31,487 research outputs found
Elasticity of Filamentous Kagome Lattice
The diluted kagome lattice, in which bonds are randomly removed with
probability , consists of straight lines that intersect at points with a
maximum coordination number of four. If lines are treated as semi-flexible
polymers and crossing points are treated as crosslinks, this lattice provides a
simple model for two-dimensional filamentous networks. Lattice-based effective
medium theories and numerical simulations for filaments modeled as elastic
rods, with stretching modulus and bending modulus , are used to
study the elasticity of this lattice as functions of and . At
, elastic response is purely affine, and the macroscopic elastic modulus
is independent of . When , the lattice undergoes a
first-order rigidity percolation transition at . When ,
decreases continuously as decreases below one, reaching zero at a
continuous rigidity percolation transition at that is the
same for all non-zero values of . The effective medium theories predict
scaling forms for , which exhibit crossover from bending dominated response
at small to stretching-dominated response at large
near both and , that match simulations with no adjustable
parameters near . The affine response as is identified
with the approach to a state with sample-crossing straight filaments treated as
elastic rods.Comment: 15 pages, 10 figure
The size of the largest fluctuations in a market model with Markovian switching
This paper considers the size of the large fluctuations of a stochastic differential equation with Markovian switching. We concentrate on processes which obey the Law of the Iterated Logarithm, or obey upper and lower iterated logarithm growth bounds on their almost sure partial maxima. The results are applied to financial market models which are subject to random regime shifts. We prove that the security exhibits the same long-run growth properties and deviations from the trend rate of growth as conventional geometric Brownian motion, and also that the returns, which are non-Gaussian, still exhibit the same growth rate in their almost sure large deviations as stationary continuous-time Gaussian processes
On Optimal Service Differentiation in Congested Network Markets
As Internet applications have become more diverse in recent years, users
having heavy demand for online video services are more willing to pay higher
prices for better services than light users that mainly use e-mails and instant
messages. This encourages the Internet Service Providers (ISPs) to explore
service differentiations so as to optimize their profits and allocation of
network resources. Much prior work has focused on the viability of network
service differentiation by comparing with the case of a single-class service.
However, the optimal service differentiation for an ISP subject to resource
constraints has remained unsolved. In this work, we establish an optimal
control framework to derive the analytical solution to an ISP's optimal service
differentiation, i.e. the optimal service qualities and associated prices. By
analyzing the structures of the solution, we reveal how an ISP should adjust
the service qualities and prices in order to meet varying capacity constraints
and users' characteristics. We also obtain the conditions under which ISPs have
strong incentives to implement service differentiation and whether regulators
should encourage such practices
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