共查询到20条相似文献,搜索用时 117 毫秒
1.
Nicolae Tarfulea 《应用数学和力学(英文版)》2000,21(3):283-290
IntroductionInthispaper,weconsidertheellipticsystem(1λ) -Δu=f(λ,x,u)-v (inΩ),-Δv=δu-γv(inΩ),u=v=0(onΩ),whereΩisasmoothboundeddomaininRN(N≥2)andλisarealparameter.Thesolutions(u,v)ofthissystemrepresentsteadystatesolutionsofreactiondiffusionsystemsderivedfromseveralap… 相似文献
2.
Nai-Yi Zhu Li-Shun Huang Bin Wu Xi-Long Yu Run-Hui Wu Gang Meng Ai-Min Ren Xin-Tian Hu 《Acta Mechanica Sinica》2013,29(2):189-195
One of the key factors for solving the problems of re-entry communication interruption is electromagnetic(EM) wave transmission characteristics in a plasma.Theoretical and experimental studies were carried out on specific transmission characteristics for different plasma sheath characteristic under thin sheath condition in re-entry state.The paper presents systematic studies on the variations of wave attenuation characteristics versus plasma sheath thickness L,collision frequency ν,electron density n e and wave working frequency f in a φ 800 mm high temperature shock tube.In experiments,L is set to 4 cm and 38 cm.ν is 2 GHz and 15 GHz.n e is from 1×10 10 cm(-3) to 1×10 13 cm(-3),and f is set to 2,5,10,14.6 GHz,respectively.Meanwhile,Wentzel-Kramers-Brillouin(WKB) and finite-difference time-domain(FDTD) methods are adopted to carry out theoretical simulation for comparison with experimental results.It is found that when L is much larger than EM wavelength λ(thick sheath) and ν is large,the theoretical result is in good agreement with experimental one,when sheath thickness L is much larger than λ,while ν is relatively small,two theoretical results are obviously different from the experimental ones.It means that the existing theoretical model can not fully describe the contribution of ν.Furthermore,when L and λ are of the same order of magnitude(thin sheath),the experimental result is much smaller than the theoretical values,which indicates that the current model can not properly describe the thin sheath effect on EM attenuation characteristics. 相似文献
3.
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
4.
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
5.
R. Lewandowski 《Journal of Mathematical Fluid Mechanics》2006,8(3):398-422
This paper is devoted to the study of a LES model to simulate turbulent 3D periodic flow. We focus our attention on the vorticity
equation derived from this LES model for small values of the numerical grid size δ. We obtain entropy inequalities for the
sequence of corresponding vorticities and corresponding pressures independent of δ, provided the initial velocity u0 is in Lx2 while the initial vorticity ω0 = ∇ × u0 is in Lx1. When δ tends to zero, we show convergence, in a distributional sense, of the corresponding equations for the vorticities
to the classical 3D equation for the vorticity. 相似文献
6.
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
7.
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8.
The lift force experienced by a spinning sphere moving in a viscous fluid, with constant linear and angular velocities, is
measured by means of a trajectographic technique. Measurements are performed in the range of dimensionless angular velocities
γ=aω/V lying between 1 and 6, and in the range of Reynolds numbers Re=2aV/ν lying between 10 and 140 (a sphere radius, ω angular velocity, V relative velocity of the sphere centre, ν fluid kinematic viscosity). A notable departure from the theoretical relationship
at low Reynolds number, C
L
=2γ, is obtained, the ratio C
L
/γ being found to significantly decrease with increasing γ and increasing Re. The following correlation is finally proposed to estimate the lift coefficient in the range 10<Re<140:
C
L
≅0.45+(2γ−0.45) exp (−0.075γ0.4
Re
0.7)
Received: 20 May 1996/Accepted: 9 November 1997 相似文献
9.
The problem of the self-similar boundary flow of a “Darcy-Boussinesq fluid” on a vertical plate with temperature distribution
T
w(x) = T
∞+A·x
λ and lateral mass flux v
w(x) = a·x
(λ−1)/2, embedded in a saturated porous medium is revisited. For the parameter values λ = 1,−1/3 and −1/2 exact analytic solutions
are written down and the characteristics of the corresponding boundary layers are discussed as functions of the suction/ injection
parameter in detail. The results are compared with the numerical findings of previous authors.
Received on 8 March 1999 相似文献
10.
Gero Friesecke Richard D. James Stefan Müller 《Archive for Rational Mechanics and Analysis》2006,180(2):183-236
We derive a hierarchy of plate models from three-dimensional nonlinear elasticity by Γ-convergence. What distinguishes the
different limit models is the scaling of the elastic energy per unit volume ∼hβ, where h is the thickness of the plate. This is in turn related to the strength of the applied force ∼hα. Membrane theory, derived earlier by Le Dret and Raoult, corresponds to α=β=0, nonlinear bending theory to α=β=2, von Kármán theory to α=3, β=4 and linearized vK theory to α>3. Intermediate values of α lead to certain theories with constraints. A key ingredient in the proof is a generalization to higher derivatives of our
rigidity result [29] which states that for maps v:(0,1)3→ℝ3, the L2 distance of ∇v from a single rotation is bounded by a multiple of the L2 distance from the set SO(3) of all rotations. 相似文献
11.
Optimization of the deflagration to detonation transition: reduction of length and time of transition 总被引:1,自引:1,他引:1
The aim of this experimental investigation is the study of Deflagration to Detonation Transition (DDT) in tubes in order to (i) reduce both run-up distance and time of transition (L
DDT and t
DDT) in connection with Pulsed Detonation Engine applications and to (ii) attempt to scale L
DDT with λCJ (the detonation cellular structure width). In DDT, the production of turbulence during the long flame run-up can lead to L
DDT values of several meters. To shorten L
DDT, an experimental set-up is designed to quickly induce highly turbulent initial flow. It consists of a double chamber terminated with a perforated plate of high Blockage Ratio (BR) positioned at the beginning of a 26 mm inner diameter tube containing a “Shchelkin spiral” of BR ≈ 0.5. The study involves stoichiometric reactive mixtures of H2, CH4, C3H8, and C2H4 with oxygen and diluted with N2 in order to obtain the same cell width λCJ≈10 mm at standard conditions. The results show that a shock-flame system propagating with nearly the isobaric speed of sound of combustion products, called the choking regime, is rapidly obtained. This experimental set-up allows a L
DDT below 40 cm for the mixtures used and a ratio L
DDT/λCJ ranging from 23 to 37. The transition distance seems to depend on the reduced activation energy (E
a/RT
c) and on the normalized heat of reaction (Q/a
0
2). The higher these quantities are, the shorter the ratio L
DDT/λCJ is.
PACS 47.40.Rs · 47.60.+i · 47.70.Pq · 47.80.CbThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003. 相似文献
12.
In this paper, we consider v(t) = u(t) − e
tΔ
u
0, where u(t) is the mild solution of the Navier–Stokes equations with the initial data
u0 ? L2(\mathbb Rn)?Ln(\mathbb Rn){u_0\in L^2({\mathbb R}^n)\cap L^n({\mathbb R}^n)} . We shall show that the L
2 norm of D
β
v(t) decays like
t-\frac |b|-1 2-\frac n4{t^{-\frac {|\beta|-1} {2}-\frac n4}} for |β| ≥ 0. Moreover, we will find the asymptotic profile u
1(t) such that the L
2 norm of D
β
(v(t) − u
1(t)) decays faster for 3 ≤ n ≤ 5 and |β| ≥ 0. Besides, higher-order asymptotics of v(t) are deduced under some assumptions. 相似文献
13.
Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the
axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR
λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized
second-order structure functions show a continuous evolution withR
λ. In particular, the scaling exponentζ
v
, corresponding to the v structure function, continues to increase with R
λ in contrast to the nearly unchanged value of ζ
u
. The Kolmogorov constant for δu shows a smaller rate of increase with R
λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR
λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the
centreline of a fully developed channel flow.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
Giovanni Romeo Giovanni Filippone Alberto Fernández-Nieves Pietro Russo Domenico Acierno 《Rheologica Acta》2008,47(9):989-997
We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based
on a mixture of titanium dioxide (TiO2) nanoparticles and polypropylene. Above a critical volume fraction, Φ
c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects
the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition,
the elasticity of the hybrids shows critical behavior around Φ
c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle
clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters.
For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G′, scaling with frequency, ω, as G′∼ω
0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of
the components could be superimposed. 相似文献
15.
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
16.
K. Arakawa T. Mada H. Komatsu T. Shimizu M. Satou K. Takehara G. Etoh 《Experimental Mechanics》2006,46(6):691-697
The oblique impact between a golf ball and a rigid steel target was studied using a high-speed video camera. Video images
recorded before and after the impact were used to determine the inbound velocity v
i, rebound velocity v
r, inbound angle θi, rebound angle θr, and the coefficient of restitution e. The results showed that θr and e decreased as v
i increased. The maximum compression ratio ηc, contact time t
c, average angular velocity
, and tangential velocity
, along the target were determined from images obtained during the impact. The images demonstrated that ηc increased with v
i while t
c decreased. In addition,
and
increased almost linearly as v
i increased. A rigid body model was used to estimate the final angular velocity ω* and tangential velocity νt* at the end of the impact; these results were then compared with experimental data. 相似文献
17.
Nadina Müller-Fischer Philip Tobler Marco Dressler Peter Fischer Erich J. Windhab 《Experiments in fluids》2008,45(5):917-926
Experiments in a parallel band apparatus and a transparent concentric cylinder device allow the observation of bubble deformation
(shape and orientation) and breakup as a function of the viscosity ratio λ and the Capillary number Ca. For viscosity ratios between 3.1 × 10−7 and 6.7 × 10−8, critical Capillary numbers Ca
c for bubble breakup between 29 and 45 are found. It is furthermore shown that in the given parameter space no clear distinction
between tip breakup and fracture can be made for bubbles.
An erratum to this article can be found at 相似文献
18.
The optimal dimensions of convective-radiating circular fins with variable profile, heat-transfer coefficient and thermal
conductivity, as well as internal heat generation are obtained. A profile of the form y=(w/2) [1+(r
o/r)
n
] is studied, while variation of thermal conductivity is of the form k=k
o[1+ɛ((T−T
∞)/ (T
b−T
∞))
m
]. The heat-transfer coefficient is assumed to vary according to a power law with distance from the bore, expressed as h=K[(r−r
o)/(r
e−r
o)]λ. The results for λ=0 to λ=1.9, and −0.4≤ɛ≤0.4, have been expressed by suitable dimensionless parameters. A correlation for
the optimal dimensions of a constant and variable profile fins is presented in terms of reduced heat-transfer rate. It is
found that a (quadratic) hyperbolic circular fin with n=2 gives an optimum performance. The effect of radiation on the fin performance is found to be considerable for fins operating
at higher base temperatures, whereas the effect of variable thermal conductivity on the optimal dimensions is negligible for
the variable profile fin. It is also observed, in general, that the optimal fin length and the optimal fin base thickness
are greater when compared to constant fin thickness.
Received on 22 February 1999 相似文献
19.
Florian J. Stadler Christian Piel Joachim Kaschta Sascha Rulhoff Walter Kaminsky Helmut Münstedt 《Rheologica Acta》2006,45(5):755-764
Linear high-density polyethylenes with molar masses M
w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η0 covered a range from 2.5×10−3 to around 108 Pas. Above a critical molar mass of M
c≈2,900 g/mol, the experimental results can be described by the relation η0 ∼ M
w3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M
w but not on M
w/M
n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M
w and also on M
w/M
n.
相似文献
Helmut MünstedtEmail: Phone: +49-9131-8527604Fax: +49-9131-8528321 |
20.
The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical
measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM
i
is analyzed and the variations of the incidence angle ω
i
of the impinging shock and the reflection angle ω
r
with the distanceL
* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya. 相似文献