Comment on “A new model of charge transfer during ice–ice collisions”: [C. R. Physique 3 (2002) 1293–1303]

A model which proposes modifications of a theory of collisional charging of ice is criticized. To cite this article: J.G. Dash, J.S. Wettlaufer, C. R. Physique 4 (2003).     

Study of inverse a.c. Josephson effect in Y–Ba–Cu–O and Y–8a–Sr–Cu–O

Microwave induced d.c. voltage due to inverse a.c. Josephson effect has been observed across bulk samples of Y-Ba-Cu-O and Y-Ba-Sr-Cu-O. The d.c. voltage is found to vary with microwave power, frequency and also with small external magnetic fields. Although the resistivity curve of Y-Ba-Cu-O does not show any appreciable resistance drop around 230 K, the microwave induced d.c. voltage due to the inverse a.c. Josephson effect has been found to exist upto 230 K. The resistivity behaviour of Y-Ba-Sr-Cu-O shows a sharp resistivity drop above 230 K. In this sample the inverse Josephson effect is found to exist upto +26 °C, indicating the presence of a phase having a superconducting onset around this temperature.     

Academician A.N. Sissakian 14.10.1944–01.05.2010

Chronicle

Academician A.N. Sissakian 14.10.1944–01.05.2010     

Implementation of the Jacobian-free Newton–Krylov method for solving the first-order ice sheet momentum balance

We have implemented the Jacobian-free Newton–Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8–3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.     

Kagomé ice state in the dipolar spin ice Dy2Ti2O7

We have investigated the kagomé ice behavior of the dipolar spin-ice compound Dy2Ti2O7 in a magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagomé ice behavior predicted for the nearest-neighbor interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagomé lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the nearest-neighbor model.     

Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton–Krylov method

We have implemented the Jacobian-free Newton–Krylov (JFNK) method to solve the sea ice momentum equation with a viscous-plastic (VP) formulation. The JFNK method has many advantages: the system matrix (the Jacobian) does not need to be formed and stored, the method is parallelizable and the convergence can be nearly quadratic in the vicinity of the solution. The convergence rate of our JFNK implementation is characterized by two phases: an initial phase with slow convergence and a fast phase for which the residual norm decreases significantly from one Newton iteration to the next. Because of this fast phase, the computational gain of the JFNK method over the standard solver used in existing VP models increases with the required drop in the residual norm (termination criterion). The JFNK method is between 3 and 6.6 times faster (depending on the spatial resolution and termination criterion) than the standard solver using a preconditioned generalized minimum residual method. Resolutions tested in this study are 80, 40, 20 and 10 km. For a large required drop in the residual norm, both JFNK and standard solvers sometimes do not converge. The failure rate for both solvers increases as the grid is refined but stays relatively small (less than 2.3% of failures). With increasing spatial resolution, the velocity gradients (sea ice deformations) get more and more important. Nonlinear solvers such as the JFNK method tend to have difficulties when there are such sharp structures in the solution. This lack of robustness of both solvers is however a debatable problem as it mostly occurs for large required drops in the residual norm. Furthermore, when it occurs, it usually affects only a few grid cells, i.e., the residual is small for all the velocity components except in very localized regions. Globalization approaches for the JFNK solver, such as the line search method, have not yet proven to be successful. Further investigation is needed.     

Reply to L. Fernandez–Jambrina

We reply to the comment by L. Fernandez–Jambrina.     

On Ruelle–Perron–Frobenius Operators.¶I. Ruelle Theorem

We study Ruelle–Perron–Frobenius operators for locally expanding and mixing dynamical systems on general compact metric spaces associated with potentials satisfying the Dini condition. In this paper, we give a proof of the Ruelle Theorem on Gibbs measures. It is the first part of our research on the subject. The rate of convergence of powers of the operator will be presented in a forthcoming paper. Received: 31 May 2000 / Accepted: 1 June 2001     

On Ruelle–Perron–Frobenius Operators.¶II. Convergence Speeds

We study Ruelle operators on expanding and mixing dynamical systems with potential function satisfying the Dini condition. We give an estimate for the convergence speed of the iterates of a Ruelle operator. Our proof avoids Markov partitions. This is the second part of our research on Ruelle operators. Received: 31 May 2000 / Accepted: 1 June 2001     

On Quantum Phase Transition. II. The Falicov–Kimball Model

The Falicov–Kimball (FK) model⁽¹⁾ involves two types of interacting particles: first the itinerant spinless electrons are quantum particles, secondly the static ions are classical particles. It is striking to see that, despite the simplicity of its hamiltonian, the phase diagram of the FK model is highly sophisticated, moreover it remains in great part conjectural. An antiferromagnetic phase transition was proven for the FK model on a square lattice in the seminal paper of T. Kennedy and E. Lieb.⁽²⁾ This result was extended by Lebowitz and Macris⁽³⁾ to small magnetic field. Then the same result was obtained by using a new method.⁽⁴⁾ The main results of this paper concerns the two dimensional FK model on a square lattice, for which we apply the general results contained in ref. 5. First there exists an effective hamiltonian which is a long range many body Ising model, and which governs the behaviour of the ions. Secondly we compute explicitly the truncated effective hamiltonian up to the fourth order w.r.t. a small parameter (the inverse of the on site energy). Finally we use the classical Pirogov–Sinai theory, to get the hierarchy of the phase diagrams up to the fourth order. More precisely, we show that, when the chemical potential varies, the FK model exhibits, at low temperature, a sequence of phase transitions: first between phases of period two, then of period three, then of period four, and finally of period five. In each case the completeness of the phase diagram is proved. This paper supports the conjecture that the phase diagram of the FK model contains periodic phases outside of a Cantor set.     

On the occurrence of b.c.c.–h.c.p. structural phase transition in Mo under pressure

Abstract

To resolve the controversy on the occurrence of a b.c.c.–h.c.p. transition in shock as well as static measurements in Mo, we have done more accurate total energy electronic structure calculations. Our results show that this phasetransition should occur at much higher pressures than suggested by earlier calculations.     

Transport and relaxation properties of isotopomeric hydrogen–helium binary mixtures. I. H2–He mixtures

An extensive comparison has been carried out between calculated and measured bulk properties of H₂–helium mixtures. Detailed comparisons are presented for the interaction second virial coefficient, binary diffusion, mixture shear viscosity and thermal conductivity, rotational relaxation, thermal diffusion field-effects, collision broadening of the depolarized Rayleigh light scattering spectrum, and flow birefringence. Scattering calculations have been carried out for the ab initio potential energy surfaces obtained by Tao (1994, J. chem. Phys., 100, 4947) and Schaefer and Köhler (1985, Physica A, 129, 469). The values for the various bulk gas properties calculated from these two potential surfaces are generally found to lie within or near the experimental uncertainties.     

The activation and the spreading of deformation in a fully lamellar Ti–47 at.% Al–1 at.% Cr–0.2 at.% Si Alloy

The spreading of deformation in a lamellar Ti–47?at.% Al–1?at.% Cr–0.2?at.% Si alloy deformed under compression is studied at 25°C and 600°C. This microstructure is largely dominated by twin-related variants which are separated by either twin interfaces or thin α ₂ slabs. The alloy deforms at both temperatures by ordinary dislocations and twins. Deformation in a particular γ variant and its adjacent twin-related variant involves the same kind of glide system, either ordinary dislocations or twins. This property is found to be true for all twin-related lamellae. The occurrence of this correlated glide is explained by the introduction of the notion of pilot and driven orientations. The lamellar orientation in which the operating glide system is activated on the basis of Schmid factor considerations is termed the pilot orientation. It imposes its deformation system on to the twin-related lamella, called the driven orientation, whose deformation may not involve the slip system most favoured by the applied stress.