On final states of 2D decaying turbulence

Numerical and analytical studies of "final states" of two-dimensional (2D) decaying turbulence are reported. The first part of this work is trying to give a definition for final states of 2D decaying turbulence. Although the functional relation of $\omega-\psi$ is frequently used as the characterization of those "final states," it is just a sufficient but not necessary condition so it is not proper to be used as the definition. It is found the way through the value of the effective area S covered by the scatter $\omega-\psi$ plot, which is initially suggested by Read, is more general, and more suitable for the definition. Based on this concept, we gave out a definition that can cover all existing results in late states of decaying 2D flows, including some weird double-valued $\omega-\psi$ scatter plots that can not be explained before. The rest part of the paper is trying to further investigate 2D decaying turbulence with the assistance of our new definition. Some new numerical results, which lead to "bar" final states and further verify the predictive ability of statistical mechanics [2], are reported. It is realized that some simulations with narrow-band energy spectral initial conditions, which can be called "turbulence" doubtfully, lead to some final states that can not be very well explained by the statistical theory (in the meanwhile, they are still in the scope of our new definition of the "final state"). For those simulations with initial conditions of broadband energy spectra that lead to the famous dipole, we give out a mathematical re-interpreting for the so-called sin-hyperbolic ("sinh") $\omega-\psi$ scatter plot in final states. We suggest the term "sinh" here should be replaced by "sinh-like." The corresponding physical meaning of this re-interpreting will also be discussed.Comment: 19 pages, 10 figures, submitted to "physics of fluids

The principle of least action and the geometric basis of D-branes

We analyze thoroughly the boundary conditions allowed in classical non-linear sigma models and derive from first principle the corresponding geometric objects, i.e. D-branes. In addition to giving classical D-branes an intrinsic and geometric foundation, D-branes in nontrivial H flux and D-branes embedded within D-branes are precisely defined. A well known topological condition on D-branes is replaced

Large bipartite Bell violations with dichotomic measurements

In this paper we introduce a simple and natural bipartite Bell scenario, by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations can be obtained in this context. Since such violations cannot occur when both parties use dichotomic measurements, our setting can be considered as the simplest one where this phenomenon can be observed. Our example is essentially optimal in terms of the outputs and the Hilbert space dimension

Rational material design of mixed-valent high Tc_c superconductors

We design, from first principles calculations, a novel family of thallium halide-based compounds as candidates for new high temperature superconductors, whose superconductivity is mediated by the recently proposed mechanism of non-local correlation-enhanced strong electron-phonon coupling. Two prototype compounds namely CsTlF$_3$ and CsTlCl$_3$ are studied with various hole doping levels and volumes. The critical superconducting temperature T$_c$ are predicted to be about 30 K and 20 K with $\sim$0.35/f.u. hole doping and require only modest pressures ($\sim$10 and $\sim$2 GPa), respectively. Our procedure of designing this class of superconductors is quite general and can be used to search for other "other high temperature superconductors".Comment: 6- ages, EPL 101, 27002 (2013