Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Chromosomal fragile site FRA16D and DNA instability in cancer

It has been proposed that common aphidicolin-inducible fragile sites, in general, predispose to specific chromosomal breakage associated with deletion, amplification, and/or translocation in certain forms of cancer. Although this appears to be the case for the fragile site FRA3B and may be the case for FRA7G, it is not Set clear whether this association is a general property of this class of fragile site. The major aim of the present study was to determine whether the FRA16D chromosomal fragile site locus has a role to play in predisposing DNA sequences within and adjacent to the fragile site to DNA instability (such as deletion or translocation), which could lead to or be associated with neoplasia. We report the localization of FRA16D within a contig of cloned DNA and demonstrate that this fragile site coincides with a region of homozygous deletion in a gastric adenocarcinoma cell line and is bracketed by translocation breakpoints in multiple myeloma, as reported previously (Chesi, M., et al., Blood, 91: 4457-4463, 1998), Therefore, given similar findings at the FRA3B and FRA7G fragile sites, it is likely that common aphidicolin-inducible fragile sites exhibit the general property of localized DNA instability in cancer cells.

Kinematic and non-linear analysis of foldable barrel vaults

Kinematic analysis is conducted to derive the geometric constraints for the geometric design of foldable barrel vaults (FBV) composed of polar or angulated scissor units. Non-linear structural analysis is followed to determine the structural response of FBVs in the fully deployed configuration under static loading. Two load cases are considered: cross wind and longitudinal wind. The effect of varying member sizes, depth-to-span ratio and geometric imperfections is examined. (C) 2000 Elsevier Science Ltd. All rights reserved.

Large amplitude folding in finely layered viscoelastic rock structures

We analyze folding phenomena in finely layered viscoelastic rock. Fine is meant in the sense that the thickness of each layer is considerably smaller than characteristic structural dimensions. For this purpose we derive constitutive relations and apply a computational simulation scheme (a finite-element based particle advection scheme; see MORESI et al., 2001) suitable for problems involving very large deformations of layered viscous and viscoelastic rocks. An algorithm for the time integration of the governing equations as well as details of the finite-element implementation is also given. We then consider buckling instabilities in a finite, rectangular domain. Embedded within this domain, parallel to the longer dimension we consider a stiff, layered plate. The domain is compressed along the layer axis by prescribing velocities along the sides. First, for the viscous limit we consider the response to a series of harmonic perturbations of the director orientation. The Fourier spectra of the initial folding velocity are compared for different viscosity ratios. Turning to the nonlinear regime we analyze viscoelastic folding histories up to 40% shortening. The effect of layering manifests itself in that appreciable buckling instabilities are obtained at much lower viscosity ratios (1:10) as is required for the buckling of isotropic plates (1:500). The wavelength induced by the initial harmonic perturbation of the director orientation seems to be persistent. In the section of the parameter space considered here elasticity seems to delay or inhibit the occurrence of a second, larger wavelength. Finally, in a linear instability analysis we undertake a brief excursion into the potential role of couple stresses on the folding process. The linear instability analysis also provides insight into the expected modes of deformation at the onset of instability, and the different regimes of behavior one might expect to observe.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Theoretical and numerical analyses of convective instability in porous media with temperature-dependent viscosity

Exact analytical solutions of the critical Rayleigh numbers have been obtained for a hydrothermal system consisting of a horizontal porous layer with temperature-dependent viscosity. The boundary conditions considered are constant temperature and zero vertical Darcy velocity at both the top and bottom of the layer. Not only can the derived analytical solutions be readily used to examine the effect of the temperature-dependent viscosity on the temperature-gradient driven convective flow, but also they can be used to validate the numerical methods such as the finite-element method and finite-difference method for dealing with the same kind of problem. The related analytical and numerical results demonstrated that the temperature-dependent viscosity destabilizes the temperature-gradient driven convective flow and therefore, may affect the ore body formation and mineralization in the upper crust of the Earth. Copyright (C) 2003 John Wiley Sons, Ltd.

Utilizing encoding in scalable linear optics quantum computing

We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme and Milburn, and makes use of an incremental approach to the error encoding to boost probability of success.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone system.

High-breakdown linear discriminant analysis

The classification rules of linear discriminant analysis are defined by the true mean vectors and the common covariance matrix of the populations from which the data come. Because these true parameters are generally unknown, they are commonly estimated by the sample mean vector and covariance matrix of the data in a training sample randomly drawn from each population. However, these sample statistics are notoriously susceptible to contamination by outliers, a problem compounded by the fact that the outliers may be invisible to conventional diagnostics. High-breakdown estimation is a procedure designed to remove this cause for concern by producing estimates that are immune to serious distortion by a minority of outliers, regardless of their severity. In this article we motivate and develop a high-breakdown criterion for linear discriminant analysis and give an algorithm for its implementation. The procedure is intended to supplement rather than replace the usual sample-moment methodology of discriminant analysis either by providing indications that the dataset is not seriously affected by outliers (supporting the usual analysis) or by identifying apparently aberrant points and giving resistant estimators that are not affected by them.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

Anisotropy-based performance analysis of linear discrete time invariant control systems

The anisotropic norm of a linear discrete-time-invariant system measures system output sensitivity to stationary Gaussian input disturbances of bounded mean anisotropy. Mean anisotropy characterizes the degree of predictability (or colouredness) and spatial non-roundness of the noise. The anisotropic norm falls between the H-2 and H-infinity norms and accommodates their loss of performance when the probability structure of input disturbances is not exactly known. This paper develops a method for numerical computation of the anisotropic norm which involves linked Riccati and Lyapunov equations and an associated special type equation.