Magnetic field generation by convective flows in a plane layer

Hydrodynamic and magnetohydrodynamic convective attractors in a plane horizontal layer 0≤z≤1 are investigated numerically. We consider Rayleigh-Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period L in the x and y directions. Computations have been performed for the Prandtl number P=1 for and Rayleigh numbers 0<R≤4000, and for L=4, 0<R≤2000. Fifteen different types of hydrodynamic attractors are found, including two types of steady states distinct from rolls, travelling waves, periodic and quasiperiodic flows, and chaotic attractors of heteroclinic nature. Kinematic dynamo problem has been solved for the computed convective attractors. Out of the 15 types of the observed attractors only 6 can act as kinematic dynamos. Nonlinear magnetohydrodynamic regimes have been explored assuming as initial conditions convective attractors capable of magnetic field generation, and a small seed magnetic field. After initial exponential growth, in the saturated regime magnetic energy remains much smaller than the flow kinetic energy. The final magnetohydrodynamic attractors are either quasiperiodic or chaotic.     

Singularity of the Velocity Distribution Function in Molecular Velocity Space

We study the boundary singularity of the solutions to the Boltzmann equation in the kinetic theory. The solution has a jump discontinuity in the microscopic velocity \({\zeta}\) on the boundary and a secondary singularity of logarithmic type around the velocity tangential to the boundary, \({\zeta_{n} \sim 0_{-}}\), where \({\zeta_{n}}\) is the component of molecular velocity normal to the boundary, pointing to the gas. We demonstrate this secondary singularity by obtaining an asymptotic formula for the derivative of the solution on the boundary with respect to \({\zeta_{n}}\) that diverges logarithmically when \({\zeta_{n} \sim 0_{-}}\). Our study is for the thermal transpiration problem between two plates for the hard sphere gases with sufficiently large Knudsen number and with the diffuse reflection boundary condition. The solution is constructed and its singularity is studied by an iteration procedure.     

Exact Solution of the Six-Vertex Model with Domain Wall Boundary Conditions. Disordered Phase

The six-vertex model, or the square ice model, with domain wall boundary conditions (DWBC) has been introduced and solved for finite N by Korepin and Izergin. The solution is based on the Yang–Baxter equations and it represents the free energy in terms of an N × N Hankel determinant. Paul Zinn–Justin observed that the Izergin– Korepin formula can be re-expressed in terms of the partition function of a random matrix model with a nonpolynomial interaction. We use this observation to obtain the large N asymptotics of the six-vertex model with DWBC in the disordered phase. The solution is based on the Riemann–Hilbert approach and the Deift–Zhou nonlinear steepest descent method. As was noticed by Kuperberg, the problem of enumeration of alternating sign matrices (the ASM problem) is a special case of the six-vertex model. We compare the obtained exact solution of the six-vertex model with known exact results for the 1, 2, and 3 enumerations of ASMs, and also with the exact solution on the so-called free fermion line. We prove the conjecture of Zinn–Justin that the partition function of the six-vertex model with DWBC has the asymptotics, as N → ∞, and we find the exact value of the exponent κ.The first author is supported in part by the National Science Foundation (NSF) Grant DMS-0354962.     

Non-linear rheology of lamellar liquid crystals

We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C₁₂E₅ /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of a lamellar or smectic phase is proposed with a prediction ∼ σ^3/2 , where is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent.     

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (T_c) the Casimir force for this non-interacting system decreases with temperature (T) and at , it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

An experimental study of impulsively started turbulent axisymmetric jets

An impulsively started turbulent jet injected into quiescent surroundings with a constant inlet velocity has been studied experimentally. Results show that the jet length increases linearly with the square-root of time, over a wide range of Reynolds number calculated with respect to the jet diameter. The celerity factor, x_f/t U, has been found to be nearly constant at 2.47 throughout with a 5% variance. Here, x_f is the jet length, t is the time and U is the jet exit velocity. These results compare favourably with earlier results reported at lower Reynolds numbers. Finally, we present a simple model based on the integral energy balance of the turbulent boundary layer equation for an impulsively started turbulent axisymmetric jet. The model predicts a jet length that scales as, where d is the nozzle diameter and B(≈6.0) is the velocity-decay constant. This gives a celerity factor, in close agreement with the experiments.     

Mixing and sorting of bidisperse two-dimensional bubbles

We have examined a number of candidates for the minimum-surface-energy arrangement of two-dimensional clusters composed of N bubbles of area 1 and N bubbles of area λ ( λ≤1). These include hexagonal bubbles sorted into two monodisperse honeycomb tilings, and various mixed periodic tilings with at most four bubbles per unit cell. We identify, as a function of λ, the minimal configuration for N → ∞. For finite N, the energy of the external (i.e., cluster-gas) boundary and that of the interface between honeycombs in “phase-separated” clusters have to be taken into account. We estimate these contributions and find the lowest total energy configuration for each pair (N,λ). As λ is varied, this alternates between a circular cluster of one of the mixed tilings, and “partial wetting” of the monodisperse honeycomb of bubble area 1 by the monodisperse honeycomb of bubble area λ. Received 1 August 2002 RID="a" ID="a"e-mail: paulo@ist.utl.pt     

Genetic Algorithms as a tool in the study of aperiodic order,with application to the case of X-Ray diffraction spectra of GaAs-AlAs multilayer heterostructures

We present the first application of Genetic Algorithms to the analysis of data from an aperiodically ordered system, high resolution X-Ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme. This method paves the way to the solution of the “inverse problem”, that is the retrieval of the generating disorder from the investigation of the spectra of an unknown sample having non crystallographic, non quasi-crystallographic order. Received 18 March 2002 / Received in final form 3 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Evelyne.Lutton@inria.fr RID="b" ID="b"CNRS UMR 8502     

The lateral extension of radiation damage in ion-implanted semiconductors

Implantation into a confined surface area produces considerable radiation damage even outside the implanted area. The distance between the damage boundary and the implantation boundary can be determined by simultaneously recording the sample current and the characteristic x-ray signal in a scanning electron microscope. This method was applied to investigate the lateral extent of radiation damage in Si, GaAs, and GaP. Annealing studies were performed with Si. It was found that the lateral excess of damage over the implanted area can be more than 1 m even if the projected range is less than 0.1 m. In Si, this marginal damage, except for oxidation induced stacking faults, can be annealed under the same conditions as necessary for the annealing of the implanted zone itself. Experimental support is given to the prediction of Campisano and Barbarino [1] that within the implanted region the recrystallization rate of the amorphous layer reaches a maximum within a range of concentration near the maximal solid solubility.     

A Stochastic Perturbation of Inviscid Flows

We prove existence and regularity of the stochastic flows used in the stochastic Lagrangian formulation of the incompressible Navier-Stokes equations (with periodic boundary conditions), and consequently obtain a C ^k,α local existence result for the Navier-Stokes equations. Our estimates are independent of viscosity, allowing us to consider the inviscid limit. We show that as ν → 0, solutions of the stochastic Lagrangian formulation (with periodic boundary conditions) converge to solutions of the Euler equations at the rate of .     

A quasi-elastic regime for vibrated granular gases

Using simple scaling arguments and two-dimensional numerical simulations of a granular gas excited by vibrating one of the container boundaries, we study a double limit of small 1-r and large L, where r is the restitution coefficient and L the size of the container. We show that if the particle density n₀ and (1-r²)(n₀ Ld) where d is the particle diameter, are kept constant and small enough, the granular temperature, i.e. the mean value of the kinetic energy per particle, 〈E 〉/N, tends to a constant whereas the mean dissipated power per particle, 〈D 〉/N, decreases like when N increases, provided that (1-r²)(n₀ Ld)² < 1. The relative fluctuations of E, D and the power injected by the moving boundary, I, have simple properties in that regime. In addition, the granular temperature can be determined from the fluctuations of the power I(t) injected by the moving boundary.     

Boundary entropy can increase under bulk RG flow

The boundary entropy log(g)$\log (g)$ of a critical one-dimensional quantum system (or two-dimensional conformal field theory) is known to decrease under renormalization group (RG) flow of the boundary theory. We study instead the behavior of the boundary entropy as the bulk theory flows between two nearby critical points. We use conformal perturbation theory to calculate the change in g   due to a slightly relevant bulk perturbation and find that it has no preferred sign. The boundary entropy log(g)$\log (g)$ can therefore increase during appropriate bulk flows. This is demonstrated explicitly in flows between minimal models. We discuss the applications of this result to D-branes in string theory and to impurity problems in condensed matter.     

The Phase Transitions from Chiral Nematic Toward Smectic Liquid Crystals

A Chen-Lubensky energy is used to investigate phase transitions from chiral nematic to smectic C* and smectic A* liquid crystal phases. We consider a liquid crystalline material Ω confined between two parallel plates, where the dimensions of Ω are assumed to be large relative both to the width of a smectic layer and the material’s chiral pitch. We take boundary conditions so that the smectic phase melts at the plates’ surfaces and prove the existence of energy minimizers in an admissible set consisting of order parameters and molecular directors . Then under the physically observed assumption that the Frank elasticity constants become large near a phase transition, we establish estimates for the transition region separating phases. In particular we derive analytic estimates proving that chirality lowers the transition temperature regime above which minimizers are nematic and below which minimizers are in a smectic phase.Research supported by NSF grants DMS-0306516 and DMS-0456286.     

Boundary Solutions of the Classical Yang--Baxter Equation

We define a new class of unitary solutions to the classical Yang--Baxter equation (CYBE). These boundary solutions are those which lie in the closure of the space of unitary solutions of the modified classical Yang--Baxter equation (MCYBE). Using the Belavin--Drinfel'd classification of the solutions to the MCYBE, we are able to exhibit new families of solutions to the CYBE. In particular, using the Cremmer--Gervais solution to the MCYBE, we explicitly construct for all n 3 a boundary solution based on the maximal parabolic subalgebra of obtained by deleting the first negative root. We give some evidence for a generalization of this result pertaining to other maximal parabolic subalgebras whose omitted root is relatively prime to n. We also give examples of nonboundary solutions for the classical simple Lie algebras.     

Brick walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren’s algebraic holography (and in other ‘fixed-background’, QFT-based, approaches to holography) and in mainstream string-theoretic ‘Maldacena AdS/CFT’. Especially, we contrast the understanding of black-hole entropy from the point of view of QFT in curved spacetime—in the framework of ’t Hooft’s ‘brick wall’ model—with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein–Gordon field in the Hartle–Hawking–Israel state on $1+2$ dimensional Schwarzschild AdS has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren’s algebraic holography and mainstream AdS/CFT and the puzzle embodied in the ‘complementarity principle’ proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein–Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author’s proposed resolution to the Mukohyama–Israel puzzle based on his ‘matter–gravity entanglement hypothesis’, we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the ‘same’—the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.     

Upper bounds on the convective heat transport in a rotating fluid layer of infinite Prandtl number: case of large Taylor numbers

By means of the Howard-Busse method of the optimum theory of turbulence we obtain upper bounds on the convective heat transport in a horizontal fluid layer heated from below and rotating about a vertical axis. We consider the interval of large Taylor numbers where the intermediate layers of the optimum fields expand in the direction of the corresponding internal layers. We consider the 1 - α-solution of the arising variational problem for the cases of rigid-stress-free, stress-free, and rigid boundary conditions. For each kind of boundary condition we discuss four cases: two cases where the boundary layers are thinner than the Ekman layers of the optimum field and two cases where the boundary layers are thicker than the Ekman layers. In most cases we use an improved solution of the Euler-Lagrange equations of the variational problem for the intermediate layers of the optimum fields. This solution leads to corrections of the thicknesses of the boundary layers of the optimum fields and to lower upper bounds on the convective heat transport in comparison to the bounds obtained by Chan [J. Fluid Mech. 64, 477 (1974)] and Hunter and Riahi [J. Fluid Mech. 72, 433 (1975)]. Compared to the existing experimental data for the case of a fluid layer with rigid boundaries the corresponding upper bounds on the convective heat transport is less than two times larger than the experimental results, the corresponding upper bound on the convective heat transport, obtained by Hunter and Riahi is about 10% higher than the bound obtained in this article. When Rayleigh number and Taylor number are high enough the upper bound on the convective heat transport ceases to depend on the boundary conditions. Received 30 January 2001 and Received in final form 28 May 2001     

Grain boundary diffusion of Cu in TiN film by X-ray photoelectron spectroscopy

In this study, the grain boundary diffusion of Cu through a TiN layer with columnar structure was investigated by X-ray photoelectron spectroscopy (XPS). It was observed that Cu atoms diffuse from the Cu layer to the surface along the grain boundaries in the TiN layer at elevated temperature. In order to estimate the grain boundary diffusion constants, we used the surface accumulation method. The diffusivity of Cu through TiN layer with columnar structure from 400 °C to 650 °C is D_b≈6×10⁻¹¹exp(−0.29/(k_BT )) cm²/s. Received: 18 May 1999 / Accepted: 8 September 1999 / Published online: 23 February 2000     

Simulation of microchannel flow using the lattice Boltzmann method

For microchannel flow simulation, the slip boundary model is very important to guarantee the accuracy of the solution. In this paper, a new slip model, the Langmuir slip model, instead of the popularly used Maxwell slip model, is incorporated into the lattice Boltzmann (LB) method through the non-equilibrium extrapolation scheme to simulate the rarefied gas flow. Its feasibility and accuracy are examined by simulations of microchannel flow. Although, for simplicity, in this paper our recently developed LB model is used to solve the flow field, this does not prevent the present boundary scheme from easily incorporating other LB models, for example the more advanced collision model with multiple relaxation times. In addition, the existing non-equilibrium extrapolation LB boundary scheme for macroscopic flows can be recovered naturally from the present scheme when the Knudsen number .     

The Solutions for the Boundary Layer Problem of Boltzmann Equation in a Half-Space

We study the half space boundary layer problem for Boltzmann equation with cut-off potentials in all the cases −3<γ≤1, while the boundary condition is imposed on the incoming particles of Dirichlet type, and the solution is assumed to approach to a global Maxwellian at the far field. The same as for cut-off hard sphere model, there is an implicit solvability condition on the boundary data which gives the co-dimensions of the boundary data in terms of positive characteristic speeds.