3,288 research outputs found
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specular pattern of patches.Comment: This article has been withdrawn because of critical errors in the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) (defined in the text) where 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 . 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 and Type
and their duals, MacDonald codes, and Reed-Muller codes over
.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
with respect to homogenous distance. We also determine the covering
radius of various Repetition codes, Simplex codes (Type and Type
) and their dual and give bounds on the covering radii for MacDonald
codes of both types over .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 = 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
- …