Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation

Dynamics of ordering in Ising model, following quench to zero temperature, have been studied via Glauber spin-flip Monte Carlo simulations in space dimensions $d=2$ and $3$. One of the primary objectives has been to understand phenomena associated with the persistent spins, viz., time decay in the number of unaffected spins, growth of the corresponding pattern and its fractal dimensionality, for varying correlation length in the initial configurations, prepared at different temperatures, at and above the critical value. It is observed that the fractal dimensionality and the exponent describing the power-law decay of persistence probability are strongly dependent upon the relative values of nonequilibrium domain size and the initial equilibrium correlation length. Via appropriate scaling analyses, these quantities have been estimated for quenches from infinite and critical temperatures. The above mentioned dependence is observed to be less pronounced in higher dimension. In addition to these findings for the local persistence, we present results for the global persistence as well. Further, important observations on the standard domain growth problem are reported. For the latter, a controversy in $d=3$, related to the value of the exponent for the power-law growth of the average domain size with time, has been resolved.Comment: 10 pages, 16 figure

Rational homotopy of maps between certain complex Grassmann manifolds

Let $G_{n,k}$ denote the complex Grassmann manifold of $k$-dimensional vector subspaces of $\mathbb{C}^n$. Assume $l,k\le \lfloor n/2\rfloor$. We show that, for sufficiently large $n$, any continuous map $h:G_{n,l}\to G_{n,k}$ is rationally null homotopic if $(i)~ 1\le k< l,$ $(ii)~2<l<k< 2(l-1)$, $(iii)~1<l<k$, $l$ divides $n$ but $l$ does not divide $k$.Comment: 15 page

Kinetics of Ferromagnetic Ordering in 3D Ising Model: Do we understand the case of zero temperature quench?

We study phase ordering dynamics in the three-dimensional nearest-neighbor Ising model, following rapid quenches from infinite to zero temperature. Results on various aspects, viz., domain growth, persistence, aging and pattern, have been obtained via the Glauber Monte Carlo simulations of the model on simple cubic lattice. These are analyzed via state-of-the-art methods, including the finite-size scaling, and compared with those for quenches to a temperature above the roughening transition. Each of these properties exhibit remarkably different behavior at the above mentioned final temperatures. Such a temperature dependence is absent in the two-dimensional case for which there is no roughening transition

Persistence in Ferromagnetic Ordering: Dependence upon initial configuration

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of the Ising model, employing the Glauber spin-flip mechanism, in space dimensions $d=2$ and $3$. Results for the persistence probability and the domain growth are discussed for quenches to various temperatures ($T_f$) below the critical one ($T_{c}$), from different initial temperatures $T_{i} \geq T_{c}$. In long time limit, for $T_{i} > T_{c}$, the persistence probability exhibits power-law decay with exponents $\theta \simeq 0.22$ and $\simeq 0.18$ in $d=2$ and $3$, respectively. For finite $T_i$, the early time behavior is a different power-law whose life-time diverges and exponent decreases as $T_{i} \rightarrow T_{c}$. The crossover length between the two steps diverges as the equilibrium correlation length. $T_i=T_c$ is expected to provide a {\it{new universality class}} for which we obtain $\theta \simeq 0.035$ in $d=2$ and $\simeq 0.10$ in $d=3$. The time dependence of the average domain size $\ell$, however, is observed to be rather insensitive to the choice of $T_i$.Comment: 8 pages, 9 figure

Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points

We have studied the dynamical polarization and collective excitations in an anisotropic two-dimensional system undergoing a quantum phase transition with merging of two Dirac points. Analytical results for the one-loop polarization function are obtained at the finite momentum, frequency, and chemical potential. The evolution of the plasmon dispersion across the phase transition is then analyzed within the random phase approximation. We derive analytically the long-wavelength dispersion of the undamped anisotropic collective mode and find that it evolves smoothly at the critical merging point. The effects of the van Hove singularity on the plasmon excitations are explored in detail.Comment: 8 pages, 5 figures; published version: minor changes, one reference and insets to Figs. 2 and 3 adde

On a Fixed Point Theorem for a Cyclical Kannan-type Mapping

This paper deals with an extension of a recent result by the authors generalizing Kannan's fixed point theorem based on a theorem of Vittorino Pata. The generalization takes place via a cyclical condition.Comment: 7 pages, No figure

Coarsening in 3D Nonconserved Ising Model at Zero Temperature: Anomalies in structure and relaxation of order-parameter autocorrelation

Via Monte Carlo simulations we study pattern and aging during coarsening in nonconserved nearest neighbor Ising model, following quenches from infinite to zero temperature, in space dimension $d=3$. The decay of the order-parameter autocorrelation function is observed to obey a power-law behavior in the long time limit. However, the exponent of the power-law, estimated accurately via a state-of-art method, violates a well-known lower bound. This surprising fact has been discussed in connection with a quantitative picture of the structural anomaly that the 3D Ising model exhibits during coarsening at zero temperature. These results are compared with those for quenches to a temperature above that of the roughening transition.Comment: 15 pages, 6 figure

Categorical Accommodation of Graded Fuzzy Topological System, Graded Frame and Fuzzy Topological Space with Graded inclusion

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded inclusion were obtained via fuzzy geometric logic with graded con- sequence. As an off shoot the notion of graded frame has been developed. This paper deals with a detailed categorical study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion and their interrelation

Intrinsic Shapes of Very Flat Elliptical Galaxies

Photometric data from the literature is combined with triaxial mass models to derive variation in the intrinsic shapes of the light distribution of elliptical galaxies NGC 720, 2768 and 3605. The inferred shape variation in given by a Bayesian probability distribution, assuming a uniform prior. The likelihood of obtaining the data is calculated by using ensemble of triaxial models. We apply the method to infer the shape variation of a galaxy, using the ellipticities and the difference in the position angles at two suitably chosen points from the profiles of the photometric data. Best constrained shape parameters are found to be the short to long axial ratios at small and large radii, and the absolute values of the triaxiallity difference between these radii.Comment: Accepted in MNRA

On the energy spectrum of rapidly rotating forced turbulence

In this paper, we investigate the statistical features of the fully developed, forced, rapidly rotating, {turbulent} system using numerical simulations, and model {the} energy {spectrum} that {fits} well with the numerical data. Among the wavenumbers ($k$) larger than the Kolmogorov dissipation wavenumber, the energy is distributed such that the suitably non-dimensionized energy spectrum is ${\bar E}({\bar k})\approx \exp(-0.05{\bar k})$, where overbar denotes appropriate non-dimensionalization. {For the wavenumbers smaller than that of forcing, the energy in a horizontal plane is much more than that along the vertical rotation-axis.} {For} such wavenumbers, we find that the anisotropic energy spectrum, $E(k_\perp,k_\parallel)$ follows the power law scaling, $k_\perp^{-5/2}k_\parallel^{-1/2}$, where `$\perp$' and `$\parallel$' respectively refer to the directions perpendicular and parallel to the rotation axis; this result is in line with the Kuznetsov--Zakharov--Kolmgorov spectrum predicted by the weak inertial-wave turbulence theory for the rotating fluids.Comment: 11 pages, 7 figures, accepted in Physics of FLuid