Interaction of two edge dislocations in free-space propagation

This paper studies in detail the interaction of two edge dislocations nested in a Gaussian beam propagating in free space. It shows that in free-space propagation the edge dislocations are unstable and vanish, and two noncanonical vortices with opposite topological charge take place when off-axis distances c₁ and c₂ of two edge dislocations are non-zero, and the condition k²w₀⁸+32c₁c₂(w₀²-2c₁c₂)z²>0 is fulfilled (k-wave number, w₀-waist width). A noncanonical vortex appears when one off-axis distance is zero. However, one edge dislocation is stable when two edge dislocations are perpendicular and one off-axis distance is zero. Two perpendicular edge dislocations both with zero off-axis distance are also stable. The analytical results are illustrated by numerical examples.     

Performance optimization analysis of a thermoelectric refrigerator with two resonances

Based on electron transport theory,the performance of k x and k r filtered thermoelectric refrigerators with two resonances are studied in this paper.The performance characteristic curves between the cooling rate and the coefficient of performance are plotted by numerical calculation.It is shown that the maximum cooling rate of the thermoelectric refrigerator with two resonances increases but the maximum coefficient of performance decreases compared with those with one resonance.No matter which resonance mechanism is used(k x or k r filtered),the cooling rate and the performance coefficient of the k r filtered refrigerator are much better than those of the k x filtered one.     

Real Kasner and related complex “windmill” vacuum spacetime metrics

The Kasner family of vacuum solutions of Einstein's field equations admits a simply-transitiveH ₄, a four-parameter local homothetic group of motions which has an AbelianG ₃ subgroup. It is shown that a complex transformation of coordinates and constants exists which maps this family from the normal Kasner form into a form of vacuum metrics whose Weyl tensors are each Petrov type I and which were published in 1932 by Lewis. These metrics also admit a similarH ₄; however for one particular metric (for one parameter value) theH ₄ becomes aG ₄ and the resultant metric is one which was rediscovered by Petrov in 1962. These Lewis metrics are thus shown to be Kasner metrics over complex fields. Here they are calledwindmill metrics because of the rotating relationship between the coordinates and the Killing vector fields admitted. The principal null directions of thereal Kasner and the windmill metrics are discussed; the two families then provide illustrations of two degenerate classes of spacetime metrics whose Weyl tensors are of Petrov type I, as discussed elsewhere by Arianrhod and McIntosh. An extension of the windmill-type generation of metrics to some other families of metrics is also discussed.     

Geometrical Tools for Quantum Euclidean Spaces

We apply one of the formalisms of noncommutative geometry to ℝ ^N _q , the quantum space covariant under the quantum group SO _q (N). Over ℝ ^N _q there are two SO _q (N)-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of ℝ³ _q . As in the case N=3, one has to slightly enlarge the algebra ℝ ^N _q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N=3 there is a conformal ambiguity in the natural metrics on the differential calculi over ℝ ^N _q . While in our previous article the frame was found “by hand”, here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of ℝ ^N _q with U _q so(N) into ℝ ^N _q , an interesting result in itself. Received: 4 March 2000 / Accepted: 11 October 2000     

采用Lennard-Jones原子间势研究(C60)N分子团簇的结构演化行为

采用描述原子间相互作用的Lennard-Jones势来描述C₆₀分子间的相互作用,考虑了每个C₆₀分子的一定位置取向,并采用最速下降法计算了IH,fcc,hcp,DH及SC五种典型结构满壳层(C₆₀)_N团簇(N<2000)的能量.结果显示:当尺寸较小(N<20)时,IH结构最稳定;当尺寸处于中等(50<N<300)时,HCP结构最稳定;当尺寸较大(300<N 关键词： 60团簇')" href="#">C₆₀团簇 取向 最速下降法 结构演化     

Doppler-free two-color spectroscopy of the 62 S 1/2–82 S 1/2 cesium transition using semiconductor diode lasers

We report an experimental investigation of the 6S–8S transition of cesium atoms by using Doppler-free two-color spectroscopy. We consider the case in which one of the laser frequencies is nearly resonant with the 6S _1/2–6P _3/2 transition while a second one is swept around the 6P _3/2–8S _1/2 transition. The lineshapes of two-photon absorption spectra are analyzed taking into account the effects of saturation and collisions. Both counterpropagating and copropagating laser-beam schemes are studied. Although for the linewidths are broader copropagating beams, such a scheme has proved advantageous to fully resolve the hyperfine structure of the final state 8S _1/2 and, hence, to measure the dipole magnetic constantA of this state.     

Flux-driven cellular precipitation in open system to form porous Cu3Sn

Recently, a new morphology of porous Cu₃Sn with lamellar structure is observed. Several possible explanations of the formation are proposed and compared. The most reasonable one seems to be the one based on a theory of flux-driven cellular precipitation in open system. Outflux of Sn from Cu₆Sn₅ generates simultaneously supersaturation with vacancies and with copper leading to the eutectoid-like transformation β → α + γ (where γ is void). The transformation is complete due to a complete outflux of Sn from the Cu₆Sn₅ phase. Simple formulae for prediction of the lamellar structure parameters and the propagation velocity are obtained and compared reasonably with experimental data. The suggested model can be interpreted as one more case of the flux-driven phase transformations in open systems.     

Eigenvalues of graphs with twofold symmetry

There are many cases in which the spectrum of a graph contains the complete spectrum of a smaller graph. The larger (composite) graph and the smaller (component) graph are said to be subspectral. It is shown here that whenever a composite graph G has a twofold symmetry operation which defines two equivalent sets of vertices r and s, it is possible to construct two subspectral components G ₊ and G _-, whose eigenvalues, taken jointly, comprise the full spectrum of G. The following rules are given for constructing the components. (1) Draw the r set of vertices and all the edges connecting the members of the set. Then examine in G the vertices through which r and s are connected (the so-called bridging vertices). (2) If a bridging vertex r ₁ is connected to its symmetry-equivalent partner s ₁, then r ₁ is weighted +1 in G ₊ and -1 in G _-. (3) If r ₁ is connected to a vertex s ₂ which is symmetry-equivalent to a second bridging vertex r ₂ in r, then the weight of the edge between r ₁ and r ₂ in G (+1 if they are connected, zero if they are not) is increased by one unit in G ₊ and decreased by one unit in G _-. The derivation of these rules is shown, and the relationship between the spectrum of G and the spectra of G ₊ and G _- is explained in terms of the symmetry properties of the adjacency matrix of G.     

Diagnostics for the structure of AGNs’ broad line regions with reverberation mapping data: confirmation of the two-component broad line region model

We re-examine the ten Reverberation Mapping (RM) sources with public data based on the two-component model of the Broad Line Region (BLR). In fitting their broad Hβ Mlines, six of them only need one Gaussian component, one of them has a double-peak profile, one has an irregular profile, and only two of them need two components, i.e., a Very Broad Gaussian Component (VBGC) and an Inter-Mediate Gaussian Component (IMGC). The Gaussian components are assumed to come from two distinct regions in the two-component model; they are the Very Broad Line Region (VBLR) and the Inter-Mediate Line region (IMLR). The two sources with a two-component profile are Mrk 509 and NGC 4051. The time lags of the two components of both sources satisfy t _IMLR/t _VBLR=V ² _VBLR/V ² _IMLR, where t _IMLR and t _VBLR are the lags of the two components while V _IMLR and V _VBLR represent the mean gas velocities of the two regions, supporting the two-component model of the BLR of Active Galactic Nuclei (AGNs). The fact that most of these ten sources only have the VBGC confirms the assumption that RM mainly measures the radius of the VBLR; consequently, the radius obtained from the R-L relationship mainly represents the radius of VBLR. Moreover, NGC 4051, with a lag of about 5 days in the one component model, is an outlier on the R-L relationship as shown in Kaspi et al. (2005); however this problem disappears in our two-component model with lags of about 2 and 6 days for the VBGC and IMGC, respectively.

     

Fermion Mass and Mixing in a Simple Extension of the Standard Model Based on T7 Flavor Symmetry

We build a simple Standard Model extension based on T₇ flavor symmetry which accommodates lepton mass, mixing with non-zero θ₁₃, and CP violation phase. The lepton mixing matrix is obtained from three triplets and one singlet under T₇ symmetry, and the charged-lepton mass is derived through the spontaneous symmetry breaking by just one T₇ triplet (φ), while neutrinos get small masses from one SU(2) _L doublet and two SU(2)_L singlets in which one is in 1 and the two others are in 3 and 3* under T₇, respectively. There exist viable parameters of the model that predict the effective Majorana neutrino mass with values m_β ≃ 10⁻² eV and 4.95 × 10⁻² eV as well as a lightest neutrino mass m_light ≃ 4.97 × 10⁻³ eV and 1.61 × 10⁻³ eV for the normal and inverted neutrino mass hierarchies, respectively. The model also gives a remarkable prediction of Dirac CP violation δ_CP ≃ 303.3° in the normal hierarchy and δ_CP ≃ 56.69° in the inverted hierarchy which is still missing in the neutrino mixing matrix. The quark mixing angles of the model are closed to the experimental data, whereas the obtained values for the quark masses are consistent with with the experimental data at the tree level.

     

LETTER: On a Class of Solutions for Null Dust

In stationary metrics depending on two spacelike coordinates the field equations permit one to choose a radial coordinate r such that D ² := –g ₃₃ g ₄₄ + g ₃₄ ² = r ², leading to solutions with axial symmetry. However, solutions exist also for the case in which D ² = 1. These solutions are examined in this paper, and, if physically realistic, are found to refer to null dust or vacuum. This is at variance with the interpretation of Hoenselaers and Vishveshwara [4] who examined one of the solutions and concluded that it described non-null dust or vacuum.     

Studies on the cell structure of quasicrystals

The geometric and crystallographic ideas for cell models and tilings in non-periodic ordered structures are outlined. The basic concepts, among them the cell geometry and duality in a lattice are explained for the example of a one dimensional section through the root lattice A ₂. The corresponding constructions for 3D icosahedral sections through the 6D face-centered hypercubic lattice, equivalent to the root lattice D ₆, are described. Two different tilings, one with equivalent, one with three inequivalent vertex positions, are derived and discussed.     

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

Hydromagnetic surface waves in a moving compressible plasma column

Summary The dispersive characteristic of hydromagnetic surface waves along a plasma-plasma interface when one of the fluids has a relative motion has been studied as a function of the compressibility factors ₁/V ₁, wheres ₁ andV ₁ are the acoustic and Alfvén wave speed in one of the media. Both slow and fast magnetosonic surface waves for each symmetric and asymmetric modes can exist. The nature and existence of these modes depend on the values ofs ₁/V ₁ and ϑ, the angle of wave propagation. The phase velocity of the slow wave increases whereas for the fast wave it decreases with increase in the angle ϑ. The authors of this paper have agreed to not receive the proofs for correction.     

Absence of the partially ordered phase in theq-state models

We investigate theq-state models called (N ,N ) model using an infinitesimal Migdal-Kadanoff renormalization-group method. We distinguish two cases namely the isotropic model and the anisotropic model. The first one presents a critical value ofq,q _c such that forq _c we obtain an Ashkin-Teller phase diagrams while forq>q _c the partially ordered phase disappears then the model exhibits only phase transition between ferromagnetic phase and disordered one. The phase diagrams in the second case are qualitatively similar to one obtained forZ(6) model for all values ofq.     

57Fe Mössbauer study of Eu1−x Sr x FeO3−y

The samples of Eu_1–x Sr _x FeO_3–y (x=0.0–1.0) were prepared by the solid state reaction method. Their X-ray diffraction patterns and⁵⁷Fe Mössbauer spectra at room temperature were measured. It is found that Sr ions incorporate in the lattice of EuFeO₃, the change of crystal structure is related to the dopant.⁵⁷Fe Mössbauer spectra consist of one magnetic, one doublet and one single paramagnetic components. The Fe ions in the cubic phase are in intermediate valence state between Fe(III) and Fe(IV) and may participate in electron hopping.     

supersymmetric 3-particles Calogero model

We constructed the most general N=4 superconformal 3-particles systems with translation invariance. In the basis with decoupled center of mass the supercharges and Hamiltonian possess one arbitrary function which defines all potential terms. We have shown that with the proper choice of this function one may describe the standard, A₂ Calogero model as well as G₂ and BC₂ Calogero models, which, by construction, possess N=4 superconformal symmetry. The main property of all these systems is that even with the coupling constant equal to zero they still contain nontrivial interactions in the fermionic sector. In other words, there are infinitely many non-equivalent N=4 supersymmetric extensions of the free action depending on one arbitrary function. We also considered quantization and explicitly showed how the supercharges and Hamiltonian are modified. In the quantum case the constructed systems exhibit only invariance with respect to N=4 Poincaré supersymmetry.     

Nonstandard q-deformation of the Euclidean Lie algebra and its representations

A nonstandard q-deformed Euclidean algebra U _q(iso _n ), based on the definition of the twisted q-deformed algebra U _qso_n) (different from the Drinfeld–Jimbo algebra U _q(so _n )), is defined. Infinite dimensional representations R of U _q(iso _n ) are described. Explicit formulas for operators of these representations in the orthonormal basis are given. The spectra of the operators R(T _n) corresponding to a q-analogue of the infinitesimal operator of shifts along the n-th axis are described. Contrary to the case of the classical Euclidean Lie algebra iso _n , these spectra are discrete and spectral points have one point of accumulation.     

XOR gate response in a mesoscopic ring with embedded quantum dots

We address XOR gate response in a mesoscopic ring threaded by a magnetic flux . The ring, composed of identical quantum dots, is symmetrically attached to two semi-infinite one-dimensional metallic electrodes and two gate voltages, viz, V_a and V_b, are applied, respectively, in each arm of the ring which are treated as the two inputs of the XOR gate. The calculations are based on the tight-binding model and the Green’s function method, which numerically compute the conductance–energy and current–voltage characteristics as functions of the ring-electrodes coupling strengths, magnetic flux and gate voltages. Quite interestingly it is observed that, for =₀/2 (₀=ch/e, the elementary flux-quantum) a high output current (1) (in the logical sense) appears if one, and only one, of the inputs to the gate is high (1), while if both inputs are low (0) or both are high (1), a low output current (0) appears. It clearly demonstrates the XOR behavior and this aspect may be utilized in designing the electronic logic gate.     

NaZn13型结构LaFe13－xAlxCy化合物的磁熵变与磁相变的研究

研究了NaZn₁₃型结构LaFe_13-xAl_xC_0.1(x=1.6，1.8)间隙化合物的磁制冷能力和磁相变.利用麦克斯韦关系式计算得到，高Al含量LaFe_13-xAl_x碳化物的最大磁熵变值|ΔS|_m低于低Al含量碳化物的最大磁熵变值.随Al含量的增加，化合物的磁熵变峰展宽，但由于磁熵变大幅降低，衡量磁制冷能力的q值随之降低.基于朗道相变原理，考虑到自旋涨落的影响，磁自由能可以展开到磁化强度的6次方项，材料的相变类型由磁化强度的4次方项系数a₃(T)的符号来进行判断.随着Al含量的增加，研究的碳化物相变由弱的一级相变转为二级相变. 关键词： 13-xAl_x碳化物')" href="#">LaFe_13-xAl_x碳化物 磁制冷能力 磁相变