13,255 research outputs found
Asymptotic analysis and spectrum of three anyons
The spectrum of anyons confined in harmonic oscillator potential shows both
linear and nonlinear dependence on the statistical parameter. While the
existence of exact linear solutions have been shown analytically, the nonlinear
dependence has been arrived at by numerical and/or perturbative methods. We
develop a method which shows the possibility of nonlinearly interpolating
spectrum. To be specific we analyse the eigenvalue equation in various
asymptotic regions for the three anyon problem.Comment: 28 pages, LaTeX, 2 Figure
High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution
In many wireless systems, interference is the main performance-limiting
factor, and is primarily dictated by the locations of concurrent transmitters.
In many earlier works, the locations of the transmitters is often modeled as a
Poisson point process for analytical tractability. While analytically
convenient, the PPP only accurately models networks whose nodes are placed
independently and use ALOHA as the channel access protocol, which preserves the
independence. Correlations between transmitter locations in non-Poisson
networks, which model intelligent access protocols, makes the outage analysis
extremely difficult. In this paper, we take an alternative approach and focus
on an asymptotic regime where the density of interferers goes to 0. We
prove for general node distributions and fading statistics that the success
probability \p \sim 1-\gamma \eta^{\kappa} for , and
provide values of and for a number of important special
cases. We show that is lower bounded by 1 and upper bounded by a value
that depends on the path loss exponent and the fading. This new analytical
framework is then used to characterize the transmission capacity of a very
general class of networks, defined as the maximum spatial density of active
links given an outage constraint.Comment: Submitted to IEEE Trans. Info Theory special issu
A Tractable Approach to Coverage and Rate in Cellular Networks
Cellular networks are usually modeled by placing the base stations on a grid,
with mobile users either randomly scattered or placed deterministically. These
models have been used extensively but suffer from being both highly idealized
and not very tractable, so complex system-level simulations are used to
evaluate coverage/outage probability and rate. More tractable models have long
been desirable. We develop new general models for the multi-cell
signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under
very general assumptions, the resulting expressions for the downlink SINR CCDF
(equivalent to the coverage probability) involve quickly computable integrals,
and in some practical special cases can be simplified to common integrals
(e.g., the Q-function) or even to simple closed-form expressions. We also
derive the mean rate, and then the coverage gain (and mean rate loss) from
static frequency reuse. We compare our coverage predictions to the grid model
and an actual base station deployment, and observe that the proposed model is
pessimistic (a lower bound on coverage) whereas the grid model is optimistic,
and that both are about equally accurate. In addition to being more tractable,
the proposed model may better capture the increasingly opportunistic and dense
placement of base stations in future networks.Comment: Submitted to IEEE Transactions on Communication
Queueing analysis of a canonical model of real-time multiprocessors
A logical classification of multiprocessor structures from the point of view of control applications is presented. A computation of the response time distribution for a canonical model of a real time multiprocessor is presented. The multiprocessor is approximated by a blocking model. Two separate models are derived: one created from the system's point of view, and the other from the point of view of an incoming task
Brownian Motion on a Sphere: Distribution of Solid Angles
We study the diffusion of Brownian particles on the surface of a sphere and
compute the distribution of solid angles enclosed by the diffusing particles.
This function describes the distribution of geometric phases in two state
quantum systems (or polarised light) undergoing random evolution. Our results
are also relevant to recent experiments which observe the Brownian motion of
molecules on curved surfaces like micelles and biological membranes. Our
theoretical analysis agrees well with the results of computer experiments.Comment: 11 pages, two figures, Fig2 in Colour,references update
Characterization of real-time computers
A real-time system consists of a computer controller and controlled processes. Despite the synergistic relationship between these two components, they have been traditionally designed and analyzed independently of and separately from each other; namely, computer controllers by computer scientists/engineers and controlled processes by control scientists. As a remedy for this problem, in this report real-time computers are characterized by performance measures based on computer controller response time that are: (1) congruent to the real-time applications, (2) able to offer an objective comparison of rival computer systems, and (3) experimentally measurable/determinable. These measures, unlike others, provide the real-time computer controller with a natural link to controlled processes. In order to demonstrate their utility and power, these measures are first determined for example controlled processes on the basis of control performance functionals. They are then used for two important real-time multiprocessor design applications - the number-power tradeoff and fault-masking and synchronization
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