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1.
The objective of this article is to derive a macroscopic Darcy’s law for a fluid-saturated moving porous medium whose matrix
is composed of two solid phases which are not in direct contact with each other (weakly coupled solid phases). An example of this composite medium is the case of a solid matrix, unfrozen water, and an ice matrix within the pore space.
The macroscopic equations for this type of saturated porous material are obtained using two-space homogenization techniques
from microscopic periodic structures. The pore size is assumed to be small compared to the macroscopic scale under consideration.
At the microscopic scale the two weakly coupled solids are described by the linear elastic equations, and the fluid by the linearized Navier–Stokes equations with appropriate
boundary conditions at the solid–fluid interfaces. The derived Darcy’s law contains three permeability tensors whose properties
are analyzed. Also, a formal relation with a previous macroscopic fluid flow equation obtained using a phenomenological approach
is given. Moreover, a constructive proof of the existence of the three permeability tensors allows for their explicit computation
employing finite elements or analogous numerical procedures. 相似文献
2.
Adriano Montanaro 《Archive for Rational Mechanics and Analysis》1998,143(4):375-400
We consider equilibria arising in a model for phase transitions which correspond to stable critical points of the constrained
variational problem Here W is a double‐well potential and is a strictly convex domain. For ε small, this is closely related to the problem of partitioning Ω into two subdomains of fixed volume, where the subdomain boundaries correspond to the transitional boundary between phases.
Motivated by this geometry problem, we show that in a strictly convex domain, stable critical points of the original variational
problem have a connected, thin transition layer separating the two phases. This relates to work in [GM] where special geometries
such as cylindrical domains were treated, and is analogous to the results in [CHo] which show that
in a convex domain, stable critical points of the corresponding unconstrained problem are constant. The proof of connectivity employs tools from geometric measure theory including the co‐area formula
and the isoperimetric inequality on manifolds. The thinness of the transition layer follows from a separate calculation establishing
spatial decay of solutions to the pure phases.
(Accepted July 15, 1996) 相似文献
3.
This paper presents an experimental investigation of one-dimensional moving shock waves in vertical soap films. The shock
waves were generated by bursting the films with a perforating spark. Images of propagating shock waves and small disturbances
were recorded using a fast line scan CCD camera. An aureole and a shock wave preceding the rim of the expanding hole were
clearly observed. These images are similar to the x-t diagrams in gas dynamics and give the velocities of shock and sound waves. The moving shock waves cause jumps in thickness.
The variations of the induced Mach number, M2 and the ratio of film thickness across the shock wave, δ
2/δ
1, are plotted versus the shock Mach number, M
s. Both results suggest that soap films are analogous to compressible gases with a specific heat ratio of γ≅1.0.
Published online: 15 October 2002 相似文献
4.
In this paper we investigate a subgrid model based on an anisotropic version of the NS-α model using a lid-driven cavity flow at a Reynolds number of 10,000. Previously the NS-α model has only been used numerically in the isotropic form. The subgrid model is developed from the Eulerian-averaged anisotropic
equations (Holm, Physica D 133:215, 1999). It was found that when α
2 was based on the mesh numerical oscillations developed which manifested themselves in the appearance of streamwise vortices
and a ‘mixing out’ of the velocity profile. This is analogous to the Craik–Leibovich mechanism, with the difference being
that the oscillations here are not physical but numerical. The problem could be traced back to the discontinuity in α
2 encountered when α
2 = 0 on the endwalls. A definition of α
2 based on velocity gradients, rather than mesh spacing, is proposed and tested. Using this definition the results with the
model show a significant improvement. The splitting of the downstream wall jet, rms and shear stress profiles are correctly
captured a coarse mesh. The model is shown to predict both positive and negative energy transfer in the jet impingement region,
in qualitative agreement with DNS results. 相似文献
5.
Using a normal mode analysis, we predict the infinite dilution linear viscoelastic properties of single-strand (ss) DNA molecules
and compare the results to the linear viscoelastic data of Shusterman et al. (Phys Rev Let 92(4):048303, 2004) obtained by
monitoring the diffusion of a fluorescently labeled terminus of the molecule. To compute the overall best global fit, we constrain
the hydrodynamic interaction parameter, h*, equilibrium root mean square spring extension, b, and the number of Kuhn steps per spring, N
K,S, to be equal for the strands compared. The fits using the bead-spring model for all but 23,100 base ss-DNA strands match
the experimental data at long times with significant deviations at intermediate and short times. However, parameters fitted
separately to all individual strand lengths predict results well. The best fits to data for 2,400 and 6,700 base pairs yield
N
K,S ∼12 and h* = 0.12. These values are similar to those found for conventional polymers such as polystyrene which have been successfully
modeled with N
K,S ∼7 and h* = 0.15, indicating ss-DNA and polystyrene exhibit analogous hydrodynamic behavior. 相似文献
6.
7.
The classical Fokker–Planck equation is a linear parabolic equation which describes the time evolution of the probability
distribution of a stochastic process defined on a Euclidean space. Corresponding to a stochastic process, there often exists
a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential
and an entropy. In recent years, it has been shown that the Fokker–Planck equation is the gradient flow of the free energy
functional defined on the Riemannian manifold of probability distributions whose inner product is generated by a 2-Wasserstein
distance. In this paper, we consider analogous matters for a free energy functional or Markov process defined on a graph with
a finite number of vertices and edges. If N ≧ 2 is the number of vertices of the graph, we show that the corresponding Fokker–Planck equation is a system of N
nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. However, in contrast to stochastic
processes defined on Euclidean spaces, the situation is more subtle for discrete spaces. We have different choices for inner
products on the space of probability distributions resulting in different Fokker–Planck equations for the same process. It
is shown that there is a strong connection but there are also substantial discrepancies between the systems of ordinary differential
equations and the classical Fokker–Planck equation on Euclidean spaces. Furthermore, both systems of ordinary differential
equations are gradient flows for the same free energy functional defined on the Riemannian manifolds of probability distributions
with different metrics. Some examples are also discussed. 相似文献
8.
The exact linear three-dimensional equations for a elastically monoclinic (13 constant) plate of constant thickness are reduced
without approximation to a single 4th order differential equation for a thickness-weighted normal displacement plus two auxiliary equations for
weighted thickness integrals of a stress function and the normal strain. The 4th order equation is of the same form as in
classical (Kirchhoff) theory except the unknown is not the midsurface normal displacement. Assuming a solution of these plate
equations, we construct so-called modified Saint-Venant solutions—“modified” because they involve non-zero body and surface
loads. That is, solutions of the exact three-dimensional elasticity equations that exhibit no boundary layers and that are
subject to a special set of body and surface loads that leave the analogous plate loads arbitrary. 相似文献
9.
We consider a linear system of thermoelasticity in a compact, C
infin, n-dimensional connected Riemannian manifold. This system consists of a wave equation coupled to a heat equation. When the boundary
of the manifold is non‐empty, Dirichlet boundary conditions are considered. We study the controllability properties of this
system when the control acts in the hyperbolic equation (and not in the parabolic one) and has its support restricted to an
open subset of the manifold. We show that, if the control time and the support of the control satisfy the geometric control
condition for the wave equation, this system of thermoelasticity is null-controllable. More precisely, any finite‐energy solution
can be driven to zero at the control time. An analogous result is proved when the control acts on the parabolic equation.
Finally, when the manifold has no boundary, the null‐controllability of the linear system of three‐dimensional thermoelastic
ity is proved.
(Accepted June 13, 1996) 相似文献
10.
G. A. Kluitenberg 《Applied Scientific Research》1972,25(1):383-398
A generalization is given of the author's theory for plasticity phenomena. The theory includes the possibility of both stress
and strain relaxation in the preplastic range. Methods of non-equilibrium thermodynamics are used. The plasticity phenomenon
is explained by introducing a physical assumption concerning the phenomenological coefficients. A yield function is proposed
which includes the Bauschinger effect and strain hardening. If the free energy f has the form f=f
(1)+f
(2), where f
(1) is a function of the temperature and the elastic strains and f
(2) is a function of the temperature and the inelastic strains, and if cross effects between the plastic flow and elastic relaxation
phenomena may be neglected, the proposed yield function is such that the derivative with respect to time of the deviator of
the plastic strain tensor is given by
, where Φ is the yield function, ταβ is the mechanical stress tensor, and η is a coefficient which vanishes in the preplastic
range. If the equations of state may be linearized the proposed yield function reduces to a function which is analogous to
a yield function proposed by Freudenthal. If the plastic flow phenomenon is not associated with changes in the microscopic
structure of the medium the proposed yield function reduces to the Von Mises function. It follows from the theory that in
a first approximation elastic relaxation phenomena in the preplastic range may be described by the equation for Poynting-Thomson
media (standard linear solids). An equation which characterizes Schofield-Scott Blair media is also derived from the developed
theory. 相似文献
11.
The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable
defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic
obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected,
having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to
establish sufficient conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong
to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the
mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that
(i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle
and the background solid are heterogeneous, and (ii) they are dimensionally consistent, i.e., invariant under the choice of
physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier
studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective
of the vibration frequency. When applied to the situation where both the scatterer and the background medium are viscoelastic, i.e., dissipative, on the other hand, the same type of analysis
shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the “viscoelastic-viscoelastic”
case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically
insulated from its surroundings—a feature that is particularly cloaked in situations when either the background medium or
the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions
for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results
indicate that the set of transmission values is indeed empty in the “elastic-viscoelastic” case, and countable for “elastic-elastic”
and “viscoelastic-viscoelastic” configurations. 相似文献
12.
Particles have been shown to adsorb at the interface between immiscible homopolymer melts and to affect the morphology of
blends of those homopolymers. We examined the effect of such interfacially active particles on the morphology of droplet/matrix
blends of model immiscible homopolymers. Experiments were conducted on blends of polydimethylsiloxane and 1,4-polyisoprene
blended in either a 20:80 or 80:20 weight ratio. The effects of three different particle types, fluoropolymer particles, iron
particles, and iron oxyhydroxide particles, all at a loading of 0.5 vol.%, were examined by rheology and by direct flow visualization.
Particles were found to significantly affect the strain recovery behavior of polymer blends, increasing or decreasing the
ultimate recovery, slowing down or accelerating the recovery kinetics, and changing the dependence of these parameters on
the applied stress prior to cessation of shear. These rheological observations were found to correlate reasonably well with
particle-induced changes in drop size. The particles can both increase as well as decrease the drop size, depending on the
particle type, as well as on which phase is continuous. The cases in which particles cause a decrease in drop size are analogous
to the particle stabilization of “Pickering emulsions” well-known from the literature on oil/water systems. We hypothesize
that cases in which particles increase drop size are analogous to the “bridging–dewetting” mechanism known in the aqueous
foam literature. 相似文献
13.
Very general weak forms may be developed for dynamic systems, the most general being analogous to a Hu-Washizu three-field
formulation, thus paralleling well-established weak methods of solid mechanics. In this work two different formulations are
developed: a pure displacement formulation and a two-field mixed formulation. With the objective of developing a thorough
understanding of the peculiar features of finite elements in time, the relevant methodologies associated with this approach
for dynamics are extensively discussed. After having laid the theoretical bases, the finite element approximation and the
linearization of the resulting forms are developed, together with a method for the treatment of holonomic and nonholonomic
constraints, thus widening the horizons of applicability over the vast world of multibody system dynamics. With the purpose
of enlightening on the peculiar numerical behavior of the different approaches, simple but meaningful examples are illustrated.
To this aim, significant parallels with elastostatics are emphasized.
Paper presented at the ‘International Technical Specialists' Meeting on Rotorcraft Basic Research’, March 25–27, 1991, Georgia Institute of Technology, Atlanta, Georgia, USA. 相似文献
14.
A thre-dimensional direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed
annular rotor-stator cavity characterized by a large aspect ratio G = (b − a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Ω considered is equivalent to the rotational Reynolds number Re = Ωb
2/ν= 9 .5 × 104 (ν the kinematic viscosity of water). This corresponds to a value at which experiment has revealed that the stator boundary
layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the computed solution with velocity
measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence
by comparing the turbulence properties with available data in the literature (Lygren and Andersson, J Fluid Mech 426:297–326,
2001). An approximately self-similar boundary layer behavior is observed along the stator. The wall-normal variations of the structural
parameter and of characteristic angles confirm that this boundary layer is three-dimensional. A quadrant analysis (Kang et
al., Phys Fluids 10:2315–2322, 1998) of conditionally averaged velocities shows that the asymmetries obtained are dominated by Reynolds stress-producing events
in the stator boundary layer. Moreover, Case 1 vortices (with a positive wall induced velocity) are found to be the major
source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson (J Fluid Mech 426:297–326,
2001). 相似文献
15.
The results of a theoretical and experimental investigation of nonsymmetric flow around a V-wing with supersonic leading edges
are presented. The range of the angles of attack and yaw, on which additional singular lines are formed on the windward cantilever
of the wing, are experimentally determined using different techniques of flow diagnostics. These are one convergence line
and two divergence lines in the transverse flow which were not previously observable in the calculations of ideal-gas flow
around wings. It is established that the appearance of the three new alternating singular lines located between the central
chord of the wing and a convergence line, exterior to them and occurring within the framework of the ideal gas model, is associated
with the relation between the intensities of two contact discontinuities. One of these proceeds from the branching point of
the bow shock above the leeward cantilever, while the second issues out of the triple point of a λ-shaped shock configuration accompanying developed turbulent-boundary-layer separation generated by an internal shock incident
on the leeward cantilever surface. If the intensity of the contact discontinuity proceeding from the branching point of the
bow shock is large as compared with that of the contact discontinuity of the λ-configuration, then the flow pattern realized on the windward cantilever is analogous to that obtained within the framework
of the ideal gas model, that is, it includes one convergence line on the wing surface. Under these conditions, the results
of the calculations within the framework of the ideal gas model are applicable for understanding the phenomena occurring in
the wing shock layer in a considerable part of the control parameter range, including the regimes with intense internal shocks
generating turbulent boundary layer separation from the leeward cantilever. Corrections should be made only for a carachteristic
pressure distribution in the separation zone and, as a consequence of separation, for an elevated pressure level in the vicinity
of the central chord which is the stagnation line of the transverse flow that has passed across the oblique and terminating
shocks of the λ-configuration and possesses a higher stagnation pressure than the flow that has passed in an ideal gas across the internal
shock incident normally on the leeward cantilever. This is possible only when the divergence line, at which the stream surface
enclosing the turbulent boundary layer separation zone enters, does not go over from the leeward onto the windward cantilever. 相似文献
16.
Giovanni P. Galdi 《Archive for Rational Mechanics and Analysis》2006,180(1):97-126
In this paper we show that every solution of the three-dimensional exterior Navier-Stokes boundary-value problem, corresponding
to a given non-zero, constant velocity at infinity (flow past a body) and belonging to a very general functional class, , can be determined by a finite number of parameters. Our results extend the analogous classical results by Foiaş & Temam
[6, 7], and by Jones & Titi [14] for the interior problem. This extension is by no means trivial, in that all fundamental
tools used in the case of the interior problem – such as compactness of the Sobolev embeddings, Poincaré's inequality, and
the special basis constituted by eigenfunctions of the Stokes operator – are no longer available for the exterior problem.
An important consequence of our results is that any solution in is uniquely determined by the knowledge of the associated velocity field only ``near' the boundary. Just how ``near' it
has to be depends only on the Reynolds number and on the body.
Dedicated to John Heywood on the occasion of his 65th birthday 相似文献
17.
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
18.
Carlo Marchioro Evelyne Miot Mario Pulvirenti 《Archive for Rational Mechanics and Analysis》2011,201(1):1-26
In this paper we establish global existence and uniqueness of the solution to the three-dimensional Vlasov–Poisson system
in the presence of point charges with repulsive interaction. The present analysis extends an analogous two-dimensional result
(Caprino and Marchioro in Kinet. Relat. Models 3(2):241–254, 2010). 相似文献
19.
Although literature presents several alternatives, an approach based on the electronic analogy was still not considered for
the implementation of an inductor-free realization of the double scroll Chua’s circuit. This paper presents a new inductor-free
configuration of the Chua’s circuit based on the electronic analogy. This proposal results in a versatile and functional inductorless
implementation of the Chua’s circuit that offers new and interesting features for several applications. The analogous circuit
is implemented and used to perform an experimental mapping of a large variety of attractors. 相似文献
20.
Chien-Hsin Chen 《Heat and Mass Transfer》2006,42(9):853-860
Forced convection flow in a microchannel with constant wall temperature is studied, including viscous dissipation effect. The slip-flow regime is considered by incorporating both the velocity-slip and the temperature-jump conditions at the surface. The energy equation is solved for the developing temperature field using finite integral transform. To increase βv
Kn is to increase the slip velocity at the wall surface, and hence to decrease the friction factor. Effects of the parameters βv
Kn, β, and Br on the heat transfer results are illustrated and discussed in detail. For a fixed Br, the Nusselt number may be either higher or lower than those of the continuum regime, depending on the competition between the effects of βv
Kn and β. At a given βv
Kn the variation of local Nusselt number becomes more even when β becomes larger, accompanied by a shorter thermal entrance length. The fully developed Nusselt number decreases with increasing β irrelevant to βv
Kn. The increase in Nusselt number due to viscous heating is found to be more pronounced at small βv
Kn. 相似文献