Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

Extraction of thermal and electromagnetic properties in 45Ti

The level density and gamma-ray strength function of 45Ti have been determined by use of the Oslo method. The particle-gamma coincidences from the 46Ti(p,d gamma)45Ti pick-up reaction with 32 MeV protons are utilized to obtain gamma-ray spectra as function of excitation energy. The extracted level density and strength function are compared with models, which are found to describe these quantities satisfactorily. The data do not reveal any single-particle energy gaps of the underlying doubly magic 40Ca core, probably due to the strong quadruple deformation

Evolution in random fitness landscapes: the infinite sites model

We consider the evolution of an asexually reproducing population in an uncorrelated random fitness landscape in the limit of infinite genome size, which implies that each mutation generates a new fitness value drawn from a probability distribution $g(w)$. This is the finite population version of Kingman's house of cards model [J.F.C. Kingman, \textit{J. Appl. Probab.} \textbf{15}, 1 (1978)]. In contrast to Kingman's work, the focus here is on unbounded distributions $g(w)$ which lead to an indefinite growth of the population fitness. The model is solved analytically in the limit of infinite population size $N \to \infty$ and simulated numerically for finite $N$. When the genome-wide mutation probability $U$ is small, the long time behavior of the model reduces to a point process of fixation events, which is referred to as a \textit{diluted record process} (DRP). The DRP is similar to the standard record process except that a new record candidate (a number that exceeds all previous entries in the sequence) is accepted only with a certain probability that depends on the values of the current record and the candidate. We develop a systematic analytic approximation scheme for the DRP. At finite $U$ the fitness frequency distribution of the population decomposes into a stationary part due to mutations and a traveling wave component due to selection, which is shown to imply a reduction of the mean fitness by a factor of $1-U$ compared to the $U \to 0$ limit.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday. Submitted to JSTAT. Error in Section 3.2 was correcte

String Breaking in Lattice Quantum Chromodynamics

The separation of a heavy quark and antiquark pair leads to the formation of a tube of flux, or string, which should break in the presence of light quark-antiquark pairs. This expected zero temperature phenomenon has proven elusive in simulations of lattice QCD. We present simulation results that show that the string does break in the confining phase at nonzero temperature.Comment: 11 pages RevTeX, including 4 encapsulated Postscript figures. version2: minor corrections to reference

Single-crossover dynamics: finite versus infinite populations

Populations evolving under the joint influence of recombination and resampling (traditionally known as genetic drift) are investigated. First, we summarise and adapt a deterministic approach, as valid for infinite populations, which assumes continuous time and single crossover events. The corresponding nonlinear system of differential equations permits a closed solution, both in terms of the type frequencies and via linkage disequilibria of all orders. To include stochastic effects, we then consider the corresponding finite-population model, the Moran model with single crossovers, and examine it both analytically and by means of simulations. Particular emphasis is on the connection with the deterministic solution. If there is only recombination and every pair of recombined offspring replaces their pair of parents (i.e., there is no resampling), then the {\em expected} type frequencies in the finite population, of arbitrary size, equal the type frequencies in the infinite population. If resampling is included, the stochastic process converges, in the infinite-population limit, to the deterministic dynamics, which turns out to be a good approximation already for populations of moderate size.Comment: 21 pages, 4 figure

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Level densities and γ\gamma-ray strength functions in Sn isotopes

The nuclear level densities of $^{118,119}$Sn and the $\gamma$-ray strength functions of $^{116,118,119}$Sn below the neutron separation energy are extracted with the Oslo method using the ($^3$He, \,$\alpha \gamma$) and ($^3$He,$^3$He$^\prime\gamma$) reactions. The level density function of $^{119}$Sn displays step-like structures. The microcanonical entropies are deduced from the level densities, and the single neutron entropy of $^{119}$Sn is determined to be $(1.7 \pm 0.2)\,k_B$. Results from a combinatorial model support the interpretation that some of the low-energy steps in the level density function are caused by neutron pair-breaking. An enhancement in all the $\gamma$-ray strength functions of $^{116-119}$Sn, compared to standard models for radiative strength, is observed for the $\gamma$-ray energy region of $\simeq (4 -11)$ MeV. These small resonances all have a centroid energy of 8.0(1) MeV and an integrated strength corresponding to $1.7(9)\%$ of the classical Thomas-Reiche-Kuhn sum rule. The Sn resonances may be due to electric dipole neutron skin oscillations or to an enhancement of the giant magnetic dipole resonance

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy