From Open Quantum Systems to Open Quantum Maps

For a class of quantized open chaotic systems satisfying a natural dynamical assumption we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincaré map associated with the flow near the set of trapped trajectories.     

Branch-and-Cut-and-Price for Capacitated Connected Facility Location

We consider a generalization of the Connected Facility Location Problem (ConFL), suitable to model real world network extension scenarios such as fiber-to-the-curb. In addition to choosing a set of facilities and connecting them by a Steiner tree as in ConFL, we aim to maximize the resulting profit by potentially supplying only a subset of all customers. Furthermore, capacity constraints on potential facilities need to be considered. We present two mixed integer programming based approaches which are solved using branch-and-cut and branch-and-cut-and-price, respectively. By studying the corresponding polyhedra we analyze both approaches theoretically and show their advantages over previously presented models. Furthermore, using a computational study we are able to additionally show significant advantages of our models over previously presented ones from a practical point of view.     

Communication and Collective Consensus Making in?Animal Groups via Mechanical Interactions

Mechanical constraints have a strong influence on the dynamics and structure of granular aggregations. The contact forces within dense suspensions of active particles may give rise to intriguing phenomena, including anomalous density fluctuations, long-range orientational ordering, and spontaneous pattern formation. Various authors have proposed that these physical phenomena contribute to the ability of animal groups to move coherently. Our systematic numerical simulations confirm that spontaneous interactions of elongated individuals can trigger oriented motion in small groups. They are, however, insufficient in larger ones, despite their significant imprint on the group’s internal structure. It is also demonstrated that preferred directions of motion of a minority of group members can be communicated to others solely by mechanical interactions. These findings strengthen the link between pattern formation in active nematics and the collective decision making of social animals.     

Critical percolation: the expected number of clusters in a rectangle

We show that for critical site percolation on the triangular lattice two new observables have conformally invariant scaling limits. In particular the expected number of clusters separating two pairs of points converges to an explicit conformal invariant. Our proof is independent of earlier results and SLE techniques, and might provide a new approach to establishing conformal invariance of percolation.     

Esterification with orthophosphoric acid of cellulose samples with different extents of structural heterogeneity

Modification of cellulose samples with different extents of structural heterogeneity by esterification with orthophosphoric acid in the temperature range 140?C160??C was studied. The reaction yielded cellulose phosphates containing 3.2?C6.0 wt % P, with the ion-exchange capacity of 2.2?C3.0 mg-equiv g^?1. Introduction of phosphorus into cellulose leads to a slight decrease in the structural heterogeneity. The polymer with the lower ordering index is characterized by the higher phosphorus content, which suggests that the reaction mainly occurs in the amorphous part of the polymer.     

Nuclear relativistic hartree-fock approximation with effective pions

The effect of an interaction between the ??- and ??-meson fields, as well as that of the mixture of pseudoscalar (PS) and pseudovector (PV) couplings for the ??N vertex on the shell structure of finite nuclei are analyzed in the framework of different nonlinear nuclearmodels based on the relativistic Hartree-Fock approximation. For the case of a dominant ??N PV coupling, it is found that if the ??-?? interaction generates an effective pion mass increasing with the nuclear density, the unrealistic effect of pions on the shell structure can be strongly reduced, keeping, roughly, the contribution of pions to the total binding energy. The ??N PS coupling increases slightly the spin-orbit splittings and the binding energy of the single-particle levels.     

Codimension and pseudometric in co-Heyting algebras

In this paper, we introduce a notion of dimension and codimension for every element of a bounded distributive lattice L. These notions prove to have a good behavior when L is a co-Heyting algebra. In this case the codimension gives rise to a pseudometric on L which satisfies the ultrametric triangle inequality. We prove that the Hausdorff completion of L with respect to this pseudometric is precisely the projective limit of all its finite dimensional quotients. This completion has some familiar metric properties, such as the convergence of every monotonic sequence in a compact subset. It coincides with the profinite completion of L if and only if it is compact or equivalently if every finite dimensional quotient of L is finite. In this case we say that L is precompact. If L is precompact and Hausdorff, it inherits many of the remarkable properties of its completion, specially those regarding the join/meet irreducible elements. Since every finitely presented co-Heyting algebra is precompact Hausdorff, all the results we prove on the algebraic structure of the latter apply in particular to the former. As an application, we obtain the existence for every positive integers n, d of a term t _{n, d} such that in every co-Heyting algebra generated by an n-tuple a, t _{n, d} (a) is precisely the maximal element of codimension d.     

A p-nilpotency criterion

Let G be a finite group, p a fixed prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, then G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.