Closed geodesics on orbifolds

In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of the existence of infinitely many geometrically distinct closed geodesics. In the classical case the solution of those problems involve the consideration of the homotopy groups of $M$ and the homology properties of the free loop space on $M$(Morse theory). Those notions have their analogue in the case of orbifolds (see [7]). The main part of this paper will be to recall those notions and to show how the classical techniques can be adapted to the case of orbifolds.Comment: Improved version which takes into account the comments of the refree. In particular, we extend to compact simply connected Riemannian orbifolds the result of Gromoll-Meye

Residual stress development and evolution in two-phase crystalline material: a discrete dislocation study

Crystalline materials undergo heterogeneous deformation upon the application of external load, which results in the development of incompatible elastic strains in the material as soon as the load is removed. The presence of heterogeneous distribution of elastic strains in the absence of any form of external load results in the building up of stresses referred to as residual stresses. The heterogeneity of strain is attributed either to the presence of multiple phases or to the orientation gradients across the sample volume. This paper is an endeavour to model the presence of second phase in a two-dimensional discrete dislocation dynamics framework, which already contains constitutive rules to include three-dimensional mechanisms, such as line tension and dynamic junction formation. The model is used to investigate residual stress development in single crystals subjected to plane strain loading and then subsequently unloaded to study residual stresses. The dislocation accumulation around the second phase and its effect on the mechanical properties is studied. The orientation dependence of residual stresses as a function of the underlying defect substructure has also been explored. A variety of results are obtained. In particular, the development of stresses as a function of underlying defect substructure is also presented and found to depend upon the orientation of the crystal

Local cloning of Bell states and distillable entanglement

The necessary and sufficient amount of entanglement required for cloning of orthogonal Bell states by local operation and classical communication is derived, and using this result, we provide here some additional examples of reversible, as well as irreversible states.Comment: 5 pages, two columns, Latex. Few typos have been corrected. An explanation of the teleportation map (eqn. (3) in the manuscript) has been provide

Symmetry and stability of orientationally ordered collective motions of self-propelled, semiflexible filaments

Ordered, collective motions commonly arise spontaneously in systems of many interacting, active units, ranging from cellular tissues and bacterial colonies to self-propelled colloids and animal flocks. Active phases are especially rich when the active units are sufficiently anisotropic to produce liquid crystalline order and thus active nematic phenomena, with important biophysical examples provided by cytoskeletal filaments including microtubules and actin. Gliding assay experiments have provided a testbed to study the collective motions of these cytoskeletal filaments and unlocked diverse collective active phases, including states with long-range orientational order. However, it is not well-understood how such long-range order emerges from the interplay of passive and active aligning mechanisms. We use Brownian dynamics simulations to study the collective motions of semiflexible filaments that self-propel in quasi-two dimensions, in order to gain insights into the aligning mechanisms at work in these gliding assay systems. We find that, without aligning torques in the microscopic model, long-range orientational order can only be achieved when the filaments are able to overlap. The symmetry (nematic or polar) of the long-range order that first emerges is shown to depend on the energy cost of filament overlap and on filament flexibility. However, our model also predicts that a long-range-ordered active nematic state is merely transient, whereas long-range polar order is the only active dynamical steady state in systems with finite filament rigidity.Comment: Main text: 9 pages, 6 figures. Supplementary Material: 5 pages, 5 figures. For associated video files, see https://livejohnshopkins-my.sharepoint.com/:f:/g/personal/mathani1_jh_edu/EmZKBH1qRzJFmK1mXTr32BUBfu2xJk1yesRJ3NyUo1ueRQ?e=LPRud

On a notion of maps between orbifolds, I. function spaces

This is the first of a series of papers which are devoted to a comprehensive theory of maps between orbifolds. In this paper, we define the maps in the more general context of orbispaces, and establish several basic results concerning the topological structure of the space of such maps. In particular, we show that the space of such maps of C^r-class between smooth orbifolds has a natural Banach orbifold structure if the domain of the map is compact, generalizing the corresponding result in the manifold case. Motivations and applications of the theory come from string theory and the theory of pseudoholomorphic curves in symplectic orbifolds.Comment: Final version, 46 pages. Accepted for publication in Communications in Contemporary Mathematics. A preliminary version of this work is under a different title "A homotopy theory of orbispaces", arXiv: math. AT/010202

Study of the causes of non-acceptance of VBAC in patients with previous one LSCS in a tertiary institution

Background: Many women who are eligible candidates for a VBAC (Vaginal Birth after Caesarean) in the current pregnancy opt for a repeat LSCS (Lower Segment Caesarean Section) as a mode of delivery. We decided to evaluate the proportion of patients who opt out of a VBAC and to study the causality of this trend.Methods: All patients who presented to the Dept. of OBG in our institution and were eligible to have a VBAC were included in the study till the sample size of 100 cases was met. Consultant opinion was sought prior to deciding the mode of delivery.Results: Incidence of patients of previous one LSCS who were not willing for VBAC was 4%, out of total number of deliveries and 30.7%, out of all cases of patients with previous one LSCS. The reason for not opting for a VBAC in the current pregnancy in the majority of the eligible patients was the desire for a concurrent sterilization procedure. Others cited apprehension of a scar rupture or fear of labor pain or both as their primary reason for opting out of a VBAC.Conclusions: The high incidence of ERC (Elective Repeat Caesarean) as compared to TOLAC (Trial of Labour after Caesarean) has long-term clinical and financial implications. Counseling given to the pregnant woman with an emphasis on the advantages of VBAC in order that she opts for a VBAC with confidence and enthusiasm is the only way forward

Degree of Complementarity Determines the Nonlocality in Quantum Mechanics

Complementarity principle is one of the central concepts in quantum mechanics which restricts joint measurement for certain observables. Of course, later development shows that joint measurement could be possible for such observables with the introduction of a certain degree of unsharpness or fuzziness in the measurement. In this paper, we show that the optimal degree of unsharpness, which guarantees the joint measurement of all possible pairs of dichotomic observables, determines the degree of nonlocality in quantum mechanics as well as in more general no-signaling theories.Comment: Close to published versio

Broadcasting of entanglement and universal quantum cloners

We study broadcasting of entanglement where we use universal quantum cloners (in general less optimal) to perform local cloning operations. We show that there is a lower bound on the fidelity of the universal quantum cloners that can be used for broadcasting. We prove that an entanglement is optimally broadcast only when optimal quantum cloners are used for local copying. We also show that broadcasting of entanglement into more than two entangled pairs is forbidden using only local operations.Comment: 8 pages, Latex,final version, to appear in Physical Review

Entanglement teleportation via Bell Mixture

We investigate the teleportation of the bipartite entangled states through two equally noisy quantum channels, namely mixture of Bell states. There is a particular mixed state channel for which all pure entanglement in a known Schmidt basis remain entangled after teleportation and it happens till the channel state remains entangled. Werner state channel lacks both these features. The relation of these noisy channels with violation of Bell's inequality and 2-E inequality is studied.Comment: 7 pages, late