On the stability of the primordial closed string gas

We recast the study of a closed string gas in a toroidal container in the physical situation in which the single string density of states is independent of the volume because energy density is very high. This includes the gas for the well known Brandenberger-Vafa cosmological scenario. We describe the gas in the grandcanonical and microcanonical ensembles. In the microcanonical description, we find a result that clearly confronts the Brandenberger-Vafa calculation to get the specific heat of the system. The important point is that we use the same approach to the problem but a different regularization. By the way, we show that, in the complex temperature formalism, at the Hagedorn singularity, the analytic structure obtained from the so-called F-representation of the free energy coincides with the one computed using the S-representation.Comment: 20 pages and 1 figure. The final version that appeared in JHE

On the inequivalence of statistical ensembles

We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.Comment: 4 pages, 4 figure

Universal physics of 2+1 particles with non-zero angular momentum

The zero-energy universal properties of scattering between a particle and a dimer that involves an identical particle are investigated for arbitrary scattering angular momenta. For this purpose, we derive an integral equation that generalises the Skorniakov - Ter-Martirosian equation to the case of non-zero angular momentum. As the mass ratio between the particles is varied, we find various scattering resonances that can be attributed to the appearance of universal trimers and Efimov trimers at the collisional threshold.Comment: 6 figure

A new displacement-based approach to calculate stress intensity factors with the boundary element method

The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs). The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has be-come very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM) in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes

Metal Surface Energy: Persistent Cancellation of Short-Range Correlation Effects beyond the Random-Phase Approximation

The role that non-local short-range correlation plays at metal surfaces is investigated by analyzing the correlation surface energy into contributions from dynamical density fluctuations of various two-dimensional wave vectors. Although short-range correlation is known to yield considerable correction to the ground-state energy of both uniform and non-uniform systems, short-range correlation effects on intermediate and short-wavelength contributions to the surface formation energy are found to compensate one another. As a result, our calculated surface energies, which are based on a non-local exchange-correlation kernel that provides accurate total energies of a uniform electron gas, are found to be very close to those obtained in the random-phase approximation and support the conclusion that the error introduced by the local-density approximation is small.Comment: 5 pages, 1 figure, to appear in Phys. Rev.

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange