(2+1) gravity for higher genus in the polygon model

We construct explicitly a (12g-12)-dimensional space P of unconstrained and independent initial data for 't Hooft's polygon model of (2+1) gravity for vacuum spacetimes with compact genus-g spacelike slices, for any g >= 2. Our method relies on interpreting the boost parameters of the gluing data between flat Minkowskian patches as the lengths of certain geodesic curves of an associated smooth Riemann surface of the same genus. The appearance of an initial big-bang or a final big-crunch singularity (but never both) is verified for all configurations. Points in P correspond to spacetimes which admit a one-polygon tessellation, and we conjecture that P is already the complete physical phase space of the polygon model. Our results open the way for numerical investigations of pure (2+1) gravity.Comment: 35 pages, 22 figure

Local representations of the loop braid group

We study representations of the loop braid group LBn from the perspective of extending representations of the braid group Bn. We also pursue a generalization of the braid/Hecke/Temperlely-Lieb paradigm-uniform finite dimensional quotient algebras of the loop braid group algebras

Boundary conditions and symplectic structure in the Chern-Simons formulation of (2+1)-dimensional gravity

We propose a description of open universes in the Chern-Simons formulation of (2+1)-dimensional gravity where spatial infinity is implemented as a puncture. At this puncture, additional variables are introduced which lie in the cotangent bundle of the Poincar\'e group, and coupled minimally to the Chern-Simons gauge field. We apply this description of spatial infinity to open universes of general genus and with an arbitrary number of massive spinning particles. Using results of [9] we give a finite dimensional description of the phase space and determine its symplectic structure. In the special case of a genus zero universe with spinless particles, we compare our result to the symplectic structure computed by Matschull in the metric formulation of (2+1)-dimensional gravity. We comment on the quantisation of the phase space and derive a quantisation condition for the total mass and spin of an open universe.Comment: 44 pages, 3 eps figure

Polygon model from first order gravity

The gauge fixed polygon model of 2+1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the first order formalism of the theory in terms of the triad and the spin connection. The induced symplectic structure is calculated and shown to agree with the canonical one in terms of the variables.Comment: 20 pages, presentation improved, typos correcte

Timelike surfaces in Lorentz covariant loop gravity and spin foam models

We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop approach to quantize the theory we derive the spectrum of the area operator of a two-dimensional surface. Its different branches are naturally associated to spacelike and timelike surfaces. The results are compared with the predictions of Lorentzian spin foam models. A restriction of the representations labeling spin networks leads to perfect agreement between the states as well as the area spectra in the two approaches.Comment: a wrong sign corrected in equation (65

A locally finite model for gravity

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate matter of a form that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Globally, however, the model is not finite, because solutions tend to generate infinite fractals. The model is not (yet) quantized, but could serve as an interesting setting for analytical approaches to classical general relativity, as well as a possible stepping stone for quantum models. Details of its properties are explained, but some problems remain unsolved, such as a complete description of the most violent interactions, which can become quite complex.Comment: 26 pages, 9 figure

Port site herniation of the small bowel following laparoscopy-assisted distal gastrectomy: a case report

<p>Abstract</p> <p>Introduction</p> <p>Port-site herniation is a rare but potentially dangerous complication after laparoscopic surgery. Closure of port sites, especially those measuring 10 mm or more, has been recommended to avoid such an event.</p> <p>Case presentation</p> <p>We herein report the only case of a port site hernia among a series 52 consecutive cases of laparoscopy-assisted distal gastrectomy (LADG) carried out by our unit between July 2002 and March 2007. In this case the small bowel herniated and incarcerated through the port site on day 4 after LADG despite closure of the fascia. Initial manifestations experienced by the patient, possibly due to obstruction, and including mild abdominal pain and nausea, occurred on the third day postoperatively. The definitive diagnosis was made on day 4 based on symptoms related to leakage from the duodenal stump, which was considered to have developed after severe obstruction of the bowel. Re-operation for reduction of the incarcerated bowel and tube duodenostomy with peritoneal drainage were required to manage this complication.</p> <p>Conclusion</p> <p>We present this case report and review of literature to discuss further regarding methods of fascial closure after laparoscopic surgery.</p

Entanglement study of the 1D Ising model with Added Dzyaloshinsky-Moriya interaction

We have studied occurrence of quantum phase transition in the one-dimensional spin-1/2 Ising model with added Dzyaloshinsky-Moriya (DM) interaction from bi- partite and multi-partite entanglement point of view. Using exact numerical solutions, we are able to study such systems up to 24 qubits. The minimum of the entanglement ratio R $\equiv$ \tau 2/\tau 1 < 1, as a novel estimator of QPT, has been used to detect QPT and our calculations have shown that its minimum took place at the critical point. We have also shown both the global-entanglement (GE) and multipartite entanglement (ME) are maximal at the critical point for the Ising chain with added DM interaction. Using matrix product state approach, we have calculated the tangle and concurrence of the model and it is able to capture and confirm our numerical experiment result. Lack of inversion symmetry in the presence of DM interaction stimulated us to study entanglement of three qubits in symmetric and antisymmetric way which brings some surprising results.Comment: 18 pages, 9 figures, submitte

Atmospheric processing outside clouds increases soluble iron in mineral dust

Iron (Fe) is a key micronutrient regulating primary productivity in many parts of the global ocean. Dust deposition is an important source of Fe to the surface ocean, but most of this Fe is biologically unavailable. Atmospheric processing and reworking of Fe in dust aerosol can increase the bioavailable Fe inputs to the ocean, yet the processes are not well understood. Here, we experimentally simulate and model the cycling of Fe-bearing dust between wet aerosol and cloud droplets. Our results show that insoluble Fe in dust particles readily dissolves under acidic conditions relevant to wet aerosols. By contrast, under the higher pH conditions generally relevant to clouds, Fe dissolution tends to stop, and dissolved Fe precipitates as poorly crystalline nanoparticles. If the dust-bearing cloud droplets evaporated again (returning to the wet aerosol stage with low pH), those neo-formed Fe nanoparticles quickly redissolve, while the refractory Fe-bearing phases continue to dissolve gradually. Overall, the duration of the acidic, wet aerosol stage ultimately increases the amount of potentially bioavailable Fe delivered to oceans, while conditions in clouds favor the formation of Fe-rich nanoparticles in the atmosphere