Universality of Long-Range Correlations in Expansion-Randomization Systems

We study the stochastic dynamics of sequences evolving by single site mutations, segmental duplications, deletions, and random insertions. These processes are relevant for the evolution of genomic DNA. They define a universality class of non-equilibrium 1D expansion-randomization systems with generic stationary long-range correlations in a regime of growing sequence length. We obtain explicitly the two-point correlation function of the sequence composition and the distribution function of the composition bias in sequences of finite length. The characteristic exponent $\chi$ of these quantities is determined by the ratio of two effective rates, which are explicitly calculated for several specific sequence evolution dynamics of the universality class. Depending on the value of $\chi$, we find two different scaling regimes, which are distinguished by the detectability of the initial composition bias. All analytic results are accurately verified by numerical simulations. We also discuss the non-stationary build-up and decay of correlations, as well as more complex evolutionary scenarios, where the rates of the processes vary in time. Our findings provide a possible example for the emergence of universality in molecular biology.Comment: 23 pages, 15 figure

Ferromagnetism in Fe-doped Ba6Ge25 Chiral Clathrate

We have successfully synthesized a Ba6Ge25 clathrate, substituting 3 Fe per formula unit by Ge. This chiral clathrate has Ge sites forming a framework of closed cages and helical tunnel networks. Fe atoms randomly occupy these sites, and exhibit high-spin magnetic moments. A ferromagnetic transition is observed with Tc = 170 K, the highest observed Tc for a magnetic clathrate. However, the magnetic phase is significantly disordered, and exhibits a transformation to a re-entrant spin glass phase. This system has a number of features in common with other dilute magnetic semiconductors.Comment: Submitted to Applied Physics Letters. Fig. 1 resolution reduced for online archive versio

Hot Nuclear Matter Equation of State with a Three-body Force

The finite temperature Brueckner-Hartree-Fock approach is extended by introducing a microscopic three-body force. In the framework of the extended model, the equation of state of hot asymmetric nuclear matter and its isospin dependence have been investigated. The critical temperature of liquid-gas phase transition for symmetric nuclear matter has been calculated and compared with other predictions. It turns out that the three-body force gives a repulsive contribution to the equation of state which is stronger at higher density and as a consequence reduces the critical temperature of liquid-gas phase transition. The calculated energy per nucleon of hot asymmetric nuclear matter is shown to satisfy a simple quadratic dependence on asymmetric parameter $\beta$ as in the zero-temperature case. The symmetry energy and its density dependence have been obtained and discussed. Our results show that the three-body force affects strongly the high-density behavior of the symmetry energy and makes the symmetry energy more sensitive to the variation of temperature. The temperature dependence and the isospin dependence of other physical quantities, such as the proton and neutron single particle potentials and effective masses are also studied. Due to the additional repulsion produced by the three-body force contribution, the proton and neutron single particle potentials are correspondingly enhanced as similar to the zero-temperature case.Comment: 16 pages, 8 figure