Numerical Complete Solution for Random Genetic Drift by Energetic Variational Approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.Comment: 22 pages, 11 figures, 2 table

Systematic analysis of the incoming quark energy loss in cold nuclear matter

The investigation into the fast parton energy loss in cold nuclear matter is crucial for a good understanding of the parton propagation in hot-dense medium. By means of four typical sets of nuclear parton distributions and three parametrizations of quark energy loss, the parameter values in quark energy loss expressions are determined from a leading order statistical analysis of the existing experimental data on nuclear Drell-Yan differential cross section ratio as a function of the quark momentum fraction. It is found that with independence on the nuclear modification of parton distributions, the available experimental data from lower incident beam energy rule out the incident-parton momentum fraction quark energy loss. Whether the quark energy loss is linear or quadratic with the path length is not discriminated. The global fit of all selected data gives the quark energy loss per unit path length {\alpha} = 1.21\pm0.09 GeV/fm by using nuclear parton distribution functions determined only by means of the world data on nuclear structure function. Our result does not support the theoretical prediction: the energy loss of an outgoing quark is three times larger than that of an incoming quark approaching the nuclear medium. It is desirable that the present work can provide useful reference for the Fermilab E906/SeaQuest experiment

Quark energy loss and shadowing in nuclear Drell-Yan process

The energy loss effect in nuclear matter is another nuclear effect apart from the nuclear effects on the parton distribution as in deep inelastic scattering process. The quark energy loss can be measured best by the nuclear dependence of the high energy nuclear Drell-Yan process. By means of three kinds of quark energy loss parameterizations given in literature and the nuclear parton distribution extracted only with lepton-nucleus deep inelastic scattering experimental data, measured Drell-Yan production cross sections are analyzed for 800GeV proton incident on a variety of nuclear targets from FNAL E866. It is shown that our results with considering the energy loss effect are much different from these of the FNAL E866 who analysis the experimental data with the nuclear parton distribution functions obtained by using the deep inelastic lA collisions and pA nuclear Drell-Yan data . Considering the existence of energy loss effect in Drell-Yan lepton pairs production,we suggest that the extraction of nuclear parton distribution functions should not include Drell-Yan experimental data.Comment: 12 page

Nuclear geometry effect and transport coefficient in semi-inclusive lepton-production of hadrons off nuclei

Hadron production in semi-inclusive deep-inelastic scattering of leptons from nuclei is an ideal tool to determine and constrain the transport coefficient in cold nuclear matter. The leading-order computations for hadron multiplicity ratios are performed by means of the SW quenching weights and the analytic parameterizations of quenching weights based on BDMPS formalism. The theoretical results are compared to the HERMES positively charged pions production data with the quarks hadronization occurring outside the nucleus. With considering the nuclear geometry effect on hadron production, our predictions are in good agreement with the experimental measurements. The extracted transport parameter from the global fit is shown to be $\hat{q} = 0.74\pm0.03 GeV^2/fm$ for the SW quenching weight without the finite energy corrections. As for the analytic parameterization of BDMPS quenching weight without the quark energy E dependence, the computed transport coefficient is $\hat{q} = 0.20\pm0.02 GeV^2/fm$. It is found that the nuclear geometry effect has a significant impact on the transport coefficient in cold nuclear matter. It is necessary to consider the detailed nuclear geometry in studying the semi-inclusive hadron production in deep inelastic scattering on nuclear targets.Comment: 14 pages, 3 figures. arXiv admin note: text overlap with arXiv:1310.569

Density-functional calculations of the electronic structure and lattice dynamics of superconducting LaO0.5_{0.5}F0.5_{0.5}BiS2_{2}: Evidence for an electron-phonon interaction near the charge-density-wave instability

We discuss the electronic structure, lattice dynamics and electron-phonon interaction of newly discovered superconductor LaO$_{0.5}$F$_{0.5}$BiS$_{2}$ using density functional based calculations. A strong Fermi surface nesting at $\mathbf{k}$=($\pi$,$\pi$,0) suggests a proximity to charge density wave instability and leads to imaginary harmonic phonons at this $\mathbf{k}$ point associated with in-plane displacements of S atoms. Total energy analysis resolves only a shallow double-well potential well preventing the appearance of static long-range order. Both harmonic and anharmonic contributions to electron-phonon coupling are evaluated and give a total coupling constant $\lambda \simeq 0.85$ prompting this material to be a conventional superconductor contrary to structurally similar FeAs materials.Comment: Supplementary Materials is adde