共查询到20条相似文献,搜索用时 31 毫秒
1.
G. H. Keetels W. Kramer H. J. H. Clercx G. J. F. van Heijst 《Theoretical and Computational Fluid Dynamics》2011,25(5):293-300
Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z μ Re0.8{Z\propto{\rm Re}^{0.8}} and P μ Re2.25{P\propto {\rm Re}^{2.25}} for 5 × 102 ≤ Re ≤ 2 × 104 and Z μ Re0.5{Z\propto{\rm Re}^{0.5}} and P μ Re1.5{P\propto{\rm Re}^{1.5}} for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Re
c
(here, Rec ? 2×104{{\rm Re}_c\approx 2\times 10^4}) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity
ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following
scaling relations are obtained: Z μ Re3/4, P μ Re9/4{Z\propto{\rm Re}^{3/4}, P\propto {\rm Re}^{9/4}} , and dP/dt μ Re11/4{\propto {\rm Re}^{11/4}} in agreement with the numerically obtained scaling laws. For Re ≥ Re
c
the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate
boundary-layer theory, this yields: Z μ Re1/2{Z\propto{\rm Re}^{1/2}} and P μ Re3/2{P\propto {\rm Re}^{3/2}}. 相似文献
2.
This study investigates the displacement of SO4-2{{\rm SO}_{4}^{-2}} and Ca+2 ions in a red-clay ceramic, simulating the process of efflorescence. Ceramic bodies were molded (70 × 27 × 9 mm3) by vacuum extrusion formulated with different contents of CaSO4 · 2H2O (0, 2, 4, 8, and 16% in weight) and burnt at different temperatures (800, 850, 900, and 950°C) for 12 h. Ceramic bodies
were characterized in terms of water absorption, apparent porosity, and pore size distribution. Efflorescence was evaluated
according to the norms of ASTM C67/2003 and by testing the solubilization of SO4-2{{\rm SO}_{4}^{-2}} and Ca+2 ions after 1 h with the ceramic bodies immersed in hot water as well as after 7, 14, and 28 consecutive days with the ceramic
bodies immersed in cold water. In the quantification of efflorescence, a new image analysis methodology was developed by using
the graphic software Image Tools 3.0. The results allowed in establishing a relationship between the efflorescence of the
investigated ions, physical properties (water absorption and apparent porosity), pore size distribution, and solubilization. 相似文献
3.
This study investigates the displacement of SO4-2{{\rm SO}_{4}^{-2}} and Ca+2 ions in a red-clay ceramic, simulating the process of efflorescence. Ceramic bodies were molded (70 × 27 × 9mm3) by vacuum extrusion formulated with different contents of CaSO4· 2H2O (0, 2, 4, 8, and 16% in weight) and burnt at different temperatures (800, 850, 900, and 950°C) for 12 h. Ceramic bodies
were characterized in terms of water absorption, apparent porosity and pore size distribution. Efflorescence was evaluated
according to the norms of ASTM C67/2003 and by testing the solubilization of SO4-2{{\rm SO}_{4}^{-2}} and Ca+2 ions after 1 h with the ceramic bodies immersed in hot water as well as after 7, 14, and 28 consecutive days with the ceramic
bodies immersed in cold water. In the quantification of efflorescence, a new image analysis methodology was developed by using
the graphic software Image Tools 3.0. The results allowed in establishing a relationship between the efflorescence of the
investigated ions, physical properties (water absorption and apparent porosity), pore size distribution, and solubilization. 相似文献
4.
We prove a regularity result for the anisotropic linear elasticity equation ${P u := {\rm div} \left( \boldmath\mathsf{C} \cdot \nabla u\right) = f}We prove a regularity result for the anisotropic linear elasticity equationP u : = div ( C ·?u) = f{P u := {\rm div} \left( \boldmath\mathsf{C} \cdot \nabla u\right) = f} , with mixed (displacement and traction) boundary conditions on a curved polyhedral domain
W ì \mathbbR3{\Omega \subset \mathbb{R}^3} in weighted Sobolev spaces Km+1a+1(W){\mathcal {K}^{m+1}_{a+1}(\Omega)} , for which the weight is given by the distance to the set of edges. In particular, we show that there is no loss of Kma{\mathcal {K}^{m}_{a}} -regularity. Our curved polyhedral domains are allowed to have cracks. We establish a well-posedness result when there are
no neighboring traction boundary conditions and |a| < η, for some small η > 0 that depends on P, on the boundary conditions, and on the domain Ω. Our results extend to other strongly elliptic systems and higher dimensions. 相似文献
5.
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
6.
Yuji Aoki Kentaro Hirayama Koji Kikuchi Masataka Sugimoto Kiyohito Koyama 《Rheologica Acta》2010,49(10):1071-1076
A poly(vinyl chloride) (PVC, Mw = 102×103)(\mbox{PVC,}\;{\rm M}_{\rm w} =102\times 10^3) di-octyl phthalate (DOP) gel with PVC content of 20 wt.% was prepared by a solvent evaporation method. The dynamic viscoelsticity
and elongational viscosity of the PVC/DOP gel were measured at various temperatures. The gel exhibited a typical sol–gel transition
behavior with elevating temperature. The critical gel temperature (Tgel) characterized with a power–law relationship between the storage and loss moduli, G′ and G″, and frequency ω, G¢=G¢¢/tan ( np/2 ) μ wn{G}^\prime={G}^{\prime\prime}{\rm /tan}\;\left( {{n}\pi {\rm /2}} \right)\propto \omega ^{n}, was observed to be 152°C. The elongational viscosity of the gel was measured below the Tgel. The gel exhibited strong strain hardening. Elongational viscosity against strain plot was independent of strain rate. This
finding is different from the elongational viscosity behavior of linear polymer solutions and melts. The stress–strain relations
were expressed by the neo-Hookean model at high temperature (135°C) near the Tgel. However, the stress–strain curves were deviated from the neo-Hookean model at smaller strain with decreasing temperature.
These results indicated that this physical gel behaves as the neo-Hookean model at low cross-linking point, and is deviated
from the neo-Hookean model with increasing of the PVC crystallites worked as the cross-linking junctions. 相似文献
7.
S. I. Maksymenko 《Nonlinear Oscillations》2010,13(2):196-227
Let
D2 ì \mathbbR2 {D^2} \subset {\mathbb{R}^2} be a closed unit 2-disk centered at the origin
O ? \mathbbR2 O \in {\mathbb{R}^2} and let F be a smooth vector field such that O is a unique singular point of F and all other orbits of F are simple closed curves wrapping once around O. Thus, topologically O is a “center” singularity. Let q:D2\{ O } ? ( 0, + ¥ ) \theta :D2\backslash \left\{ O \right\} \to \left( {0, + \infty } \right) be the function associating with each z ≠ O its period with respect to F. In general, such a function cannot be even continuously defined at O. Let also D+ (F) {\mathcal{D}^{+} }(F) be the group of diffeomorphisms of D
2 that preserve orientation and leave invariant each orbit of F. It is proved that θ smoothly extends to all of D
2 if and only if the 1-jet of F at O is a “rotation,” i.e.,
j1F(O) = - y\frac??x + x\frac??y {j^1}F(O) = - y\frac{\partial }{{\partial x}} + x\frac{\partial }{{\partial y}} . Then D+ (F) {\mathcal{D}^{+} }(F) is homotopy equivalent to a circle. 相似文献
8.
IntroductionInthispaper,weshallconsiderthefollowingsingularboundaryvalueproblems (BVP)u″ g(t)f(u) =0 , 0 <t<1 ,αu(0 ) -βu′(0 ) =0 , γu(1 ) δu′(1 ) =0 ,(1 )whereα ,β,γ ,δ≥ 0 ,ρ:=βγ αγ αδ>0 ,f∈C([0 ,∞ ) ,[0 ,∞ ) ) ,gmaybesingularatt=0and/ort=1 .Thisproblemarisesnaturallyinthestudyofradiallysymmet… 相似文献
9.
10.
Weon Shik Han Kue-Young Kim Richard P. Esser Eungyu Park Brian J. McPherson 《Transport in Porous Media》2011,90(3):807-829
The primary purpose of this study is to understand quantitative characteristics of mobile, residual, and dissolved CO2 trapping mechanisms within ranges of systematic variations in different geologic and hydrologic parameters. For this purpose,
we conducted an extensive suite of numerical simulations to evaluate the sensitivities included in these parameters. We generated
two-dimensional numerical models representing subsurface porous media with various permutations of vertical and horizontal
permeability (k
v and k
h), porosity (f{\phi}), maximum residual CO2 saturation (Sgrmax{S_{\rm gr}^{\max}}), and brine density (ρ
br). Simulation results indicate that residual CO2 trapping increases proportionally to kv, kh, Sgrmax{k_{\rm v}, k_{\rm h}, S_{\rm gr}^{\max}} and ρ
br but is inversely proportional to f.{\phi.} In addition, the amount of dissolution-trapped CO2 increases with k
v and k
h, but does not vary with f{\phi } , and decreases with Sgrmax{S_{\rm gr}^{\max}} and ρ
br. Additionally, the distance of buoyancy-driven CO2 migration increases proportionally to k
v and ρ
br only and is inversely proportional to kh, f{k_{\rm h}, \phi } , and Sgrmax{S_{\rm gr}^{\max}} . These complex behaviors occur because the chosen sensitivity parameters perturb the distances of vertical and horizontal
CO2 plume migration, pore volume size, and fraction of trapped CO2 in both pores and formation fluids. Finally, in an effort to characterize complex relationships among residual CO2 trapping and buoyancy-driven CO2 migration, we quantified three characteristic zones. Zone I, expressing the variations of Sgrmax{S_{\rm gr}^{\max}} and k
h, represents the optimized conditions for geologic CO2 sequestration. Zone II, showing the variation of f{\phi} , would be preferred for secure CO2 sequestration since CO2 has less potential to escape from the target formation. In zone III, both residual CO2 trapping and buoyancy-driven migration distance increase with k
v and ρ
br. 相似文献
11.
In association with multi-inhomogeneity problems, a special class of eigenstrains is discovered to give rise to disturbance
stresses of interesting nature. Some previously unnoticed properties of Eshelby’s tensors prove useful in this accomplishment.
Consider the set of nested similar ellipsoidal domains {Ω1, Ω2,⋯,Ω
N+1}, which are embedded in an infinite isotropic medium. Suppose that
in which and ξ
t
a
p
, p=1,2,3 are the principal half axes of Ω
t
. Suppose, the distribution of eigenstrain, ε
ij
*(x) over the regions Γ
t
=Ω
t+1−Ω
t
, t=1,2,⋯,N can be expressed as
where x
k
x
l
⋯x
m
is of order n, and f
ijkl ⋯m
(t) represents 3N(n+2)(n+1) different piecewise continuous functions whose arguments are ∑
p=1
3
x
p
2 /a
p
2. The nature of the disturbance stresses due to various classes of the piecewise nonuniform distribution of eigenstrains,
obtained via superpositions of Eq. (‡) is predicted and an infinite number of impotent eigenstrains are introduced. The present theory not only provides a general
framework for handling a broad range of nonuniform distribution of eigenstrains exactly, but also has great implications in
employing the equivalent inclusion method (EIM) to study the behavior of composites with functionally graded reinforcements.
The paper is dedicated to professor Toshio Mura. 相似文献
(‡) |
12.
Joel Avrin 《Journal of Dynamics and Differential Equations》2008,20(2):479-518
We obtain attractor and inertial-manifold results for a class of 3D turbulent flow models on a periodic spatial domain in
which hyperviscous terms are added spectrally to the standard incompressible Navier–Stokes equations (NSE). Let P
m
be the projection onto the first m eigenspaces of A =−Δ, let μ and α be positive constants with α ≥3/2, and let Q
m
=I − P
m
, then we add to the NSE operators μ A
φ in a general family such that A
φ≥Q
m
A
α in the sense of quadratic forms. The models are motivated by characteristics of spectral eddy-viscosity (SEV) and spectral
vanishing viscosity (SVV) models. A distinguished class of our models adds extra hyperviscosity terms only to high wavenumbers
past a cutoff λ
m0
where m
0 ≤ m, so that for large enough m
0 the inertial-range wavenumbers see only standard NSE viscosity.
We first obtain estimates on the Hausdorff and fractal dimensions of the attractor (respectively and ). For a constant K
α on the order of unity we show if μ ≥ ν that and if μ ≤ ν that where ν is the standard viscosity coefficient, l
0 = λ1−1/2 represents characteristic macroscopic length, and is the Kolmogorov length scale, i.e. where is Kolmogorov’s mean rate of dissipation of energy in turbulent flow. All bracketed constants and K
α are dimensionless and scale-invariant. The estimate grows in m due to the term λ
m
/λ1 but at a rate lower than m
3/5, and the estimate grows in μ as the relative size of ν to μ. The exponent on is significantly less than the Landau–Lifschitz predicted value of 3. If we impose the condition , the estimates become for μ ≥ ν and for μ ≤ ν. This result holds independently of α, with K
α and c
α independent of m. In an SVV example μ ≥ ν, and for μ ≤ ν aspects of SEV theory and observation suggest setting for 1/c within α orders of magnitude of unity, giving the estimate where c
α is within an order of magnitude of unity. These choices give straight-up or nearly straight-up agreement with the Landau–Lifschitz
predictions for the number of degrees of freedom in 3D turbulent flow with m so large that (e.g. in the distinguished-class case for m
0 large enough) we would expect our solutions to be very good if not virtually indistinguishable approximants to standard NSE
solutions. We would expect lower choices of λ
m
(e.g. with a > 1) to still give good NSE approximation with lower powers on l
0/l
ε, showing the potential of the model to reduce the number of degrees of freedom needed in practical simulations. For the choice
, motivated by the Chapman–Enskog expansion in the case m = 0, the condition becomes , giving agreement with Landau–Lifschitz for smaller values of λ
m
then as above but still large enough to suggest good NSE approximation. Our final results establish the existence of a inertial
manifold for reasonably wide classes of the above models using the Foias/Sell/Temam theory. The first of these results obtains such
an of dimension N > m for the general class of operators A
φ if α > 5/2.
The special class of A
φ such that P
m
A
φ = 0 and Q
m
A
φ ≥ Q
m
A
α has a unique spectral-gap property which we can use whenever α ≥ 3/2 to show that we have an inertial manifold of dimension m if m is large enough. As a corollary, for most of the cases of the operators A
φ in the distinguished-class case that we expect will be typically used in practice we also obtain an , now of dimension m
0 for m
0 large enough, though under conditions requiring generally larger m
0 than the m in the special class. In both cases, for large enough m (respectively m
0), we have an inertial manifold for a system in which the inertial range essentially behaves according to standard NSE physics,
and in particular trajectories on are controlled by essentially NSE dynamics.
相似文献
13.
Dongho Chae 《Journal of Mathematical Fluid Mechanics》2010,12(2):171-180
Let v and ω be the velocity and the vorticity of the a suitable weak solution of the 3D Navier–Stokes equations in a space-time
domain containing z0=(x0, t0)z_{0}=(x_{0}, t_{0}), and let Qz0,r = Bx0,r ×(t0 -r2, t0)Q_{z_{0},r}= B_{x_{0},r} \times (t_{0} -r^{2}, t_{0}) be a parabolic cylinder in the domain. We show that if either $\nu
\times \frac{\omega}{|\omega|} \in
L^{\gamma,\alpha}_{x,t}(Q_{z_{0},r})$\nu
\times \frac{\omega}{|\omega|} \in
L^{\gamma,\alpha}_{x,t}(Q_{z_{0},r}) with $\frac{3}{\gamma} + \frac{2}{\alpha} \leq 1, {\rm or} \omega \times
\frac{\nu} {|\nu|} \in L^{\gamma,\alpha}_{x,t} (Q_{z_{0},r})$\frac{3}{\gamma} + \frac{2}{\alpha} \leq 1, {\rm or} \omega \times
\frac{\nu} {|\nu|} \in L^{\gamma,\alpha}_{x,t} (Q_{z_{0},r}) with
\frac3g + \frac2a £ 2\frac{3}{\gamma} + \frac{2}{\alpha} \leq 2, where Lγ, αx,t denotes the Serrin type of class, then z0 is a regular point for ν. This refines previous local regularity criteria for the suitable weak solutions. 相似文献
14.
This paper deals with the rational function approximation of the irrational transfer function
G(s) = \fracX(s)E(s) = \frac1[(t0s)2m + 2z(t0s)m + 1]G(s) = \frac{X(s)}{E(s)} = \frac{1}{[(\tau _{0}s)^{2m} + 2\zeta (\tau _{0}s)^{m} + 1]} of the fundamental linear fractional order differential equation
(t0)2m\fracd2mx(t)dt2m + 2z(t0)m\fracdmx(t)dtm + x(t) = e(t)(\tau_{0})^{2m}\frac{d^{2m}x(t)}{dt^{2m}} + 2\zeta(\tau_{0})^{m}\frac{d^{m}x(t)}{dt^{m}} + x(t) = e(t), for 0<m<1 and 0<ζ<1. An approximation method by a rational function, in a given frequency band, is presented and the impulse and
the step responses of this fractional order system are derived. Illustrative examples are also presented to show the exactitude
and the usefulness of the approximation method. 相似文献
15.
Katrin Schumacher 《Journal of Mathematical Fluid Mechanics》2009,11(4):552-571
We investigate the solvability of the instationary Navier–Stokes equations with fully inhomogeneous data in a bounded domain
W ì \mathbbRn \Omega \subset {{\mathbb{R}}^{n}} . The class of solutions is contained in Lr(0, T; Hb, qw (W))L^{r}(0, T; H^{\beta, q}_{w} (\Omega)), where Hb, qw (W){H^{\beta, q}_{w}} (\Omega) is a Bessel-Potential space with a Muckenhoupt weight w. In this context we derive solvability for small data, where this smallness can be realized by the restriction to a short
time interval. Depending on the order of this Bessel-Potential space we are dealing with strong solutions, weak solutions,
or with very weak solutions. 相似文献
16.
Jingchi Huang Marius Paicu Ping Zhang 《Archive for Rational Mechanics and Analysis》2013,209(2):631-682
In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier–Stokes equations with initial data ${a_0 \in L^\infty (\mathbb{R}^d), u_0 = (u_0^h, u_0^d) \in \dot{B}^{-1+\frac{d}{p}}_{p, r} (\mathbb{R}^d)}$ , which satisfy ${(\mu \| a_0 \|_{L^\infty} + \|u_0^h\|_{\dot{B}^{-1+\frac{d}{p}}_{p, r}}) {\rm exp}(C_r{\mu^{-2r}}\|u_0^d\|_{\dot{B}^{-1+\frac{d}{p}}_{p,r}}^{2r}) \leqq c_0\mu}$ for some positive constants c 0, C r and 1 < p < d, 1 < r < ∞. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity fields. Furthermore, with additional regularity assumptions on the initial velocity or on the initial density, we can also prove the uniqueness of such a solution. We should mention that the classical maximal L p (L q ) regularity theorem for the heat kernel plays an essential role in this context. 相似文献
17.
18.
Let Ω be a bounded smooth domain in ${{\bf R}^N, N\geqq 3}Let Ω be a bounded smooth domain in
RN, N\geqq 3{{\bf R}^N, N\geqq 3}, and Da1,2(W){D_a^{1,2}(\Omega)} be the completion of C0¥(W){C_0^\infty(\Omega)} with respect to the norm:
||u||a2=òW |x|-2a|?u|2dx.||u||_a^2=\int_\Omega |x|^{-2a}|\nabla u|^2{d}x. 相似文献
19.
We study the global attractor of the non-autonomous 2D Navier–Stokes (N.–S.) system with singularly oscillating external force of the form . If the functions g
0(x, t) and g
1 (z, t) are translation bounded in the corresponding spaces, then it is known that the global attractor is bounded in the space H, however, its norm may be unbounded as since the magnitude of the external force is growing. Assuming that the function g
1 (z, t) has a divergence representation of the form where the functions (see Section 3), we prove that the global attractors of the N.–S. equations are uniformly bounded with respect to for all . We also consider the “limiting” 2D N.–S. system with external force g
0(x, t). We have found an estimate for the deviation of a solution of the original N.–S. system from a solution u
0(x, t) of the “limiting” N.–S. system with the same initial data. If the function g
1 (z, t) admits the divergence representation, the functions g
0(x, t) and g
1 (z, t) are translation compact in the corresponding spaces, and , then we prove that the global attractors converges to the global attractor of the “limiting” system as in the norm of H. In the last section, we present an estimate for the Hausdorff deviation of from of the form: in the case, when the global attractor is exponential (the Grashof number of the “limiting” 2D N.–S. system is small).
相似文献
20.
Alessio Figalli 《Archive for Rational Mechanics and Analysis》2010,195(2):533-560
Given two densities f and g, we consider the problem of transporting a fraction ${m \in [0,\min\{\|f\|_{L^1},\|g\|_{L^1}\}]}
|