共查询到20条相似文献,搜索用时 31 毫秒
1.
Leonid Brevdo 《Journal of Elasticity》1997,49(3):201-237
We solve the initial-boundary-value linear stability problem for small localised disturbances in a homogeneous elastic waveguide
formally by applying a combined Laplace – Fourier transform. An asymptotic evaluation of the solution, expressed as an inverse
Laplace – Fourier integral, is carried out by means of the mathematical formalism of absolute and convective instabilities.
Wave packets, triggered by perturbations localised in space and finite in time, as well as responses to sources localised
in space, with the time dependence satisfying e−iωt
+ O(e−ɛt
), for t → ∞, where Im ω0 = 0 and ω > 0 , that is, the signaling problem, are treated. For this purpose, we analyse the dispersion relation of the
problem analytically, and by solving numerically the eigenvalue stability problem. It is shown that due to double roots in
a wavenumber k of the dispersion relation function D(k, ω), for real frequencies ω, that satisfy a collision criterion, wave packets with an algebraic temporal decay and signaling
with an algebraic temporal growth, that is, temporal resonances, are present in a neutrally stable homogeneous waveguide.
Moreover, for any admissible combination of the physical parameters, a homogeneous waveguide possesses a countable set of
temporally resonant frequencies. Consequences of these results for modelling in seismology are discussed.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
This paper describes a numerical simulation of bow shock formation ahead of a sphere at steady supersonic flow in the Mach
number range of 1.025–1.20. Turbulent viscous flow results are presented using the Spalart–Allmaras turbulence model. The
purpose of this study is to determine the shock standoff distance for a spherical projectile at slightly supersonic free flight
speeds. Results are compared to experimental data, including double exposure holographic interferograms obtained from a 40 mm
polycarbonate sphere launched by a light gas gun. The shock standoff distance was determined from the interferograms. The
present numerical simulations were found to agree with previously published data, and reached down to M = 1.025—a range where almost no previously published data exists. The computed flow structure and shock wave locations agree
well with recently obtained free-flight interferograms. 相似文献
3.
Yoshihiro Ueda Tohru Nakamura Shuichi Kawashima 《Archive for Rational Mechanics and Analysis》2010,198(3):735-762
This paper is concerned with the asymptotic stability of degenerate stationary waves for viscous gases in the half space.
We discuss the following two cases: (1) viscous conservation laws and (2) damped wave equations with nonlinear convection.
In each case, we prove that the solution converges to the corresponding degenerate stationary wave at the rate t
−α/4 as t → ∞, provided that the initial perturbation is in the weighted space
L2a=L2(\mathbb R+; (1+x)a dx){L^2_\alpha=L^2({\mathbb R}_+;\,(1+x)^\alpha dx)} . This convergence rate t
−α/4 is weaker than the one for the non-degenerate case and requires the restriction α < α*(q), where α*(q) is the critical value depending only on the degeneracy exponent q. Such a restriction is reasonable because the corresponding linearized operator for viscous conservation laws cannot be dissipative
in L2a{L^2_\alpha} for α > α*(q) with another critical value α*(q). Our stability analysis is based on the space–time weighted energy method in which the spatial weight is chosen as a function
of the degenerate stationary wave. 相似文献
4.
Chitiur Hadinata Claus Gabriel Maximilian Ruellmann Nhol Kao Hans-Martin Laun 《Rheologica Acta》2006,45(5):631-639
A comparison between two quantities concerning quiescent crystallization of polymer melts, namely the quiescent crystallization onset time (t
on,q) and gel time (t
gel), is performed using rheological methods. It was found that t
gel as measured from the evolution of loss angle (tan δ) occurs slightly earlier than t
on,q, defined as the time required for the viscosity to reach twice its steady-state value. The change of viscosity with time was measured with Small Amplitude Oscillatory Shear (SAOS) method. Two alternative methods to measure t
on,q are studied: by continuous shear at a very small shear rate and by creep method. A very good agreement from all the three methods was achieved, indicating the robust nature of this quantity. Finally, the gel times for different PB-1 samples are considered. When the difference in crossover angular frequencies (ω
x
) of the samples is taken into account in performing t
gel experiments, it can be shown that the temperature dependence of t
gel for the samples are the same. However, for samples having high molecular weight t
gel measurements are problematic. In this case, t
on,q serves as an easier tool to compare the crystallization behaviour of different samples. 相似文献
5.
V. K. Kedrinskii P. A. Fomin S. P. Taratuta 《Journal of Applied Mechanics and Technical Physics》1999,40(2):292-299
The influence of inert and chemically reactive additives in the form of microdrops on the dynamics of a single bubble filled
with an active gas mixture and collapsing under the action of a shock wave is considered. The development of a reaction during
formation of the mixture is analyzed for instantaneous and dynamic evaporation of drops with allowance for various phases
of their injection t
inj
. It is shown that in instantaneous evaporation, an increase in the fraction of gaseous argon in the H2+O2 system raises the final temperature of the system under cryogenic conditions, lowers it under ordinary conditions, and causes
appreciable oscillations of the values of γ, heat release, and molecular weight. It is noted that there are values of t
inj
and D0 at which the final temperature of the mixture decreases practically to the initial temperature.
Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 119–127, March–April. 1999. 相似文献
6.
This paper considers the analysis of transient heating of a hemispherical solid plate of finite thickness during impingement
of a free liquid jet. A constant heat flux was imposed at the inner surface of the hemispherical plate at t = 0 and heat transfer was monitored for the entire duration of the transient until a steady state condition was reached.
Calculations were done for Reynolds number (Re) ranging from 500 to 1,500 and dimensionless plate thicknesses to nozzle diameter ratio (b/d
n) from 0.083 to 1.5. Results are presented for local and average Nusselt number using water as the coolant and various solid
materials such as silicon, constantan, and copper. It was detected that increasing the Reynolds number decreases the time
for the plate to achieve the steady-state condition. Also, a higher Reynolds number increases the Nusselt number. Hemispherical
plate materials with higher thermal conductivity maintain lower temperature non-uniformity at the solid–fluid interface. Increasing
the plate thickness decreases the maximum temperature in the solid and increases the time to reach the steady-state condition. 相似文献
7.
The existence of projective-dual-anticipating, projective-dual, and projective-dual-lag synchronization in a coupled time-delayed
systems with modulated delay time is investigated via nonlinear observer design approach. Transition from projective-dual-anticipating
to projective-dual synchronization and from projective-dual to projective-dual-lag synchronization as a function of variable
coupling delay τ
p
(t) is discussed. Using Krasovskii–Lyapunov stability theory, a general condition for projective-dual synchronization is derived.
Numerical simulations on the chaotic Ikeda and Mackey–Glass systems are given to demonstrate the effectiveness of the theoretical
results. 相似文献
8.
Hai-Liang Li Akitaka Matsumura Guojing Zhang 《Archive for Rational Mechanics and Analysis》2010,196(2):681-713
The compressible Navier–Stokes–Poisson (NSP) system is considered in ${\mathbb {R}^3}The compressible Navier–Stokes–Poisson (NSP) system is considered in
\mathbb R3{\mathbb {R}^3} in the present paper, and the influences of the electric field of the internal electrostatic potential force governed by
the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating
effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that
the density of the NSP system converges to its equilibrium state at the same L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 respectively as the compressible Navier–Stokes system, but the momentum of the NSP system decays at the L
2-rate
(1+t)-\frac 14{(1+t)^{-\frac {1}{4}}} or L
∞-rate (1 + t)−1 respectively, which is slower than the L
2-rate
(1+t)-\frac 34{(1+t)^{-\frac {3}{4}}} or L
∞-rate (1 + t)−3/2 for compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm
Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and the L
∞-rate (1 + t)−p
with p ? (1, 3/2){p \in (1, 3/2)} for irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be
optimal for the compressible NSP system. 相似文献
9.
W. D. Thacker S. Sarkar T. B. Gatski 《Theoretical and Computational Fluid Dynamics》2007,21(3):171-199
The influence of compressibility on the rapid pressure–strain rate tensor is investigated using the Green’s function for the
wave equation governing pressure fluctuations in compressible homogeneous shear flow. The solution for the Green’s function
is obtained as a combination of parabolic cylinder functions; it is oscillatory with monotonically increasing frequency and
decreasing amplitude at large times, and anisotropic in wave-vector space. The Green’s function depends explicitly on the
turbulent Mach number M
t
, given by the root mean square turbulent velocity fluctuations divided by the speed of sound, and the gradient Mach number
M
g
, which is the mean shear rate times the transverse integral scale of the turbulence divided by the speed of sound. Assuming
a form for the temporal decorrelation of velocity fluctuations brought about by the turbulence, the rapid pressure–strain
rate tensor is expressed exactly in terms of the energy (or Reynolds stress) spectrum tensor and the time integral of the
Green’s function times a decaying exponential. A model for the energy spectrum tensor linear in Reynolds stress anisotropies
and in mean shear is assumed for closure. The expression for the rapid pressure–strain correlation is evaluated using parameters
applicable to a mixing layer and a boundary layer. It is found that for the same range of M
t
there is a large reduction of the pressure–strain correlation in the mixing layer but not in the boundary layer. Implications
for compressible turbulence modeling are also explored.
相似文献
10.
This paper uses a variational approach to establish existence of solutions (σ
t
, v
t
) for the 1-d Euler–Poisson system by minimizing an action. We assume that the initial and terminal points σ
0, σ
T
are prescribed in , the set of Borel probability measures on the real line, of finite second-order moments. We show existence of a unique minimizer
of the action when the time interval [0,T] satisfies T < π. These solutions conserve the Hamiltonian and they yield a path t → σ
t
in . When σ
t
= δ
y(t) is a Dirac mass, the Euler–Poisson system reduces to . The kinetic version of the Euler–Poisson, that is the Vlasov–Poisson system was studied in Ambrosio and Gangbo (Comm Pure
Appl Math, to appear) as a Hamiltonian system.
WG gratefully acknowledges the support provided by NSF grants DMS-02-00267,
DMS-03-54729 and DMS-06-00791.
TN gratefully acknowledges the postdoctoral support provided by NSF grants DMS-03-
54729 and the School of Mathematics.
AT gratefully acknowledges the support provided by the School of Mathematics. 相似文献
11.
The combined effect of rotation and magnetic field is investigated for the axisymmetric flow due to the motion of a sphere
in an inviscid, incompressible electrically conducting fluid having uniform rotation far upstream. The steady-state linearized
equations contain a single parameter α=1/2βR
m, β being the magnetic pressure number and R
m the magnetic Reynolds number. The complete solution for the flow field and magnetic field is obtained and the distribution
of vorticity and current density is found. The induced vorticity is O(α4) and the current density is O(R
m) on the sphere. 相似文献
12.
V. Ya. Ternovoi K. V. Khishchenko A. A. Charakhch’yan 《Journal of Applied Mechanics and Technical Physics》2009,50(3):371-379
This paper considers the interaction between an absolutely rigid wall or a steel plate and the rarefaction wave arising in
solid deuterium when a 30–150 GPa shock wave arrives at the free surface. It is shown that, in the entropy trace near the wall or interface with the plate,
a high-temperature plasma arises, in which a thermonuclear fusion is possible, at least, for shock-wave pressures above 70 GPa. The dimension of the plasma region and the time of its establishment are proportional to the distance between the free surface
and the wall. Estimates of the proportionality coefficients are given. It is noted that, in this case, unlike in other methods
of high-temperature plasma generation, the time of existence of the plasma may not depend on the sound velocity in it. It
is shown that, by using a conical solid-state target wit an exit hole, the shock-wave pressure in solid deuterium can be increased
from 10 to 100 GPa.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 15–24, May–June, 2009. 相似文献
13.
V. M. Kulik 《Journal of Applied Mechanics and Technical Physics》2007,48(2):221-228
The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued
onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two
components corresponding to two components of surface displacement. The dimensionless compliance components depend only on
the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the
wave velocity to the velocity of propagation of shear oscillations V/C
t
0
. Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C
t
0
< 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure.
The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous
behavior of the compliance with the wave velocity being greater than a certain critical value is explained.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007. 相似文献
14.
John R. de Bruyn 《Rheologica Acta》2006,45(6):803-811
The drag force on a sphere moving through an aqueous foam is measured as the foam ages. After an initial period, the steady-state drag decreases with age T as T
−0.54±0.14. As the mean bubble size R in the foam coarsens as T
0.5, this implies that the drag force scales as The transient buildup of the force when the sphere starts to move is described by a single exponential approach to the steady-state drag while its relaxation when the motion stops is described by the sum of three exponential relaxations. This is as for fresh foam, but the coefficients and time constants vary systematically with age. For the most part, these quantities also show a power law scaling with T. The age dependence of the quantities determined in this study is discussed in terms of the mean bubble size. 相似文献
15.
D.V. Bel’skii 《Nonlinear Oscillations》2006,9(2):166-172
We establish new properties of C
1[−1, +∞)-solutions of the linear functional differential equation ẋ(t) = ax(t) + bx(qt) + hx(t−1) + cẋ(qt) + rẋ(t−1) in the neighborhood of the singular point t = +∞.
__________
Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 170–177, April–June, 2006. 相似文献
16.
Shahram Pouya Manoochehr M. Koochesfahani Andrew B. Greytak Moungi G. Bawendi Daniel G. Nocera 《Experiments in fluids》2008,44(6):1035-1038
Near-surface velocity measurements are carried out with quantum dot (QD) nanoparticles using evanescent wave illumination.
Relying on the small size of QDs, their correspondingly small hydrodynamic radius and high Brownian diffusion coefficient,
we consider the situation where the tracer diffusion length over the inter-frame time Δt is large compared to the size of the interrogation region next to the wall. While keeping all other experimental parameters
fixed, we systematically increase Δt by as much as a factor of 25, resulting in an increase of the QD diffusion length by a factor of 5. Data indicate a significant
overestimation of the “apparent” mean velocity measured experimentally. These results provide a direct confirmation of the
phenomenon of diffusion-induced bias described by the simulations of Sadr et al. (2007). 相似文献
17.
We study the interaction of a shock with a density-stratified gaseous interface (Richtmyer–Meshkov instability) with localized
jagged and irregular perturbations, with the aim of developing an analytical model of the vorticity deposition on the interface
immediately after the passage of the shock. The jagged perturbations, meant to simulate machining errors on the surface of
a laser fusion target, are characterized using Haar wavelets. Numerical solutions of the Euler equations show that the vortex
sheet deposited on the jagged interface rolls into multiple mushroom-shaped dipolar structures which begin to merge before
the interface evolves into a bubble-spike structure. The peaks in the distribution of x-integrated vorticity (vorticity integrated in the direction of the shock motion) decay in time as their bases widen, corresponding
to the growth and merger of the mushrooms. However, these peaks were not seen to move significantly along the interface at
early times i.e. t < 10 τ, where τ is the interface traversal time of the shock. We tested our analytical model against inviscid simulations
for two test cases – a Mach 1.5 shock interacting with an interface with a density ratio of 3 and a Mach 10 shock interacting
with a density ratio of 10. We find that this model captures the early time (t/τ ∼ 1) vorticity deposition (as characterized by the first and second moments of vorticity distributions) to within 5% of
the numerical results.
PACS 47.40.Nm; 47.20.Ma 相似文献
18.
A new experimental approach to the study of the two-dimensional compressible flow phenomena is presented. In this technique,
a variety of compressible flows were generated by bursting plane vertical soap films. An aureole and a “shock wave” preceding
the rim of the expanding hole were clearly observed using traditional high-speed flash photography and a fast line-scan charge
coupled device (CCD) camera. The moving shock wave images obtained from the line-scan CCD camera were similar to the x–t diagrams in gas dynamics. The moving shock waves cause thickness jumps and induce supersonic flows. Photographs of the supersonic
flows over a cylinder and a wedge are presented. The results suggest clearly the feasibility of the “soap film shock tube”.
Received: 11 May 2000/Accepted: 2 November 2000 相似文献
19.
Thermo-mechanical analysis of functionally graded hollow sphere subjected to mechanical loads and one-dimensional steady-state
thermal stresses is carried out in this study. The material properties are assumed to vary non-linearly in the radial direction,
and the Poisson’s ratio is assumed constant. The temperature distribution is assumed to be a function of radius, with general
thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the analysis presented here,
the effect of non-homogeneity in FGM thick sphere was implemented by choosing a dimensionless parameter, named β
i
(i = 1, . . . , 3), which could be assigned an arbitrary value affecting the stresses in the sphere. It is observed that the
solution process for β
i
(i = 3) = −1 are different from those obtained for other values of β
i
(i = 1, . . . , 3). Cases of pressure, temperature, and combined loadings were considered separately. It is concluded that by
changing the value of β
i
(i = 1 . . . 3), the properties of FGM can be so modified that the lowest stress levels are reached. The present results agree
well with existing results. Using FEM simulations, the analytical findings for FGM spheres under the influence of internal
pressure and temperature gradient were compared to finite element results. 相似文献
20.
Assume that A1, A2 ⊂ ℝ are closed intervals containing 0, ϕ is an increasing odd homeomorphism with ϕ (ℝ) = ℝ, and T ∈ (0, ∞). We study a singular Dirichlet problem of the form {fx080-01} and prove the existence of its smooth solution satisfying
the conditions {fx080-02}, where ƒ satisfies the Carathéodory conditions on the set (0, T) × D and can have time singularities
at t = 0 and t = T and space singularities at x = 0, y = 0.
Published in Neliniini Kolyvannya, Vol. 11, No. 1, pp. 81–95, January–March, 2007. 相似文献