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

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-C1^1, NIMROD and JOREK

In recent years, the nonlinear 3D magnetohydrodynamic codes JOREK, M3D-C$^1$ 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