Charge reversal of colloidal particles

A theory is presented for the effective charge of colloidal particles in suspensions containing multivalent counterions. It is shown that if colloids are sufficiently strongly charged, the number of condensed multivalent counterion can exceed the bare colloidal charge leading to charge reversal. Charge renormalization in suspensions with multivalent counterions depends on a subtle interplay between the solvation energies of the multivalent counterions in the bulk and near the colloidal surface. We find that the effective charge is {\it not} a monotonically decreasing function of the multivalent salt concentration. Furthermore, contrary to the previous theories, it is found that except at very low concentrations, monovalent salt hinders the charge reversal. This conclusion is in agreement with the recent experiments and simulations

Theory of Diamagnetism in the Pseudogap Phase: Implications from the Self energy of Angle Resolved Photoemission

In this paper we apply the emerging- consensus understanding of the fermionic self energy deduced from angle resolved photoemisssion spectroscopy (ARPES) experiments to deduce the implications for orbital diamagnetism in the underdoped cuprates. Many theories using many different starting points have arrived at a broadened BCS-like form for the normal state self energy associated with a d-wave excitation gap, as is compatible with ARPES data. Establishing compatibility with the f-sum rules, we show how this self energy, along with the constraint that there is no Meissner effect in the normal phase are sufficient to deduce the orbital susceptibility. We conclude, moreover, that diamagnetism is large for a d-wave pseudogap. Our results should apply rather widely to many theories of the pseudogap, independent of the microscopic details.Comment: 15 pages, 8 figure

Normal zone in YBa2Cu3O6+xYBa_2Cu_3O_{6+x}-coated conductors

We consider the distribution of an electric field in YBCO-coated conductors for a situation in which the DC transport current is forced into the copper stabilizer due to a weak link -- a section of the superconducting film with a critical current less than the transport current. The electric field in the metal substrate is also discussed. The results are compared with recent experiments on normal zone propagation in coated conductors for which the substrate and stabilizer are insulated from each other. The potential difference between the substrate and stabilizer, and the electric field in the substrate outside the normal zone can be accounted for by a large screening length in the substrate, comparable to the length of the sample. During a quench, the electric field inside the interface between YBCO and stabilizer, as well as in the buffer layer, can be several orders of magnitude greater than the longitudinal macroscopic electric field inside the normal zone. We speculate on the possibility of using possible microscopic electric discharges caused by this large ($\sim$kV/cm) electric field as a means to detect a quench.Comment: 8 pages, 4 figure

The effects of superconductor-stabilizer interfacial resistance on quench of a pancake coil made out of coated conductor

We present the results of numerical analysis of normal zone propagation in a stack of $YBa_2Cu_3O_{7-x}$ coated conductors which imitates a pancake coil. Our main purpose is to determine whether the quench protection quality of such coils can be substantially improved by increased contact resistance between the superconducting film and the stabilizer. We show that with increased contact resistance the speed of normal zone propagation increases, the detection of a normal zone inside the coil becomes possible earlier, when the peak temperature inside the normal zone is lower, and stability margins shrink. Thus, increasing contact resistance may become a viable option for improving the prospects of coated conductors for high $T_c$ magnets applications.Comment: 9 pages, 4 figure

Curing singularities: From the big bang to black holes

Singular spacetimes are a natural prediction of Einstein's theory. Most memorable are the singular centers of black holes and the big bang. However, dilatonic extensions of Einstein's theory can support nonsingular spacetimes. The cosmological singularities can be avoided by dilaton driven inflation. Furthermore, a nonsingular black hole can be constructed in two dimensions.Comment: To appear as a brief report in Phys. Rev.

Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

The effects of superconductor-stabilizer interfacial resistance on quench of current-carrying coated conductor

We present the results of numerical analysis of a model of normal zone propagation in coated conductors. The main emphasis is on the effects of increased contact resistance between the superconducting film and the stabilizer on the speed of normal zone propagation, the maximum temperature rise inside the normal zone, and the stability margins. We show that with increasing contact resistance the speed of normal zone propagation increases, the maximum temperature inside the normal zone decreases, and stability margins shrink. This may have an overall beneficial effect on quench protection quality of coated conductors. We also briefly discuss the propagation of solitons and development of the temperature modulation along the wire.Comment: To be published in Superconductor Science and Technology. This preprint contains one animated figure (Fig. 6(a)). when asked whether you want to play the content, click "Play". Acrobat Reader (Windows and Mac, but not Linux) will play embedded flash movies. In the printed copy Fig. 6(b) will show the temperature profile at gamma t=15

Statistical Mechanics of Unbound Two Dimensional Self-Gravitating Systems

We study, using both theory and molecular dynamics simulations, the relaxation dynamics of a microcanonical two dimensional self-gravitating system. After a sufficiently large time, a gravitational cluster of N particles relaxes to the Maxwell-Boltzmann distribution. The time to reach the thermodynamic equilibrium, however, scales with the number of particles. In the thermodynamic limit, $N\to\infty$ at fixed total mass, equilibrium state is never reached and the system becomes trapped in a non-ergodic stationary state. An analytical theory is presented which allows us to quantitatively described this final stationary state, without any adjustable parameters

Monopole solutions to the Bogomolny equation as three-dimensional generalizations of the Kronecker series

The Dirac monopole on a three-dimensional torus is considered as a solution to the Bogomolny equation with non-trivial boundary conditions. The analytical continuation of the obtained solution is shown to be a three-dimensional generalization of the Kronecker series. It satisfies the corresponding functional equation and is invariant under modular transformations.Comment: 13 pages, 1 figur