2,583 research outputs found
Spectrum of the three dimensional fuzzy well
We develop the formalism of quantum mechanics on three dimensional fuzzy
space and solve the Schr\"odinger equation for a free particle, finite and
infinite fuzzy wells. We show that all results reduce to the appropriate
commutative limits. A high energy cut-off is found for the free particle
spectrum, which also results in the modification of the high energy dispersion
relation. An ultra-violet/infra-red duality is manifest in the free particle
spectrum. The finite well also has an upper bound on the possible energy
eigenvalues. The phase shifts due to scattering around the finite fuzzy
potential well have been calculated
Domination Integrity of Some Path Related Graphs
The stability of a communication network is one of the important parameters for network designers and users. A communication network can be considered to be highly vulnerable if the destruction of a few elements cause large damage and only few members are able to communicate. In a communication network several vulnerability measures like binding number, toughness, scattering number, integrity, tenacity, edge tenacity and rupture degree are used to determine the resistance of network to the disruption after the failure of certain nodes (vertices) or communication links (edges). Domination theory also provides a model to measure the vulnerability of a graph network. The domination integrity of a simple connected graph is one such measure. Here we determine the domination integrity of square graph of path as well as the graphs obtained by composition (lexicographic product) of two paths
Relativistic Green functions in a plane wave gravitational background
We consider a massive relativistic particle in the background of a
gravitational plane wave. The corresponding Green functions for both spinless
and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti
\cite{Barducci3}, are reobtained here by alternative methods, as for example,
the Fock-Schwinger proper-time method and the algebraic method. In analogy to
the electromagnetic case, we show that for a gravitational plane wave
background a semiclassical approach is also sufficient to provide the exact
result, though the lagrangian involved is far from being a quadratic one.Comment: Last paper by Professor Arvind Narayan Vaidya, 18 pages, no figure
Asymptotically Flat Radiating Solutions in Third Order Lovelock Gravity
In this paper, we present an exact spherically symmetric solution of third
order Lovelock gravity in dimensions which describes the gravitational
collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter
or flat depending on the choice of the cosmological constant. Using the
asymptotically flat solution for with a power-law form of the mass
as a function of the null coordinate, we present a model for a gravitational
collapse in which a null dust fluid radially injects into an initially flat and
empty region. It is found that a naked singularity is inevitably formed whose
strength is different for the and cases. In the case,
the limiting focusing condition for the strength of curvature singularity is
satisfied. But for , the strength of curvature singularity depends on
the rate of increase of mass of the spacetime. These considerations show that
the third order Lovelock term weakens the strength of the curvature
singularity.Comment: 15 pages, no figure, references added, two appendix adde
Distributed Algorithms for Consensus and Coordination in the Presence of Packet-Dropping Communication Links - Part I: Statistical Moments Analysis Approach
This two-part paper discusses robustification methodologies for
linear-iterative distributed algorithms for consensus and coordination problems
in multicomponent systems, in which unreliable communication links may drop
packets. We consider a setup where communication links between components can
be asymmetric (i.e., component j might be able to send information to component
i, but not necessarily vice-versa), so that the information exchange between
components in the system is in general described by a directed graph that is
assumed to be strongly connected. In the absence of communication link
failures, each component i maintains two auxiliary variables and updates each
of their values to be a linear combination of their corresponding previous
values and the corresponding previous values of neighboring components (i.e.,
components that send information to node i). By appropriately initializing
these two (decoupled) iterations, the system components can asymptotically
calculate variables of interest in a distributed fashion; in particular, the
average of the initial conditions can be calculated as a function that involves
the ratio of these two auxiliary variables. The focus of this paper to
robustify this double-iteration algorithm against communication link failures.
We achieve this by modifying the double-iteration algorithm (by introducing
some additional auxiliary variables) and prove that the modified
double-iteration converges almost surely to average consensus. In the first
part of the paper, we study the first and second moments of the two iterations,
and use them to establish convergence, and illustrate the performance of the
algorithm with several numerical examples. In the second part, in order to
establish the convergence of the algorithm, we use coefficients of ergodicity
commonly used in analyzing inhomogeneous Markov chains.Comment: University of Illinois at Urbana-Champaign. Coordinated Sciences
Laboratory technical repor
Distributed Algorithms for Consensus and Coordination in the Presence of Packet-Dropping Communication Links - Part II: Coefficients of Ergodicity Analysis Approach
In this two-part paper, we consider multicomponent systems in which each
component can iteratively exchange information with other components in its
neighborhood in order to compute, in a distributed fashion, the average of the
components' initial values or some other quantity of interest (i.e., some
function of these initial values). In particular, we study an iterative
algorithm for computing the average of the initial values of the nodes. In this
algorithm, each component maintains two sets of variables that are updated via
two identical linear iterations. The average of the initial values of the nodes
can be asymptotically computed by each node as the ratio of two of the
variables it maintains. In the first part of this paper, we show how the update
rules for the two sets of variables can be enhanced so that the algorithm
becomes tolerant to communication links that may drop packets, independently
among them and independently between different transmission times. In this
second part, by rewriting the collective dynamics of both iterations, we show
that the resulting system is mathematically equivalent to a finite inhomogenous
Markov chain whose transition matrix takes one of finitely many values at each
step. Then, by using e a coefficients of ergodicity approach, a method commonly
used for convergence analysis of Markov chains, we prove convergence of the
robustified consensus scheme. The analysis suggests that similar convergence
should hold under more general conditions as well.Comment: University of Illinois at Urbana-Champaign. Coordinated Sciences
Laboratory technical repor
Formation damage due to colloidally induced fines migration
The in-situ release of fine particles in a porous medium resulting from changes in the colloidal character of fines induced by changes in the electrolytic condition of the permeating fluid and its effects on processes related to enhanced oil recovery (EOR) are examined. Experimental results show that high pH and low salinity cause fines to be released which, in turn, causes a drastic decline in the permeability of the medium. These results and other key experiments establish the interplay between salinity changes, cation exchange, and pH during a water shock, and elucidate the vital role of the ion-exchange process in formation damage. A physico-chemical model based on the fundamental principles of ion exchange and colloidal chemistry shows qualitative agreement with experimental observations. The results of this study will find use in various areas such as: bacteria migration in soils, failure of earthen embankments, and contaminant transport during ground water flow.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28839/1/0000674.pd
Scattering and Bound State Green's Functions on a Plane via so(2,1) Lie Algebra
We calculate the Green's functions for the particle-vortex system, for two
anyons on a plane with and without a harmonic regulator and in a uniform
magnetic field. These Green's functions which describe scattering or bound
states (depending on the specific potential in each case) are obtained exactly
using an algebraic method related to the SO(2,1) Lie group. From these Green's
functions we obtain the corresponding wave functions and for the bound states
we also find the energy spectra.Comment: 21 Latex pages. Typos corrected. Results unchanged. Version to appear
in JM
Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes
We study scalar field and electromagnetic perturbations on Locally
Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently
developed covariant and gauge-invariant perturbation formalism. From the
Klein-Gordon equation and Maxwell's equations, respectively, we derive
covariant and gauge-invariant wave equations for the perturbation variables and
thereby find the generalised Regge-Wheeler equations for these LRS class II
spacetime perturbations. As illustrative examples, the results are discussed in
detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes
of dust Universes.Comment: 22 pages; v3 has minor changes to match published versio
Local correlations in a strongly interacting 1D Bose gas
We develop an analytical method for calculating local correlations in
strongly interacting 1D Bose gases, based on the exactly solvable Lieb-Liniger
model. The results are obtained at zero and finite temperatures. They describe
the interaction-induced reduction of local many-body correlation functions and
can be used for achieving and identifying the strong-coupling Tonks-Girardeau
regime in experiments with cold Bose gases in the 1D regime.Comment: 8 pages, REVTeX4, published in the New Journal of Physic
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