大散射角散斑场中有关相位奇异新特性的研究

利用散斑场和参考光的干涉提取散斑场复振幅和相位, 研究了不同散射角下散斑场相位的分布规律以及相位奇异处光波复振幅实部零值线和虚部零值线夹角、光强等值线离心率的统计特性. 在大散射角散斑中发现了一种新的相位奇异现象, 即相位奇异线; 研究了相位在跨越奇异线时的突变规律及涡旋状相位的分布特征, 发现在相位奇异线处存在着呈双曲线或抛物线状的光强等值线.     

Surface currents on a perfect conductor, induced by a magnetic dipole

An oscillating magnetic dipole located near a perfect conductor induces a current density on the surface of the metal. We have derived an expression for this current density, and studied its field line patterns for various orientations of the dipole moment. When the dipole moment is perpendicular to the surface, the field lines are circles which run clockwise and counterclockwise. For a linear dipole oriented parallel to the surface, the field line pattern is much more complex, and it contains singular points. When the dipole moment rotates in a plane parallel to the surface, the field lines are spirals. A field line spirals inward from infinity to some given point, after which it spirals outward back to infinity. We have also considered the Poynting vector of the electromagnetic field near the surface, and we found that its field lines can have singular points or exhibit a vortex.     

Asymptotic silence of generic cosmological singularities

In this Letter we investigate the nature of generic cosmological singularities using the framework developed by Uggla et al. We study the past asymptotic dynamics of general vacuum G2 cosmologies, which are expected to capture the singular behavior of generic cosmologies with no symmetries at all. Our results indicate that asymptotic silence holds, i.e., particle horizons along all time lines shrink to zero for generic solutions. Moreover, we provide evidence that spatial derivatives become dynamically insignificant along generic time lines, and that the evolution into the past along such time lines is governed by an asymptotic dynamical system which is associated with an invariant set-the silent boundary. We identify an attracting subset on the silent boundary that organizes the oscillatory dynamics of generic time lines in the singular regime. Finally, we discuss the dynamics associated with recurring spike formation.     

Spectral Anomalies in the Fraunhofer Diffraction Pattern

We study the spectral characteristics theoretically and experimentally in the Fraunhofer diffraction pattern formed by the diffraction of a spatially coherent, polychromatic light through a slit. It is found that the spectrum in some diffraction directions close to the singular direction is redshifted, compared to the spectrum of the incident polychromatic light, and blueshifted in other directions, and splits into two lines at the singular direction. We show that the experimental results are consistent with the theoretical expectations.     

Disclinations in the nematic phase of a magnet with spin 1

Two-dimensional topological defects, spin disclinations, exist for a magnet with spin 1 and strong biquadratic interaction, in which the spin nematic state is realized. The spin disclinations have a nonsingular macroscopic core with a saturated magnetic moment and destroyed nematic order. These singular lines have common features with disclinations in nematic liquid crystals, singular disclinations in antiferromagnets, and magnetic vortices. However, significant differences of their properties from the above-mentioned topological defects also exist. The dynamic properties of a disclination in the spin nematic are characterized by the “freezing in the condensate” and by the gyroscopic force.     

Mikromagnetisch singuläre punkte in bubbles

The magnetization pattern of a vertical Bloch line in a bubble wall containing a singular point in its center is investigated by a variational method. Introducing a hypothetical intermediate structure, the energy of such a configuration can be separated into two parts: one which describes a local embedding energy for the singular point, and one which may be derived from the structure of the domain wall only. The results indicate that above a critical film thickness Bloch lines containing a singular point represent, in agreement with a prediction by Slonczewski, the energetically most favourable configuration.     

On new complex soliton structures of the nonlinear partial differential equation describing the pulse narrowing nonlinear transmission lines

The present paper studies the pulse narrowing nonlinear transmission lines equation, describing pulse narrowing in the field of communication engineering. More precisely, the pulse narrowing nonlinear transmission line equation is solved analytically using the recently developed techniques viz the modified Kudraysov method, the sine-Gordon equation expansion method and the extended sinh-Gordon equation expansion method. As a result, a wide range of dark, bright, dark–bright, singular or combined singular and optical soliton solutions for the pulse narrowing nonlinear transmission lines equation is formally obtained. All solutions have been verified back into its corresponding equation with the aid of maple package program.     

Existence and Dynamics of Bounded Traveling Wave Solutions to Getmanou Equation

In this paper, we study the existence and dynamics of bounded traveling wave solutions to Getmanou equations by using the qualitative theory of differential equations and the bifurcation method of dynamical systems. We show that the corresponding traveling wave system is a singular planar dynamical system with two singular straight lines, and obtain the bifurcations of phase portraits of the system under different parameters conditions. Through phase portraits, we show the existence and dynamics of several types of bounded traveling wave solutions including solitary wave solutions, periodic wave solutions, compactons, kink-like and antikink-like wave solutions. Moreover, the expressions of solitary wave solutions are given. Additionally, we confirm abundant dynamical behaviors of the traveling wave s olutions to the equation, which are summarized as follows: i) We confirm that two types of orbits give rise to solitary wave solutions, that is, the homoclinic orbit passing the singular point, and the composed homoclinic orbit which is comprised of two heteroclinic orbits and tangent to the singular line at the singular point of associated system. ii) We confirm that two types of orbits correspond to periodic wave solutions, that is, the periodic orbit surrounding a center, and the homoclinic orbit of associated system, which is tangent to the singular line at the singular point of associated system.     

Annihilation of quantized vortex lines in rotating<Superscript>3</Superscript>He-A

The maximum number of vortex lines at a given angular velocity Ω is obtained during deceleration when vortices annihilate at the wall of the container. The width of the vortex-free region in the decelerated state has been measured by cw NMR for vortex lines with singular and continuous core structures. It corresponds to the limit of stability of peripheral vortices for single and double quantization respectively.     

Optical Möbius strips in three-dimensional ellipse fields: I. Lines of circular polarization

The major and minor axes of the polarization ellipses that surround singular lines of circular polarization in three-dimensional optical ellipse fields are shown to be organized into Möbius strips (twisted ribbons). These strips can have either one or three half-twists, and can be either right- or left-handed. The normals to the surrounding ellipses generate cone-like structures. Two special projections, and eight new indices are developed to characterize the rather complex structures of the Möbius strips and cones. These eight indices, together with the two well-known indices used until now to characterize singular lines of circular polarization, could, if independent, generate 16,384 different index combinations. Geometric constraints and 15 selection rules are discussed that reduce the number of combinations to 1676. Of these 1150 have been observed in 10⁶ independent realizations of a simulated random ellipse field. Statistical probabilities are presented for the most important index combinations. It is argued that it is presently feasible to perform experimental measurements of the Möbius strips and cones described here theoretically.     

Long-range Jastrow correlations

We develop a promising many-body method to evaluate the equation of state for dense neutron matter and liquid helium. The ground state of the Fermi fluid is described by a conventional Jastrow ansatz. We admit the presence of short- and long-range correlations. Under this assumption we study the generating function which has been introduced by Wu and Feenberg. We employ a graphic formulation and develop the diagrammatic expansion of the generating function and the radial distribution function. If long-range correlations are assumed, the diagrams have singular parts. We give a proof that the total contribution of such diagrams to the generating function which contain two, three, and four correlation lines is of finite value. The same property is shown for a selected class of singular diagrams containing α correlation lines (α>4). To verify the cancellation phenomenon we introduce a two-body function which serves graphically as an insertion into selected singular diagrams. For the remaining classes of diagrams we need three-, four-, ?, n-body insertions. The result is cast into the form of a theorem. The cancellation rests on the exclusion principle and does not depend on the special shape of the correlation function. Finally, a generalized hypernetted-chain summation of diagrams which represent the radial distribution function is executed. The procedure includes exchange contributions and can be employed if short-and/or long-range correlations are present.     

Generation of superthermal plasma flows in current sheets

The profiles of the He II 3203 Å and He II 4686 Å spectral lines of helium ions have been detected and analyzed. Using these data, the processes of acceleration and heating of a plasma in current sheets that are formed in magnetic configurations with X-type singular lines have been analyzed. The generation of plasma flows with energies of 400–1300 eV, which are much higher than the thermal energy of ions, has been revealed. The acceleration of the plasma induced by Ampere forces is likely spatially inhomogeneous, which should lead to shear plasma flows in a current sheet.     

Transition micromagnetic structures in asymmetric vortexlike domain walls (Static solutions and dynamic reconstructions)

The possible types of transition structures with a three-dimensional magnetization distribution over regions in the vortex asymmetric domain walls that exist in magnetically uniaxial soft magnetic films with in-plane anisotropy are studied by computer simulation in terms of a micromagnetic approach. It is shown that the possible structure types include both the type of vertical Bloch lines that was discussed earlier in other works and new types, namely, singular (Bloch) points and clusters consisting of vertical Bloch lines and Bloch points. The spatial configurations of the transition structures are calculated and their topological properties are found. The numerical simulation of the dynamics of closely spaced substructure regions reveals various scenarios of their interaction, including annihilation accompanied by energy release and the excitation of nonlinear waves.     

A Proof of Factorization Theorem of Drell–Yan Process at Operator Level

An alternative proof of factorization theorem for Drell–Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines.     

Transmission of electric dipole radiation through an interface

We consider the transmission of electric dipole radiation through an interface between two dielectrics, for the case of a vertical dipole. Energy flows along the field lines of the Poynting vector, and in the optical near field these field lines are curves (as opposed to optical rays). When the radiation passes through the interface into a thicker medium, the field lines bend to the normal (as rays do), but the transmission angle is not related to the angle of incidence. The redirection of the radiation at the interface is determined by the angle dependence of the transmission coefficient. This near-field redistribution is responsible for the far-field angular power pattern. When the transmission medium is thinner than the embedding medium of the dipole, some energy flows back and forth through the interface in an oscillating fashion. In each area where field lines dip below the interface, an optical vortex appears just above the interface. The centers of these vortices are concentric singular circles around the dipole axis.     

Fluctuation-induced broadening of Mn2+ EPR lines in the incommensurate phase of Rb2ZnCl4 crystals

The EPR spectra of Mn²⁺ ions in Rb₂ZnCl₄ crystals is investigated in the vicinity of the transition from the paraelectric phase to an incommensurate modulated phase. When these crystals are cooled below the transition temperature T _i =304 K, a splitting of the resonance lines is observed in the singular spectrum. A one-harmonic model is used to discuss the contributions that fluctuations in the amplitude and phase of the incommensurate displacement wave make to the local width of the singular spectra. It is shown that anomalies in the local width of the low-temperature singular peaks observed in the vicinity of T _i are caused by amplitude fluctuations. Fiz. Tverd. Tela (St. Petersburg) 41, 1668–1674 (September 1999)     

Visualization of Dynamic Vortex Structures in Magnetic Films with Uniaxial Anisotropy (Micromagnetic Simulation)

Three-dimensional computer simulation of dynamic processes in a moving domain boundary separating domains in a soft magnetic uniaxial film with planar anisotropy is performed by numerical solution of Landau-Lifshitz-Gilbert equations. The developed visualization methods are used to establish the connection between the motion of surface vortices and antivortices, singular (Bloch) points, and core lines of intrafilm vortex structures. A relation between the character of magnetization dynamics and the film thickness is found. The analytical models of spatial vortex structures for imitation of topological properties of the structures observed in micromagnetic simulation are constructed.     

Dispersion study of open slot-lines taking into account conductor thickness and substrate width

By means of singular integral equations' method we've studied dispersion of open slot lines having nonstandard cross-section geometry. Peculiar dependence of eigenmodes' number and slot width between conductor strips has been found.     

Synthesis and analysis of SAW dispersive ladder transducers by the modified method of coupled modes

A method for the synthesis and analysis of SAW filters and delay lines that use dispersive ladderinterdigital transducers is described. A method for designing SAW devices that relies on modified equations forcoupled waves is proposed. A singular integral equation for the surface current density in the transducer’s electrodes is derived and solved. Theoretical data are compared with experimental results.