共查询到20条相似文献,搜索用时 31 毫秒
1.
Andrej Zlatoš 《Archive for Rational Mechanics and Analysis》2010,195(2):441-453
We study KPP pulsating front speed-up and effective diffusivity enhancement by general periodic incompressible flows. We prove
the existence of and determine the limits c*e(A)/A{c^*_{e}(A)/A} and D
e
(A)/A
2 as the flow amplitude A → ∞, with c*e(A){c^*_{e}(A)} the minimal front speed and D
e
(A) the effective diffusivity in direction e. 相似文献
2.
Hiroshi Watanabe Tomohiro Sato Motoyuki Hirose Kunihiro Osaki Ming-Long Yao 《Rheologica Acta》1999,38(2):100-107
Rheo-dielectric behavior was examined for 4−4′−n-octyl-cyanobiphenyl (8CB) having large dipoles parallel to its principal axis (in the direction of the C≡N bond). In the
quiescent state at all temperatures (T) examined, orientational fluctuation of the 8CB molecules was observed as dielectric dispersions at characteristic frequencies
ωc>106 s−1. In the isotropic state at high T, no detectable changes of the complex dielectric constant ɛ*(ω) were found under slow flow at shear rates ˙γ≫ωc. In the nematic state at intermediate T, the terminal relaxation intensity of ɛ*(ω) was decreased under such slow flow. In the smectic state at lower T, the flow effect became much less significant. These results were related to the flow-induced changes of the liquid crystalline
textures in the nematic and smectic states, and the differences of the rheo-dielectric behavior in these states are discussed
in relation to a difference of the symmetry of molecular arrangements in the nematic and smectic textures.
Received: 1 October 1998 Accepted: 13 January 1999 相似文献
3.
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
4.
MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING 总被引:8,自引:0,他引:8
These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m*ζ), or a high mass-damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ 0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*. 相似文献
5.
Alain Haraux 《Journal of Dynamics and Differential Equations》2007,19(4):915-933
Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A
* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A
1/2) et λ, c sont des constantes positives, tandis que .
By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A
* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A
1/2) and λ, c are positive constants, while .
相似文献
6.
In a bounded domain of R n+1, n ≧ 2, we consider a second-order elliptic operator, ${A=-{\partial_{x_0}^2} - \nabla_x \cdot (c(x) \nabla_x)}In a bounded domain of R
n+1, n ≧ 2, we consider a second-order elliptic operator, A=-?x02 - ?x ·(c(x) ?x){A=-{\partial_{x_0}^2} - \nabla_x \cdot (c(x) \nabla_x)}, where the (scalar) coefficient c(x) is piecewise smooth yet discontinuous across a smooth interface S. We prove a local Carleman estimate for A in the neighborhood of any point of the interface. The “observation” region can be chosen independently of the sign of the
jump of the coefficient c at the considered point. The derivation of this estimate relies on the separation of the problem into three microlocal regions
and the Calderón projector technique. Following the method of Lebeau and Robbiano (Comm Partial Differ Equ 20:335–356, 1995)
we then prove the null controllability for the linear parabolic initial problem with Dirichlet boundary conditions associated
with the operator ?t - ?x ·(c(x) ?x){{\partial_t - \nabla_x \cdot (c(x) \nabla_x)}} . 相似文献
7.
H. Watanabe Tomohiro Sato Motoyuki Hirose Kunihiro Osaki Ming-Long Yao 《Rheologica Acta》1998,37(6):519-527
Dielectric relaxation behavior was examined for 4-4′-n-pentyl-cyanobiphenyl (5CB) and 4-4′-n-heptyl-cyanobiphenyl (7CB) under flow. In quiescent states at all temperatures examined, both 5CB and 7CB exhibited dispersions
in their complex dielectric constant ε*(ω) at characteristic frequencies ω
c
above 106 rad s–1. This dispersion reflected orientational fluctuation of individual 5CB and 7CB molecules having large dipoles parallel to
their principal axis (in the direction of C≡N bond). In the isotropic state at high temperatures, these molecules exhibited no detectable changes of ε*(ω) under flow at
shear rates . In contrast, in the nematic state at lower temperatures the terminal relaxation intensity of ε*(ω) as well as the static
dielectric constant ε′(0) decreased under flow at . This rheo-dielectric change was discussed in relation to the flow effects on the nematic texture (director distribution)
and anisotropy in motion of individual molecules with respect to the director.
Received: 14 April 1998 Accepted: 29 July 1998 相似文献
8.
We study the values e
σ(f) of the best approximation of integrals of functions from the spaces L
p
(A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies
on the unit ball U
p
(A) of the space L
p
(A, dμ). We consider applications of the obtained results to approximation problems in the spaces S
p
ϕ.
__________
Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007. 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.
Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A- such that (AA-)*=AA- and B has a generalized inverse B- such that (B-B)*=B-B,the general characteristic forms for the critical points of the map Fp:X→‖AXB-C‖pp(1
p=2. Similarly, the same question has been discussed for several operators. 相似文献
11.
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
12.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
13.
14.
H. Watanabe Kunihiro Osaki Mutsuo Matsumoto Dobrin P. Bossev Cathy E. McNamee Masaru Nakahara Ming-Long Yao 《Rheologica Acta》1998,37(5):470-485
Nonlinear rheological features were investigated for an aqueous solution of tetraethylammonium perfluorooctyl sulfonate (C8F17SO3
–N+(C2H5)4; abbreviated as FOSTEA). In the solution (c=0.045 mol/l; 28.3 g/l), spherical micelles of FOSTEA were connected with each other to form threads of pearl-necklace shape.
These threads were further organized into a transient network to exhibit linear relaxation characteristic of living polymers,
single-mode terminal relaxation widely separated from faster relaxation processes. Nonlinear relaxation experiments against
large step-strains γ(≤8) revealed that the terminal relaxation mode had a γ-insensitive relaxation time but its relaxation
intensity exhibited significant damping (much stronger than that for entangled polymers). In contrast, the relaxation time
and intensity for the fast relaxation modes first increased and then decreased with increasing γ. Under shear flow, the FOSTEA
threads exhibited strong thinning of the viscosity. These nonlinear features of the FOSTEA threads were compared with those
of other threadlike micelles, analyzed on the basis of an empirically introduced constitutive equation, and discussed in relation
to strain/low-induced scission of the living threads.
Received: 20 February 1998 Accepted: 30 July 1998 相似文献
15.
The steady mixed convection boundary-layer flow over a vertical impermeable surface in a porous medium saturated with water
at 4°C (maximum density) when the surface heat flux varies as x
m
and the velocity outside the boundary layer varies as x
(1+2m)/2, where x measures the distance from the leading edge, is discussed. Assisting and opposing flows are considered with numerical solutions
of the governing equations being obtained for general values of the flow parameters. For opposing flows, there are dual solutions
when the mixed convection parameter λ is greater than some critical value λ
c
(dependent on the power-law index m). For assisting flows, solutions are possible for all values of λ. A lower bound on m is found, m > −1 being required for solutions. The nature of the critical point λ
c
is considered as well as various limiting forms; the forced convection limit (λ = 0), the free convection limit (λ → ∞) and
the limits as m → ∞ and as m → −1. 相似文献
16.
Yoshihisa Morita Hirokazu Ninomiya 《Journal of Dynamics and Differential Equations》2006,18(4):841-861
We deal with a reaction–diffusion equation u
t
= u
xx
+ f(u) which has two stable constant equilibria, u = 0, 1 and a monotone increasing traveling front solution u = φ(x + ct) (c > 0) connecting those equilibria. Suppose that u = a (0 < a < 1) is an unstable equilibrium and that the equation allows monotone increasing traveling front solutions u = ψ1(x + c
1
t) (c
1 < 0) and ψ2(x + c
2
t) (c
2 > 0) connecting u = 0 with u = a and u = a with u = 1, respectively. We call by an entire solution a classical solution which is defined for all
. We prove that there exists an entire solution such that for t≈ − ∞ it behaves as two fronts ψ1(x + c
1
t) and ψ2(x + c
2
t) on the left and right x-axes, respectively, while it converges to φ(x + ct) as t→∞. In addition, if c > − c
1, we show the existence of an entire solution which behaves as ψ1( − x + c
1
t) in
and φ(x + ct) in
for t≈ − ∞. 相似文献
17.
The unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder is considered with combined buoyancy
force effects, for the situation in which the surface temperature T
′
w(x) and C
′
w(x) are subjected to the power-law surface heat and mass flux as K(T
′/r) = −ax
n
and D(C
′/r) = −bx
m
. The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results are
obtained for different values of Prandtl number, Schmidt number ‘n’ and ‘m’. The velocity, temperature and concentration profiles, local and average skin-friction, Nusselt and Sherwood numbers are
shown graphically. The local Nusselt and Sherwood number of the present study are compared with the available result and a
good agreement is found to exist.
Received on 7 July 1998 相似文献
18.
If a pair of material line elements, passing through a typical particle P in a body, subtend an angle Θ before deformation, and Θ+γ after deformation, the pair of material elements is said to be
sheared by the amount γ. Here all pairs of material elements at P are considered for arbitrary deformations. Two main problems are addressed and solved. The first is the determination of
all pairs of material line elements at P which are unsheared. The second is the determination of that pair of material line elements at P which suffers the maximum shear.
All unsheared pairs of material elements in a given plane π(S) with normal S passing through P are considered. Provided π(S) is not a plane of central circular section of the C-ellipsoid at P (where C is the right Cauchy-Green strain tensor), it is seen that corresponding to any material element in π(S) there is, in general, one companion material element in π(S) such that the element and its companion are unsheared.
There are, however, two elements in π(S) which have no companions. We call their corresponding directions \textit{limiting directions.} Equally inclined to the direction
of least stretch in the plane π(S), the limiting directions play a central role. It is seen that, in a given plane π(S), the pair of material line elements which suffer the maximum shear lie along the limiting directions in π(S). If Θ
L
is the acute angle subtended by the limitig directions in π(S) before deformation, then this angle is sheared into its supplement π−Θ
L
so that the maximum shear γ*;(S) is γ*=π− 2 Θ
L
. If S is given and C is known, then Θ
L
may be determined immediately. Its calculation does not involve knowing the eigenvectors or eigenvalues of C.
When all possible planes through P are considered, it is seen that the global maximum shear γ*
G
occurs for material elements lying along the limiting directions in the plane spanned by the eigenvectors of C corresponding to the greatest principal stretch λ3 and the least λ1. The limiting directions in this principal plane of C subtend the angle and . Generally the maximum shear does not occur for a pair of material elements which are originally orthogonal.
For a given material element along the unit vector N, there is, in general, in each plane π(S passing through N at P, a companion vector M such that material elements along N and M are unsheared. A formula, originally due to Joly (1905), is presented for M in terms of N and S.
Given an unsheared pair π(S), the limiting directions in π(S) are seen to be easily determined, either analytically or geometrically.
Planar shear, the change in the angle between the normals of a pair of material planar elements at X, is also considered. The theory of planar shear runs parallel to the theory of shear of material line elements. Corresponding
results are presented.
Finally, another concept of shear used in the geology literature, and apparently due to Jaeger, is considered. The connection
is shown between Cauchy shear, the change in the angle of a pair of material elements, and the Jaeger shear, the change in
the angle between the normal N to a planar element and a material element along the normal N. Although Jaeger's shear is described in terms of one direction N, it is seen to implicitly include a second material line element orthogonal to N.
Accepted: May 25, 1999 相似文献
19.
The mechanism of precursor ionization ahead of strong shock waves has been studied in a low density shock tube. The experimental
results are illustrated with Arrhenius plots with kink points dividing them into two parts with apparent activation energy
ratio 1:2, namely with the values 7.7 eV and 15.3 eV, and varying with first and third power of the density respectively.
A model is proposed to interpret the facts where the process taking place in the precursor region, is a two step photo ionization
accompanied with the drift flow effect of the gas relative to the shock wave or the ionization recombination effect according
to whether the shock speed and initial density are low enough. The product of the A-A collision excitation cross section coefficientS
* multiplied by the radiation cross sectionQ
* of ArgonS
*×Q
*=1×10−36 (cm4eV−1) and the three body recombination coefficient of Argon at room temperaturek
ra
=1×10−24 (cm−6s−1).
The project supported by the National Natural Science Foundation of China 相似文献
20.
Roger Young 《Transport in Porous Media》1993,12(3):261-278
Two-phase flows of boiling water and steam in geothermal reservoirs satisfy a pair of conservation equations for mass and energy which can be combined to yield a hyperbolic wave equation for liquid saturation changes. Recent work has established that in the absence of conduction, the geothermal saturation equation is, under certain conditions, asymptotically identical with the Buckley-Leverett equation of oil recovery theory. Here we summarise this work and show that it may be extended to include conduction. In addition we show that the geothermal saturation wave speed is under all conditions formally identical with the Buckley-Leverett wave speed when the latter is written as the saturation derivative of a volumetric flow.Roman Letters
C(P, S,q)
geothermal saturation wave speed [ms–1] (14)
-
c
t
(P, S)
two-phase compressibility [Pa–1] (10)
-
D(P, S)
diffusivity [m s–2] (8)
-
E(P, S)
energy density accumulation [J m–3] (3)
-
g
gravitational acceleration (positive downwards) [ms–2]
-
h
w
(P),h
w
(P)
specific enthalpies [J kg–1]
-
J
M
(P, S,P)
mass flow [kg m–2 s–1] (5)
-
J
E
(P, S,P)
energy flow [J m–2s–1] (5)
-
k
absolute permeability (constant) [m2]
-
k
w
(S),k
s
(S)
relative permeabilities of liquid and vapour phases
-
K
formation thermal conductivity (constant) [Wm–1 K–1]
-
L
lower sheetC<0 in flow plane
-
m, c
gradient and intercept
-
M(P, S)
mass density accumulation [kg m–3] (3)
-
O
flow plane origin
-
P(x,t)
pressure (primary dependent variable) [Pa]
-
q
volume flow [ms–1] (6)
-
S(x, t)
liquid saturation (primary dependent variable)
-
S
*(x,t)
normalised saturation (Appendix)
-
t
time (primary independent variable) [s]
-
T
temperature (degrees Kelvin) [K]
-
T
sat(P)
saturation line temperature [K]
-
TdT
sat/dP
saturation line temperature derivative [K Pa–1] (4)
-
T
c
,T
D
convective and diffusive time constants [s]
-
u
w
(P),u
s
(P),u
r
(P)
specific internal energies [J kg–1]
-
U
upper sheetC > 0 in flow plane
-
U(x,t)
shock velocity [m s–1]
- x
spatial position (primary independent variable) [m]
-
X
representative length
-
x, y
flow plane coordinates
-
z
depth variable (+z vertically downwards) [m]
Greek Letters
P
,
S
remainder terms [Pa s–1], [s–1]
-
double-valued saturation region in the flow plane
- h =h
s
–h
w
latent heat [J kg–1]
- =
w
–
s
density difference [kg m–3]
-
line envelope
-
=D
K
/D
0
diffusivity ratio
-
porosity (constant)
-
w
(P),
s
(P),
t
(P, S)
dynamic viscosities [Pa s]
-
v
w
(P),v
s
(P)
kinematic viscosities [m2s–1]
-
v
0 =kh/KT
kinematic viscosity constant [m2 s–1]
-
0 =v
0
dynamic viscosity constant [m2 s–1]
-
w
(P),
s
(P)
density [kg m–3]
Suffixes
r
rock matrix
-
s
steam (vapour)
-
w
water (liquid)
-
t
total
- av
average
- 0
without conduction
-
K
with conduction 相似文献