Spectral/hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L₂ least-squares functional and L₂ error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.     

Fluorescence emission enhancement in substituted 3-styrylindoles in the solid state

Fluorescence emission properties of substituted 3-styrylindoles viz 3-(2-phenylethenyl-E)-NH-indole (1), 3-[2-(4-cyanophenyl)ethenyl-E]-NH-indole (2), and 3-(2-cyano-2-phenylethenyl-Z]-NH-indole (3) in n-hexane, THF–H₂O binary mixtures and solid state are reported. In general, fluorescence efficiency in solid state is found to be much higher than in n-hexane solution. The fluorescence enhancement in solid state is attributed to restricted intramolecular motions. Interestingly, the molecules of 3 in solid state are also bound together through intermolecular hydrogen bonds yielding polymer like structure, leading to further enhancement of fluorescence emission. In THF–H₂O binary mixtures, drastic enhancement of fluorescence efficiency is observed due to aggregate formation.     

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.     

Transparent Boundary Conditions for Split-Step Padé Approximations of the One-Way Helmholtz Equation

In this paper, we generalize the nonlocal discrete transparent boundary condition introduced by F. Schmidt and P. Deuflhard (1995, Comput. Math. Appl.29, 53–76) and by F. Schmidt and D. Yevick (1997, J. Comput. Phys.134, 96–107) to propagation methods based on arbitrary Padé approximations of the two-dimensional one-way Helmholtz equation. Our approach leads to a recursive formula for the coefficients appearing in the nonlocal condition, which then yields an unconditionally stable propagation method.     

The Adjoint Method for an Inverse Design Problem in the Directional Solidification of Binary Alloys

This paper presents a systematic procedure based on the adjoint method for solving a class of inverse directional alloy solidification design problems in which a desired growth velocityv_fis achieved under stable growth conditions. To the best of our knowledge, this is the first time that a continuum adjoint formulation is proposed for the solution of an inverse problem with simultaneous heat and mass transfer, thermo-solutal convection, and phase change. In this paper, the interfacial stability is considered to imply a sharp solid–liquid freezing interface. This condition is enforced using the constitutional undercooling criterion in the form of an inequality constraint between the thermal and solute concentration gradients,GandG_c, respectively, at the freezing front. The main unknowns of the design problem are the heating and/or cooling boundary conditions on the mold walls. The inverse design problem is formulated as a functional optimization problem. The cost functional is defined by the square of theL₂norm of the deviation of the freezing interface temperature from the temperature corresponding to thermodynamic equilibrium. A continuum adjoint system is derived to calculate the adjoint temperature, concentration, and velocity fields such that the gradient of the cost functional can be expressed analytically. The cost functional minimization process is realized by the conjugate gradient method via the finite element method solutions of the continuum direct, sensitivity, and adjoint problems. The developed formulation is demonstrated with an example of designing the directional solidification of a binary aqueous solution in a rectangular mold such that a stable vertical interface advances from left to right with a desired growth velocity.     

Study of the Katz–Lebowitz–Spohn model. The influence of an oscillatory driving field

The classic Katz–Lebowitz–Spohn (KLS) model is a lattice gas driven by an external field. In this paper, we study the critical behavior of the KLS model driven by an oscillatory field of strength E and period τ by means of both, Monte Carlo simulations and a coupled-map-lattice mean-field approach. It is found that, keeping the amplitude constant and changing the period, a novel phase transition between a non-equilibrium-stationary-state and an almost equilibrium-stationary-state takes place at a certain critical value τ_c.     

Spin Echo Analysis of Restricted Diffusion under Generalized Gradient Waveforms: Planar, Cylindrical, and Spherical Pores with Wall Relaxivity

A simple matrix formalism presented by Callaghan [J. Magn. Reson.129, 74–84 (1997)], and based on the multiple propagator approach of Caprihanet al.[J. Magn. Reson. A118, 94–102 (1996)], allows for the calculation of the echo attenuation,E(q), in spin echo diffusion experiments, for practically all gradient waveforms. We have extended the method to the treatment of restricted diffusion in parallel plate, cylindrical, and spherical geometries, including the effects of fluid–surface interactions. In particular, theq-space coherence curves are presented for the finite-width gradient pulse PGSE experiment and the results of the matrix calculations compare precisely with published computer simulations. It is shown that the use of long gradient pulses (δ a²/D) create the illusion of smaller pores if a narrow pulse approximation is assumed, while ignoring the presence of significant wall relaxation can lead to both an underestimation of the pore dimensions and a misidentification of the pore geometry.     

Angular Flow in Toroid Cavity Probes

NMR signals from samples that rotate uniformly about the central conductor of a TCD (toroid cavity detector) exhibit frequency shifts that are directly proportional to the sample's angular velocity. This newly observed effect is based on the unique radiofrequency field inside TCDs, which is variable in direction. If a liquid sample is pumped through a capillary tube wound about the central conductor, the frequency shift is proportional to the flow rate. A mathematical relationship between a volumetric flow rate and the frequency shift is established and experimentally verified to high precision. Additionally, two-dimensional flow-resolved NMR spectroscopy for discrimination between components with different flow velocities yet retaining chemical shift information for structural analysis is presented. The application of the two-dimensional method in chromatographic NMR is suggested. Furthermore, utilization of the frequency-shift effect for rheologic studies if combined with toroid-cavity rotating-frame imaging is proposed.     

First passage time in a two-layer system

As a first step in the first passage problem for passive tracer in stratified porous media, we consider the case of a two-dimensional system consisting of two layers with different convection velocities. Using a lattice generating function formalism and a variety of analytic and numerical techniques, we calculate the asymptotic behavior of the first passage time probability distribution. We show analytically that the asymptotic distribution is a simple exponential in time for any choice of the velocities. The decay constant is given in terms of the largest eigenvalue of an operator related to a half-space Green's function. For the anti-symmetric case of opposite velocities in the layers, we show that the decay constant for system lengthL crosses over fromL ^–2 behavior in the diffusive limit toL ^–1 behavior in the convective regime, where the crossover lengthL ^* is given in terms of the velocities. We also have formulated a general self-consistency relation, from which we have developed a recursive approach which is useful for studying the short-time behavior.     

Critical velocities in superfluids and the nucleation of vortices

The problem of critical velocities in superfluids, that is the comprehension of superfluidity breakdown by flow, has been long standing. One difficulty stems from the existence of several breakdown mechanisms. A major advance has come from the observation of single 2π phase slips, which arise from the nucleation of quantised vortices, that is, their creation ex nihilo. The statistical properties of the nucleation process in both the thermal regime and the quantum regime are identified and analysed: vortex nucleation provides a well-documented case of macroscopic quantum tunnelling (MQT). In particular, a close scrutiny of the experimental data obtained on ultra-pure ⁴He reveals the influence of damping on tunnelling, a rare occurrence where the effect of the environment on MQT can be studied. To cite this article: É. Varoquaux, C. R. Physique 7 (2006).     

Formation of monoclinic zirconia at the anodic face of tetragonal zirconia polycrystalline solid electrolytes

The stability of yttria tetragonal zirconia polycrystalline (Y-TZP) materials with and without the addition of alumina has been investigated during charge flow in solid electrolyte cells. A considerable amount of monoclinic zirconia is formed (up to 50–60%) on the anodic side of the solid electrolyte discs during current flow. The thickness of the surface layer in which maximum transformation takes place was determined to be 3–4.5 m. On the cathodic side, the amount of monoclinic zirconia detected was relatively small (< 5%). The amount of monoclinic formed on the anodic side varied with the microstructure of the ceramic and was considerably less in materials free of pores and with uniform grain size distribution. Relaxation experiments indicate that the tetragonal to monoclinic zirconia phase transformation is related to the oxygen evolution reaction and is not due to oxygenion transport within the solid electrolyte. The observed behaviour has been explained in terms of the creation of space charge layers at the electrode/electrolyte interface leading to the saturation of vacancies by oxygen ions and instability of the tetragonal phase in the surface region on the anodic side of the solid electrolyte.     

Removal of J-coupling peak distortion in PGSE experiments

Peak distortion caused by homonuclear J-coupling is a major problem that limits the utility of the pulsed-field gradient spin–echo (PGSE) method for studying translational diffusion. This unwanted effect can be removed by incorporation of anti-phase magnetization purging pulse elements at the end of the spin–echo sequence. Three methods, namely, trim-pulse, homospoil pulse gradient and chirp based z-filter were evaluated as potential candidates for an improved NMR diffusion method that is less sensitive to J-coupling peak distortion. The chirp based z-filter was found to be excellent in suppressing anti-phase magnetization while leaving the in-phase magnetization basically intact in spin–echo and stimulated-echo based experiments. The incorporation of chirp based z-filter into PGSE could allow diffusion analysis that would otherwise be impossible by conventional means.     

Growth and studies of Hg1−xCdxTe based low dimensional structures

The band structure of HgTe quantum wells (QWs) has been determined from absorption experiments on superlattices in conjunction with calculations based on an 8×8 k·p model. The band structure combined with self-consistent Hartree calculations has enabled transport results to be quantitatively explained.Rashba spin–orbit, (SO) splitting has been investigated in n-type modulation doped HgTe QWs by means of Shubnikov–de Haas oscillations (SdH) in gated Hall bars. The heavy hole nature of the H1 conduction subband in QWs with an inverted band structure greatly enhances the Rashba SO splitting, with values up to 17 meV.By analyzing the SdH oscillations of a magnetic two-dimensional electron gas (2DEG) in modulation-doped n-type Hg_1−xMn_xTe QWs, we have been able to separate the gate voltage-dependent Rashba SO splitting from the temperature-dependent giant Zeeman splitting, which are of comparable magnitudes. In addition, hot electrons and Mn ions in a magnetic 2DEG have been investigated as a function of current.Nano-scale structures of lower dimensions are planned and experiments on sub-micrometer magneto-transport structures have resulted in the first evidence for ballistic transport in quasi-1D HgTe QW structures.     

Elastic properties of mono- and polycrystalline ( and Lu) under pressure effect

The structural and elastic properties of perovskite-type RCRh₃, with R=Sc, Y, La and Lu, under pressure effects have been investigated using the pseudo-potential plane-wave method based on the density functional theory within the generalized gradient approximation. For monocrystalline RCRh₃, the optimized lattice constants, elastic constants and directional elastic wave velocities are calculated and analyzed in comparison with the available experimental and theoretical data. An increase in the lattice constant has been found with increasing atomic size of the R element and a corresponding decrease in the hardness. The anisotropic elastic constants and directional elastic wave velocities increase linearly with increasing pressure. A set of elastic parameters and related properties, namely bulk and shear moduli, Young’s modulus, Poisson’s ratio, Lamé’s coefficients, average sound velocity and Debye temperature are predicted in the framework of the Voigt–Reuss–Hill approximation for polycrystalline RCRh₃. We have found that the toughness of RCRh₃ compounds can be improved at high pressure.     

Multi-carrier transport properties in p-type ZnO thin films

By the aid of temperature- and magnetic-field-dependent Hall effect measurements, we have extracted the multi-carrier transport information in N-doped and N–In codoped p- ZnO thin films grown on Si substrates through mobility spectrum analysis. It is found that owing to the compensation between free electrons and holes, the two-dimensional hole gas from ZnO/Si interface layers becomes determinant and results in the high p-type conductivity and high hole mobility in the ZnO samples. Compared with N-doping, the N–In codoping introduces many In donors and increases acceptor incorporation, as well as enhancing the free hole mobility due to the short-range dipole-like scattering.     

Origin of the blueshift in the infrared absorbance of intersubband transitions in N/GaN multiple quantum wells

A self-consistent calculation of the subband energy levels of n-doped quantum wells is studied. A comparison is made between theoretical results and experimental data. In order to account for the deviations between them, the ground-state electron–electron exchange interactions, the ground-state direct Coulomb interactions, the depolarization effect, and the exciton-like effect are considered in the simulations. The agreement between theory and experiment is greatly improved when all these aspects are taken into account. The ground-to-excited-state energy difference increases by 8 meV from its self-consistent value if one considers the depolarization effect and the exciton-like effect only. It appears that the electron–electron exchange interactions account for most of the observed residual blueshift for the infrared intersubband absorbance in Al_xGa_1-xN/GaN multiple quantum wells. It seems that electrons on the surface of the k-space Fermi gas make the main contribution to the electron–electron exchange interactions, while for electrons further inside the Fermi gas it is difficult to exchange their positions.     

D-branes from matrix factorizations

B-type D-branes can be obtained from matrix factorizations of the Landau–Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi–Yau compactifications. We discuss the grading of the D-branes, and present applications in two examples: the two-dimensional torus, and the quintic. To cite this article: K. Hori, J. Walcher, C. R. Physique 5 (2004).

Résumé

Les D-branes de type B peuvent être décrites à partir de factorisations matricielles du super-potentiel de Landau–Ginzburg. On revoit ici cette approche prometteuse pour étudier le super-potentiel en espace-temps de compactifications de Calabi–Yau. On discute la graduation des D-branes, et présente deux exemples : le tore en deux dimensions, ainsi que la quintique. Pour citer cet article : K. Hori, J. Walcher, C. R. Physique 5 (2004).     

Accurate Measurement of Small Spin–Spin Couplings in Partially Aligned Molecules Using a Novel J-Mismatch Compensated Spin-State-Selection Filter

The accurate measurement of small spin–spin coupling constants in macromolecules dissolved in a liquid crystalline phase is important in the context of molecular structure investigation by modern liquid state NMR. A new spin-state-selection filter, DIPSAP, is presented with significantly reduced sensitivity to J-mismatch of the filter delays compared to previously proposed pulse sequences. DIPSAP presents an attractive new approach for the accurate measurement of small spin–spin coupling constants in molecules dissolved in anisotropic solution. Application to the measurement of ¹⁵N–¹³C′ and ¹H^N–¹³C′ coupling constants in the peptide planes of ¹³C, ¹⁵N labeled proteins demonstrates the high accuracy obtained by a DIPSAP-based experiment.