outlined. Variations of the ratio T
L
/τ
L
in the plane skewness-flatness (S, F) are shown and a connection with the statistical constraint F ≥S
2 + 1 is evidenced.
The Lagrangian autocorrelation function ρ(t) of particle velocity was computed for some values of (S, F). It is shown that for small times, say t < T
L
, the influence of non-Gaussianity is negligible and ρ(t) presents the same behaviour as in the Gaussian case regardless of variations in (S, F).As the time increases, departures from Gaussianity are observed and autocorrelation turns out to be always larger than in
the Gaussiancase. This is supported by some considerations in terms of information entropy, which is shown to decrease with
increasing departures from Gaussianity.
Spectral analysis of Lagrangian velocity shows that non-Gaussianity is relevant only to large scales of the stochastic process
and that the expected inertial subrange decay ω−2 is attained by spectra of all simulations, except for one case in which the model probability density function is bimodal,
due to the vicinity to the statistical limit.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献