共查询到19条相似文献,搜索用时 46 毫秒
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We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadratic and cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopes of two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification are derived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-mode equations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due to the optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears when the frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands. 相似文献
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We studied the formation of χ disclination lines in planar cholesteric samples placed in a temperature gradient near the cholesteric
to smectic A phase transition. We observed that the first simple line which forms close to the smectic-cholesteric front zigzags
when it is perpendicular to the direction of planar anchoring and is straight for other orientations. This instability is
similar to Herring instability for crystalline surfaces. We show numerically that it originates from a strong increase of
the elastic anisotropy close to the transition. In addition, we propose a new method to measure the pitch divergence at the
smectic to cholesteric phase transition. 相似文献
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Topological Aspect and Bifurcation of Disclination Lines in Two—Dimensional Liquid Crystals 总被引:2,自引:0,他引:2
Using φ-mapping method and topological current theory,the topological structure and bifurcation of disclination lines in two-dimensional liquid crystals are studied.By introducing the strength density and the topological current of many disclination lines,the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes,the origin,annihilation and bifurcation processes of disclination lines are studied in the neighborhoods of the limit points and bifurcation points,respectively.The branch solutions at the limit point and the different directions of all branch curves at the bifurcation point are calculated with the conservation law of the topological quantum numbers.It is pointed out that a disclination line with a higher strength is unstable and it will evolve to the lower strength state through the bifurcation process. 相似文献
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Topological Properties of Urban Public Traffic Networks in Chinese Top-Ten Biggest Cities 总被引:2,自引:0,他引:2 下载免费PDF全文
We investigate the topological characteristics of complex networks as exemplified by the urban public traffic network (UPTN) in Chinese top-ten biggest cities. It is found that the UPTNs have small world behaviour, by the examination of their topological parameters. The quantitative analysis of the transport efficiency of the UPTNs reveals their higher local efficiency El and lower global efficiency Eg, which coincide well with the status quo of those Chinese cities still at their developing stage. Furthermore, the topological properties of efficiency in the UPTNs are also examined, and the findings indicate that, on the one hand, the UPTNs show robustness to random attacks and frangibility to malicious attacks on a global scale; on the other hand, the interrelation between UPTN efficiency and network motifs deserves our attention. The motifs which interrelate the UPTN efficiency are always triangular-formed patterns, e.g. motifs ID 238, ID 174 and ID 102, etc. 相似文献
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By decomposing SU(2) gauge potential in four-dimensional Euclidean SU(2) Yang-Mills theory in a new way, we find that the instanton number related to the isospin defects of a doublet order parameter can be topologically quantized by the Hopf index and Brouwer degree. It is also shown that the instanton number is just the sum of the topological charges of the isospin defects in the non-trivial sector of Yang-Mills theory. 相似文献
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The Topological Structure of the SU(2) Chern-Simons Topological Current in the Four-Dimensional Quantum Hall Effect 下载免费PDF全文
In the light of the decomposition of the SU(2) gauge potential for I = 1/2, we obtain the SU(2) Chern-Simons current over S4, i.e. the vortex current in the effective field for the four-dimensional quantum Hall effect. Similar to the vortex excitations in the two-dimensional quantum Hall effect (2D FQH) which are generated from the zero points of the complex scalar field, in the 4D FQH, we show that the SU(2) Chern-Simons vortices are generated from the zero points of the two-component wave functions ψ, and their topological charges are quantized in terms of the Hopf indices and Brouwer degrees of Ф-mapping under the condition that the zero points of field ψ are regular points. 相似文献
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Guo-Hong Yang Hui Zhang Yi-Shi Duan 《International Journal of Theoretical Physics》2002,41(6):991-1005
Using -mapping method and topological current theory, the properties and behaviors of disclination points in three-dimensional liquid crystals are studied. By introducing the strength density and the topological current of many disclination points, the total disclination strength is topologically quantized by the Hopf indices and Brouwer degrees at the singularities of the general director field when the Jacobian determinant of the general director field does not vanish. When the Jacobian determinant vanishes, the origin, annihilation, and bifurcation of disclination points are detailed in the neighborhoods of the limit point and bifurcation point, respectively. The branch solutions at the limit point and the different directions of all branch curves at the first- and second-order degenerated points are calculated. It is pointed out that a disclination point with a higher strength is unstable and will evolve to the lower strength state through the bifurcation process. An original disclination point can split into at most four disclination points at one time. 相似文献
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DUAN Yi-Shi ZHAO Li ZHANG Xin-Hui SI Tie-Yan 《理论物理通讯》2007,47(6):1125-1128
A topological theory of liquid crystal films in the presence of defects is developed based on the Ф-mapping topological current theory. By generalizing the free-energy density in "one-constant" approximation, a covariant free- energy density is obtained, from which the U(1) gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of Ф-mapping. 相似文献
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By using topological current theory, this paper studies the inner
topological structure of disclinations during the melting of
two-dimensional systems. From two-dimensional elasticity theory, it
finds that there are topological currents for topological defects in
homogeneous equation. The evolution of disclinations is studied, and
the branch conditions for generating, annihilating, crossing,
splitting and merging of disclinations are given. 相似文献
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By generalizing the topological current of Abelian Chern--Simons (CS)
vortices, we present a topological tensor current of CS p-branes
based on the \phi -mapping topological current theory. It is
revealed that CS p-branes are located at the isolated zeros of the
vector field \phi(x), and the topological structure of CS
p-branes is characterized by the winding number of the
\phi-mappings. Furthermore, the Nambu--Goto action and the equation
of motion for multi CS p-branes are obtained. 相似文献
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We present experiments where opposed pairs of planar parallel disclination lines of topological strength s=+/-1 move due to their mutual attraction. Our measurements show that their motion is clearly asymmetric, with +1 defects moving up to twice as fast as -1 ones. This is a clear indication of backflow, given the intrinsic isotropic elasticity of our system. A phenomenological model is able to account for the experimental observations by renormalizing the orientational diffusivity estimated from the velocity of each defect. 相似文献
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In the light of φ-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kπ /2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director field at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field of liquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density. 相似文献
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YANGGuo-Hong WANGYu-Sheng DUANYi-Shi 《理论物理通讯》2004,42(2):185-188
In the light of C-mapping method and topological current theory, the contribution of disclination lines to free energy density of liquid crystals is studied in the single-elastic constant approximation. It is pointed out that the total free energy density can be divided into two parts. One is the usual distorted energy density of director field around the disclination lines. The other is the free energy density of disclination lines themselves, which is shown to be centralized at the disclination lines and to be topologically quantized in the unit of kn/2. The topological quantum numbers are determined by the Hopf indices and Brouwer degrees of the director l~eld at the disclination lines, i.e. the disclination strengths. From the Lagrange‘s method of multipliers, the equilibrium equation and the molecular field ofliquid crystals are also obtained. The physical meaning of the Lagrangian multiplier is just the distorted energy density. 相似文献
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Thermomechanical mechanism of the director reorientation in twisted nematic liquid crystals caused by the one-dimensional longitudinal temperature gradient is predicted and studied theoretically. The calculated director reorientations are in the range that can be measured experimentally very easily. 相似文献
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We study here a mean field model to obtain the phase diagram (concentration versus temperature) near the NAC* point in a binary mixture of liquid crystal. We have fitted our phase line equations to the experimental data for the mixture of SCE9 + SCE10 liquid crystals. We deduce from our analysis that there should exist a tricritical point close to the NAC* point on the AC* phase line. 相似文献