We report the first global study of dynamic correlation energies (DCEs) associated with rotational motion and quadrupole shape vibrational motion in a covariant energy density functional (CEDF) for 575 even-even nuclei with proton numbers ranging from $Z=8$ to $Z=108$ by solving a five-dimensional collective Hamiltonian, the collective parameters of which are determined from triaxial relativistic mean-field plus BCS calculation using the PC-PK1 force. After taking into account these beyond mean-field DCEs, the root-mean-square (rms) deviation with respect to nuclear masses is reduced significantly down to 1.14 MeV, which is smaller than those of other successful CEDFs: NL3* (2.96 MeV), DD-ME2 (2.39 MeV), DD-ME$delta$ (2.29 MeV) and DD-PC1 (2.01 MeV). Moreover, the rms deviation for two-nucleon separation energies is reduced by $sim34%$ in comparison with cranking prescription.
Studying the virtual Euler characteristic of the moduli space of curves, Harer and Zagier compute the generating function $C_g(z)$ of unicellular maps of genus $g$. They furthermore identify coefficients, $kappa^{star}_{g}(n)$, which fully determine the series $C_g(z)$. The main result of this paper is a combinatorial interpretation of $kappa^{star}_{g}(n)$. We show that these enumerate a class of unicellular maps, which correspond $1$-to-$2^{2g}$ to a specific type of trees, referred to as O-trees. O-trees are a variant of the C-decorated trees introduced by Chapuy, F{e}ray and Fusy. We exhaustively enumerate the number $s_{g}(n)$ of shapes of genus $g$ with $n$ edges, which is a specific class of unicellular maps with vertex degree at least three. Furthermore we give combinatorial proofs for expressing the generating functions $C_g(z)$ and $S_g(z)$ for unicellular maps and shapes in terms of $kappa^{star}_{g}(n)$, respectively. We then prove a two term recursion for $kappa^{star}_{g}(n)$ and that for any fixed $g$, the sequence ${kappa_{g,t}}_{t=0}^g$ is log-concave, where $kappa^{star}_{g}(n)= kappa_{g,t}$, for $n=2g+t-1$.
The multiferroic RMn2O5 family, where R is rare-earth ion or Y, exhibits rich physics of multiferroicity which has not yet well understood, noting that multiferroicity is receiving attentions for promising application potentials. DyMn2O5 is a representative member of this family. The ferroelectric polarization in DyMn2O5 is claimed to have two anti-parallel components: one (PDM) from the symmetric exchange striction between the Dy3+-Mn4+ interactions and the other (PMM) from the symmetric exchange striction between the Mn3+-Mn4+ interactions. We investigate the evolutions of the two components upon a partial substitution of Mn3+ by nonmagnetic Al3+ in order to tailor the Mn-Mn interactions and then to modulate component PMM in DyMn2-x/2Alx/2O5. It is revealed that the ferroelectric polarization can be successfully reversed by the Al-substitution via substantially suppressing the Mn3+-Mn4+ interactions and thus the PMM. The Dy3+-Mn4+ interactions and the polarization component PDM can sustain against the substitution until a level as high as x=0.2. In addition, the independent Dy spin ordering is shifted remarkably down to an extremely low temperature due to the Al3+ substitution. The present work not only confirms the existence of the two anti-parallel polarization components but also unveils the possibility of tailoring them independently.
In this paper we consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference schemes are developed to approximate the solution of the mathematical model. The convergence of the approximations to a unique weak solution with bounded total variation is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin-McCamy-type size-structured model in the weak$^*$ topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation occurs in the distributed model as well.
High-quality superconducting KxFeySe2 single crystals were synthesized using an easy one-step method. Detailed annealing studies were performed to make clear the phase formation process in KxFeySe2. Compatible observations were found in temperature-dependent X-ray diffraction patterns, back-scattered electron images and corresponding electromagnetic properties, which proved that good superconductivity performance was close related to the microstructure of superconducting component. Analysis based on the scaling behavior of flux pinning force indicated that the dominant pinning mechanism was delta(Tc) pinning and independent of connectivity. The annealing dynamics studies were also performed, which manifested that the humps in temperature-dependent resistance (RT) curves were induced by competition between the metallic/superconducting and the semiconducting/insulating phases.
The electric polarization and its magnetic origins in multiferroic RMn2O5, where R is rare-earth ion, are still issues under debate. In this work, the temperature-dependent electric polarization of DyMn2O5, the most attractive member of this RMn2O5 family, is investigated using the pyroelectric current method upon varying endpoint temperature of the electric cooling, plus the positive-up-negative-down (PUND) technique. It is revealed that DyMn2O5 at low temperature does exhibit the unusual ferrielectricity rather than ferroelectricity, characterized by two interactive and anti-parallel ferroelectric sublattices which show different temperature-dependences. The two ferroelectric sublattices are believed to be generated from the symmetric exchange-striction mechanisms associated with the Mn-Mn spin interactions and Dy-Mn spin interactions, respectively. The path-dependent electric polarization reflects the first-order magnetic transitions in the low temperature regime. The magnetoelectric effect is mainly attributed to the Dy spin order which is sensitive to magnetic field. The present experiments may be helpful for clarifying the puzzling issues on the multiferroicity in DyMn2O5 and probably other RMn2O5 multiferroics.
We present a method for accurate determination of atomic transition matrix elements at the 10^{-3} level. Measurements of the ac Stark (light) shift around magic-zero wavelengths, where the light shift vanishes, provide precise constraints on the matrix elements. We make the first measurement of the 5s-6p matrix elements in rubidium by measuring the light shift around the 421 nm and 423 nm zeros with a sequence of standing wave pulses. In conjunction with existing theoretical and experimental data, we find 0.3236(9) e a_0 and 0.5230(8) e a_0 for the 5s-6p_{1/2} and 5s-6p_{3/2} elements, respectively, an order of magnitude more accurate than the best theoretical values. This technique can provide needed, accurate matrix elements for many atoms, including those used in atomic clocks, tests of fundamental symmetries, and quantum information.
In this paper we study $gamma$-structures filtered by topological genus. $gamma$-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time folding of RNA pseudoknot structures. A $gamma$-structure is composed by specific building blocks, that have topological genus less than or equal to $gamma$, where composition means concatenation and nesting of such blocks. Our main results are the derivation of a new bivariate generating function for $gamma$-structures via symbolic methods, the singularity analysis of the solutions and a central limit theorem for the distribution of topological genus in $gamma$-structures of given length. In our derivation specific bivariate polynomials play a central role. Their coefficients count particular motifs of fixed topological genus and they are of relevance in the context of genus recursion and novel folding algorithms.
The shape evolution and shape coexistence phenomena in neutron-rich nuclei at $Napprox60$, including Kr, Sr, Zr, and Mo isotopes, are studied in the covariant density functional theory (DFT) with the new parameter set PC-PK1. Pairing correlations are treated using the BCS approximation with a separable pairing force. Sharp rising in the charge radii of Sr and Zr isotopes at N=60 is observed and shown to be related to the rapid changing in nuclear shapes. The shape evolution is moderate in neighboring Kr and Mo isotopes. Similar as the results of previous Hartree-Fock-Bogogliubov (HFB) calculations with the Gogny force, triaxiality is observed in Mo isotopes and shown to be essential to reproduce quantitatively the corresponding charge radii. In addition, the coexistence of prolate and oblate shapes is found in both $^{98}$Sr and $^{100}$Zr. The observed oblate and prolate minima are related to the low single-particle energy level density around the Fermi surfaces of neutron and proton respectively. Furthermore, the 5-dimensional (5D) collective Hamiltonian determined by the calculations of the PC-PK1 energy functional is solved for $^{98}$Sr and $^{100}$Zr. The resultant excitation energy of $0^+_2$ state and E0 transition strength $rho^2(E0;0^+_2rightarrow0^+_1)$ are in rather good agreement with the data. It is found that the lower barrier height separating the two competing minima along the $gamma$ deformation in $^{100}$Zr gives rise to the larger $rho^2(E0;0^+_2rightarrow0^+_1)$ than that in $^{98}$Sr.
The ratio of shear viscosity ($eta$) to entropy density ($s$) for an equilibrated system is investigated in intermediate energy heavy ion collisions below 100$A$ MeV within the framework of the Boltzmann-Uehling-Uhlenbeck (BUU) model . After the collision system almost reaches a local equilibration, the temperature, pressure and energy density are obtained from the phase space information and {$eta/s$} is calculated using the Green-Kubo formulas. The results show that {$eta$}/$s$ decreases with incident energy and tend towards a smaller value around 0.5, which is not so drastically different from the BNL Relativistic Heavy Ion Collider results in the present model.
