Nonlinear Airy Light Bullets in a 3D Self‐Defocusing Medium

The (3+1)‐dimensional [(3+1)D] nonlinear Schrödinger (NLS) equation is investigated, describing the propagation of nonlinear spatiotemporal wave packets in a self‐defocusing medium, and a new type of Airy spatiotemporal solutions is presented. By using the reductive perturbation method, the (3+1)D NLS equation is reduced to the spherical Kortewegde Vries (SKdV) equation. Based on the Hirota's bilinear method, the bilinear form of the SKdV equation is constructed and Airy light bullet (LB) solutions of different orders are obtained, which depend on the sets of two free constants associated with the amplitude and initial phase. The results show that these Airy LBs can exist in the self‐defocusing medium and their intensities can be controlled by selecting the suitable free parameters along the propagation distance. As examples, three types of low‐order approximate LB solutions are presented and their intensity profiles numerically discussed. The obtained results are helpful in exploring nonlinear phenomena in a self‐defocusing medium and providing a new approach for possible experimental verification of LBs.     

Comment on ‘Stationary perfect fluid solutions with differential rotation’

We vindicate our results in Mars and Senovilla (Phys Rev D 54, 6166–6180, 1996), which have been recently put in doubt or misunderstood in García and Ulloa (Gen Rel Grav 39, 1639–1650, 2007). In particular, we maintain that there indeed exist axially symmetric differentially rotating perfect-fluid solutions satisfying all energy conditions within the family of solutions presented in Senovilla (Class Quant Grav 9, L167–L169, 1992). We remark that the existence of an axis of symmetry can never be “re-interpreted” as the existence of a Killing horizon, and vice versa. We prove that such horizons are simply impossible for the perfect fluids within the family, and that regular axes of symmetry (or curvature singularities) are the only possibilities. Other inaccuracies or misunderstandings appeared in García and Ulloa (Gen Rel Grav 39, 1639–1650, 2007) are clarified.     

Symmetry Analysis and Exact Solutions of the 2D Unsteady Incompressible Boundary-Layer Equations

To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations(ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown.     

Neutron stars in relativistic hadron-quark models

Neutron star properties are computed in relativistic models that contain both hadron and quark degrees of freedom. Neutron matter is assumed to have a low-density phase described by quantum hadrodynamics (QHD) and a high-density phase described by quantum chromodynamics (QCD). Several different QHD models and approximations are employed; all use parameters that reproduce the binding energy and density of equilibrium nuclear matter. Calculated neutron star properties depend primarily on the high-density equation of state and cannot be inferred from the symmetry energy or compressibility of equilibrium nuclear matter. If interactions are neglected in the QCD phase, the density of the hadron-quark phase transition is determined by one free parameters, which is the energy/volume needed to create a “bubble” that confines the quarks and gluons. Observed neutron star masses do not constrain this parameter, but stable neutron stars with quark cores can exist only for a limited range of parameter values. When second-order gluon-exchange corrections are included in the QCD phase, these conclusions are unchanged, and the parameter values that lead to stable hadronquark stars are restricted even further.     

On noncircularly symmetric self-trapped light beams

Self-trapping solutions of the nonlinear scalar wave equation with arbitrary transverse symmetry (e.g., elliptical) do not exist.     

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of (3+1)-dimensional (3D) generalized nonlinear Schrdinger (NLS) equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.     

Description of Chiral Doublet Bands in Odd-Odd Cs Isotopes

Properties of the chair doublet bands of the odd-odd Cs isotopes built on the π h_11/2 \otimes ν h_11/2 configuration are investigated systematicallywithin the supersymmetry scheme including many-body interactions andpossessing the SO(5)(or SU(5)) symmetry on the rotational symmetry.Quantitatively good results of the energy spectra, the energy staggering parameter as a function of the spin are obtained. The calculation shows that the stronger competition between the pairing and anti-pairing effects and the SU(3) symmetry broking more seriously exist in the stable chiral structure.     

Symmetry Reduction and Exact Solutions of the (3+1)-Dimensional Breaking Soliton Equation

By means of the generalized direct method, a relationship is constructed between the new solutions and the old ones of the (3+1)-dimensional breaking soliton equation. Based on the relationship, a new solution is obtained by using a given solution of the equation. The symmetry is also obtained for the (3+1)-dimensional breaking soliton equation. By using the equivalent vector of the symmetry, we construct a seven-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, the (3+1)-dimensional breaking soliton equation is reduced and some solutions to the reduced equations are obtained. Furthermore, some new explicit solutions are found for the (3+1)-dimensional breaking soliton equation.     

Metastable ringlike semitopological solitons

We show the existence of new stable ringlike localized scalar field configurations whose stability is due to a combination of topological and nontopological charges. In that sense these defects may be called semitopological. These rings are Noether charged and also carry Noether current (they are superconducting). They are local minima of the energy in scalar field theories with an unbroken U(1) global symmetry. We obtain numerical solutions of the field configuration corresponding to large rings and derive virial theorems demonstrating their stability. We also derive the minimum energy field configurations in 3D and simulate the evolution of a finite size Q ring on a three dimensional lattice.     

Singularities of regular black holes and the monodromy method for asymptotic quasinormal modes

We use the monodromy method to investigate the asymptotic quasinormal modes of regular black holes based on the explicit Stokes portraits. We find that, for regular black holes with spherical symmetry and a single shape function, the analytical forms of the asymptotic frequency spectrum are not universal and do not depend on the multipole number but on the presence of complex singularities and the trajectory of asymptotic solutions along the Stokes lines.     

A Two-Parameter Deformed Two-Dimensional Interacting Boson Model With Uqp(U3)Uqp(U2)Uqp(SO2) Symmetry

A two-parameter deformed two-dimensional interacting boson model with U_qp(U₃) U_qp(U₂) U_qp(SO₂)symmetry is constructed.It is found that the energy spectrum and transition matrix elements depend very sensitively on the second parameter of deformation.     

Global monopole in general relativity

We consider the gravitational properties of a global monopole on the basis of the simplest Higgs scalar triplet model in general relativity. We begin with establishing some common features of hedgehog-type solutions with a regular center, independent of the choice of the symmetry-breaking potential. There are six types of qualitative behaviors of the solutions; we show, in particular, that the metric can contain at most one simple horizon. For the standard Mexican hat potential, the previously known properties of the solutions are confirmed and some new results are obtained. Thus, we show analytically that solutions with the monotonically growing Higgs field and finite energy in the static region exist only in the interval 1 < λ < 3, where λ is the squared energy of spontaneous symmetry breaking in Planck units. The cosmological properties of these globally regular solutions apparently favor the idea that the standard Big Bang might be replaced with a nonsingular static core and a horizon appearing as a result of some symmetry-breaking phase transition at the Planck energy scale. In addition to the monotonic solutions, we present and analyze a sequence of families of new solutions with the oscillating Higgs field. These families are parametrized by n, the number of knots of the Higgs field, and exist for λ < γ_n=6/[(2n + 1)(n + 2)]; all such solutions possess a horizon and a singularity beyond it.     

Ih和D5h对称的三金属氮化物富勒烯Sc3N@C80的几何结构、电子结构和磁学特性

采用密度泛函理论（density functional theory, DFT）方法对具有Ih和D5h对称的三金属氮化物富勒烯Sc3 N＠C80的几何结构、电子结构及其磁学特性进行了计算研究。几何结构优化显示掺杂Sc3 N之后,C80的结构只是发生了细微的变化,仍然保持了Ih 和D5h对称性。能级图和局部态密度图表明Sc原子对能级的变化贡献最大,掺杂之后能隙增加,简并度下降,增强了两种异构体的稳定性。磁学特性分析指出掺杂之后,Sc3 N的磁性完全淬灭,两种异构体均没有磁矩,都不能作为磁性材料。     

Ih和D5h对称的三金属氮化物富勒烯Sc3N@C80的几何结构、电子结构和磁学特性

采用密度泛函理论（density functional theory, DFT）方法对具有Ih和D5h对称的三金属氮化物富勒烯Sc3N@C80的几何结构、电子结构及其磁学特性进行了计算研究.几何结构优化显示掺杂Sc3N之后,C80的结构只是发生了细微的变化,仍然保持了Ih和D5h对称性.能级图和局部态密度图表明Sc原子对能级的变化贡献最大,掺杂之后能隙增加,简并度下降,增强了两种异构体的稳定性.磁学特性分析指出掺杂之后,Sc3N的磁性完全淬灭,两种异构体均没有磁矩,都不能作为磁性材料.     

Entropy and equilibrium state of free market models

Large adiabatic polarons in anisotropic crystals in the presence of constant magnetic field have been studied within the Holstein molecular crystal model in the continuum approximation. It was shown that magnetic field directed along the symmetry axis induces transverse confinement which may stabilize large polarons. They represent localized (soliton-like) nonlinear structure uniformly propagating along the symmetry axis and rotating around it in the same time. Such objects exist in 3D lattice provided that coupling constant and magnetic field do not exceed certain critical values. In contrast with pure 1D systems existence of large polarons is possible in a quite wider region of the values of coupling constant which may attain considerably higher values than in the pure 1D media. Furthermore, polaron effective mass, depending on the intensity of the applied magnetic field, may be considerably lighter than that of the the pure 1D polarons for the same values of coupling constant. This is the most significant difference with respect to pure 1D systems in the absence of magnetic field and may have substantial impact on polaron transport properties.     

Two-dimensional electron gas in a periodic magnetic field

We study the energy spectrum and electronic properties of a two-dimensional (2D) spinless electron gas in a periodic magnetic field which has the symmetry of a triangular lattice. We show that the energy bands depend strongly on the value of the magnetic field. For large field the low-energy electrons are localized on closed rings where the magnetic field vanishes. This results in the appearance of persistent currents around these rings. We also calculate the intrinsic Hall conductivity, which is quantized when the Fermi level is in a gap.     

Isovector Q balls

Finite-energy solutions rotating at a constant angular velocity in isovector space are considered within theories that possess global SO(3) symmetry (isovector theories). It is shown that, for a nonlinear O(3) model (n field), such solutions exist only in the one-dimensional case. For the isovector theory proposed by S. Weinberg in order to describe low-energy properties of the π mesons, such solutions exist at some values of parameters that appear in this theory. Some properties of these solutions are studied.     

三价铕离子配合物的激光光谱研究

利用高灵敏度的时间辨激光光谱技术研究了在配位场作用下Ｅｕ＾３＾＋的直接激发与发特性。Ｅｕ＾３＾＋的直接激发光谱（特别是７Ｆ０－５Ｄ０的超灵敏跃迁）及其发射光谱随不同的配合物的变化，同时观测到与配位对称性及配位强度有联系的７Ｆ１－５Ｄ０磁偶极跃 迁的分裂。在对７Ｆ０－５Ｄ０跃迁共振与非共振的１０ｐｓ激光脉冲的激励下，都可以立即观察到５Ｄ０－７ＦＪ（Ｊ＝２，３，４）的发射，说明Ｅｕ＾３＾＋的５Ｄ０能态     

Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.