Su (2) Poisson–Lie T Duality

Poisson–Lie target space duality is a framework where duality transformations are properly defined. In this Letter, we investigate the dual pair of -models defined by the double SO(3,1) in the Iwasawa decomposition.     

Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential

Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles.     

Cohomology theories in triangulated categories

Let C be a triangulated category with a proper class E of triangles.We prove that there exists an Avramov–Martsinkovsky type exact sequence in C,which connects E-cohomology,E-Tate cohomology and E-Gorenstein cohomology.     

On a Unified Theory of Generalized Branes Coupled to Gauge Fields,Including the Gravitational and Kalb–Ramond Fields

We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes the dynamics of the usual branes. Geometrically, coordinates and associated coordinate frame fields {} extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified. Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space.     

非线性力学场论的几个基本课题

最近10年,在变形体转动的描述和应用,应变的度量和应用,以及应力,应变的客观性导数这三个非线性力学场论中互相关联的基本课题方面,提出了许多新问题,作出了大量的研究工作.本文综合介绍了其中一些方面的情况,并概述了笔者的相应工作.      

Structure and size distribution of percolating clusters. Comparison with gelling systems

Dynamic properties of Brownian particles immersed in a periodic potential with two barriers V₁ and V₂ (symmetric bistable potential) are studied by using the Fokker-Planck equation which we solve numerically by the matrix continued fraction method. This study will therefore serve to demonstrate the influence of this form of potential, which is of great interest for superionic conductors and for many other solid systems, on the diffusion process. Thus, we have calculated the full width at half maximum (FWHM) ) of the quasi-elastic line of the dynamic structure factor, for a large range of values of the wave-vectors q. Our results show clearly that, by varying the ratio of the barriers strictly between and 1, the Fokker-Planck equation describes a diffusive process which has some characteristic of jump and liquid-like regimes. While in the limit cases, i.e. when tends to or 1, the diffusion process can be described only by a simple jump motion. However, the jump-lengths corresponding to each limit case are not equal. In general the change of the ratio is found to have a significant effect on the character of the diffusive motion. We have also performed Fokker-Planck dynamics calculations of the diffusion coefficient in a bistable potential. We have found a good agreement between numerical calculations and analytical approximation results obtained in the high friction limit. Received 25 May 1998 and Received in final form 15 November 1998     

Evolution of Grassmannian invariant-angle coherent states and nonadiabatic Hannay's angle

We show how the exact evolution and nonadiabatic Hannay's angle of Grassmannian classical mechanics of spin one half in a varying external magnetic field is associated with the evolution of Grassmannian invariant-angle coherent states. Received: 18 February 1998