The second critical point for the Perfect Bose gas in quasi-one-dimensional traps

We present a new model of quasi-one-dimensional trap with some unknown physical predictions about a second transition, including about a change in fractions of condensed coherence lengths due to the existence of a second critical temperature Tm < Tc. If this physical model is acceptable, we want to challenge experimental physicists in this regard

On the classical WN(l)W_N^{(l)} algebras

We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3 algebra is derived explicitly along these lines, thus providing further support for the conjecture. This algebra is found to be equivalent to that obtained by the method of Hamiltonian reduction. Furthermore, its twisted version reproduces the algebra associated to a certain non-principal embedding of sl(2) into sl(4), or equivalently, the u(2) quasi-superconformal algebra. The general aspects of the W_N^l algebras are also presented.Comment: 28 page

Likelihood-based inference for max-stable processes

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so likelihood-based methods remain far from providing a complete and flexible framework for inference. In this article we develop inferentially practical, likelihood-based methods for fitting max-stable processes derived from a composite-likelihood approach. The procedure is sufficiently reliable and versatile to permit the simultaneous modeling of marginal and dependence parameters in the spatial context at a moderate computational cost. The utility of this methodology is examined via simulation, and illustrated by the analysis of U.S. precipitation extremes

The Decidability Frontier for Probabilistic Automata on Infinite Words

We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\"uchi, coB\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and adaptations of proofs for probabilistic finite automata and present a complete characterization of the decidability and undecidability frontier of the quantitative and qualitative decision problems for probabilistic automata on infinite words

Utilizing osteocyte derived factors to enhance cell viability and osteogenic matrix deposition within IPN hydrogels

Many bone defects arising due to traumatic injury, disease, or surgery are unable to regenerate, requiring intervention. More than four million graft procedures are performed each year to treat these defects making bone the second most commonly transplanted tissue worldwide. However, these types of graft suffer from a limited supply, a second surgical site, donor site morbidity, and pain. Due to the unmet clinical need for new materials to promote skeletal repair, this study aimed to produce novel biomimetic materials to enhance stem/stromal cell osteogenesis and bone repair by recapitulating aspects of the biophysical and biochemical cues found within the bone microenvironment. Utilizing a collagen type I-alginate interpenetrating polymer network we fabricated a material which mirrors the mechanical and structural properties of unmineralized bone, consisting of a porous fibrous matrix with a young's modulus of 64 kPa, both of which have been shown to enhance mesenchymal stromal/stem cell (MSC) osteogenesis. Moreover, by combining this material with biochemical paracrine factors released by statically cultured and mechanically stimulated osteocytes, we further mirrored the biochemical environment of the bone niche, enhancing stromal/stem cell viability, differentiation, and matrix deposition. Therefore, this biomimetic material represents a novel approach to promote skeletal repair

The Boltzmann Equation in Classical Yang-Mills Theory

We give a detailed derivation of the Boltzmann equation, and in particular its collision integral, in classical field theory. We first carry this out in a scalar theory with both cubic and quartic interactions and subsequently in a Yang-Mills theory. Our method is not relied on a doubling of the fields, rather it is based on a diagrammatic approach representing the classical solution to the problem.Comment: 24 pages, 7 figures; v2: typos corrected, reference added, published in Eur. Phys. J.

On the deprojection of triaxial galaxies with St\"ackel potentials

A family of triaxial St\"ackel potential-density pairs is introduced. With the help of a Quadratic Programming method, a linear combination of potential-density pairs of this family which fits a given projected density distribution can be built. This deprojection strategy can be used to model the potentials of triaxial elliptical galaxies with or without dark halos. Besides, we show that the expressions for the St\"ackel triaxial density and potential are considerably simplified when expressed in terms of divided differences, which are convenient numerically. We present an example of triaxial deprojection for the galaxy NGC~5128 whose photometry follows the de Vaucouleurs law.Comment: 8 pages, to appear in A&A, postscript file with figures available at ftp://naos.rug.ac.be/pub/deprojection.ps.

Mott law as upper bound for a random walk in a random environment

We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a Boltzmann-type factor. This is an effective model for the phonon-induced hopping of electrons in disordered solids in the regime of strong Anderson localization. Under mild assumptions on the point process we prove an upper bound of the asymptotic diffusion matrix of the random walk in agreement with Mott law. A lower bound in agreement with Mott law was proved in \cite{FSS}.Comment: 22 pages. Additional results and corrections