Probabilistic study of the speed of approach to equilibrium for an inelastic Kac model

This paper deals with a one--dimensional model for granular materials, which boils down to an inelastic version of the Kac kinetic equation, with inelasticity parameter $p>0$. In particular, the paper provides bounds for certain distances -- such as specific weighted $\chi$--distances and the Kolmogorov distance -- between the solution of that equation and the limit. It is assumed that the even part of the initial datum (which determines the asymptotic properties of the solution) belongs to the domain of normal attraction of a symmetric stable distribution with characteristic exponent \a=2/(1+p). With such initial data, it turns out that the limit exists and is just the aforementioned stable distribution. A necessary condition for the relaxation to equilibrium is also proved. Some bounds are obtained without introducing any extra--condition. Sharper bounds, of an exponential type, are exhibited in the presence of additional assumptions concerning either the behaviour, near to the origin, of the initial characteristic function, or the behaviour, at infinity, of the initial probability distribution function

Antiferro-quadrupole resonance in CeB6

We report experimental observation of a new type of magnetic resonance caused by orbital ordering in a strongly correlated electronic system. Cavity measurements performed on CeB6 single crystals in a frequency range 60-100 GHz show that a crossing of the phase boundary TQ(B) between the antiferro-quadrupole and paramagnetic phases gives rise to development at T <TQ(B) of a magnetic resonance. The observed mode is gapless and correspond to g-factor 1.62.Comment: 2 pages, Submitted to SCES05 proceeding

Magnetic resonance in cerium hexaboride caused by quadrupolar ordering

Experimental evidence of the magnetic resonance in the antiferro-quadrupole phase of CeB6 is reported. We have shown that below orbital ordering temperature a new magnetic contribution from localized magnetic moments (LMM) emerge and gives rise to observed resonant phenomenon. This behaviour is hardly possible to expect in dense Kondo system, where LMM should vanish al low temperatures rather than emerge. From the other hand, in the quadrupole ordering concept, where magnetism of Ce magnetic ions is solely accounted, is difficult to explain splitting of magnetisation into components having different physical nature. Therefore an adequate theory explaining magnetic properties of CeB6 including magnetic resonance and orbital ordering appears on the agenda.Comment: 4 pages, Accepted paper for MISM05 proceeding

Proof of projective Lichnerowicz conjecture for pseudo-Riemannian metrics with degree of mobility greater than two

We prove an important partial case of the pseudo-Riemannian version of the projective Lichnerowicz conjecture stating that a complete manifold admitting an essential group of projective transformations is the round sphere (up to a finite cover).Comment: 32 pages, one .eps figure. The version v1 has a misprint in Theorem 1: I forgot to write the assumption that the degree of mobility is greater than two. The versions v3, v4 have only cosmetic changes wrt v

Soliton molecules in trapped vector Nonlinear Schrodinger systems

We study a new class of vector solitons in trapped Nonlinear Schrodinger systems modelling the dynamics of coupled light beams in GRIN Kerr media and atomic mixtures in Bose-Einstein condensates. These solitons exist for different spatial dimensions, their existence is studied by means of a systematic mathematical technique and the analysis is made for inhomogeneous media

Landscape equivalent of the shoving model

It is shown that the shoving model expression for the average relaxation time of viscous liquids follows largely from a classical "landscape" estimation of barrier heights from curvature at energy minima. The activation energy involves both instantaneous bulk and shear moduli, but the bulk modulus contributes less than 8% to the temperature dependence of the activation energy. This reflects the fact that the physics of the two models are closely related.Comment: 4 page

An interdisciplinary overview of levee setback benefits: Supporting spatial planning and implementation of riverine nature-based solutions

Nature-based solutions (NbS, and related concepts like natural infrastructure, Ecosystem-based Adaptation, and green infrastructure) are increasingly recognized as multi-benefit strategies for addressing the critical sustainability challenges of the Anthropocene, including the climate emergency and biodiversity crisis. Mainstreaming NbS in professional practice requires strategic, landscape-level planning integrating multiple sources of benefits and their synergies and trade-offs. Levee setbacks (LS) are among the best-studied riverine NbS with recognized benefits for flood risk management, drought resilience, water quality management, recreational opportunities, and ecological restoration for biodiversity. Although awareness of the multifarious benefits of LS as forms of Natural Capital is growing, implementation remains ad-hoc and opportunistic. To address this critical implementation gap for one major example of NbS, we review and synthesize literature across diverse disciplines to provide an overview of the primary social, economic, and ecological mechanisms that affect the co-benefit delivery of LS projects. Next, to make this information relevant to NbS practitioners, we link these mechanisms to spatial metrics that can be used to approximate the relative magnitude of project benefits and costs across these mechanisms. Finally, we highlight examples of key synergies and trade-offs among benefits that should be considered for LS planning. This synthetic approach is intended to familiarize readers with the diverse potential benefits of LS, and provide an understanding of how to select and prioritize potential sites for further study and implementation. Synergies and trade-offs among important benefit drivers abound, and social equity concerns will be paramount in ensuring the successful implementation of LS and other NbS in the future. This article is categorized under: Engineering Water > Sustainable Engineering of Water Engineering Water > Planning Water Water and Life > Nature of Freshwater Ecosystems. © 2024 The Author(s). WIREs Water published by Wiley Periodicals LLC.This research was conducted as part of the Network for Engineering with Nature (N-EWN, https://n-ewn.org). This work was supported by the US Army Corps of Engineers Engineering With Nature® Initiative through Cooperative Ecosystem Studies Unit Agreement W912HZ-20-2-0031. Charles B. van Rees was partially supported by NASA Ecological Conservation Grant Number 80NSSC23K1562. Damon M. Hall and Angela J. Catalano supported by the Missouri Department of Natural Resources. The use of products or trade names does not represent an endorsement by either the authors or the N-EW

Proton-Antiproton Annihilation into a Lambda_c-Antilambda_c Pair

The process p-pbar -> Lambda_c-Antilambda_c is investigated within the handbag approach. It is shown that the dominant dynamical mechanism, characterized by the partonic subprocess u-ubar -> c-cbar factorizes in the sense that only the subprocess contains highly virtual partons, a gluon to lowest order of perturbative QCD, while the hadronic matrix elements embody only soft scales and can be parameterized in terms of helicity flip and non-flip generalized parton distributions. Modelling these parton distributions by overlaps of light-cone wave functions for the involved baryons we are able to predict cross sections and spin correlation parameters for the process of interest.Comment: 39 pages, 7 figures, problems with printout of figures resolved, Ref. 33 and referring sentences in section 4 change

Atom trapping and two-dimensional Bose-Einstein condensates in field-induced adiabatic potentials

We discuss a method to create two-dimensional traps as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio frequency-induced adiabatic potentials. These are shown to form a versatile and robust tool to generate novel trapping potentials. Our shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping-stones to prepare atoms in highly-excited trap eigenstates or to study `collapse and revival phenomena'. Their creation requires gravitational effects to be compensated by applying additional optical dipole potentials. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We demonstrate the loading process for such a trap and examine experimental conditions under which a 2D condensate may be prepared.Comment: 16 pages, 10 figure