34,294 research outputs found
Modeling multi-cellular systems using sub-cellular elements
We introduce a model for describing the dynamics of large numbers of
interacting cells. The fundamental dynamical variables in the model are
sub-cellular elements, which interact with each other through phenomenological
intra- and inter-cellular potentials. Advantages of the model include i)
adaptive cell-shape dynamics, ii) flexible accommodation of additional
intra-cellular biology, and iii) the absence of an underlying grid. We present
here a detailed description of the model, and use successive mean-field
approximations to connect it to more coarse-grained approaches, such as
discrete cell-based algorithms and coupled partial differential equations. We
also discuss efficient algorithms for encoding the model, and give an example
of a simulation of an epithelial sheet. Given the biological flexibility of the
model, we propose that it can be used effectively for modeling a range of
multi-cellular processes, such as tumor dynamics and embryogenesis.Comment: 20 pages, 4 figure
Predator-prey cycles from resonant amplification of demographic stochasticity
In this paper we present the simplest individual level model of predator-prey
dynamics and show, via direct calculation, that it exhibits cycling behavior.
The deterministic analogue of our model, recovered when the number of
individuals is infinitely large, is the Volterra system (with density-dependent
prey reproduction) which is well-known to fail to predict cycles. This
difference in behavior can be traced to a resonant amplification of demographic
fluctuations which disappears only when the number of individuals is strictly
infinite. Our results indicate that additional biological mechanisms, such as
predator satiation, may not be necessary to explain observed predator-prey
cycles in real (finite) populations.Comment: 4 pages, 2 figure
Quantum revivals and carpets in some exactly solvable systems
We consider the revival properties of quantum systems with an eigenspectrum
E_{n} proportional to n^{2}, and compare them with the simplest member of this
class - the infinite square well. In addition to having perfect revivals at
integer multiples of the revival time t_{R}, these systems all enjoy perfect
fractional revivals at quarterly intervals of t_{R}. A closer examination of
the quantum evolution is performed for the Poeschel-Teller and Rosen-Morse
potentials, and comparison is made with the infinite square well using quantum
carpets.Comment: 5 pages, 5 figures (1 new), minor additions, to appear in J. Phys.
Strong coupling probe for the Kardar-Parisi-Zhang equation
We present an exact solution of the {\it deterministic} Kardar-Parisi-Zhang
(KPZ) equation under the influence of a local driving force . For substrate
dimension we recover the well-known result that for arbitrarily small
, the interface develops a non-zero velocity . Novel behaviour is
found in the strong-coupling regime for , in which must exceed a
critical force in order to drive the interface with constant velocity. We
find for . In particular,
the exponent for , but saturates at
for , indicating that for this simple problem, there exists a finite upper
critical dimension . For the surface distortion caused by the
applied force scales logarithmically with distance within a critical radius
, where . Connections
between these results, and the critical properties of the weak/strong-coupling
transition in the noisy KPZ equation are pursued.Comment: 18 pages, RevTex, to appear in J. Phys. I Franc
The Universal Cut Function and Type II Metrics
In analogy with classical electromagnetic theory, where one determines the
total charge and both electric and magnetic multipole moments of a source from
certain surface integrals of the asymptotic (or far) fields, it has been known
for many years - from the work of Hermann Bondi - that energy and momentum of
gravitational sources could be determined by similar integrals of the
asymptotic Weyl tensor. Recently we observed that there were certain overlooked
structures, {defined at future null infinity,} that allowed one to determine
(or define) further properties of both electromagnetic and gravitating sources.
These structures, families of {complex} `slices' or `cuts' of Penrose's null
infinity, are referred to as Universal Cut Functions, (UCF). In particular, one
can define from these structures a (complex) center of mass (and center of
charge) and its equations of motion - with rather surprising consequences. It
appears as if these asymptotic structures contain in their imaginary part, a
well defined total spin-angular momentum of the source. We apply these ideas to
the type II algebraically special metrics, both twisting and twist-free.Comment: 32 page
Proper conformal symmetries in SD Einstein spaces
Proper conformal symmetries in self-dual (SD) Einstein spaces are considered.
It is shown, that such symmetries are admitted only by the Einstein spaces of
the type [N]x[N]. Spaces of the type [N]x[-] are considered in details.
Existence of the proper conformal Killing vector implies existence of the
isometric, covariantly constant and null Killing vector. It is shown, that
there are two classes of [N]x[-]-metrics admitting proper conformal symmetry.
They can be distinguished by analysis of the associated anti-self-dual (ASD)
null strings. Both classes are analyzed in details. The problem is reduced to
single linear PDE. Some general and special solutions of this PDE are
presented
The spatial structure of networks
We study networks that connect points in geographic space, such as
transportation networks and the Internet. We find that there are strong
signatures in these networks of topography and use patterns, giving the
networks shapes that are quite distinct from one another and from
non-geographic networks. We offer an explanation of these differences in terms
of the costs and benefits of transportation and communication, and give a
simple model based on the Monte Carlo optimization of these costs and benefits
that reproduces well the qualitative features of the networks studied.Comment: 5 pages, 3 figure
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