Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.

Dynamical complexity in a mean-field model of human EEG

A recently proposed mean-field theory of mammalian cortex rhythmogenesis describes the salient features of electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations (Liley et al 2002). This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness (Bojak & Liley 2007) and the changes in EEG spectral power associated with general anesthetic effect (Bojak & Liley 2005). From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, various routes to chaos, fat fractals and rich bifurcation scenarios occur for physiologically relevant parameter values (van Veen & Liley 2006). The origin and the character of this complex behaviour, and its relevance for EEG activity will be illustrated. The existence of short-lived unstable brain states will also be discussed in terms of the available theoretical and experimental results. A perspective on future analysis will conclude the presentation.

Self-organized 40Hz synchronization in a physiological theory of EEG

We present evidence that large-scale spatial coherence of 40 Hz oscillations can emerge dynamically in a cortical mean field theory. The simulated synchronization time scale is about 150 ms, which compares well with experimental data on large-scale integration during cognitive tasks. The same model has previously provided consistent descriptions of the human EEG at rest, with tranquilizers, under anesthesia, and during anesthetic-induced epileptic seizures. The emergence of coherent gamma band activity is brought about by changing just one physiological parameter until cortex becomes marginally unstable for a small range of wavelengths. This suggests for future study a model of dynamic computation at the edge of cortical stability.

Instabilities in thermal gravity with a cosmological constant

It is shown that in quantum gravity at finite temperature, the effective potential evaluated in the tadpole approximation can have a local minimum below a certain critical temperature. However, when the leading higher order thermal loop corrections are included, one finds that no static solution exists at high temperature. (C) 2008 Elsevier B.V. All rights reserved.

Critical behavior of a contact process with aperiodic transition rates

We performed Monte Carlo simulations to investigate the steady-state critical behavior of a one-dimensional contact process with an aperiodic distribution of rates of transition. As in the presence of randomness, spatial fluctuations can lead to changes of critical behavior. For sufficiently weak fluctuations, we give numerical evidence to show that there is no departure from the universal critical behavior of the underlying uniform model. For strong spatial fluctuations, the analysis of the data indicates a change of critical universality class.

Dynamical noncommutativity

The model of dynamical noncommutativity is proposed. The system consists of two interrelated parts. The first of them describes the physical degrees of freedom with the coordinates q(1) and q(2), and the second corresponds to the noncommutativity eta which has a proper dynamics. After quantization, the commutator of two physical coordinates is proportional to the function of eta. The interesting feature of our model is the dependence of nonlocality on the energy of the system. The more the energy, the more the nonlocality. The leading contribution is due to the mode of noncommutativity; however, the physical degrees of freedom also contribute in nonlocality in higher orders in theta .

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which is based on Weyl symmetrically ordered operator products. By using a polydifferential representation for the deformed coordinates, xj we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth-order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.

Shared information in stationary states at criticality

We consider bipartitions of one-dimensional extended systems whose probability distribution functions describe stationary states of stochastic models. We define estimators of the information shared between the two subsystems. If the correlation length is finite, the estimators stay finite for large system sizes. If the correlation length diverges, so do the estimators. The definition of the estimators is inspired by information theory. We look at several models and compare the behaviors of the estimators in the finite-size scaling limit. Analytical and numerical methods as well as Monte Carlo simulations are used. We show how the finite-size scaling functions change for various phase transitions, including the case where one has conformal invariance.

Protecting clean critical points by local disorder correlations

We show that a broad class of quantum critical points can be stable against locally correlated disorder even if they are unstable against uncorrelated disorder. Although this result seemingly contradicts the Harris criterion, it follows naturally from the absence of a random-mass term in the associated order parameter field theory. We illustrate the general concept with explicit calculations for quantum spin-chain models. Instead of the infinite-randomness physics induced by uncorrelated disorder, we find that weak locally correlated disorder is irrelevant. For larger disorder, we find a line of critical points with unusual properties such as an increase of the entanglement entropy with the disorder strength. We also propose experimental realizations in the context of quantum magnetism and cold-atom physics. Copyright (C) EPLA, 2011

A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local; they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows us to check the universality of non-local observables in the raise and peel model. An example is given.

Quantum toy model for black-hole backreaction

We propose a simple quantum field theoretical toy model for black-hole evaporation and study the backreaction of Hawking radiation onto the classical background. It turns out that the horizon is also pushed back in this situation (i.e., the interior region shrinks) though this backreaction is not caused by energy conservation but by momentum balance. The effective heat capacity and induced entropy variation can have both signs-depending on the parameters of the model.

On (b,c)-system at finite temperature in thermo field approach

We construct the finite temperature field theory of the two-dimensional ghost-antighost system within the framework of thermo field theory. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = partial derivative F + fAF arises besides the one of the first order treatment, F = partial derivative A - partial derivative A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L-P alpha G(2). In this application the photon mass is estimated. The SU(N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian. (c) 2006 Elsevier B.V. All rights reserved.