Analytical study of quasi-one dimensional flat band networks and slow light analogue

Exact method of analytical solution of flat, non-dispersive eigenstates in a class of quasi-one dimensional structures is reported within the tight-binding framework. The states are localized over certain sublattice sites. One such finite size cluster of atomic sites is decoupled from the rest of the system by the special non-permissible vertex having zero amplitude. This immediately leads to the self-trapping of the incoming excitation. We work out an analytical scheme to discern the localizing character of the diffraction free dispersionless modes using real space renormalization group technique. Supportive numerical calculations of spectral profile and transport are demonstrated to substantiate the essence of compact localized states. Possible experimental scope regarding the photonic analogue of the tight-binding electronic case is also discussed elaborately. This eventually unfolds the concepts of slow light and the related re-entrant mode switching from the study of optical dispersion.Comment: 11 pages, 11 eps figures (Accepted in Acta Physica Polonica A). arXiv admin note: text overlap with arXiv:1901.0924

Flux modulated flat band engineering in square-kagome ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagome ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical divider formed by the sites with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.Comment: 10 pages, 12 eps figures (Revision submitted to Physics Letters A

A Data Driven, Zero-Dimensional Time Delay Model with Radiative Forcing for Simulating Global Climate

Several complicated non-linear models exist which simulate the physical processes leading to fluctuations in global climate. Some of these more advanced models use observations to constrain various parameters involved. However, they tend to be very computationally expensive. Also, the exact physical processes that affect the climate variations have not been completely comprehended. Therefore, to obtain an insight into global climate, we have developed a physically motivated reduced climate model. The model utilizes a novel mathematical formulation involving a non-linear delay differential equation to study temperature fluctuations when subjected to imposed radiative forcing. We have further incorporated simplified equations to test the effect of speculated mechanisms of climate forcing and evaluated the extent of their influence. The findings are significant in our efforts to predict climate change and help in policy framing necessary to tackle it

On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacation

Due to the widespread applicability of discrete-time queues in wireless networks or telecommunication systems, this paper analyzes an infinite-buffer batch-service queue with single and multiple vacation where customers/messages arrive according to the Bernoulii process and service time varies with the batch-size. The foremost focal point of this analysis is to get the complete joint distribution of queue length and server content at service completion epoch, for which first the bivariate probability generating function has been derived. We also acquire the joint distribution at arbitrary slot. We also provide several marginal distributions and performance measures for the utilization of the vendor. Transmission of data through a particular channel is skipped due to the high transmission error. As the discrete phase type distribution plays a noteworthy role to control this error, we include numerical example where service time distribution follows discrete phase type distribution. A comparison between batch-size dependent and independent service has been drawn through the graphical representation of some performance measures and total system cost.Comment: 28 pages, 5 figure

An Analytical Study of different Document Image Binarization Methods

Document image has been the area of research for a couple of decades because of its potential application in the area of text recognition, line recognition or any other shape recognition from the image. For most of these purposes binarization of image becomes mandatory as far as recognition is concerned. Throughout couple decades standard algorithms have already been developed for this purpose. Some of these algorithms are applicable to degraded image also. Our objective behind this work is to study the existing techniques, compare them in view of advantages and disadvantages and modify some of these algorithms to optimize time or performance.Comment: National Conference on Computing and Communication Systems (COCOSYS-09), UIT, Burdwan, January 02-04, 2009, pp. 71-7

Higher order Soliton Complexes in Coupled Nonlinear Schr\"odinger Equation with Variable Coefficients

We present the explicit dark-bright three soliton solution and the associated spectral problem for the variable coefficient integrable coupled NLS equation. Using asymptotic analysis as well as graphical analysis we study the interactions in soliton complexes. We present a correlation between the soliton parameters and the interaction pattern in three soliton complexes. Using asymptotic analysis, we present a few interesting features of complex three soliton bound state and interaction of dark-bright two soliton complex with a regular soliton. Using three soliton interactions we have shown that the energy sharing take place between soliton even when the soliton do not collide with each other. The results found by us might be useful for the development of soliton control, all optical gates as well as all optical switching devices. We hope that the analysis of three soliton complexes would be useful for a better understanding of soliton interactions in nonlinear fiber as well as in a bulk medium.Comment: 25 page

Double ring algorithm of solar active region eruptions within the framework of kinematic dynamo model

Recent results indicate that the Babcock-Leighton mechanism for poloidal field creation plays an important role in the solar cycle. However, modelling this mechanism has not always correctly captured the underlying physics. In particular, it has been demonstrated that using a spatially distributed near-surface alpha-effect to parametrize the Babcock-Leighton mechanism generates results which do not agree with observations. Motivated by this, we are developing a physically more consistent model of the solar cycle in which we model poloidal field creation by the emergence and flux dispersal of double-rings structures. Here we present preliminary results from this new dynamo model.Comment: To appear in proceedings of the ISSTP 2012, 4 Pages,3 figure

Generative Modeling of Hidden Functional Brain Networks

Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human functional brain networks, the network structure is often inferred from functional magnetic resonance imaging (fMRI) blood oxygen level dependent (BOLD) signal. Since the BOLD signal is a proxy for neuronal activity, it is of interest to learn the latent functional network structure. Additionally, despite a core set of observations about functional networks such as small-worldness, modularity, exponentially truncated degree distributions, and presence of various types of hubs, very little is known about the computational principles which can give rise to these observations. This paper introduces a Hidden Markov Random Field framework for the purpose of representing, estimating, and evaluating latent neuronal functional relationships between different brain regions using fMRI data

Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.Comment: 3 figures, version published in Phys. Rev.

Hyperskewness of (1+1)(1+1)-dimensional KPZ Height Fluctuations

We evaluate the fifth order normalized cumulant, known as hyperskewness, of height fluctuations dictated by the $(1+1)$-dimensional KPZ equation for the stochastic growth of a surface on a flat geometry in the stationary state. We follow a diagrammatic approach and invoke a renormalization scheme to calculate the fifth cumulant given by a connected loop diagram. This, together with the result for the second cumulant, leads to the hyperskewness value $\widetilde{S} = 0.0835$.Comment: 11 pages, 2 figures, version accepted for publication in J. Stat. Mech.: Theory and Ex