A novel multi-objective evolutionary algorithm based on space partitioning

To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks

Averaged null energy condition in Loop Quantum Cosmology

Wormhole and time machine are very interesting objects in general relativity. However, they need exotic matters which are impossible in classical level to support them. But if we introduce the quantum effects of gravity into the stress-energy tensor, these peculiar objects can be constructed self-consistently. Fortunately, loop quantum cosmology (LQC) has the potential to serve as a bridge connecting the classical theory and quantum gravity. Therefore it provides a simple way for the study of quantum effect in the semiclassical case. As is well known, loop quantum cosmology is very successful to deal with the behavior of early universe. In the early stage, if taken the quantum effect into consideration, inflation is natural because of the violation of every kind of local energy conditions. Similar to the inflationary universe, the violation of the averaged null energy condition is the necessary condition for the traversable wormholes. In this paper, we investigate the averaged null energy condition in LQC in the framework of effective Hamiltonian, and find out that LQC do violate the averaged null energy condition in the massless scalar field coupled model.Comment: 5 page

Mixing of quasiparticle excitations and gamma-vibrations in transitional nuclei

Evidence of strong coupling of quasiparticle excitations with gamma-vibration is shown to occur in transitional nuclei. High-spin band structures in [166,168,170,172]Er are studied by employing the recently developed multi-quasiparticle triaxial projected shell model approach. It is demonstrated that a low-lying K=3 band observed in these nuclei, the nature of which has remained unresolved, originates from the angular-momentum projection of triaxially deformed two-quasiparticle (qp) configurations. Further, it is predicted that the structure of this band depends critically on the shell filling: in [166]Er the lowest K=3 2-qp band is formed from proton configuration, in [168]Er the K=3 neutron and proton 2-qp bands are almost degenerate, and for [170]Er and [172]Er the neutron K=3 2-qp band becomes favored and can cross the gamma-vibrational band at high rotational frequencies. We consider that these are few examples in even-even nuclei, where the three basic modes of rotational, vibrational, and quasi-particle excitations co-exist close to the yrast line.Comment: 7 pages, 6 figure

A Codazzi-like equation and the singular set for C1C^{1} smooth surfaces in the Heisenberg group

In this paper, we study the structure of the singular set for a $C^{1}$ smooth surface in the $3$-dimensional Heisenberg group $\boldsymbol{H}_{1}$. We discover a Codazzi-like equation for the $p$-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify that Codazzi-like equation by proving a fundamental theorem for local surfaces in $\boldsymbol{H}_{1}$.Comment: 64 pages, 17 figure

Infrared anomalous Hall effect in SrRuO3_3: Evidence for crossover to intrinsic behavior

The origin of the Hall effect in many itinerant ferromagnets is still not resolved, with an anomalous contribution from the sample magnetization that can exhibit extrinsic or intrinsic behavior. We report the first mid-infared (MIR) measurements of the complex Hall ($\theta_H$), Faraday ($\theta_F$), and Kerr ($\theta_K$) angles, as well as the Hall conductivity ($\sigma_{xy}$) in a SrRuO$_3$ film in the 115-1400 meV energy range. The magnetic field, temperature, and frequency dependence of the Hall effect is explored. The MIR magneto-optical response shows very strong frequency dependence, including sign changes. Below 200 meV, the MIR $\theta_H (T)$ changes sign between 120 and 150 K, as is observed in dc Hall measurements. Above 200 meV, the temperature dependence of $\theta_H$ is similar to that of the dc magnetization and the measurements are in good agreement with predictions from a band calculation for the intrinsic anomalous Hall effect (AHE). The temperature and frequency dependence of the measured Hall effect suggests that whereas the behavior above 200 meV is consistent with an intrinsic AHE, the extrinsic AHE plays an important role in the lower energy response.Comment: The resolution of figures is improve

Spin waves in the block checkerboard antiferromagnetic phase

Motivated by the discovery of new family 122 iron-based superconductors, we present the theoretical results on the ground state phase diagram, spin wave and dynamic structure factor of the extended $J_{1}-J_{2}$ Heisenberg model. In the reasonable physical parameter region of $K_{2}Fe_{4}Se_{5}$, we fi{}nd the block checkerboard antiferromagnetic order phase is stable. There are two acoustic branches and six optical branches spin wave in the block checkerboard antiferromagnetic phase, which has analytic expression in the high symmetry points. To compare the further neutron scattering experiments, we discuss the saddlepoint structure in the magnetic excitation spectrum and calculate the predicted inelastic neutron scattering pattern based on linear spin wave theory