Kolmogorov equations for randomly perturbed generalized Newtonian fluids

We consider incompressible generalized Newtonian fluids in two space dimensions perturbed by an additive Gaussian noise. The velocity field of such a fluid obeys a stochastic partial differential equation with fully nonlinear drift due to the dependence of viscosity on the shear rate. In particular, we assume that the extra stress tensor is of power law type, i.e. a polynomial of degree , , i.e. the shear thinning case. We prove that the associated Kolmogorov operator K admits at least one infinitesimally invariant measure μ satisfying certain exponential moment estimates. Moreover, K is L²‐unique w.r.t. μ provided , where is the second root of , approximately .     

Well-posedness and time-decay for compressible viscoelastic fluids in critical Besov space

In this paper, we construct local solution with highly oscillating initial velocity and then get the global strong solution in the L^p$L^p$ based Besov space which improves the result of J. Qian, Z. Zhang (2010) [25] and X. Hu, D. Wang (2011) [14]. The local existence and uniqueness lies on the Lagrange coordinate transform and the contraction mapping theorem. The global result lies on a decomposition of the system and some commutator estimates. In the last part, we prove a time-decay in the critical Besov space framework which seems to have little investigation. The proof is based on the properties of the Green's matrix and various interpolations between Besov type spaces.     

Numerical simulations of miscible fluids on a rotating Hele–Shaw cell with effects of Coriolis forces

The effects of Coriolis forces to interfacial stabilities on miscible rotating Hele–Shaw flows are investigated by means of highly accurate numerical schemes. Two major influences on the interfaces, i.e. the stabilization of circumferential fingerings and the unstable body distortion of droplets, are observed. These two phenomena can be represented by two characteristic measurements, i.e. interfacial length and radius of gyration, respectively. Without an additional injection, the miscible interface is found to be more stable at higher Coriolis factors, based on both the judgments of growths in interfacial length and the radius of gyration. However, with an additional injection, a visible body distortion with suppressed interfacial fingerings at higher Coriolis factors leads to inconsistent developments in these two characteristic measurements. The stabilized effect of interfacial fingering delays and weakens the growth in interfacial length at higher Coriolis factors, while faster and greater growth in the radius of gyration is observed because of the significant body distortion. As a result, the effects of the Coriolis forces on the miscible interfacial instabilities should be addressed with great caution. Copyright © 2005 John Wiley & Sons, Ltd.     

The one-dimensional extended Bose-Hubbard model

We use the finite-size, density-matrix-renormalization-group(DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson densityρ = 1, in theU-V plane (U andV are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator(MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases. Dedicated to Professor C N R Rao on his 70th birthday     

On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal‐order interpolation for the velocity and pressure fields. Finally, we show by counterexample that a direct equivalence between subgrid‐based stabilized finite element methods and Galerkin methods enriched by bubble functions cannot be constructed for quadrilateral and hexahedral elements using standard bubble functions. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydrodynamics and cell motion during the rounding of two dimensional hydra cell aggregates

Using a two dimensional experimental geometry, we study hydrodynamics and cell motion during the rounding-up of three kinds of hydra aggregates (ectodermal, endodermal and mixed). The relaxation of initially elongated aggregates toward a circular shape is exponential and the relaxation time is proportional to the aggregate size as expected from hydrodynamics laws. As for viscous liquids, aggregate rounding is driven by tissue surface tensions σ and resisted by tissue viscosity η. The ratio η/σ is the same for the three kinds of aggregates. With a reasonable value σ = 1 mN/m, we obtain an estimate larger than 10⁴ Pa s for the tissue viscosity. Cell motion during rounding is strongly cooperative and cell displacements exhibit some specific patterns in each aggregate. These results point out the role of adhesive bonds in the observed kinetics. Received 21 December 2001     

Evolutionary optimization techniques as versatile solvers for hard‐to‐converge problems in computational fluid dynamics

Evolutionary algorithms mimic the process of natural evolution governed by the ‘survival of the fittest’ principle. In this work, a genetic algorithm (GA) is successfully used to solve problems in potential flow in a gradual contraction, viscous flow over a backward facing step, and non‐Newtonian flow using the power law model. Specifically, the GA heuristically searches the domain for potential solutions, precluding many convergence difficulties associated with the stiffness of a problem. The GA was able to solve problems that the gradient‐based method could not mainly because of its relative indifference to regions of high gradients when performing the search and that systems of discretized equations are never actually solved. The GA exhibited excellent scalability properties for solving problems with a large number of nodes. These results show evolutionary techniques to be of great utility in solving stiff problems in fluid flow. Copyright © 2006 John Wiley & Sons, Ltd.     

The topology of stirred fluids

There are simple idealized mathematical models representing the stirring of fluids. The models we consider involve two fluids entering a chamber, with the overflow leaving it. The stirring creates a Cantor-like, but connected, boundary between the fluids that is best described point-set topologically. We prove that in many cases the boundary between the fluids is an indecomposable continuum.     

磁流变智能液场致微结构变化的Monte Carlo模拟

从磁流变液中存在的各种相互作用势出发，对Ｎ＝１００个球形羰基铁颗粒均匀分布于一正方形二维体系之中的物理模型，利用ＭｏｎｔｅＣａｒｌｏ方法和Ｍｅｔｒｏｐｌｉｓ算法着重计算了磁流变智能液的场致微结构变化。计算结果表明，磁流变液（ＭＲＦ）的流变效应在外磁场中的变化是由于其ＭＲＦ中磁性颗粒的成链团簇有序化所致。这与磁流变液在外磁场中熵的下降和对ＭＲＦ的光学显微镜观察结果是一致的。     

On the interaction of mesoscopic quantum systems with gravity

We review the different aspects of the interaction of mesoscopic quantum systems with gravitational fields. We first discuss briefly the foundations of general relativity and quantum mechanics. Then, we consider the non‐relativistic expansions of the Klein‐Gordon and Dirac equations in the post‐Newtonian approximation. After a short overview of classical gravitational waves, we discuss two proposed interaction mechanisms: (i) the use of quantum fluids as generator and/or detector of gravitational waves in the laboratory, and (ii) the inclusion of gravitomagnetic fields in the study of the properties of rotating superconductors. The foundations of the proposed experiments are explained and evaluated.