Field Theories on Null Manifolds

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges

Scaling and universality in coupled driven diffusive models

Inspired by the physics of magnetohydrodynamics (MHD) a simplified coupled Burgers-like model in one dimension (1d), a generalization of the Burgers model to coupled degrees of freedom, is proposed to describe 1dMHD. In addition to MHD, this model serves as a 1d reduced model for driven binary fluid mixtures. Here we have performed a comprehensive study of the universal properties of the generalized d-dimensional version of the reduced model. We employ both analytical and numerical approaches. In particular, we determine the scaling exponents and the amplitude-ratios of the relevant two-point time-dependent correlation functions in the model. We demonstrate that these quantities vary continuously with the amplitude of the noise cross-correlation. Further our numerical studies corroborate the continuous dependence of long wavelength and long time-scale physics of the model on the amplitude of the noise cross-correlations, as found in our analytical studies. We construct and simulate lattice-gas models of coupled degrees of freedom in 1d, belonging to the universality class of our coupled Burgers-like model, which display similar behavior. We use a variety of numerical (Monte-Carlo and Pseudospectral methods) and analytical (Dynamic Renormalization Group, Self-Consistent Mode-Coupling Theory and Functional Renormalization Group) approaches for our work. The results from our different approaches complement one another. Possible realizations of our results in various nonequilibrium models are discussed.Comment: To appear in JSTAT (2009); 52 pages in JSTAT format. Some figure files have been replace

Fixed-Energy Sandpiles Belong Generically to Directed Percolation

Fixed-energy sandpiles with stochastic update rules are known to exhibit a nonequilibrium phase transition from an active phase into infinitely many absorbing states. Examples include the conserved Manna model, the conserved lattice gas, and the conserved threshold transfer process. It is believed that the transitions in these models belong to an autonomous universality class of nonequilibrium phase transitions, the so-called Manna class. Contrarily, the present numerical study of selected (1+1)-dimensional models in this class suggests that their critical behavior converges to directed percolation after very long time, questioning the existence of an independent Manna class.Comment: article (4 pages, 9 eps figures) + Supplement (8 pages, 9 eps figures); Phys. Rev. Lett. 201

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models

Helioseismic analysis of the hydrogen partition function in the solar interior

The difference in the adiabatic gradient gamma_1 between inverted solar data and solar models is analyzed. To obtain deeper insight into the issues of plasma physics, the so-called ``intrinsic'' difference in gamma_1 is extracted, that is, the difference due to the change in the equation of state alone. Our method uses reference models based on two equations of state currently used in solar modeling, the Mihalas-Hummer-Dappen (MHD) equation of state, and the OPAL equation of state (developed at Livermore). Solar oscillation frequencies from the SOI/MDI instrument on board the SOHO spacecraft during its first 144 days in operation are used. Our results confirm the existence of a subtle effect of the excited states in hydrogen that was previously studied only theoretically (Nayfonov & Dappen 1998). The effect stems from internal partition function of hydrogen, as used in the MHD equation of state. Although it is a pure-hydrogen effect, it takes place in somewhat deeper layers of the Sun, where more than 90% of hydrogen is ionized, and where the second ionization zone of helium is located. Therefore, the effect will have to be taken into account in reliable helioseismic determinations of the astrophysically relevant helium-abundance of the solar convection zone.Comment: 30 pages, 4 figures, 1 table. Revised version submitted to Ap

Relation between concurrence and Berry phase of an entangled state of two spin 1/2 particles

We have studied here the influence of the Berry phase generated due to a cyclic evolution of an entangled state of two spin 1/2 particles. It is shown that the measure of formation of entanglement is related to the cyclic geometric phase of the individual spins. \\Comment: 6 pages. Accepted in Europhys. Letters (likely to be published in vol 73, pp1-6 (2006)

Topological Aspect of high-TcT_c Superconductivity, Fractional Quantum Hall Effect and Berry Phase

We have analysed here the equivalence of RVB states with $\nu=1/2$ FQH states in terms of the Berry Phase which is associated with the chiral anomaly in 3+1 dimensions. It is observed that the 3-dimensional spinons and holons are characterised by the non-Abelian Berry phase and these reduce to 1/2 fractional statistics when the motion is confined to the equatorial planes. The topological mechanism of superconductivity is analogous to the topological aspects of fractional quantum Hall effect with $\nu=1/2$.Comment: 12 pages latex fil

Reaction diffusion processes on random and scale-free networks

We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.Comment: 8 pages, 7 figure

Structure of the near-surface layers of the Sun: asphericity and time variation

We present results on the structure of the near-surface layers of the Sun obtained by inverting frequencies of high-degree solar modes from "ring diagrams". We have results for eight epochs between June 1996 and October 2003. The frequencies for each epoch were obtained from ring diagrams constructed from MDI Dopplergrams spanning complete Carrington rotations. We find that there is a substantial latitudinal variation of both sound speed and the adiabatic index Gamma_1 in the outer 2% of the Sun. We find that both the sound-speed and Gamma_1 profiles change with changes in the level of solar activity. In addition, we also study differences between the northern and southern hemispheres of the Sun and find a small asymmetry that appears to reflect the difference in magnetic activity between the two hemispheres.Comment: To appear in ApJ (January 2007

A synoptic comparison of the MHD and the OPAL equations of state

A detailed comparison is carried out between two popular equations of state (EOS), the Mihalas-Hummer-Dappen (MHD) and the OPAL equations of state, which have found widespread use in solar and stellar modeling during the past two decades. They are parts of two independent efforts to recalculate stellar opacities; the international Opacity Project (OP) and the Livermore-based OPAL project. We examine the difference between the two equations of state in a broad sense, over the whole applicable rho-T range, and for three different chemical mixtures. Such a global comparison highlights both their differences and their similarities. We find that omitting a questionable hard-sphere correction, tau, to the Coulomb interaction in the MHD formulation, greatly improves the agreement between the MHD and OPAL EOS. We also find signs of differences that could stem from quantum effects not yet included in the MHD EOS, and differences in the ionization zones that are probably caused by differences in the mechanisms for pressure ionization. Our analysis do not only give a clearer perception of the limitations of each equation of state for astrophysical applications, but also serve as guidance for future work on the physical issues behind the differences. The outcome should be an improvement of both equations of state.Comment: 33 pages, 26 figures. Corrected discussion of Basu & Antia, 2004, ApJ, 606, L85-L8