5,534 research outputs found
Complex Behavior in Simple Models of Biological Coevolution
We explore the complex dynamical behavior of simple predator-prey models of
biological coevolution that account for interspecific and intraspecific
competition for resources, as well as adaptive foraging behavior. In long
kinetic Monte Carlo simulations of these models we find quite robust 1/f-like
noise in species diversity and population sizes, as well as power-law
distributions for the lifetimes of individual species and the durations of
quiet periods of relative evolutionary stasis. In one model, based on the
Holling Type II functional response, adaptive foraging produces a metastable
low-diversity phase and a stable high-diversity phase.Comment: 8 pages, 5 figure
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C, NIMROD and JOREK
In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C
and NIMROD developed the capability of modelling realistic 3D vertical
displacement events (VDEs) including resistive walls. In this paper, a
comprehensive 3D VDE benchmark is presented between these state of the art
codes. The simulated case is based on an experimental NSTX plasma but with a
simplified rectangular wall. In spite of pronounced differences between physics
models and numerical methods, the comparison shows very good agreement in the
relevant quantities used to characterize disruptions such as the 3D wall forces
and energy decay. This benchmark does not only bring confidence regarding the
use of the mentioned codes for disruption studies, but also shows differences
with respect to the used models (e.g. reduced versus full MHD models). The
simulations show important 3D features for a NSTX plasma such as the
self-consistent evolution of the halo current and the origin of the wall
forces. In contrast to other reduced MHD models based on an ordering in the
aspect ratio, the ansatz based JOREK reduced MHD model allows capturing the 3D
dynamics even in the spherical tokamak limit considered here
Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input
We investigate with the help of analytical and numerical methods the reaction
A+A->A on a one-dimensional lattice opened at one end and with an input of
particles at the other end. We show that if the diffusion rates to the left and
to the right are equal, for large x, the particle concentration c(x) behaves
like As/x (x measures the distance to the input end). If the diffusion rate in
the direction pointing away from the source is larger than the one
corresponding to the opposite direction the particle concentration behaves like
Aa/sqrt(x). The constants As and Aa are independent of the input and the two
coagulation rates. The universality of Aa comes as a surprise since in the
asymmetric case the system has a massive spectrum.Comment: 27 pages, LaTeX, including three postscript figures, to appear in J.
Stat. Phy
Lianas Have A Seasonal Growth Advantage Over Co‐Occurring Trees
The seasonal growth advantage hypothesis posits that plant species that grow well during seasonal drought will increase in abundance in forests with increasing seasonality of rainfall both in absolute numbers and also relative to co‐occurring plant species that grow poorly during seasonal drought. That is, seasonal drought will give some plant species a growth advantage that they lack in aseasonal forests, thus allowing them attain higher abundance. For tropical forest plants, the seasonal growth advantage hypothesis may explain the distribution of drought‐adapted species across large‐scale gradients of rainfall and seasonality. We tested the seasonal growth advantage hypothesis with lianas and trees in a seasonal tropical forest in central Panama. We measured the dry‐season and wet‐season diameter growth of 1,117 canopy trees and 648 canopy lianas from 2011 to 2016. We also evaluated how lianas and trees responded to the 2015–2016 El Niño, which was the third strongest el Niño drought on record in Panama. We found that liana growth rate was considerably higher during the dry‐season months than the wet‐season months in each of the five years. Lianas achieved one‐half of their annual growth during the 4‐month dry season. By contrast, trees grew far more during the wet season; they realized only one‐quarter of their annual growth during the dry season. During the strong 2015–2016 El Niño dry season, trees essentially stopped growing, whereas lianas grew unimpeded and as well as during any of the previous four dry seasons. Our findings support the hypothesis that seasonal growth gives lianas a decided growth advantage over trees in seasonal forests compared to aseasonal forests, and may explain why lianas peak in both absolute and relative abundance in highly seasonal tropical forests. Furthermore, the ability of lianas to grow during a strong el Niño drought suggests that lianas will benefit from the predicted increasing drought severity, whereas trees will suffer, and thus lianas are predicted to increase in relative abundance in seasonal tropical forests
Stochastic Models on a Ring and Quadratic Algebras. The Three Species Diffusion Problem
The stationary state of a stochastic process on a ring can be expressed using
traces of monomials of an associative algebra defined by quadratic relations.
If one considers only exclusion processes one can restrict the type of algebras
and obtain recurrence relations for the traces. This is possible only if the
rates satisfy certain compatibility conditions. These conditions are derived
and the recurrence relations solved giving representations of the algebras.Comment: 12 pages, LaTeX, Sec. 3 extended, submitted to J.Phys.
Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C1, NIMROD and JOREK
A benchmark exercise for the modeling of vertical displacement events(VDEs) is presented and applied to the 3D nonlinear magneto-hydrodynamic codesM3D-C1, JOREK and NIMROD. The simulations are based on a vertically unstableNSTX equilibrium enclosed by an axisymmetric resistive wall with rectangular crosssection. A linear dependence of the linear VDE growth rates on the resistivity ofthe wall is recovered for sufficiently large wall conductivity and small temperatures inthe open field line region. The benchmark results show good agreement between theVDE growth rates obtained from linear NIMROD and M3D-C1simulations as wellas from the linear phase of axisymmetric nonlinear JOREK, NIMROD and M3D-C1simulations. Axisymmetric nonlinear simulations of a full VDE performed with thethree codes are compared and excellent agreement is found regarding plasma locationand plasma currents as well as eddy and halo currents in the wall.</p
The duality relation between Glauber dynamics and the diffusion-annihilation model as a similarity transformation
In this paper we address the relationship between zero temperature Glauber
dynamics and the diffusion-annihilation problem in the free fermion case. We
show that the well-known duality transformation between the two problems can be
formulated as a similarity transformation if one uses appropriate (toroidal)
boundary conditions. This allow us to establish and clarify the precise nature
of the relationship between the two models. In this way we obtain a one-to-one
correspondence between observables and initial states in the two problems. A
random initial state in Glauber dynamics is related to a short range correlated
state in the annihilation problem. In particular the long-time behaviour of the
density in this state is seen to depend on the initial conditions. Hence, we
show that the presence of correlations in the initial state determine the
dependence of the long time behaviour of the density on the initial conditions,
even if such correlations are short-ranged. We also apply a field-theoretical
method to the calculation of multi-time correlation functions in this initial
state.Comment: 15 pages, Latex file, no figures. To be published in J. Phys. A.
Minor changes were made to the previous version to conform with the referee's
Repor
Solution of classical stochastic one dimensional many-body systems
We propose a simple method that allows, in one dimension, to solve exactly a
wide class of classical stochastic many-body systems far from equilibrium. For
the sake of illustration and without loss of generality, we focus on a model
that describes the asymmetric diffusion of hard core particles in the presence
of an external source and instantaneous annihilation. Starting from a Master
equation formulation of the problem we show that the density and multi-point
correlation functions obey a closed set of integro-differential equations which
in turn can be solved numerically and/or analyticallyComment: 2 figure
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