共查询到20条相似文献,搜索用时 937 毫秒
1.
Lawrence Markus 《Journal of Dynamics and Differential Equations》2007,19(1):133-154
In a celebrated theorem H?lder proved that the Euler Γ-function is differential transcendental, i.e. Γ(z) is not a solution of any (non-trivial) algebraic ordinary differential equation with coefficients that are complex numbers; and we extend his methods to the Riemann ζ-function. Moreover, we conjecture that Γ and ζ are differential independent, i.e. Γ(z) is not a solution of any such algebraic differential equation—even allowing coefficients that are differential polynomials in ζ(z). However, we are able to demonstrate only the partial result that Γ(z) and ζ(sin 2πz) are differential independent. 相似文献
2.
In this paper we study the two-dimensional hydrostatic Euler equations in a periodic channel. We prove the local existence
and uniqueness of H
s
solutions under the local Rayleigh condition. This extends Brenier’s (Nonlinearity 12(3):495–512, 1999) existence result by removing an artificial condition and proving uniqueness. In addition, we prove weak–strong uniqueness,
mathematical justification of the formal derivation and stability of the hydrostatic Euler equations. These results are based
on weighted H
s
a priori estimates, which come from a new type of nonlinear cancellation between velocity and vorticity. 相似文献
3.
Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively. 相似文献
4.
In this work, we measured 14 horizontal velocity profiles along the vertical direction of a rectangular microchannel with
aspect ratio α = h/w = 0.35 (h is the height of the channel and w is the width of the channel) using microPIV at Re = 1.8 and 3.6. The experimental velocity profiles are compared with the full 3D theoretical solution, and also with a Poiseuille
parabolic profile. It is shown that the experimental velocity profiles in the horizontal and vertical planes are in agreement
with the theoretical profiles, except for the planes close to the wall. The discrepancies between the experimental data and
3D theoretical results in the center vertical plane are less than 3.6%. But the deviations between experimental data and Poiseuille’s
results approaches 5%. It indicates that 2D Poiseuille profile is no longer a perfect theoretical approximation since α = 0.35. The experiments also reveal that, very near the hydrophilic wall (z = 0.5–1 μm), the measured velocities are significantly larger than the theoretical velocity based on the no-slip assumption.
A proper discussion on some physical effects influencing the near wall velocity measurement is given. 相似文献
5.
Charles M. Elliott Reiner Schätzle Barbara E. E. Stoth 《Archive for Rational Mechanics and Analysis》1998,145(2):99-127
In a Type‐II superconductor the magnetic field penetrates the superconducting body through the formation of vortices. In
an extreme Type‐II superconductor these vortices reduce to line singularities. Because the number of vortices is large it
seems feasible to model their evolution by an averaged problem, known as the mean-field model of superconductivity. We assume
that the evolution law of an individual vortex, which underlies the averaging process, involves the current of the generated
magnetic field as well as the curvature vector. In the present paper we study a two‐dimensional reduction, assuming all vortices
to be perpendicular to a given direction. Since both the magnetic field H and the averaged vorticity ω are curl‐free, we may represent them via a scalar magnetic potential q and a scalar stream function ψ, respectively. We study existence, uniqueness and asymptotic behaviour of solutions (ψ, q) of the resulting degenerate elliptic‐parabolic system (with curvature taken into account or not) by means of viscosity and
weak solutions. In addition we relate (ψ, q) to solutions (ω, H) of the mean‐field equations without curvature. Finally we construct special solutions of the corresponding stationary equations
with two or more superconducting phases.
(Accepted August 8, 1997) 相似文献
6.
Weakly R-KKM mappings——intersection theorems and minimax inequalities in topological spaces 总被引:1,自引:0,他引:1
In this paper, we introduce the concepts of weakly R-KKM mappings, R-convex and ,R-β-quasiconvex in general topological spaces without any convex structure. Relating to these, we obtain an extension to general topological spaces of Fan's matching theorem, namely that Lemma 1.2 in this paper. On this basis, two intersection theorems are proved in topological spaces. By using intersection theorems, some minimax inequalities of Ky Fan type are also proved in topological spaces. Our results generalize and improve the corresponding results in the literature. 相似文献
7.
One of the most promising approaches to characterizing the stable tearing process for lower constraint configurations in metallic
materials has been indicated to be the crack tip opening angle (CTOA) criterion. In this paper we examine the effect of measurement
distance selection and the impact of measurement procedures/analysis on the experimental CTOA-Δa resistance curve behavior of a Ti-6Al-4V and an Al5083 alloy. A new, systematic procedure for carrying out the experimental,
surface CTOA measurement process has been used, which has uncovered artifacts of measurement distance selection that have
not been presented prior to this study. By studying the CTOA-Δa behavior using a rigidly defined and consistent method, it is apparent that the measurement distance behind the crack tip
at which angles are measured has a direct impact on the shape of the early transitional behavior of the CTOA-Δa behavior as well as the critical, experimental CTOA values produced. 相似文献
8.
9.
Linear and nonlinear viscoelastic properties were examined for aqueous suspensions of monodisperse poly(methyl methacrylate-co-styrene) (MS) particles having the radius a
0
=45 nm and the volume fractions φ=0.428−0.448. These particles had surface charges and the resulting electrostatic surface
layer (electric double layer) had a thickness of ts=5.7 nm. At low frequencies in the linear viscoelastic regime, the MS particles behaved approximately as the Brownian hard
particles having an effective radius a
eff=a
0 + ts, and the dependence of their zero-shear viscosity η0 on an effective volume fraction φeff (={a
eff/a
0}3φ) agreed with the φ dependence of η0 of ideal hard-core silica suspensions. In a range of φeff < 0.63, this φeff dependence was well described by the Brady theory. However, the φeff dependence of the high-frequency plateau modulus was weaker and the terminal relaxation mode distribution was narrower for
the MS suspensions than for the hard-core suspensions. This result suggested that the electrostatic surface layer of the MS
particles was soft and penetrable (at high frequencies). In fact, this “softness” was more clearly observed in the nonlinear
regime: the nonlinear damping against step strain was weaker and the thinning under steady shear was less significant for
the MS suspension than for the hard-core silica suspensions having the same φeff. These weaker nonlinearities of the concentrated MS particles with φeff∼ 0.63 (maximum volume fraction for random packing) suggested that the surface layers of those particles were mutually penetrating
to provide the particles with a rather large mobility.
Received: 10 July 2001 Accepted: 2 November 2001 相似文献
10.
Yu. A. Abzaev 《Journal of Applied Mechanics and Technical Physics》2007,48(4):599-604
The temperature dependence of the yield stress τ*
Ni
3
Ge single crystals is studied. The temperature dependence τ*(T) in the high-temperature region (above 420 K) is found to be conditioned by thermally activated accumulation of the density of non-screw components of superdislocations.
Interaction of point defects with edge dislocations and its effect on the temperature anomaly of the yield stress in Ni
3
Ge single crystals are analyzed. The calculated results are found to agree with experimental data.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 154–161, July–August, 2007. 相似文献
11.
In this paper, a non-isobaric Marangoni boundary layer flow that can be formed along the interface of immiscible nanofluids
in surface driven flows due to an imposed temperature gradient, is considered. The solution is determined using a similarity
solution for both the momentum and energy equations and assuming developing boundary layer flow along the interface of the
immiscible nanofluids. The resulting system of nonlinear ordinary differential equations is solved numerically using the shooting
method along with the Runge-Kutta-Fehlberg method. Numerical results are obtained for the interface velocity, the surface
temperature gradient as well as the velocity and temperature profiles for some values of the governing parameters, namely
the nanoparticle volume fraction φ (0≤φ≤0.2) and the constant exponent β. Three different types of nanoparticles, namely Cu, Al2O3 and TiO2 are considered by using water-based fluid with Prandtl number Pr =6.2. It was found that nanoparticles with low thermal conductivity,
TiO2, have better enhancement on heat transfer compared to Al2O3 and Cu. The results also indicate that dual solutions exist when β<0.5. The paper complements also the work by Golia and Viviani (Meccanica 21:200–204, 1986) concerning the dual solutions in the case of adverse pressure gradient. 相似文献
12.
Avner Friedman Bei Hu Juan J. L. Velazquez 《Archive for Rational Mechanics and Analysis》2000,152(2):103-139
When a crack Γ
s
propagates in an elastic medium the stress intensity factors evolve with the tip x(s) of Γ
s
. In this paper we derive formulae which describe the evolution of these stress intensity factors for a homogeneous isotropic
elastic medium under plane strain conditions. Denoting by ψ=ψ(x,s) the stress potential (ψ is biharmonic and has zero traction along the crack Γ
s
) and by κ(s) the curvature of the crack at the tip x(s), we prove that the stress intensity factors A
1(s), A
2(s), as functions of s, satisfy:
where , are stress intensity factors of the tangential derivative of in the polar coordinate system at x(s) with θ=0 in the direction of the crack at x(s). The case of antiplane shearing is also briefly considered; in this case ψ is harmonic. 相似文献
13.
Using the extension of Krasnoselskii's fixed point theorem in a cone, we prove the existence of at least one positive solution to the nonlinear nth order m-point boundary value problem with dependence on the first order derivative. The associated Green's function for the nth order m-point boundary value problem is given, and growth conditions are imposed on the nonlinear term f which ensures the existence of at least one positive solution. A simple example is presented to illustrate applications of the obtained results. 相似文献
14.
Matthew Dobson Mitchell Luskin Christoph Ortner 《Archive for Rational Mechanics and Analysis》2010,197(1):179-202
Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are popular tools in computational
physics. For example, the force-based quasicontinuum (QCF) approximation is the only known pointwise consistent quasicontinuum
approximation for coupling a general atomistic model with a finite element continuum model. In this paper, we present a detailed
stability and error analysis of this method. Our optimal order error estimates provide a theoretical justification for the
high accuracy of the QCF approximation: they clearly demonstrate that the computational efficiency of continuum modeling can
be utilized without a significant loss of accuracy if defects are captured in the atomistic region. The main challenge we
need to overcome is the fact that the linearized QCF operator is typically not positive definite. Moreover, we prove that no uniform inf-sup stability condition holds for discrete versions of the W
1,p
-W
1,q
“duality pairing” with 1/p + 1/q = 1, if 1 ≤ p < ∞. However, we were able to establish an inf-sup stability condition for a discrete version of the W
1,∞-W
1,1 “duality pairing” which leads to optimal order error estimates in a discrete W
1,∞-norm. 相似文献
15.
16.
The generalized second-grade fluids, which have been used for modeling the creep of ice and the flow of coal-water and coal-oil
slurries, are among the simplest non-Newtonian fluid models that can describe shear-thinning/thickening and exhibit normal
stress effects. In this article, we conduct thermodynamic analysis on a class of generalized second-grade fluids, one distinguishing
feature of which is the existence of a constitutive function Φ that describes frictional heating. We work within the framework
of Serrin’s original formulation of neoclassical thermodynamics, where internal energy and entropy functions, if they exist
for a continuous body at all, are to be derived from the classical First Law and (quantitatively reformulated) Second Law
of thermodynamics for cycles. For the class of generalized second-grade fluids in question, we show from the First Law that
an internal energy density u exists, and we derive the equation of energy balance; from the Second Law, we demonstrate the existence of an entropy density
s and derive the Clausius–Duhem inequality that it satisfies. We obtain explicit expressions for u, s and the frictional heating Φ, and derive thermodynamic restrictions on the material functions of temperature μ, α
1, and α
2 that appear in the constitutive relation for the Cauchy stress. For the special case of second-grade fluids, our expressions
for u and s agree with those which Dunn and Fosdick [6] derived under the theoretical framework of the rational thermodynamics of Coleman
and Noll. 相似文献
17.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2007,9(4):506-516
In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R
3 must be smooth if the direction of the vorticity is Lipschitz continuous with respect to the space variables. In reference
[5] the authors improve the above result by showing that Lipschitz continuity may be replaced by 1/2-H?lder continuity. A
central point in the proofs is to estimate the integral of the term (ω · ∇)u · ω, where u is the velocity and ω = ∇ × u is the vorticity. In reference [4] we extend the main estimates on the above integral term to solutions under the slip boundary
condition in the half-space R
+3. This allows an immediate extension to this problem of the 1/2-H?lder sufficient condition.
The aim of these notes is to show that under the non-slip boundary condition the above integral term may be estimated as well
in a similar, even simpler, way. Nevertheless, without further hypotheses, we are not able now to extend to the non slip (or
adherence) boundary condition the 1/2-H?lder sufficient condition. This is not due to the “nonlinear" term (ω · ∇)u · ω but to a boundary integral which is due to the combination of viscosity and adherence to the boundary. On the other hand,
by appealing to the properties of Green functions, we are able to consider here a regular, arbitrary open set Ω.
相似文献
18.
Hideyuki Uematsu Yuji Aoki Masataka Sugimoto Takashi Taniguchi Kiyohito Koyama 《Rheologica Acta》2008,47(2):237-242
We investigated the dynamic viscoelasticity and elongational viscosity of polypropylene (PP) containing 0.5 wt% of 1,3:2,4-bis-O-(p-methylbenzylidene)-d-sorbitol (PDTS). The PP/PDTS system exhibited a sol–gel transition (T
gel) at 193 °C. The critical exponent n was nearly equal to 2/3, in agreement with the value predicted by a percolation theory. This critical gel is due to a three-dimensional
network structure of PDTS crystals. The elongational viscosity behavior of neat PP followed the linear viscosity growth function
3η
+
(t), where η
+
(t) is the shear stress growth function in the linear viscoelastic region. The elongational viscosity of the PP/PDTS system
also followed the 3η
+
(t) above T
gel but did not follow the 3η
+
(t) and exhibited strong strain-softening behavior below T
gel. This strain softening can be attributed to breakage of the network structure of PDTS with a critical stress (σ
c) of about 104 Pa. 相似文献
19.
TheT
ε
*
integral was calculated on the surface of single edge notched, three-point bend (SE(B)) specimens using experimentally obtained
displacements. Comparison was made withT
ε
*
calculated with the measured surface displacements andT
ε
*
calculated at several points through the thickness of a finite element (FE) model of the SE(B) specimen. Good comparison
was found between the surfaceT
ε
*
calculated from displacements extracted from the FE model and the surfaceT
ε
*
calculated from experimentally obtained displacements. The computedT
ε
*
integral was also observed to decrease as the crack front was traversed from the surface to the mid-plane of the specimen.
Mid-planeT
ε
*
values tend to be approximately 10% of the surface values. 相似文献