Driven 3D Ising Interface: its fluctuation, Devil's staircase, and effect of interface geometry

Enchanting ripple pattern exist on interface, and manifest them self in it's fluctuation profile as well. These ripples apparently flow as the interface struck with inhomogeneous externally driven field interface, moves fluctuating about it on a rectangular 3D Ising system. Ripple structure and flow have temporal periodicity, eventually with some modulation, and have signature of geometry of field interface. Dramatic transitions occur in fluctuation profile as a function of dynamics and geometry of the force field interface and is divided into two spatial regions : rippled and smooth. For the velocity we are concerned with, the interface is pinned with field interface, and for arbitrary orientations of the field profile local slope of the rippled part of the interface gets locked in to a combination of few rational values (Devil's staircase) which most closely approximate the profile, thereby generating specular pattern of patches.Comment: This article has been withdrawn because of critical errors in the manuscrip

Equilibrium configuration of self-gravitating charged dust clouds: Particle approach

A three dimensional Molecular Dynamics (MD) simulation is carried out to explore the equilibrium configurations of charged dust particles. These equilibrium configuration are of astrophysical significance for the conditions of molecular clouds and the interstellar medium. The interaction among the dust grains is modeled by Yukawa repulsion and gravitational attraction. The spherically symmetric equilibria are constructed which are characterized characterized by three parameters: (i) the number of particles in the cloud, (ii) $\Gamma_g$ (defined in the text) where $\Gamma_g^{-1}$ is the short range cutoff of the interparticle potential, and (iii) the temperature of the grains. The effects of these parameters on dust cloud are investigated using radial density profile. The problem of equilibrium is also formulated in the mean field limit where total dust pressure which is the sum of kinetic pressure and electrostatic pressure, balances the self-gravity. The mean field solutions agree well with the results of MD simulations. Astrophysical significance of the results is briefly discussed.Comment: 10 page

On Octonary Codes and their Covering Radii

This paper introduces new reduction and torsion codes for an octonary code and determines their basic properties. These could be useful for the classification of self-orthogonal and self dual codes over $\mathbb{Z}_8$. We also focus our attention on covering radius problem of octonary codes. In particular, we determine lower and upper bounds of the covering radius of several classes of Repetition codes, Simplex codes of Type $\alpha$ and Type $\beta$ and their duals, MacDonald codes, and Reed-Muller codes over $\mathbb{Z}_8$.Comment: 16 pages, some errors fixe

Optimal Scheduling of Water Distribution Systems

With dynamic electricity pricing, the operation of water distribution systems (WDS) is expected to become more variable. The pumps moving water from reservoirs to tanks and consumers, can serve as energy storage alternatives if properly operated. Nevertheless, optimal WDS scheduling is challenged by the hydraulic law, according to which the pressure along a pipe drops proportionally to its squared water flow. The optimal water flow (OWF) task is formulated here as a mixed-integer non-convex problem incorporating flow and pressure constraints, critical for the operation of fixed-speed pumps, tanks, reservoirs, and pipes. The hydraulic constraints of the OWF problem are subsequently relaxed to second-order cone constraints. To restore feasibility of the original non-convex constraints, a penalty term is appended to the objective of the relaxed OWF. The modified problem can be solved as a mixed-integer second-order cone program, which is analytically shown to yield WDS-feasible minimizers under certain sufficient conditions. Under these conditions, by suitably weighting the penalty term, the minimizers of the relaxed problem can attain arbitrarily small optimality gaps, thus providing OWF solutions. Numerical tests using real-world demands and prices on benchmark WDS demonstrate the relaxation to be exact even for setups where the sufficient conditions are not met.Comment: Accepted for publication in IEEE Trans. on Control of Network System

Natural Gas Flow Equations: Uniqueness and an MI-SOCP Solver

The critical role of gas fired-plants to compensate renewable generation has increased the operational variability in natural gas networks (GN). Towards developing more reliable and efficient computational tools for GN monitoring, control, and planning, this work considers the task of solving the nonlinear equations governing steady-state flows and pressures in GNs. It is first shown that if the gas flow equations are feasible, they enjoy a unique solution. To the best of our knowledge, this is the first result proving uniqueness of the steady-state gas flow solution over the entire feasible domain of gas injections. To find this solution, we put forth a mixed-integer second-order cone program (MI-SOCP)-based solver relying on a relaxation of the gas flow equations. This relaxation is provably exact under specific network topologies. Unlike existing alternatives, the devised solver does not need proper initialization or knowing the gas flow directions beforehand, and can handle gas networks with compressors. Numerical tests on tree and meshed networks with random gas injections indicate that the relaxation is exact even when the derived conditions are not met

RNA as a Permutation

RNA secondary structure prediction and classification are two important problems in the field of RNA biology. Here, we propose a new permutation based approach to create logical non-disjoint clusters of different secondary structures of a single class or type. Many different types of techniques exist to classify RNA secondary structure data but none of them have ever used permutation based approach which is very simple and yet powerful. We have written a small JAVA program to generate permutation, apply our algorithm on those permutations and analyze the data and create different logical clusters. We believe that these clusters can be utilized to untangle the mystery of RNA secondary structure and analyze the development patterns of unknown RNA.Comment: 9 pages, 5 figures, 3 table

On the Covering Radius of Some Modular Codes

This paper gives lower and upper bounds on the covering radius of codes over $\Z_{2^s}$ with respect to homogenous distance. We also determine the covering radius of various Repetition codes, Simplex codes (Type $\alpha$ and Type $\beta$) and their dual and give bounds on the covering radii for MacDonald codes of both types over $\Z_4$.Comment: revise

On the Flow Problem in Water Distribution Networks: Uniqueness and Solvers

Increasing concerns on the security and quality of water distribution systems (WDS), along with their role as smart city components, call for computational tools with performance guarantees. To this end, this work revisits the physical laws governing water flow and provides a hierarchy of solvers having complementary value. Given water injections in a WDS, finding the corresponding water flows within pipes and pumps together with the pressures at all nodes constitutes the water flow (WF) problem. The latter entails solving a set of (non)-linear equations. It is shown that the WF problem admits a unique solution even in networks hosting pumps. For networks without pumps, the WF solution can be recovered as the minimizer of a convex energy function. The latter approach is extended to networks with pumps but not in cycles, through a stitching algorithm. For networks with non-overlapping cycles, a provably exact convex relaxation of the pressure drop equations yields a mixed-integer quadratic program (MIQP)-based WF solver. A hybrid scheme combining the MIQP with the stitching algorithm can handle water networks with overlapping cycles, but without pumps on them. Each solver is guaranteed to converge regardless initialization. Two of the solvers are numerically validated on a benchmark WDS

Natural Data Storage: A Review on sending Information from now to then via Nature

Digital data explosion drives a demand for robust and reliable data storage medium. Development of better digital storage device to accumulate Zetta bytes (1 ZB = $10^{21}$ bytes ) of data that will be generated in near future is a big challenge. Looking at limitations of present day digital storage devices, it will soon be a big challenge for data scientists to provide reliable. affordable and dense storage medium. As an alternative, researcher used natural medium of storage like DNA, bacteria and protein as information storage systems. This article discuss DNA based information storage system in detail along with an overview about bacterial and protein data storage systems.Comment: draf

Bounds on Fractional Repetition Codes using Hypergraphs

In the \textit{Distributed Storage Systems} (DSSs), an encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of \textit{Fractional Repetition} (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a \textit{Maximum Distance Separable} (MDS) code and a smart replication of packets. In this work, we have shown that an FR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the associated FR code. In general, the necessary and sufficient conditions for the existence of an FR code is obtained by using the correspondence. Some of the bounds are new and FR codes meeting these bounds are unknown. It is also shown that any FR code associated with a linear hypergraph is universally good.Comment: 8 pages, 2 figure