Anomalous structural and mechanical properties of solids confined in quasi one dimensional strips

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural and mechanical properties not observed in the bulk. Depending on the density $\rho$ and the distance between the walls $L_y$, the system shows structural characteristics analogous to a weakly modulated liquid, a strongly modulated smectic, a triangular solid or a buckled phase. At fixed $\rho$, a change in $L_y$ leads to many reentrant discontinuous transitions involving changes in the number of layers parallel to the confining walls depending crucially on the commensurability of inter-layer spacing with $L_y$. The solid shows resistance to elongation but not to shear. When strained beyond the elastic limit it fails undergoing plastic deformation but surprisingly, as the strain is reversed, the material recovers completely and returns to its original undeformed state. We obtain the phase diagram from mean field theory and finite size simulations and discuss the effect of fluctuations.Comment: 14 pages, 13 figures; revised version, accepted in J. Chem. Phy

A semidefinite relaxation procedure for fault-tolerant observer design

A fault-tolerant observer design methodology is proposed. The aim is to guarantee a minimum level of closed-loop performance under all possible sensor fault combinations while optimizing performance under the nominal, fault-free condition. A novel approach is proposed to tackle the combinatorial nature of the problem, which is computationally intractable even for a moderate number of sensors, by recasting the problem as a robust performance problem, where the uncertainty set is composed of all combinations of a set of binary variables. A procedure based on an elimination lemma and an extension of a semidefinite relaxation procedure for binary variables is then used to derive sufficient conditions (necessary and sufficient in the case of one binary variable) for the solution of the problem which significantly reduces the number of matrix inequalities needed to solve the problem. The procedure is illustrated by considering a fault-tolerant observer switching scheme in which the observer outputs track the actual sensor fault condition. A numerical example from an electric power application is presented to illustrate the effectiveness of the design

Ray optics in flux avalanche propagation in superconducting films

Experimental evidence of wave properties of dendritic flux avalanches in superconducting films is reported. Using magneto-optical imaging the propagation of dendrites across boundaries between a bare NbN film and areas coated by a Cu-layer was visualized, and it was found that the propagation is refracted in full quantitative agreement with Snell's law. For the studied film of 170 nm thickness and a 0.9 mkm thick metal layer, the refractive index was close to n=1.4. The origin of the refraction is believed to be caused by the dendrites propagating as an electromagnetic shock wave, similar to damped modes considered previously for normal metals. The analogy is justified by the large dissipation during the avalanches raising the local temperature significantly. Additional time-resolved measurements of voltage pulses generated by segments of the dendrites traversing an electrode confirm the consistency of the adapted physical picture.Comment: 4 pages, 4 figure

Relativistic Coupled-Cluster Theory of Atomic Parity Nonconservation: Application to 137^{137}Ba+^+

We report the result of our {\it ab initio} calculation of the $6s ^2S_{1/2} \to 5d ^2D_{3/2}$ parity nonconserving electric dipole transition amplitude in $^{137}\text{Ba}^+$ based on relativistic coupled-cluster theory. Considering single, double and partial triple excitations, we have achieved an accuracy of less than one percent. If the accuracy of our calculation can be matched by the proposed parity nonconservation experiment in Ba$^+$ for the above transition,then the combination of the two results would provide an independent non accelerator test of the Standard Model of particle physics.Comment: 4 pages, 1 figure, Submitted to PR

Fault-tolerant Wide-area Control for Power Oscillation Damping

The effectiveness of using both local and remote (wide-area) feedback signals for power oscillation damping (POD) controllers is first demonstrated. The challenge is then to guarantee a minimum level of dynamic performance with only the local signals following a sudden loss of remote signals. A case study on the Nordic equivalent system is presented to show that the closed-loop response could deteriorate if the remote signals are lost. A fault-tolerant control (FTC) design methodology is presented to solve this problem and ensure an acceptable performance level even in case of loss of remote signals. The FTC design methodology is based on simultaneous regional pole-placement for normal and loss of (remote) signals conditions. First the problem is solved non-iteratively using a Linear Matrix Inequality (LMI) approximation and then it is shown that, although this procedure is linear and easy to implement, it has a drawback: the value of one of the control matrices is fixed before calculating the others. An iterative procedure is presented instead to ameliorate this problem and potentially improve the damping of the system. Case studies on the Nordic equivalent system confirm that the proposed iterative fault tolerant controller (FTCit) is able to improve performance against the non-iterative fault tolerant controller (FTC) and produce acceptable performance in case of loss of the remote signals while the response with a CC is unacceptable if a fault occurs

A numerical renormalization group study of laser induced freezing

We study the phenomenon of laser induced freezing, within a numerical renormalization scheme which allows explicit comparison with a recent defect mediated melting theory. Precise values for the `bare' dislocation fugacities and elastic moduli of the 2-d hard disk system are obtained from a constrained Monte Carlo simulation sampling only configurations {\em without} dislocations. These are used as inputs to appropriate renormalization flow equations to obtain the equilibrium phase diagram which shows excellent agreement with earlier simulation results. We show that the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results.Comment: Minor Corrections; Combined version of Europhys. Lett. 67 (2004) p. 814 and Europhys. Lett. 68 (2004) p. 16

Ab initio determination of the lifetime of the 62P3/26^2P_{3/2} state f or 207Pb+^{207}Pb^+ by relativistic many-body theory

Relativistic coupled-cluster(RCC) theory has been employed to calculate the life time of the $6 ^2P_{3/2}$ state of single ionized lead($^{207}Pb$) to an accurac y of 3% and compared with the corresponding value obtained using second order r elativistic many-body perturbation theory(RMBPT). This is one of the very few ap plications of this theory to excited state properties of heavy atomic systems. C ontributions from the different electron correlation effects are given explicitl y

Static and dynamic properties of a reversible gel

We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is supported by a fractal network. Gelation results in a dramatic slowing down of the dynamics, which can be used to locate the transition, which otherwise shows no structural signatures. Moreover, the equilibrium gel dynamics is highly heterogeneous as a result of the presence of particle families with different mobilities. An analysis of gel dynamics in terms of mobile and arrested particles allows us to elucidate several differences between the dynamics of equilibrium gels and that of glass-formers.Comment: 9 pages, 7 figures, paper presented at the 10th Granada Seminar on Computational and Statistical Physic

Direct test of defect mediated laser induced melting theory for two dimensional solids

We investigate by direct numerical solution of appropriate renormalization flow equations, the validity of a recent dislocation unbinding theory for laser induced freezing/melting in two dimensions. The bare elastic moduli and dislocation fugacities which are inputs to the flow equations are obtained for three different 2-d systems (hard disk, inverse $12^{th}$ power and the Derjaguin-Landau-Verwey-Overbeek potentials) from a restricted Monte Carlo simulation sampling only configurations {\em without} dislocations. We conclude that (a) the flow equations need to be correct at least up to third order in defect fugacity to reproduce meaningful results, (b) there is excellent quantitative agreement between our results and earlier conventional Monte Carlo simulations for the hard disk system and (c) while the qualitative form of the phase diagram is reproduced for systems with soft potentials there is some quantitative discrepancy which we explain.Comment: 11 pages, 14 figures, submitted to Phys. Rev.

AdS2xS2 as an exact heterotic string background

An exact heterotic string theory on an AdS2xS2 background supported by an electromagnetic flux is found as a marginal deformation of an SL(2,R)xSU(2) WZW model. Based on a talk given at NATO Advanced Study Institute and EC Summer School on String Theory: from Gauge Interactions to Cosmology, Cargese, Corsica, France, 7 Jun - 19 Jun 2004.Comment: 5 page