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1.
Although a fundamental physical parameter, surface tension is difficult to measure. Common tensiometry inaccuracy comes from
failure to control air–liquid–solid contact conditions, or account for liquid meniscus geometry and buoyancy corrections.
This paper describes an in situ tensiometry technique, based on withdrawal of a thin-walled tube from the liquid interface,
that enforces a known air–liquid–solid contact condition. This technique can be pursued at any level of experimental hygiene.
Experimental results for filtered tap water, an alcohol–water solution, and a surfactant–water solution show that results
repeatable to three significant digits are obtained with modest effort for a variety of geometrical parameters.
Received: 7 October 1997/Accepted: 23 April 1998 相似文献
2.
We show that the Reissner–Mindlin plate bending model has a wider range of applicability than the Kirchhoff–Love model for
the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the
transverse direction, the Reissner–Mindlin model solution converges to the three-dimensional linear elasticity solution in
the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect,
the Kirchhoff–Love model fails.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential
functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential
functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric
configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited,
where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy.
In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic
materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements
satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest
to the reader beyond the present application.
Dedicated to Morton E. Gurtin 相似文献
4.
The purpose of this study is to implement a new analytical method which is a combination of the homotopy analysis method (HAM)
and the Padé approximant for solving magnetohydrodynamic boundary-layer flow. The solution is compared with the numerical
solution. Comparisons between the HAM–Padé and the numerical solution reveal that the new technique is a promising tool for
solving MHD boundary-layer equations. The effects of the various parameters on the velocity and temperature profiles are presented
graphically form. Favorable comparisons with previously published works (Crane, J. Appl. Math. Phys. 21:645–647, 1970, and Vajravelu and Hadjinicolaou, Int. J. Eng. Sci. 35:1237–1244, 1997) are obtained. It is predicted that HAM–Padé can have wide application in engineering problems (especially for boundary-layer
and natural convection problems). 相似文献
5.
We establish a condition for the existence and uniqueness of a periodic solution of a system of nonlinear integro-differential
equations with pulse action. The solution is represented as the limit of periodic iterations. We give estimates for the rate
of convergence and for the exact solution of the system.
__________
Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 553–573, October–December, 2005. 相似文献
6.
Konstantin Pileckas 《Journal of Mathematical Fluid Mechanics》2008,10(2):272-309
The time-dependent Navier–Stokes system is studied in a two-dimensional domain with strip-like outlets to infinity in weighted
Sobolev function spaces. It is proved that under natural compatibility conditions there exists a unique solution with prescribed
fluxes over cross-sections of outlets to infinity which tends in each outlet to the corresponding time-dependent Poiseuille
flow. The obtained results are proved for arbitrary large norms of the data (in particular, for arbitrary fluxes) and globally
in time.
The authors are supported by EC FP6 MC–ToK programme SPADE2, MTKD–CT–2004–014508. 相似文献
7.
A new general solution in terms of two scalar potential functions for classical elastodynamics of x
3-convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of
its connection to Kovalevshi–Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the
aid of the theory of repeated wave equations and Boggio’s theorem. With the time dependence of the potentials suppressed,
the new decomposition can, unlike Lamé’s, degenerate to a complete solution for elastostatic problems.
相似文献
8.
We establish a Navier–Stokes–Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain
of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff
condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of
DiPerna–Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak
solution of a Navier–Stokes–Fourier system for all time. 相似文献
9.
The initial boundary value problem for the compressible Navier–Stokes equation is considered in an infinite layer of . It is proved that if the Reynolds and Mach numbers are sufficiently small, then strong solutions to the compressible Navier–Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations. The large time behavior of the solution is described by a solution of a one-dimensional viscous Burgers equation. The proof is given by a combination of spectral analysis of the linearized operator and a variant of the Matsumura–Nishida energy method. 相似文献
10.
We study the vanishing viscosity limit of the compressible Navier–Stokes equations to the Riemann solution of the Euler equations
that consists of the superposition of a shock wave and a rarefaction wave. In particular, it is shown that there exists a
family of smooth solutions to the compressible Navier–Stokes equations that converges to the Riemann solution away from the
initial and shock layers at a rate in terms of the viscosity and the heat conductivity coefficients. This gives the first
mathematical justification of this limit for the Navier–Stokes equations to the Riemann solution that contains these two typical
nonlinear hyperbolic waves. 相似文献
11.
The Navier–Stokes–Fourier system describing the motion of a compressible, viscous and heat conducting fluid is known to possess
global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong
solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within
the class of weak solutions. 相似文献
12.
Large Eddy Simulations Using the Subgrid-Scale Estimation Model and Truncated Navier–Stokes Dynamics
J. Andrzej Domaradzki Kuo Chieh Loh Patrick P. Yee 《Theoretical and Computational Fluid Dynamics》2002,15(6):421-450
We describe a procedure for large eddy simulations of turbulence which uses the subgrid-scale estimation model and truncated
Navier–Stokes dynamics. In the procedure the large eddy simulation equations are advanced in time with the subgrid-scale stress
tensor calculated from the parallel solution of the truncated Navier–Stokes equations on a mesh two times smaller in each
Cartesian direction than the mesh employed for a discretization of the resolved quantities. The truncated Navier–Stokes equations
are solved through a sequence of runs, each initialized using the subgrid-scale estimation model. The modeling procedure is
evaluated by comparing results of large eddy simulations for isotropic turbulence and turbulent channel flow with the corresponding
results of experiments, theory, direct numerical simulations, and other large eddy simulations. Subsequently, simplifications
of the general procedure are discussed and evaluated. In particular, it is possible to formulate the procedure entirely in
terms of the truncated Navier–Stokes equation and a periodic processing of the small-scale component of its solution.
Received 27 April 2001 and accepted 16 December 2001 相似文献
13.
A. G. Petrova 《Journal of Applied Mechanics and Technical Physics》2007,48(5):671-679
It is proved that the problem of one-dimensional motion of an emulsion under the action of thermocapillary forces has a self-similar
solution in a semi-infinite interval. The behavior of the solution is illustrated by numerical examples for aluminum-lead
emulsions, in which the carrier phase is lead or aluminum. The solution is compared with the solution of the self-similar
problem linearized in the low impurity concentration.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 61–70, September–October, 2007. 相似文献
14.
We consider a kinetic model for a system of two species of particles interacting through a long range repulsive potential
and a reservoir at given temperature. The model is described by a set of two coupled Vlasov–Fokker–Plank equations. The important
front solution, which represents the phase boundary, is a stationary solution on the real line with given asymptotic values
at infinity. We prove the asymptotic stability of the front for small symmetric perturbations. 相似文献
15.
A. M. Kovrizhnykh 《Journal of Applied Mechanics and Technical Physics》2009,50(1):147-154
A new solution for the shear angle is proposed which is a generalization of the solution Lee-Shaffer solution and allows the
determination of the cutting force and the shearing-element size. Merchant’s experimental data are processed taking into account
the resistance force at the cutting edge, and it is shown that accounting for this force leads to the need to increase the
internal friction angle in the calculated dependences in order to match theory with experiment. It is shown that the obtained
theoretical results agree well with experimental results.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 177–186, January–February, 2009. 相似文献
16.
We substantiate the application of the projection-iterative method to the solution of a boundary-value problem for integro-differential
equations with restrictions and control.
Translated from Neliniini Kolyvannya, Vol. 12, No. 1, pp. 83–91, January–March, 2009. 相似文献
17.
We consider a weakly nonlinear boundary-value problem for a system of second-order ordinary differential equations. We find
a sufficient condition for the existence of at least one solution of this problem and propose a convergent iterative algorithm
for the determination of its solution.
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Translated from Neliniini Kolyvannya, Vol. 9, No. 3, pp. 368–375, July–September, 2006. 相似文献
18.
Magnus Fontes 《Journal of Mathematical Fluid Mechanics》2010,12(3):412-434
In this work we study the fully nonhomogeneous initial boundary value problem for the two-dimensional time-dependent Navier–Stokes
equations in a general open space domain in R2 with low regularity assumptions on the initial and the boundary value data. We show that the perturbed Navier–Stokes operator
is a diffeomorphism from a suitable function space onto its own dual and as a corollary we get that the Navier–Stokes equations
are uniquely solvable in these spaces and that the solution depends smoothly on all involved data. Our source data space and
solution space are in complete natural duality and in this sense, without any smallness assumptions on the data, we solve
the equations for data with optimally low regularity in both space and time. 相似文献
19.
M. V. D’Angelo B. Semin G. Picard M. E. Poitzsch J. P. Hulin H. Auradou 《Transport in Porous Media》2010,84(2):389-408
The transport of fibers by a fluid flow is investigated in transparent channels modeling rock fractures: the experiments use
flexible polyester thread (mean diameter 280 μm) and water or a water–polymer solution. For a channel with smooth parallel walls and a mean aperture ā = 0.65 mm, both fiber segments of length ℓ = 20–150 mm and “continuous” fibers longer than the channel length have been used: in both the cases, the velocity of the
fibers and its variation with distance could be accounted for while neglecting friction with the walls. For rough self-affine
walls and a continuous gradient of the local mean aperture transverse to the flow, transport of the fibers by a water flow
is only possible in the region of larger aperture (ā ≲ 1.1 mm) and is of “stop and go” type at low velocities. With the polymer solution, the fibers move faster and more continuously
in high aperture regions and their interaction with the walls is reduced; fiber transport becomes also possible in narrower
regions where irreversible pinning occurred for water. In a third rough model with parallel walls and a low mean aperture
ā = 0.65 mm, fiber transport is only possible with the water–polymer solution. The dynamics of fiber deformations and entanglement
during pinning–depinning events and permanent pinning is analyzed. 相似文献
20.
G. M. Chernomashentsev 《Fluid Dynamics》1988,23(5):792-794
An exact solution of the Cauchy problem is constructed for the equation describing the three-dimensional molecular diffusion
of a gas. The result obtained is a natural generalization of the solution of the analogous Boussinesq problem.
Dnepropetrovsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 178–180, September–October,
1988. 相似文献