379 research outputs found
Homogenization for advection-diffusion in a perforated domain
The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor–Green velocity field
Site investigation for the effects of vegetation on ground stability
The procedure for geotechnical site investigation is well established but little attention is currently given to investigating the potential of vegetation to assist with ground stability. This paper describes how routine investigation procedures may be adapted to consider the effects of the vegetation. It is recommended that the major part of the vegetation investigation is carried out, at relatively low cost, during the preliminary (desk) study phase of the investigation when there is maximum flexibility to take account of findings in the proposed design and construction. The techniques available for investigation of the effects of vegetation are reviewed and references provided for further consideration. As for general geotechnical investigation work, it is important that a balance of effort is maintained in the vegetation investigation between (a) site characterisation (defining and identifying the existing and proposed vegetation to suit the site and ground conditions), (b) testing (in-situ and laboratory testing of the vegetation and root systems to provide design parameters) and (c) modelling (to analyse the vegetation effects)
Fluctuations in a general preferential attachment model via Stein's method
We consider a general preferential attachment model, where the probability
that a newly arriving vertex connects to an older vertex is proportional to a
sublinear function of the indegree of the older vertex at that time. It is well
known that the distribution of a uniformly chosen vertex converges to a
limiting distribution. Depending on the parameters, this model can show power
law, but also stretched exponential behaviour. Using Stein's method we provide
rates of convergence for the total variation distance. Our proof uses the fact
that the limiting distribution is the stationary distribution of a Markov chain
together with the generator method of Barbour
Modelling the potential for permafrost development on a radioactive waste geological disposal facility in Great Britain
The safety case for a geological disposal facility (GDF) for radioactive waste based in Great Britain must consider the potential impact on the repository environment of permafrost during the 1 million years following GDF closure. The depth of penetration of permafrost, defined as ground which remains at or below 0 °C for at least 2 consecutive years, has been modelled for a future climate that uses the climate of the last glacial–interglacial cycle as an analogue. Two future climates are considered; an average estimate case considered to be the best estimate of ground surface temperatures during the last glacial–interglacial cycle, and a cold estimate case considered to be an extreme cold, but plausible future climate. Maximum modelled permafrost thicknesses across Great Britain range from 20 to 180 m for the average estimate climate and 180–305 m for the cold estimate climate. The presence of ice cover is an important determinant on permafrost development. Thick permafrost evolves during long periods of cold-based ice cover and during periods of ice retreat that results in ground exposure to very cold air temperatures. Conversely, warm-based ice has an insulating effect, shielding the ground from cold air temperatures that retards permafrost development. For a GDF at a depth greater than that predicted to be directly affected by permafrost, phenomena associated with permafrost, e.g., enhanced groundwater salinity at depth, will need to be taken into account when considering the impact on the engineered and natural barriers associated with a GDF
Sub-Gaussian short time asymptotics for measure metric Dirichlet spaces
This paper presents estimates for the distribution of the exit time from
balls and short time asymptotics for measure metric Dirichlet spaces. The
estimates cover the classical Gaussian case, the sub-diffusive case which can
be observed on particular fractals and further less regular cases as well. The
proof is based on a new chaining argument and it is free of volume growth
assumptions
Ni-Cr textured substrates with reduced ferromagnetism for coated conductor applications
A series of biaxially textured Ni(1-x)Cr(x) materials, with compositions x =
0, 7, 9, 11, and 13 at % Cr, have been studied for use as substrate materials
in coated conductor applications with high temperature superconductors. The
magnetic properties were investigated, including the hysteretic loss in a Ni-7
at % Cr sample that was controllably deformed; for comparison, the loss was
also measured in a similarly deformed pure Ni substrate. Complementary X-ray
diffraction studies show that thermo-mechanical processing produces nearly
complete {100} cube texturing, as desired for applications.Comment: PDF only; 19 pp., incl 10 figure
Exponential martingales and changes of measure for counting processes
We give sufficient criteria for the Dol\'eans-Dade exponential of a
stochastic integral with respect to a counting process local martingale to be a
true martingale. The criteria are adapted particularly to the case of counting
processes and are sufficiently weak to be useful and verifiable, as we
illustrate by several examples. In particular, the criteria allow for the
construction of for example nonexplosive Hawkes processes as well as counting
processes with stochastic intensities depending on diffusion processes
A particle system with explosions: law of large numbers for the density of particles and the blow-up time
Consider a system of independent random walks in the discrete torus with
creation-annihilation of particles and possible explosion of the total number
of particles in finite time. Rescaling space and rates for
diffusion/creation/annihilation of particles, we obtain a stong law of large
numbers for the density of particles in the supremum norm. The limiting object
is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If
f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion
time
The scaling attractor and ultimate dynamics for Smoluchowski's coagulation equations
We describe a basic framework for studying dynamic scaling that has roots in
dynamical systems and probability theory. Within this framework, we study
Smoluchowski's coagulation equation for the three simplest rate kernels
, and . In another work, we classified all self-similar
solutions and all universality classes (domains of attraction) for scaling
limits under weak convergence (Comm. Pure Appl. Math 57 (2004)1197-1232). Here
we add to this a complete description of the set of all limit points of
solutions modulo scaling (the scaling attractor) and the dynamics on this limit
set (the ultimate dynamics). The main tool is Bertoin's L\'{e}vy-Khintchine
representation formula for eternal solutions of Smoluchowski's equation (Adv.
Appl. Prob. 12 (2002) 547--64). This representation linearizes the dynamics on
the scaling attractor, revealing these dynamics to be conjugate to a continuous
dilation, and chaotic in a classical sense. Furthermore, our study of scaling
limits explains how Smoluchowski dynamics ``compactifies'' in a natural way
that accounts for clusters of zero and infinite size (dust and gel)
A semantical approach to equilibria and rationality
Game theoretic equilibria are mathematical expressions of rationality.
Rational agents are used to model not only humans and their software
representatives, but also organisms, populations, species and genes,
interacting with each other and with the environment. Rational behaviors are
achieved not only through conscious reasoning, but also through spontaneous
stabilization at equilibrium points.
Formal theories of rationality are usually guided by informal intuitions,
which are acquired by observing some concrete economic, biological, or network
processes. Treating such processes as instances of computation, we reconstruct
and refine some basic notions of equilibrium and rationality from the some
basic structures of computation.
It is, of course, well known that equilibria arise as fixed points; the point
is that semantics of computation of fixed points seems to be providing novel
methods, algebraic and coalgebraic, for reasoning about them.Comment: 18 pages; Proceedings of CALCO 200
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