Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

Universality classes in anisotropic non-equilibrium growth models

We study the effect of generic spatial anisotropies on the scaling behavior in the Kardar-Parisi-Zhang equation. In contrast to its "conserved" variants, anisotropic perturbations are found to be relevant in d > 2 dimensions, leading to rich phenomena that include novel universality classes and the possibility of first-order phase transitions and multicritical behavior. These results question the presumed scaling universality in the strong-coupling rough phase, and shed further light on the connection with generalized driven diffusive systems.Comment: 4 pages, revtex, 2 figures (eps files enclosed

Evolution of a beam dynamics model for the transport lines in a proton therapy facility

Despite the fact that the first-order beam dynamics models allow an approximated evaluation of the beam properties, their contribution is essential during the conceptual design of an accelerator or beamline. However, during the commissioning some of their limitations appear in the comparison against measurements. The extension of the linear model to higher order effects is, therefore, demanded. In this paper, the effects of particle-matter interaction have been included in the model of the transport lines in the proton therapy facility at the Paul Scherrer Institut (PSI) in Switzerland. To improve the performance of the facility, a more precise model was required and has been developed with the multi-particle open source beam dynamics code called OPAL (Object oriented Particle Accelerator Library). In OPAL, the Monte Carlo simulations of Coulomb scattering and energy loss are performed seamless with the particle tracking. Beside the linear optics, the influence of the passive elements (e.g. degrader, collimators, scattering foils and air gaps) on the beam emittance and energy spread can be analysed in the new model. This allows for a significantly improved precision in the prediction of beam transmission and beam properties. The accuracy of the OPAL model has been confirmed by numerous measurements.Comment: 17 pages, 19 figure

Canonical phase space approach to the noisy Burgers equation

Presenting a general phase approach to stochastic processes we analyze in particular the Fokker-Planck equation for the noisy Burgers equation and discuss the time dependent and stationary probability distributions. In one dimension we derive the long-time skew distribution approaching the symmetric stationary Gaussian distribution. In the short time regime we discuss heuristically the nonlinear soliton contributions and derive an expression for the distribution in accordance with the directed polymer-replica model and asymmetric exclusion model results.Comment: 4 pages, Revtex file, submitted to Phys. Rev. Lett. a reference has been added and a few typos correcte

Crossover from Isotropic to Directed Percolation

Percolation clusters are probably the simplest example for scale--invariant structures which either are governed by isotropic scaling--laws (``self--similarity'') or --- as in the case of directed percolation --- may display anisotropic scaling behavior (``self--affinity''). Taking advantage of the fact that both isotropic and directed bond percolation (with one preferred direction) may be mapped onto corresponding variants of (Reggeon) field theory, we discuss the crossover between self--similar and self--affine scaling. This has been a long--standing and yet unsolved problem because it is accompanied by different upper critical dimensions: $d_c^{\rm I} = 6$ for isotropic, and $d_c^{\rm D} = 5$ for directed percolation, respectively. Using a generalized subtraction scheme we show that this crossover may nevertheless be treated consistently within the framework of renormalization group theory. We identify the corresponding crossover exponent, and calculate effective exponents for different length scales and the pair correlation function to one--loop order. Thus we are able to predict at which characteristic anisotropy scale the crossover should occur. The results are subject to direct tests by both computer simulations and experiment. We emphasize the broad range of applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from [email protected] or [email protected]), EF/UCT--94/2, to be published in Phys. Rev. E (May 1994

Warped Kaluza-Klein Dark Matter

Warped compactifications of type IIB string theory contain natural dark matter candidates: Kaluza-Klein modes along approximate isometry directions of long warped throats. These isometries are broken by the full compactification, including moduli stabilization; we present a thorough survey of Kaluza-Klein mode decay rates into light supergravity modes and Standard Model particles. We find that these dark matter candidates typically have lifetimes longer than the age of the universe. Interestingly, some choices for embedding the Standard Model in the compactification lead to decay rates large enough to be observed, so this dark matter sector may provide constraints on the parameter space of the compactification.Comment: 37pp; v2. references, minor clarificatio

Statics and Dynamics of the Wormlike Bundle Model

Bundles of filamentous polymers are primary structural components of a broad range of cytoskeletal structures, and their mechanical properties play key roles in cellular functions ranging from locomotion to mechanotransduction and fertilization. We give a detailed derivation of a wormlike bundle model as a generic description for the statics and dynamics of polymer bundles consisting of semiflexible polymers interconnected by crosslinking agents. The elastic degrees of freedom include bending as well as twist deformations of the filaments and shear deformation of the crosslinks. We show that a competition between the elastic properties of the filaments and those of the crosslinks leads to renormalized effective bend and twist rigidities that become mode-number dependent. The strength and character of this dependence is found to vary with bundle architecture, such as the arrangement of filaments in the cross section and pretwist. We discuss two paradigmatic cases of bundle architecture, a uniform arrangement of filaments as found in F-actin bundles and a shell-like architecture as characteristic for microtubules. Each architecture is found to have its own universal ratio of maximal to minimal bending rigidity, independent of the specific type of crosslink induced filament coupling; our predictions are in reasonable agreement with available experimental data for microtubules. Moreover, we analyze the predictions of the wormlike bundle model for experimental observables such as the tangent-tangent correlation function and dynamic response and correlation functions. Finally, we analyze the effect of pretwist (helicity) on the mechanical properties of bundles. We predict that microtubules with different number of protofilaments should have distinct variations in their effective bending rigidity

Melting of Colloidal Molecular Crystals on Triangular Lattices

The phase behavior of a two-dimensional colloidal system subject to a commensurate triangular potential is investigated. We consider the integer number of colloids in each potential minimum as rigid composite objects with effective discrete degrees of freedom. It is shown that there is a rich variety of phases including ``herring bone'' and ``Japanese 6 in 1'' phases. The ensuing phase diagram and phase transitions are analyzed analytically within variational mean-field theory and supplemented by Monte Carlo simulations. Consequences for experiments are discussed.Comment: 10 pages, 4 figure