2,601 research outputs found
Greedy walk on the real line
We consider a self-interacting process described in terms of a single-server
system with service stations at each point of the real line. The customer
arrivals are given by a Poisson point processes on the space-time half plane.
The server adopts a greedy routing mechanism, traveling toward the nearest
customer, and ignoring new arrivals while in transit. We study the trajectories
of the server and show that its asymptotic position diverges logarithmically in
time.Comment: Published at http://dx.doi.org/10.1214/13-AOP898 in the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The use of digital techniques to examine the intermittent region of a turbulent jet
Voltage signals, sampled at a high rate in the intermittent region of a round jet, are analyzed to provide instantaneous velocity vector information and measures of the vorticity and dissipation scales. A clustering routine to assess the feasibility of using the voltage readings to define the vortical, nonvortical state of the flow is also utilized. The results indicate that the clustering routine is partially successful; more sophisticated discrimination techniques will be required for a complete specification
A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks
In this paper, we propose a stochastic model for a file-sharing peer-to-peer
network which resembles the popular BitTorrent system: large files are split
into chunks and a peer can download or swap from another peer only one chunk at
a time. We prove that the fluid limits of a scaled Markov model of this system
are of the coagulation form, special cases of which are well-known
epidemiological (SIR) models. In addition, Lyapunov stability and settling-time
results are explored. We derive conditions under which the BitTorrent
incentives under consideration result in shorter mean file-acquisition times
for peers compared to client-server (single chunk) systems. Finally, a
diffusion approximation is given and some open questions are discussed.Comment: 25 pages, 6 figure
Non-equilibrium fixed points of coupled Ising models
Driven-dissipative systems are expected to give rise to non-equilibrium
phenomena that are absent in their equilibrium counterparts. However, phase
transitions in these systems generically exhibit an effectively classical
equilibrium behavior in spite of their non-equilibrium origin. In this paper,
we show that multicritical points in such systems lead to a rich and genuinely
non-equilibrium behavior. Specifically, we investigate a driven-dissipative
model of interacting bosons that possesses two distinct phase transitions: one
from a high- to a low-density phase---reminiscent of a liquid-gas
transition---and another to an antiferromagnetic phase. Each phase transition
is described by the Ising universality class characterized by an (emergent or
microscopic) symmetry. They, however, coalesce at a
multicritical point, giving rise to a non-equilibrium model of coupled
Ising-like order parameters described by a
symmetry. Using a dynamical renormalization-group approach, we show that a pair
of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance
critical behavior of the system. We elucidate various exotic features of these
NEFPs. In particular, we show that a generic continuous scale invariance at
criticality is reduced to a discrete scale invariance. This further results in
complex-valued critical exponents and spiraling phase boundaries, and it is
also accompanied by a complex Liouvillian gap even close to the phase
transition. As direct evidence of the non-equilibrium nature of the NEFPs, we
show that the fluctuation-dissipation relation is violated at all scales,
leading to an effective temperature that becomes "hotter" and "hotter" at
longer and longer wavelengths. Finally, we argue that this non-equilibrium
behavior can be observed in cavity arrays with cross-Kerr nonlinearities.Comment: 19+11 pages, 7+9 figure
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The Relational Antecedents of Interpersonal Helping: ‘Quantity’, ‘Quality’ or Both?
Having a large network of colleagues means having several opportunities to help those colleagues, as well as a higher chance of receiving requests for help from them. Employees with large networks are therefore expected to help more in the workplace than those with small networks. However, large networks are also associated with cognitive costs, which may reduce the focal employee's ability to both recognize the need for help and engage in helping behaviours. For these reasons, the authors assert an inverted U-shaped relation between the size of an ego's social network and engagement in helping behaviour. However, high-quality relationships imply higher mutual understanding between the actors, and hence lower cognitive costs. In turn, the position (and threshold) of the curve between network size and interpersonal helping should be influenced by the quality of the relationship between the provider and the beneficiaries of help. Analysis of employee-level, single-firm data supports these ideas, providing preliminary evidence that quality of relationship compensates for the difficulties that may arise from having large social networks
Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges
We consider the infinite directed graph with vertices the set of integers
...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or
value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k)
of integers with j<k, and assume that they are i.i.d. copies of v. The set of
edges of the graph is the set (j,k), j<k. A path in the graph from vertex j to
vertex k, j<k, is a finite sequence of edges (j(0), j(1)), (j(1), j(2)), ...,
(j(m-1), j(m)) with j(0)=j and j(m)=j; the weight of this path is taken to be
the sum v(j(0),j(1))+v(j(1),j(2))+...+v(j(m-1),j(m)) of the weights of its
edges. Let w(0,n) be the maximal weight of all paths from 0 to n. We study the
asymptotic behaviour of the sequence w(0,n), n=1, 2, ..., as n tends to
infinity, under the assumptions that P(v>0)>0, the conditional distribution of
v, given v>0, is not degenerate, and that E exp(Cv) is finite, for some C>0. We
derive local limit theorems in the normal and moderate large deviations regimes
in the case where v has an arithmetic distribution. We also derive an
integro-local theorem in the case where v has a non-lattice distribution.Comment: 16 pages, 1 figur
New Limits on Local Lorentz Invariance in Mercury and Cesium
We report new bounds on Local Lorentz Invariance (LLI) violation in Cs and
Hg. The limits are obtained through the observation of the the spin- precession
frequencies of 199Hg and 133Cs atoms in their ground states as a function of
the orientation of an applied magnetic field with respect to the fixed stars.
We measure the amplitudes of the dipole couplings to a preferred direction in
the equatorial plane to be 19(11) nHz for Hg and 9(5) microHz for Cs. The upper
bounds established here improve upon previous bounds by about a factor of four.
The improvement is primarily due to mounting the apparatus on a rotating table.
New bounds are established on several terms in the standard model extension
including the first bounds on the spin-couplings of the neutron and proton to
the z direction, <7e-30 GeV and <7e-29 GeV, respectively.Comment: 17 pages, 6 figure
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