Goldman flows on the Jacobian

We show that the Goldman flows preserve the holomorphic structure on the moduli space of homomorphisms of the fundamental group of a Riemann surface into U(1)$U\left(1\right)$, which identifies with the Jacobian.     

On the characteristics-based ACM for incompressible flows

In this paper, the revised characteristics-based (CB) method for incompressible flows recently derived by Neofytou [P. Neofytou, Revision of the characteristic-based scheme for incompressible flows, J. Comput. Phys. 222 (2007) 475–484] has been further investigated. We have derived all the formulas for pressure and velocities from this revised CB method, which is based on the artificial compressibility method (ACM) [A.J. Chorin, A numerical solution for solving incompressible viscous flow problems, J. Comput. Phys. 2 (1967) 12]. Then we analyze the formulations of the original CB method [D. Drikakis, P.A. Govatsos, D.E. Papatonis, A characteristic based method for incompressible flows, Int. J. Numer. Meth. Fluids 19 (1994) 667–685; E. Shapiro, D. Drikakis, Non-conservative and conservative formulations of characteristics numerical reconstructions for incompressible flows, Int. J. Numer. Meth. Eng. 66 (2006) 1466–1482; D. Drikakis, P.K. Smolarkiewicz, On spurious vortical structures, J. Comput. Phys. 172 (2001) 309–325; F. Mallinger, D. Drikakis, Instability in three-dimensional, unsteady stenotic flows, Int. J. Heat Fluid Flow 23 (2002) 657–663; E. Shapiro, D. Drikakis, Artificial compressibility, characteristics-based schemes for variable density, incompressible, multi-species flows. Parts I. Derivation of different formulations and constant density limit, J. Comput. Phys. 210 (2005) 584–607; Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5–7) (2000) 733–756] to investigate their consistency with the governing flow equations after convergence has been achieved. Furthermore we have implemented both formulations in an unstructured-grid finite volume solver [Y. Zhao, B. Zhang, A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids, Comput. Meth. Appl. Mech. Eng. 190 (5–7) (2000) 733–756]. Detailed numerical experiments show that both methods give almost identical solutions and convergence rates. Both can generate solutions which agree well with published results and experimental measurements. We thus conclude that both methods, being upwind schemes designed for the ACM, have the same performances in terms of accuracy and convergence speed, even though the revised method is more complex with less stringent assumptions made, while the original CB method is simpler due to the use of extra simplifying assumptions.     

On quantization of r matrices for Belavin-Drinfeld triples

We suggest a formula for quantum universal R matrices corresponding to quasitriangular classical r matrices classified by Belavin and Drinfeld for all simple Lie algebras. The R matrices are obtained by twisting the standard universal R matrix.     

On dense granular flows

The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divisés (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.Received: 12 December 2003, Published online: 31 August 2004PACS: 45.70.-n Granular systems     

On mechanism of peristaltic flows for power-law fluids

This paper presents a mathematical model for flow induced by peristaltic waves through a deformable tube. An incompressible power-law fluid is considered. The two dimensional model is formulated based upon the fundamental equation of mass conservation and momentum. Exact analytical solutions have been derived for the stream function, axial velocity and pressure gradient which is the main goal of this work. Moreover, pressure rise per wavelength has been evaluated numerically. The present analysis has been performed under long wavelength and low Reynolds number assumptions. The effects of various physical parameters are also discussed through graphs.     

On flows having constant vorticity

Constant vorticity flows of a uniform fluid in a rigid ellipsoidal container rotating at a variable rate are considered. These include librationally driven and precessionally driven flows. The well-known Poincaré solution for precessionally driven flow in a spheroid is generalized to an ellipsoid with unequal principal axes. The dynamic stability of these flows is investigated, and of other flows in which the angular velocity of the container is constant in time. Solutions for the Chandler wobble are discussed. The role of an invariant, called here the Helmholtzian, is examined.     

On relativistic electromagnetic fluid flows

In this paper we have explored certain theorems of theoretical interest in the domain of finitely conducting hydromagnetic systems. These theorems elucidate the local behavior of the congruences of magnetic (electric) field lines. Furthermore, a thermally conducting electromagnetic fluid space-time with vanishing conformal divergence is also investigated.     

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N$N$ vortices on line bundles over a closed Riemann surface Σ$\Sigma$ of genus g>1$g>1$, in the little explored situation where 1≤N<g$1\le N<g$. In the regime where the area of the surface is just large enough to accommodate N$N$ vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of Σ$\Sigma$. For N=1$N=1$, we show that the metric on the moduli space converges to a natural Bergman metric on Σ$\Sigma$. When N>1$N>1$, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel–Jacobi map of Σ$\Sigma$ at degree N$N$. We describe consequences of this phenomenon from the point of view of multivortex dynamics.     

A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios

We present an efficient time-stepping scheme for simulations of the coupled Navier–Stokes Cahn–Hilliard equations for the phase field approach. The scheme has several attractive characteristics: (i) it is suitable for large density ratios, and numerical experiments with density ratios up to 1000 have been presented; (ii) it involves only constant (time-independent) coefficient matrices for all flow variables, which can be pre-computed during pre-processing, so it effectively overcomes the performance bottleneck induced by variable coefficient matrices associated with the variable density and variable viscosity; (iii) it completely de-couples the computations of the velocity, pressure, and the phase field function. Strategy for spectral-element type spatial discretizations to overcome the difficulty associated with the large spatial order of the Cahn–Hilliard equation is also discussed. Ample numerical simulations demonstrate that the current algorithm, together with the Navier–Stokes Cahn–Hilliard phase field approach, is an efficient and effective method for studying two-phase flows involving large density ratios, moving contact lines, and interfacial topology changes.     

On polymer conformations in elongational flows

We consider various models of polymer conformations using paths of Gaussian processes such as Brownian motion. In each case, the calculation of the law of the moment of inertia of a random polymer structure (which is equivalent to the calculation of the partition function) is reduced to the problem of finding the law of a certain quadratic functional of a Gaussian process. We present a new method for computing the Laplace transforms of these quadratic functionals which exploit their special form via the Ray-Knight Theorem and which does not involve the classical method of eigenvalue expansions. We apply the method to several simple examples, then show how the same techniques can be applied to more complicated cases with the aid of a little excursion theory.     

On laminar-turbulent transition in nanofluid flows

The paper presents experimental data on the laminar-turbulent transition in the nanofluid flow in the pipe. The transition in the flows of such fluids is shown to have lower Reynolds numbers than in the base fluid. The degree of the flow destabilization increases with an increase in concentration of nanoparticles and a decrease in their size. On the other hand, in the turbulent flow regime, the presence of particles in the flow leads to the suppression of smallscale turbulent fluctuations. The correlation of the measured viscosity coefficient of considered nanofluids is presented.     

On nonlinearity in three-dimensional equatorial flows

We examine an aspect of the modelling of the underlying fluid motion in the equatorial region of the ocean. In particular, we assess whether nonlinearity is inherently vital in capturing the three-dimensional upwelling and downwelling phenomena. A recent applied mathematical approach has successfully captured these processes through an application of asymptotic approximations to the Euler equation, resulting in a simplified yet nonlinear model. This note demonstrates that any linearisation of the fluid flow will fail to capture the emergence and persistence of similar large-scale coherent structures.     

On the stability of geophysical flows

Summary The stability of the solution of two-dimensional stationary Euler equations for rotating flows with a constant Coriolis force is studied. An Arnold theorem in which some sufficient conditions for the stability are given was used for this purpose. This theorem can be applied to a large class of geophysical flows.

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Riassunto Si è studiata la stabilità delle soluzioni per le equazioni di Eulero stazionarie bidimensionali nel caso di un flusso in rotazione con una forza di Coriolis costante. A tal fine si è fatto uso di un teorema, dovuto ad Arnold, nel quale sono date le condizioni sufficienti per la stabilità del moto. Questo teorema può essere applicato ad una vasta classe di flussi geofisici.

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Work supported by a CNR grant. Progetto Finalizzato Oceanografia.     

On Knudsen flows within thin tubes

The dynamics of a test particle in an infinite tube is investigated. It is proven that the evolution tends to that of a diffusion process as the radius of the tube decreases to zero. This justifies the hypotheses underlying an experiment of Clausing (1930).Dedicated to Professor D. C. Pack.     

An efficient Jacobian scaling method for time-domain optical mammography

<正>Time-domain diffuse optical tomography can efficiently reconstruct optical parameters which can be further applied in diagnosing early breast cancer.Nevertheless,the performances of reconstructed imaging are badly influenced by different Jacobian magnitudes of absorption coefficient and reduced scattering coefficient.With the introudction of a relative data type based on generalized pulse spectrum technique, an efficient Jacobian scaling method is proposed.The interrelated simulated validation is also revealed for the enhancing performances.     

On the geometrical representation of the Jacobian in the path integral reduction problem

By using the formula for the scalar curvature of the manifold with the Kaluza-Klein metric we obtain the geometrical representation of the Jacobian resulted from the path integral reduction problem in Wiener path integrals for a scalar particle on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple Lie group.     

Jacobian elliptic Chebyshev rational maps

We introduce the Jacobian elliptic Chebyshev rational maps with the the equidistributivity property (or briefly EDP) and the semi-group property like the Chebyshev polynomial maps. Simple methods are also discussed for generating sequences of i.i.d. p-ary random variables based on the Jacobian elliptic Chebyshev rational maps. Furthermore, we give conjectures on correlational properties of a real-valued trajectory generated by the Jacobian elliptic Chebyshev rational maps.     

On the thermodynamicV-representability of one-particle density matrices

We consider thermodynamicallyV-representable one-matrices, i. e., one-particle density matrices that are obtained by reducing the Gibbs grand canonical density matrix of a quantum mechanical many-particle system subject to a suitable external potential, and show them to obey an inequality lower bounding their eigenvalues in terms of those of the one-particle kinetic energy operator. The result imposes a severe constraint on the asymptotic behavior of the eigenvalues of any one-matrix to beV-representable. For noninteracting particles, the corresponding upper bound is also proven, implying that a one-matrix can be interactionlesslyV-representable for at most one temperature. We expect the upper bound to be valid more generally, as is illustrated by a model of coupled harmonic oscillators where theV-representable one-matrices can be explicitly calculated, and discuss its implications for certain aspects of density-matrix functional theory.