Universal reconnection of non-Abelian cosmic strings

We show that local and semilocal strings in Abelian and non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.     

Global structures for the moduli of (punctured) super riemann surfaces

A fine moduli superspace for algebraic super Riemann surfaces with a level-n structure is constructed as a quotient of the split superscheme of local spin-gravitivo fields by an étale equivalence relation. This object is not a superscheme, but still has an interesting structure: it is an algebraic superspace, that is, an analytic superspace with sufficiently many meromorphic functions. The moduli of super Riemann surfaces with punctures (fixed points in the supersurface) is also constructed as an algebraic superspace. Moreover, when one only considers ordinary punctures (fixed points in the underlying ordinary curve), it turns out that the moduli is a true superscheme. We prove furthermore that this moduli superscheme is split.     

Backreaction I: The torus

We use wrapped D-brane probes to measure position dependent perturbations of compactification moduli. Due to the backreaction of the D-branes on the local geometry, we suspect that measuring the fluctuations of one modulus to high precision will generically affect the others. These considerations lead us to conjecture a novel uncertainty principle on the Calabi–Yau moduli space. We begin our investigation with a gedanken experiment on a torus.     

Contact Spheres and Hyperkähler Geometry

A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only closed manifolds admitting such structures). We also show that the moduli space of taut contact spheres embeds into the moduli space of taut contact circles.This moduli problem leads to a new viewpoint on the Gibbons-Hawking ansatz in hyperkähler geometry. The classification of taut contact spheres on closed 3-manifolds includes the known classification of 3-Sasakian 3-manifolds, but the local Riemannian geometry of contact spheres is much richer. We construct two examples of taut contact spheres on open subsets of \({\mathbb{R}^3}\) with nontrivial local geometry; one from the Helmholtz equation on the 2-sphere, and one from the Gibbons-Hawking ansatz. We address the Bernstein problem whether such examples can give rise to complete metrics.     

Shape of a wave front in a heterogenous medium

Wave propagation in a heterogeneous medium, characterized by a distribution of local elastic moduli, is studied. Both acoustic and elastic waves are considered, as are spatially random and power-law correlated distributions of the elastic moduli with nondecaying correlations. Three models--a continuum scalar model, and two discrete models--are utilized. Numerical simulations indicate the existence, at all times, of the relation, alpha = H, where alpha is the roughness exponent of the wave front in the medium, and H is the Hurst exponent that characterizes the spatial correlations in the distribution of the local elastic moduli. Hence, a direct relation between the static morphology of an inhomogeneous correlated medium and its dynamical properties is established. In contrast, for a wave front in random media, alpha = 0 (logarithmic growth) at short times, followed by a crossover to the classical value, alpha = 1/2, at long times.     

Moduli Fields in Warped Compactifications

We discuss the effective action of moduli fields in warped brane-world compactifications. For definiteness, a two-brane model with a bulk dilaton field and a power-law warp factor is considered. After deriving the classical four-dimensional effective action for the moduli, we present the calculation of the one-loop effective potential induced by bulk fields. A detailed discussion of renormalization is given, with emphasis on the local worldsheet operators which are generated. Finally, we outline the possible role of these operators in the stabilization of the moduli.     

Quadratic differentials and closed string vertices

Existence theorems for quadratic differentials on Riemann surfaces are used to explore the possible structure of local vertices in closed string field theory. The cell decomposition of the moduli space of the three-holed sphere is studied in some detail, and the problem of obtaining a single covering of moduli space is investigated.     

Geometric approach to Kac–Moody and Virasoro algebras

In this paper we show the existence of a group acting infinitesimally transitively on the moduli space of pointed-curves and vector bundles (with formal trivialization data) and whose Lie algebra is an algebra of differential operators. The central extension of this Lie algebra induced by the determinant bundle on the Sato Grassmannian is precisely a semidirect product of a Kac–Moody algebra and the Virasoro algebra. As an application of this geometric approach, we give a local Mumford-type formula in terms of the cocycle associated with this central extension. Finally, using the original Mumford formula we show that this local formula is an infinitesimal version of a general relation in the Picard group of the moduli of vector bundles on a family of curves (without any formal trivialization).     

On the solitons of the Chern-Simons-Higgs model

Several issues concerning the self-dual solutions of the Chern-Simons-Higgs model are addressed. The topology of the configuration space of the model is analysed when the space manifold is either the plane or an infinite cylinder. We study the local structure of the moduli space of self-dual solitons in the second case by means of an index computation. It is shown how to manage the non-integer contribution to the heat-kernel supertrace due to the non-compactness of the base space. A physical picture of the local coordinates parametrizing the non-topological soliton moduli space arises. Received: 9 October 1998 / Revised version: 12 December 1998 / Published online: 22 March 1999     

Moduli of ADHM sheaves and the local Donaldson-Thomas theory

The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper studies the geometry of moduli spaces of representations of the same quiver with relations in the abelian category of coherent sheaves on a smooth complex projective curve X. In particular it is proven that this moduli space is virtually smooth and related by relative Beilinson spectral sequence to the curve counting construction via stable pairs of Pandharipande and Thomas. This yields a new conjectural construction for the local Donaldson-Thomas theory of curves as well as a natural higher rank generalization.     

Global aspects of gauged Wess-Zumino-Witten models

A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with quasi-parabolic structure. Two actions of the fundamental group of the gauge group is defined: One on the space of gauge invariant local fields and the other on the moduli spaces. Applying these in the integral expression, we obtain a certain identity which relates correlation functions for configurations of different topologies. It gives an important information on the topological sum for the partition and correlation functions.     

Linear Fluid Theory for Weakly Inhomogeneous Plasmas with Strong Correlations

Linearized fluid equations for the collective modes of weakly inhomogeneous plasmas including strong coupling effects are derived from a recent kinetic theory based on an extended Singwi‐Tosi‐Land‐Sjölander (STLS) ansatz [H. Kählert, G. J. Kalman, and M. Bonitz, Phys. Rev. E 90 , 011101(R) (2014)]. The equations are analogous to the equations of linearized elasticity theory with space dependent elastic moduli that correspond to those of a bulk system with the local fluid density. The identification of the latter as infinite‐frequency elastic moduli shows that the present version of the extended STLS theory accounts for the elastic properties of the fluid but does not capture the viscous behavior. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Selberg zeta function and a new Kähler metric on the moduli space of punctured Riemann surfaces

A local index theorem for families of -operators on Riemann surfaces with functures is proved. A new Kähler metric on the moduli space of punctured surfaces is described in terms of the Eisenstein-Maass series.     

Universal elasticity and fluctuations of nematic gels

We study elasticity of spontaneously orientationally ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infrared fixed point. Namely, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible, and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local heterogeneities down to d(lc)<3.     

Time-dependent strength of colloidal gels

Colloidal silica gels are shown to stiffen with time, as demonstrated by both dynamic light scattering and bulk rheological measurements. Their elastic moduli increase as a power law with time, independent of particle volume fraction; however, static light scattering indicates that there are no large-scale structural changes. We propose that increases in local elasticity arising from bonding between neighboring colloidal particles can account for the strengthening of the network, while preserving network structure.     

Cohomological gravity

We construct a theory of cohomological gravity in arbitrary dimensions based upon a local vector supersyrnmetry algebra. The observables in this theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.This essay received an honorable mention from the Gravity Research Foundation, 1992-Ed.     

Conformal transformations and string field redefinitions

It is shown that conformal transformations of interaction vertices in Witten-type string field theories are realized to lowest order as nonlinear string field redefinitions. However, these redefinitions induce higher-order interactions. Unlike the redefinitions commonly done in local field theory, the S-matrix beyond tree level is affected. In particular, the change of variables determinant contributes integrals over different regions of moduli space.     

单壁碳纳米管杨氏模量的掺杂效应

用分子动力学方法研究了N,O,Si,P,S等5种杂质对扶手椅型(5，5)和锯齿型(9，0)单壁碳纳米管杨氏模量的影响.结果表明：直径为0.678和0.704 nm的扶手椅型(5，5)和锯齿型(9，0)碳纳米管在无掺杂时其杨氏模量分别为948和804 GPa.在掺杂浓度10％以下，碳纳米管的拉伸杨氏模量均随掺杂浓度增加近似呈线性下降规律，下降率以Si掺杂最大，N掺杂最小.对与C同周期的元素掺杂，随原子序数增加碳纳米管的杨氏模量下降率增大；与C不同周期的元素掺杂，碳纳米管的杨氏模量随掺杂浓度增加下降率更大，但 关键词： 碳纳米管 杂质 杨氏模量 分子动力学方法