6,027 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
Ab initio calculation of the Hoyle state
The Hoyle state plays a crucial role in the hydrogen burning of stars heavier
than our sun and in the production of carbon and other elements necessary for
life. This excited state of the carbon-12 nucleus was postulated by Hoyle [1]
as a necessary ingredient for the fusion of three alpha particles to produce
carbon at stellar temperatures. Although the Hoyle state was seen
experimentally more than a half century ago [2,3], nuclear theorists have not
yet uncovered the nature of this state from first principles. In this letter we
report the first ab initio calculation of the low-lying states of carbon-12
using supercomputer lattice simulations and a theoretical framework known as
effective field theory. In addition to the ground state and excited spin-2
state, we find a resonance at -85(3) MeV with all of the properties of the
Hoyle state and in agreement with the experimentally observed energy. These
lattice simulations provide insight into the structure of this unique state and
new clues as to the amount of fine-tuning needed in nature for the production
of carbon in stars.Comment: 4 pp, 3 eps figs, version accepted for publication in Physical Review
Letter
3D simulations of vertical displacement events in tokamaks: A benchmark of M3D-C<sup>1</sup>, NIMROD, and JOREK editors-pick
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
The Study of Shocks in Three-States Driven-Diffusive Systems: A Matrix Product Approach
We study the shock structures in three-states one-dimensional
driven-diffusive systems with nearest neighbors interactions using a matrix
product formalism. We consider the cases in which the stationary probability
distribution function of the system can be written in terms of superposition of
product shock measures. We show that only three families of three-states
systems have this property. In each case the shock performs a random walk
provided that some constraints are fulfilled. We calculate the diffusion
coefficient and drift velocity of shock for each family.Comment: 15 pages, Accepted for publication in Journal of Statistical
Mechanics: Theory and Experiment (JSTAT
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.
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
First Order Phase Transition in a Reaction-Diffusion Model With Open Boundary: The Yang-Lee Theory Approach
A coagulation-decoagulation model is introduced on a chain of length L with
open boundary. The model consists of one species of particles which diffuse,
coagulate and decoagulate preferentially in the leftward direction. They are
also injected and extracted from the left boundary with different rates. We
will show that on a specific plane in the space of parameters, the steady state
weights can be calculated exactly using a matrix product method. The model
exhibits a first-order phase transition between a low-density and a
high-density phase. The density profile of the particles in each phase is
obtained both analytically and using the Monte Carlo Simulation. The two-point
density-density correlation function in each phase has also been calculated. By
applying the Yang-Lee theory we can predict the same phase diagram for the
model. This model is further evidence for the applicability of the Yang-Lee
theory in the non-equilibrium statistical mechanics context.Comment: 10 Pages, 3 Figures, To appear in Journal of Physics A: Mathematical
and Genera
- …