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1.
We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase
pressure and which allows wetting layer swelling near an advancing flood front. The model incorporates a new time-dependent
algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number, mobility
ratio and contact angle distribution on waterflood displacement patterns, saturation and velocity profiles. By using large
networks, generated from a new stochastic network algorithm, we reproduce Buckley–Leverett profiles directly from pore-scale
modelling thereby providing a bridge between pore-scale and macro-scale transport. 相似文献
2.
H. Haken 《Nonlinear dynamics》2006,44(1-4):269-276
This paper establishes and studies equations of a network that is composed of neurons with their dendrites and axons. The
pulse generation in the axon is described by means of phase oscillators, whereas the dendritic currents are described by linear
damping equations with source terms as which the incoming pulses act. The equations take into account delays and noise. In
the case of phase-locking the equations have been solved previously by the author. The main objective of the present paper
is to study in how far these equations may serve for pattern recognition. It is shown that either a random phase approximation
for the stored patterns or a triple interaction term suffice to treat pattern recognition. It is pointed out how then recognized
patterns can be either encoded as completed prototype patterns or as phase-locked states. It is suggested that to understand
pattern recognition it is not only necessary to consider the whole network instead of “grandmother” cells but equally well
the whole intermediate steps. 相似文献
3.
H. Eugene Stanley Xavier Gabaix Parameswaran Gopikrishnan Vasiliki Plerou 《Nonlinear dynamics》2006,44(1-4):329-340
We present an overview of recent research applying ideas of statistical physics to try to better understand puzzles regarding
economic fluctuations. One of these puzzles is how to describe outliers, phenomena that lie outside of patterns of statistical
regularity. We review evidence consistent with the possibility that such outliers may not exist. This possibility is supported
by recent analysis of a database containing the bid, ask, and sale price of each trade of every stock. Further, the data support
the picture of economic fluctuations, due to Plerou et al., in which a financial market alternates between being in an “equilibrium
phase” where market behavior is split roughly equally between buying and selling, and an “out-of-equilibrium phase” where
the market is mainly either buying or selling. 相似文献
4.
Antonio Hernández-Garduño Ernesto A. Lacomba 《Journal of Mathematical Fluid Mechanics》2007,9(1):75-86
We study the dynamics of 3 point-vortices on the plane for a fluid governed by Euler’s equations, concentrating on the case
when the moment of inertia is zero. We prove that the only motions that lead to total collisions are self-similar and that
there are no binary collisions. Also, we give a regularization of the reduced system around collinear configurations (excluding
binary collisions) which smoothes out the dynamics.
Both authors gratefully acknowledge support from DGAPA-UNAM under project PAPIIT IN101902 and from CONACyT under grant 32167-E.
The second author thanks the hospitality of IIMAS-UNAM during the preparation of this paper. 相似文献
5.
Numerical simulation of blood flow and interstitial fluid pressure in solid tumor microcirculation based on tumor-induced angiogenesis 总被引:1,自引:0,他引:1
Gaiping Zhao Jie Wu Shixiong Xu M. W. Collins Quan Long Carola S. König Yuping Jiang Jian Wang A. R. Padhani 《Acta Mechanica Sinica》2007,23(5):477-483
A coupled intravascular–transvascular–interstitial fluid flow model is developed to study the distributions of blood flow
and interstitial fluid pressure in solid tumor microcirculation based on a tumor-induced microvascular network. This is generated
from a 2D nine-point discrete mathematical model of tumor angiogenesis and contains two parent vessels. Blood flow through
the microvascular network and interstitial fluid flow in tumor tissues are performed by the extended Poiseuille’s law and
Darcy’s law, respectively, transvascular flow is described by Starling’s law; effects of the vascular permeability and the
interstitial hydraulic conductivity are also considered. The simulation results predict the heterogeneous blood supply, interstitial
hypertension and low convection on the inside of the tumor, which are consistent with physiological observed facts. These
results may provide beneficial information for anti-angiogenesis treatment of tumor and further clinical research.
The project supported by the National Natural Science Foundation of China (10372026). 相似文献
6.
Giovanni Romeo Giovanni Filippone Alberto Fernández-Nieves Pietro Russo Domenico Acierno 《Rheologica Acta》2008,47(9):989-997
We investigate the relation between the structure and the viscoelastic behavior of a model polymer nanocomposite system based
on a mixture of titanium dioxide (TiO2) nanoparticles and polypropylene. Above a critical volume fraction, Φ
c, the elasticity of the hybrids dramatically increases, and the frequency dependence of the elastic and viscous moduli reflects
the superposition of the independent responses of the suspending polymer melt and of an elastic particle network. In addition,
the elasticity of the hybrids shows critical behavior around Φ
c. We interpret these observations by hypothesizing the formation of a transient network, which forms due to crowding of particle
clusters. Consistent with this interpretation, we find a long-time, Φ-dependent, structural relaxation, which emphasizes the transient character of the structure formed by the particle clusters.
For times below this characteristic relaxation time, the elasticity of the network is Φ-independent and reminiscent of glassy behavior, with the elastic modulus, G′, scaling with frequency, ω, as G′∼ω
0.3. We expect that our analysis will be useful for understanding the behavior of other complex fluids where the elasticity of
the components could be superimposed. 相似文献
7.
8.
Wu Shou-zhi 《应用数学和力学(英文版)》1994,15(11):1081-1085
Because of the great needs both for the research of pansystem mathematics and for the analysis of general things’ mechanism,
this paper discusses the binary relation’s transitivity confined to multirelation. The so-called “g-transitivity” a completely
new concept about transitivity—is introduced and its basic properties are investigated. The study shows that it is not only
g-transitivity a generalization of traditional transitivity, quasi-transitivity, semi-order, quasi-order and other panorder,
but also includes many important concepts such as closenss, convexity, topology, duality as its special cases. 相似文献
9.
Arnd Scheel 《Archive for Rational Mechanics and Analysis》2006,181(3):505-534
We characterize the spatial spreading of the coarsening process in the Allen–Cahn equation in terms of the propagation of
a nonlinear modulated front. Unstable periodic patterns of the Allen–Cahn equation are invaded by a front, propagating in
an oscillatory fashion, and leaving behind the homogeneous, stable equilibrium. During one cycle of the oscillatory propagation,
two layers of the periodic pattern are annihilated. Galerkin approximations and the Conley index for ill-posed spatial dynamics
are used to show existence of modulated fronts for all parameter values. In the limit of small amplitude patterns or large
wave speeds, we establish uniqueness and asymptotic stability of the modulated fronts. We show that the minimal speed of propagation
can be characterized by a dichotomy which depends on the existence of pulled fronts. The main tools here are an Evans function
type construction for the infinite-dimensional ill-posed dynamics and an analysis of the complex dispersion relation based
on Sturm–Liouville theory. 相似文献
10.
We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of
the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those
locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been
proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the
conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects
of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure
hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇2 φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct
numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations
in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction
and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the
quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered
and validated with help of our simulation results.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
The solidification of binary mixture (NH4Cl–H2O) inside a trapezoidal cavity is investigated experimentally in this study. The effect of the initial concentration of ammonium chloride (0–19.8%) and boundary temperatures (−30 to 0°C) on the solidification process was investigated. Particle image velocimetry (PIV) technique was used for the visualization of the dynamic field in the melt. Thirty-two thermocouples were used to monitor the temperature distribution inside the cavity and on the cooling walls. The convective flow field, the temperature distribution, the frozen layer thickness and the moving solid/liquid interface were obtained for different initial concentrations of ammonium chloride and various boundary temperatures. The results obtained in the course of this study reveal that: (1) the process of solidification is slower with an increase in initial concentration levels of the binary solution: as the concentration increases, the time needed to get the same thickness of frozen layer increases; (2) an increase in the initial concentration of ammonium chloride solution reduce significantly the temperature in the melt; and (3) the initial concentration play a significant role in the evolution of convection flow patterns. 相似文献
12.
A new method to pattern recognition of gas–liquid two-phase flow regimes based on improved local binary pattern (LBP) operator is proposed in this paper. Five statistic features are computed using the texture pattern matrix obtained from the improved LBP. The support vector machine and back-propagation neural network are trained to flow pattern recognition of five typical gas–liquid flow regimes. Experimental results demonstrate that the proposed method has achieved better recognition accuracy rates than others. It can provide reliable reference for other indirect measurement used to analyze flow patterns by its physical objectivity. 相似文献
13.
Measurements of the twist viscosity, γ1(DLS) and twist elastic coefficient, K22(DLS) by electric-field-dependent dynamic light scattering (EFDLS) are reported for low molar mass nematics (LMMNs) 4′-heptyl-4-cyanobiphenyl
(7CB) and 4′-octyl-4-cyanobiphenyl (8CB), and their binary mixtures at several temperatures in the nematic state. The results
are compared with values (γ1(Rheol)=α3–α2) computed from rheological measurements of the Leslie viscosities α2 and α3. For the binary mixtures, at each temperature, the measured twist viscosity γ1(DLS) and corresponding twist elastic constant K22(DLS) show approximately a linear additive dependence on concentration. The calculated twist viscosity, γ1(Rheol), agrees with γ1(DLS) for the pure components, but is significantly smaller for the binary mixtures. Our observations appear to be consistent
with a recent report of a discrepancy between values of the tumbling parameter λ, determined using a small-strain oscillatory
optical technique, vs those measured by a rheological method. These results suggest that, in the rheological measurements
at large strains, the rate of director rotation for mixtures may be affected by a flow-induced change in structure, e.g.,
shear-induced biaxiality.
Received: 17 March 2000 Accepted: 17 July 2000 相似文献
14.
Dambaru Bhatta Mallikarjunaiah S. Muddamallappa Daniel N. Riahi 《Transport in Porous Media》2010,82(2):385-399
This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability
and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing
a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability
is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition.
With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic
and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the
layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection
and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds
to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability. 相似文献
15.
Ruri Hidema Zenji Yatabe Masahiko Shoji Chihiro Hashimoto Robert Pansu Gabriel Sagarzazu Hideharu Ushiki 《Experiments in fluids》2010,49(3):725-732
Two-dimensional turbulence in flowing soap films with polymer additives is analyzed by image analysis. The power spectra of
the interference patterns of turbulent soap films are calculated. The scaling exponent of the power spectrum is −5/3 for polymer
free solution and −1 for dilute polymer solution in enstrophy cascade range, which is consistent with the results of thickness
fluctuations in previous researches. We propose a Curvature analysis method that calculates the curvatures of the interference
pattern of turbulent soap films. The results suggest that the curvature histogram describes well the shape of the interference
pattern, which is related to the shape of the vortices. The curvature histograms for different polymer concentrations can
be fitted by a stretched exponential function. 相似文献
16.
This paper presents experimental findings on the phenomenon of solidification of a binary alloy in a finned enclosure using
aqueous ammonium chloride solution. Solidification experiments are carried out over a wide range of initial composition of
binary alloy solution from hypoeutectic to hypereutectic concentration ranging from 8, 16 and 24% of ammonium chloride are
discussed. An interesting “snowing” phenomenon is observed for the hypereutectic concentration in a finned enclosure. 相似文献
17.
. We give an intrinsic definition of a heteroclinic network as a flow-invariant set that is indecomposable but not recurrent.
Our definition covers many previously discussed examples of heteroclinic behavior. In addition, it provides a natural framework
for discussing cycles between invariant sets more complicated than equilibria or limit cycles. We allow for cycles that connect
chaotic sets (cycling chaos) or heteroclinic cycles (cycling cycles). Both phenomena can occur robustly in systems with symmetry.
We analyze the structure of a heteroclinic network as well as dynamics on and near the network. In particular, we introduce
a notion of ‘depth’ for a heteroclinic network (simple cycles between equilibria have depth 1), characterize the connections
and discuss issues of attraction, robustness and asymptotic behavior near a network.
We consider in detail a system of nine coupled cells where one can find a variety of complicated, yet robust, dynamics in
simple polynomial vector fields that possess symmetries. For this model system, we find and prove the existence of depth‐2
networks involving connections between heteroclinic cycles and equilibria, and study bifurcations of such structures.
(Accepted July 6, 1998) 相似文献
18.
I. I. Ryzhkov 《Journal of Applied Mechanics and Technical Physics》2006,47(1):79-90
The group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of
first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional.
Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions
are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence
of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime
is studied.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 95–108, January–February, 2006. 相似文献
19.
We have used a third-order essentially non-oscillatory method to obtain numerical shadowgraphs for investigation of shock–vortex
interaction patterns. To search different interaction patterns, we have tested two vortex models (the composite vortex model
and the Taylor vortex model) and as many as 47 parametric data sets. By shock–vortex interaction, the impinging shock is deformed
to a S-shape with leading and lagging parts of the shock. The vortex flow is locally accelerated by the leading shock and
locally decelerated by the lagging shock, having a severely elongated vortex core with two vertices. When the leading shock
escapes the vortex, implosion effect creates a high pressure in the vertex area where the flow had been most expanded. This
compressed region spreads in time with two frontal waves, an induced expansion wave and an induced compression wave. They
are subsonic waves when the shock–vortex interaction is weak but become supersonic waves for strong interactions. Under a
intermediate interaction, however, an induced shock wave is first developed where flow speed is supersonic but is dissipated
where the incoming flow is subsonic. We have identified three different interaction patterns that depend on the vortex flow
regime characterized by the shock–vortex interaction.
相似文献
20.
Daniel N. Riahi 《Transport in Porous Media》2008,72(1):121-138
We consider the problem of mixed oscillatory and steady modes of nonlinear compositional convection in horizontal mushy layers
during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature,
we determine a number of two- and three-dimensional weakly nonlinear mixed solutions, and the stability of these solutions
with respect to arbitrary three-dimensional disturbances is then investigated. The present investigation is an extension of
the problem of mixed oscillatory and steady modes of convection, which was investigated by Riahi (J Fluid Mech 517: 71–101,
2004), where some calculated results were inaccurate due to the presence of a singular point in the equation for the linear
frequency. Here we resolve the problem and find some significant new results. In particular, over a wide range of the parameter
values, we find that the properties of the preferred and stable solution in the form of particular subcritical mixed standing
and steady hexagons appeared to be now in much better agreement with the available experimental results (Tai et al., Nature
359:406–408, 1992) than the one reported in Riahi (J Fluid Mech 517:71–101, 2004). We also determined a number of new types
of preferred supercritical solutions, which can be preferred over particular values of the parameters and at relatively higher
values of the amplitude of convection. 相似文献