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1.
Raffaella Rizzoni 《Continuum Mechanics and Thermodynamics》2011,23(4):319-335
The theory of thin wires developed in Dret and Meunier (Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 337:143–147,
2003) is adapted to phase-transforming materials with large elastic moduli in the sense discussed in James and Rizzoni (J Elast
59:399–436, 2000). The result is a one-dimensional constitutive model for shape memory wires, characterized by a small number of material
constants. The model is used to analyze self-accommodated and detwinned microstructures and to study superelasticity. It also
turns out that the model successfully reproduces the behavior of shape memory wires in experiments of restrained recovery
(Tsoi et al. in Mater Sci Eng A 368:299–310, 2004; Tsoi in 50:3535–3544, 2002; S̆ittner et al. in Mater Sci Eng A 286:298–311, 2000; vokoun in Smart Mater Struct 12:680–685, 2003; Zheng and Cui in Intermetallics 12:1305–1309, 2004; Zheng et al. in J Mater Sci Technol 20(4):390–394, 2004). In particular, the model is able to predict the shift to higher transformation temperatures on heating. The model also
captures the effect of prestraining on the evolution of the recovery stress and of the martensite volume fraction. 相似文献
2.
The turbulence structure near a wall is a very active subject of research and a key to the understanding and modeling of this
flow. Many researchers have worked on this subject since the fifties Hama et al. (J Appl Phys 28:388–394, 1957). One way to study this organization consists of computing the spatial two-point correlations. Stanislas et al. (C R Acad
Sci Paris 327(2b):55–61, 1999) and Kahler (Exp Fluids 36:114–130, 2004) showed that double spatial correlations can be computed from stereoscopic particle image velocimetry (SPIV) fields and can
lead to a better understanding of the turbulent flow organization. The limitation is that the correlation is only computed
in the PIV plane. The idea of the present paper is to propose a new method based on a specific stereoscopic PIV experiment
that allows the computation of the full 3D spatial correlation tensor. The results obtained are validated by comparison with
2D computation from SPIV. They are in very good agreement with the results of Ganapthisubramani et al. (J Fluid Mech 524:57–80,
2005a). 相似文献
3.
Recently, the tube diameter relaxation time in the evolution equation of the molecular stress function (MSF) model (Wagner
et al., J Rheol 49: 1317–1327, 2005) with the interchain pressure effect (Marrucci and Ianniruberto, Macromolecules 37:3934–3942, 2004) included was shown to be equal to three times the Rouse time in the limit of small chain stretch. From this result, an advanced
version of the MSF model was proposed, allowing modeling of the transient and steady-state elongational viscosity data of
monodisperse polystyrene melts without using any nonlinear parameter, i.e., solely based on the linear viscoelastic characterization
of the melts (Wagner and Rolón-Garrido 2009a, b). In this work, the same approach is extended to model experimental data in shear flow. The shear viscosity of two polybutadiene
solutions (Ravindranath and Wang, J Rheol 52(3):681–695, 2008), of four styrene-butadiene random copolymer melts (Boukany et al., J Rheol 53(3):617–629, 2009), and of four polyisoprene melts (Auhl et al., J Rheol 52(3):801–835, 2008) as well as the shear viscosity and the first and second normal stress differences of a polystyrene melt (Schweizer et al.,
J Rheol 48(6):1345–1363, 2004), are analyzed. The capability of the MSF model with the interchain pressure effect included in the evolution equation of
the chain stretch to model shear rheology on the basis of linear viscoelastic data alone is confirmed. 相似文献
4.
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation
matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima–Shizuta stability
condition formulated in Umeda et al. (Jpn J Appl Math 1:435–457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249–275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition.
However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko
system and the Euler–Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is
weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375–413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647–667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001–1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima–Shizuta condition,
and to analyze the weak dissipative structure for general systems with non-symmetric relaxation. 相似文献
5.
Kazemi et al. (SPE Reserv Eng 7(2):219–227, 1992) suggested an empirical matrix-fracture transfer function, verified based on experimental data of Mattax and Kyte (Trans
AIME 225(15):177–184, 1962), to model fluid flow in naturally fractured dual porosity petroleum reservoirs using a dual-porosity numerical simulator.
Their generalized shape factor should be valid for all possible irregular matrix blocks. The factor is calculated based on
the volume of the matrix block, the surface open to flow in all directions and the distances of these surfaces to the centre
of the matrix block. The summation is done over all open surfaces of a matrix block. Kazemi et al. (1992) showed that for rectangles and cylinders the formula reduces to the well-known forms of the shape factor. By the time, many
authors indicated the validity of the formula, but no theoretical proof was offered for that so far. This study derives the
Kazemi et al. (1992) shape factor using control volume finite difference discretization on the fracture-matrix dual continuum. The matrix blocks
are handled as Voronoi polyhedra. The derivation is given for both isotropic and tensorial matrix permeability. Based on this
derivation the authors conclude that the Kazemi et al. (SPE Reserv Eng 7(2):219–227, 1992) formula is exact under pseudo-steady-state conditions within the dual continuum mathematical concept of natural fractured
dual porosity systems. 相似文献
6.
Incompressible 3-D DNS is performed in non-decaying turbulence with single step chemistry to validate a new analytical expression
for turbulent burning velocity. The proposed expression is given as a sum of laminar and turbulent contributions, the latter
of which is given as a product of turbulent diffusivity in unburned gas and inverse scale of wrinkling at the leading edge.
The bending behavior of U
T at higher u′ was successfully reproduced by the proposed expression. It is due to decrease in the inverse scale of wrinkling at the leading
edge, which is related with an asymmetric profile of FSD with increasing u′. Good agreement is achieved between the analytical expression and the turbulent burning velocities from DNS throughout the
wrinkled, corrugated and thin reaction zone regimes. Results show consistent behavior with most experimental correlations
in literature including those by Bradley et al. (Philos Trans R Soc Lond A 338:359–387, 1992), Peters (J Fluid Mech 384:107–132, 1999) and Lipatnikov et al. (Progr Energ Combust Sci 28:1–74, 2002). 相似文献
7.
We study the minimal speed for a two species competition system with monostable nonlinearity. We are interested in the linear
determinacy for the minimal speed in the sense defined by (Lewis et al. J Math Biol 45:219–233, 2002). We provide more general cases for the linear determinacy than that of (Lewis et al. J Math Biol 45:219–233, 2002). For this, we study the minimal speed for the corresponding lattice dynamical system. Our approach gives one new way to
study the traveling waves of the parabolic equations through its discretization which can be applied to other similar problems. 相似文献
8.
B. D. Reddy 《Continuum Mechanics and Thermodynamics》2011,23(6):551-572
Variational formulations are constructed for rate-independent problems in small-deformation single-crystal strain-gradient
plasticity. The framework, based on that of Gurtin (J Mech Phys Solids 50: 5–32, 2002), makes use of the flow rule expressed in terms of the dissipation function. Provision is made for energetic and dissipative
microstresses. Both recoverable and non-recoverable defect energies are incorporated into the variational framework. The recoverable
energies include those that depend smoothly on the slip gradients, the Burgers tensor, or on the dislocation densities (Gurtin
et al. J Mech Phys Solids 55:1853–1878, 2007), as well as an energy proposed by Ohno and Okumura (J Mech Phys Solids 55:1879–1898, 2007), which leads to excellent agreement with experimental results, and which is positively homogeneous and therefore not differentiable
at zero slip gradient. Furthermore, the variational formulation accommodates a non-recoverable energy due to Ohno et al. (Int
J Mod Phys B 22:5937–5942, 2008), which is also positively homogeneous, and a function of the accumulated dislocation density. Conditions for the existence
and uniqueness of solutions are established for the various examples of defect energy, with or without the presence of hardening
or slip resistance. 相似文献
9.
Jens Rottmann-Matthes 《Journal of Dynamics and Differential Equations》2012,24(2):341-367
It is a well-known problem to derive nonlinear stability of a traveling wave from the spectral stability of a linearization.
In this paper we prove such a result for a large class of hyperbolic systems. To cope with the unknown asymptotic phase, the
problem is reformulated as a partial differential algebraic equation for which asymptotic stability becomes usual Lyapunov
stability. The stability proof is then based on linear estimates from (Rottmann-Matthes, J Dyn Diff Equat 23:365–393, 2011) and a careful analysis of the nonlinear terms. Moreover, we show that the freezing method (Beyn and Thümmler, SIAM J Appl
Dyn Syst 3:85–116, 2004; Rowley et al. Nonlinearity 16:1257–1275, 2003) is well-suited for the long time simulation and numerical approximation of the asymptotic behavior. The theory is illustrated
by numerical examples, including a hyperbolic version of the Hodgkin–Huxley equations. 相似文献
10.
The injection of CO2 in exploited natural gas reservoirs as a means to reduce greenhouse gas (GHG) emissions is highly attractive as it takes
place in well-known geological structures of proven integrity with respect to gas leakage. The injection of a reactive gas
such as CO2 puts emphasis on the possible alteration of reservoir and caprock formations and especially of the wells’ cement sheaths
induced by the modification of chemical equilibria. Such studies are important for injectivity assurance, wellbore integrity,
and risk assessment required for CO2 sequestration site qualification. Within a R&D project funded by Eni, we set up a numerical model to investigate the rock–cement
alterations driven by the injection of CO2 into a depleted sweet natural gas pool. The simulations are performed with the TOUGHREACT simulator (Xu et al. in Comput
Geosci 32:145–165, 2006) coupled to the TMGAS EOS module (Battistelli and Marcolini in Int J Greenh Gas Control 3:481–493, 2009) developed for the TOUGH2 family of reservoir simulators (Pruess et al. in TOUGH2 User’s Guide, Version 2.0, 1999). On the basis of field data, the system is considered in isothermal (50°C) and isobaric (128.5 bar) conditions. The effects of the evolving reservoir gas composition are taken into account before,
during, and after CO2 injection. Fully water-saturated conditions were assumed for the cement sheath and caprock domains. The gas phase does not
flow by advection from the reservoir into the interacting domains so that molecular diffusion in the aqueous phase is the
most important process controlling the mass transport occurring in the system under study. 相似文献
11.
Astigmatism or wavefront deformation, microscopic particle tracking velocimetry (A-μPTV) (Chen et al. in Exp Fluids 47:849–863,
2009; Cierpka et al. in Meas Sci Technol 21:045401, 2010b) is a method to determine the complete 3D3C velocity field in micro-fluidic devices with a single camera. By using an intrinsic
calibration procedure that enables a robust and precise calibration on the basis of the measured data itself (Cierpka et al.
in Meas Sci Technol 22:015401, doi:, 2011), accurate results without errors due to spatial averaging or bias due to the depth of correlation can be obtained. This
method takes all image aberrations into account, allows for the use of the whole CCD sensor, and is easy to apply without
expert knowledge. In this paper, a comparative study is presented to assess the uncertainties of two state-of-the-art methods
for 3C3D velocity field measurements in microscopic flows: stereoscopic micro-particle image velocimetry (S-μPIV) and astigmatism
micro-particle tracking velocimetry (A-μPTV). First, the main parameters affecting all methods’ measurement uncertainty are
identified, described, and quantified. Second, the test case of the flow over a backward-facing step is analyzed using all
methods. For comparison, standard 2D2C μPIV measurements and numerical flow simulations are shown as well. Advantages and
disadvantages of both methods are discussed. 相似文献
12.
We prove a blow-up criterion in terms of the upper bound of (ρ, ρ
−1, θ) for a strong solution to three dimensional compressible viscous heat-conductive flows. The main ingredient of the proof
is an a priori estimate for a quantity independently introduced in Haspot (Regularity of weak solutions of the compressible isentropic Navier–Stokes equation, arXiv:1001.1581, 2010) and Sun et al. (J Math Pure Appl 95:36–47, 2011), whose divergence can be viewed as the effective viscous flux. 相似文献
13.
An exact solution for the thin film flow of a third-grade fluid on an inclined plane is presented. This is a corrected version
of the solution obtained by Hayat et al. (Chaos Solitons Fractals 38:1336–1341, 2008). An alternative parametric form for the solution is also derived. The variation of the dimensionless velocity and average
velocity is given for a wide range of parameter values. An asymptotic solution for large parameter values is obtained giving
rise to a boundary-layer structure at the free surface. 相似文献
14.
We consider planar straight and curved masonry beams with the constitutive equation from Orlandi (Ph.D. thesis, 1999) and Zani (Eur. J. Mech. A, Solids 23:467–484, 2004). After stating some results about the solution to the boundary value problem, the limit analysis for this kind of bodies
is outlined, based on energetic considerations (Lucchesi et al. in Q. Appl. Math. 68:713–746, 2010). The static and kinematic theorems of limit analysis, which usually are justified in a heuristic way (Heyman in The Masonry
Arch, 1982; Kooharian in Proc. - Am. Concr. Inst. 89:317–328, 1953), are examined from this point of view. It is seen that the kinematic theorem does not always hold but can be proved under
some hypotheses that are frequently met in applications. 相似文献
15.
Nonlocal generalizations of Burgers’ equation were derived in earlier work by Hunter (Contemp Math, vol 100, pp 185–202. AMS, 1989), and more recently by Benzoni-Gavage and Rosini (Comput Math Appl 57(3–4):1463–1484, 2009), as weakly nonlinear amplitude equations for hyperbolic boundary value problems admitting linear surface waves. The local-in-time well-posedness of such equations in Sobolev spaces was proved by Benzoni-Gavage (Differ Integr Equ 22(3–4):303–320, 2009) under an appropriate stability condition originally pointed out by Hunter. The same stability condition has also been shown to be necessary for well-posedness in Sobolev spaces in a previous work of the authors in collaboration with Tzvetkov (Benzoni-Gavage et al. in Adv Math 227(6):2220–2240, 2011). In this article, we show how the verification of Hunter’s stability condition follows from natural stability assumptions on the original hyperbolic boundary value problem, thus avoiding lengthy computations in each particular situation. We also show that the resulting amplitude equation has a Hamiltonian structure when the original boundary value problem has a variational origin. Our analysis encompasses previous equations derived for nonlinear Rayleigh waves in elasticity. 相似文献
16.
In this paper we consider the asymptotic behavior of the Ginzburg–Landau model for superconductivity in three dimensions, in various energy regimes. Through an analysis via Γ-convergence, we rigorously derive a reduced model for the vortex density and deduce a curvature equation for the vortex lines. In the companion paper (Baldo et al. Commun. Math. Phys. 2012, to appear) we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H c1, and the critical angular velocity of rotating Bose–Einstein condensates. 相似文献
17.
We study the rheological response of monodomain ellipsoidal biaxial liquid crystal polymers (BLCP) as well as bent-core or
V-shaped liquid crystal polymers (VLCP) subject to steady and time-dependent small amplitude oscillatory shear in selected
regions of the model as well as flow parameter space. We adopt the two newly developed hydrodynamical kinetic theories for
ellipsoidal BLCPs and VLCPs, respectively (Sircar and Wang, PRE 78:061702, 2008, J Rheol 53:819–858, 2009; Sircar et al., Comm Math Sci (in press), 2010), in which a generalized Straley’s potential is used to represent the pairwise mean-field interaction of the mesoscopic system
in biaxial phases. Transient shear stresses and normal stress differences corresponding to steady and small amplitude oscillatory
shear are investigated; their variations with respect to the strength of the intermolecular potential, types of biaxial interaction,
and changes in the aspect ratios for ellipsoidal BLCPs and the bent angle for VLCPs are explored. 相似文献
18.
Liquid drop impacts on a smooth surface were studied at elevated chamber pressures to characterize the effect of gas pressure
on drop spreading and splashing. Five common liquids were tested at impact speeds between 1.0 and 3.5 m/s and pressure up
to 12 bars. Based on experiments at atmospheric pressure, a modification to the “free spreading” model (Scheller and Bousfield
in AIChE Paper 41(6):1357–1367, 1995) has been proposed that improves the prediction accuracy of maximum spread factors from an error of 15–5%. At high chamber
pressures, drop spreading and maximum spread factor were found to be independent of pressure. The splash ratio (Xu et al.
in Phys Rev Lett 94:184505, 2005) showed a non-constant behavior, and a power-law model was demonstrated to predict the increase in splash ratio with decreasing
impact speed in the low impact speed regime. Also, drop shape was found to affect splash promotion or suppression for an asymmetry
greater than 7–8% of the equivalent drop diameter. The observations of the current work could be especially useful for the
study of formation of deposits and wall combustion in engine cylinders. 相似文献
19.
Blast waves mitigate in foam due to various mechanisms, whose contribution to the final result is not fully understood yet.
Actually, blast waves can destroy the foam barrier that is usually prone to decay and thus subsides with time. Fortunately,
different time scales allow separating between these processes. The foam shattering, for example, could be completed within
several milliseconds, while the foam decay lasts minutes and even hours. Recently, an increasing interest in this area has
emerged, because particle-laden foams are much more stable and thus, could be applied for blast wave protection. To explore
the full advantage of these new foams, the relationship between the micro-properties of the foam structure and the blast wave
mitigation has to be clarified. In order to specify this relationship, little has been done. Information available in the
literature on this subject clearly shows that during the test, the foam structure could be changed in a wide range, which
is not usually controlled. This complicates the analysis of the occurring processes and ensures that the new factor involved
in the studied problem has to be tested one by one, after the result of the previous step is well understood. To follow this
strategy, this study continues our previous investigation (Britan et al in Colloid Surf A Physicochem Eng Aspects 309:137–150,
2007; Colloid Surf A Physicochem Eng Aspects 344:15–23, 2009; 2011), while mainly focusing on a single new factor, namely blast-shaped profile. To separate out the effect of the foam decay,
which was discussed elsewhere (Britan et al in 2011), a special effort has been spent to ensure that the tested foam is homogeneous over its height. To exclude the bubble shattering,
preference was given to weak impact conditions (Mach number of the shock generated inside the shock tube was about M
S
= 1.05). Under these circumstances, the blast wave mitigation inside the tested foam barrier solely depended on the concentration
of the solid additives. 相似文献
20.
A model for the rheological properties of a concentrated suspension in weakly viscoelastic fluid matrices is proposed. The
model is derived according to the Roscoe differential procedure described in 1952. The analytical results produced recently
by Greco et al. (J Non-Newton Fluid Mech 147:1–10, 2007) and Housiadas and Tanner (J Non-Newton Fluid Mech 162:88–92, 2009) for dilute suspensions of neutrally buoyant, non-Brownian rigid spheres in weakly viscoelastic matrix fluids are the key
results which are used as a base to predict the properties of concentrated suspensions. The results are compared with the
few available experimental data from the literature, showing promising trends for the viscometric properties of the suspensions.
In particular, one sees the rapidly increasing value of −N2/N1 as concentration increases. 相似文献