On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and discontinuous shocks

We study the generalization of the dispersionless Kadomtsev - Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2+1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel IST, and it has been recently shown to be a prototype model equation in the description of the two dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single valued discontinuous shocks. Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if $m(n-1)\le 2$. At last, the analytic aspects of such a wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a discontinuous shock. These results, contained in the 2012 master thesis of one of the authors (FS), generalize those obtained by one of the authors (PMS) and S.V.Manakov for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.Comment: 31 pages, 11 figure

Detection of entanglement between collective spins

Entanglement between individual spins can be detected by using thermodynamics quantities as entanglement witnesses. This applies to collective spins also, provided that their internal degrees of freedom are frozen, as in the limit of weakly-coupled nanomagnets. Here, we extend such approach to the detection of entanglement between subsystems of a spin cluster, beyond such weak-coupling limit. The resulting inequalities are violated in spin clusters with different geometries, thus allowing the detection of zero- and finite-temperature entanglement. Under relevant and experimentally verifiable conditions, all the required expectation values can be traced back to correlation functions of individual spins, that are now made selectively available by four-dimensional inelastic neutron scattering

Quantum-gate implementation in permanently coupled AF spin rings without need of local fields

We propose a scheme for the implementation of quantum gates which is based on the qubit encoding in antiferromagnetic molecular rings. We show that a proper engineering of the intercluster link would result in an effective coupling that vanishes as far as the system is kept in the computational space, while it is turned on by a selective excitation of specific auxiliary states. These are also shown to allow the performing of single- and two-qubit gates without an individual addressing of the rings by means of local magnetic fields.Comment: To appear in Physical Review Letter

Preference and Similarity-based Behavioral Discovery of Services

We extend Constraint Automata by replacing boolean constraints with semiring-based soft constraints. The obtained general formal tool can be used to represent preference-based and similarity-based queries, which allow a user more freedom in choosing the behavior of the service to finally use, among all possible choices. A user states his preferences through a “soft” query, and obtains results that satisfy this query with different levels of preference. The soft requirements may involve a parameter data of the service operations, or the (names of the) operations themselves. Moreover, we introduce a first implementation of the search procedure by using declarative (Soft) Constraint Programming

Diagnosis and treatment of lipodystrophy: a step‑by‑step approach

Aim : Lipodystrophy syndromes are rare heterogeneous disorders characterized by defciency of adipose tissue, usually a decrease in leptin levels and, frequently, severe metabolic abnormalities including diabetes mellitus and dyslipidemia. Purpose : To describe the clinical presentation of known types of lipodystrophy, and suggest specifc steps to recognize, diagnose and treat lipodystrophy in the clinical setting. Methods : Based on literature and in our own experience, we propose a stepwise approach for diagnosis of the diferent subtypes of rare lipodystrophy syndromes, describing its more frequent co-morbidities and establishing the therapeutical approach. Results : Lipodystrophy is classifed as genetic or acquired and by the distribution of fat loss, which can be generalized or partial. Genes associated with many congenital forms of lipodystrophy have been identifed that may assist in diagnosis. Because of its rarity and heterogeneity, lipodystrophy may frequently be unrecognized or misdiagnosed, which is concerning because it is progressive and its complications are potentially life threatening. A basic diagnostic algorithm is proposed. Efective management of lipodystrophy includes lifestyle changes and aggressive, evidence-based treatment of comorbidities. Leptin replacement therapy (metreleptin) has been found to improve metabolic parameters in many patients with lipodystrophy. Metreleptin is approved in the United States as replacement therapy to treat the complications of leptin defciency in patients with congenital or acquired generalized lipodystrophy and has been submitted for approval in Europe. Conclusions : Here, we describe the clinical presentation of known types of lipodystrophy, present an algorithm for diferential diagnosis of lipodystrophy, and suggest specifc steps to recognize and diagnose lipodystrophy in the clinical setting.S

A Bell-Evans-Polanyi principle for molecular dynamics trajectories and its implications for global optimization

The Bell-Evans-Polanyi principle that is valid for a chemical reaction that proceeds along the reaction coordinate over the transition state is extended to molecular dynamics trajectories that in general do not cross the dividing surface between the initial and the final local minima at the exact transition state. Our molecular dynamics Bell-Evans-Polanyi principle states that low energy molecular dynamics trajectories are more likely to lead into the basin of attraction of a low energy local minimum than high energy trajectories. In the context of global optimization schemes based on molecular dynamics our molecular dynamics Bell-Evans-Polanyi principle implies that using low energy trajectories one needs to visit a smaller number of distinguishable local minima before finding the global minimum than when using high energy trajectories

Comparison of energy consumption and costs of different HEVs and PHEVs in European and American context

This paper will analyse on the one hand the potential of Plug in Hybrid electric Vehicles to significantly reduce fuel consumption and displace it torward various primary energies thanks to the electricity sector. On the other hand the total cost of ownership of two different PHEV architectures will be compared to a conventional cehicle and a HEV without external charging