Novel Boron-10-based detectors for Neutron Scattering Science

Nowadays neutron scattering science is increasing its instrumental power. Most of the neutron sources in the world are pushing the development of their technologies to be more performing. The neutron scattering development is also pushed by the European Spallation Source (ESS) in Sweden, a neutron facility which has just started construction. Concerning small area detectors (1m^2), the 3He technology, which is today cutting edge, is reaching fundamental limits in its development. Counting rate capability, spatial resolution and cost-effectiveness, are only a few examples of the features that must be improved to fulfill the new requirements. On the other hand, 3He technology could still satisfy the detector requirements for large area applications (50m^2), however, because of the present 3He shortage that the world is experiencing, this is not practical anymore. The recent detector advances (the Multi-Grid and the Multi-Blade prototypes) developed in the framework of the collaboration between the Institut Laue-Langevin (ILL) and ESS are presented in this manuscript. In particular two novel 10B-based detectors are described; one for large area applications (the Multi-Grid prototype) and one for application in neutron refectometry (small area applications, the Multi-Blade prototype)

An optimal bound for nonlinear eigenvalues and torsional rigidity on domains with holes

In this paper we prove an optimal upper bound for the first eigenvalue of a Robin-Neumann boundary value problem for the p-Laplacian operator in domains with convex holes. An analogous estimate is obtained for the corresponding torsional rigidity problem

A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

Given $1\le q \le 2$ and $\alpha\in\mathbb R$, we study the properties of the solutions of the minimum problem $$\lambda(\alpha,q)=\min\left\{\dfrac{\displaystyle\int_{-1}^{1}|u'|^{2}dx+\alpha\left|\int_{-1}^{1}|u|^{q-1}u\, dx\right|^{\frac2q}}{\displaystyle\int_{-1}^{1}|u|^{2}dx}, u\in H_{0}^{1}(-1,1),\,u\not\equiv 0\right\}.$$ In particular, depending on $\alpha$ and $q$, we show that the minimizers have constant sign up to a critical value of $\alpha=\alpha_{q}$, and when $\alpha>\alpha_{q}$ the minimizers are odd

Heat fluctuations in Ising models coupled with two different heat baths

Monte Carlo simulations of Ising models coupled to heat baths at two different temperatures are used to study a fluctuation relation for the heat exchanged between the two thermostats in a time $\tau$. Different kinetics (single--spin--flip or spin--exchange Kawasaki dynamics), transition rates (Glauber or Metropolis), and couplings between the system and the thermostats have been considered. In every case the fluctuation relation is verified in the large $\tau$ limit, both in the disordered and in the low temperature phase. Finite-$\tau$ corrections are shown to obey a scaling behavior.Comment: 5 pages, 2 figures. To be published in Journal of Physics A: Mathematical and Theoretical as fast track communicatio

Singular behavior of fluctuations in a relaxation process

Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting $P(M)$ as a thermodynamic potential of a dual system obtained from the original one by applying a constraint, we discuss how the non-analytical point of $P(M)$ is the counterpart of a phase-transition in the companion system. We show the generality of such mechanism by considering both the system in equilibrium or in the non-equilibrium state following a temperature quench.Comment: 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:1404.397

Heat exchanges in coarsening systems

This paper is a contribution to the understanding of the thermal properties of aging systems where statistically independent degrees of freedom with largely separated timescales are expected to coexist. Focusing on the prototypical case of quenched ferromagnets, where fast and slow modes can be respectively associated to fluctuations in the bulk of the coarsening domains and to their interfaces, we perform a set of numerical experiments specifically designed to compute the heat exchanges between different degrees of freedom. Our studies promote a scenario with fast modes acting as an equilibrium reservoir to which interfaces may release heat through a mechanism that allows fast and slow degrees to maintain their statistical properties independent.Comment: 12 pages, 8 figure

Sharp estimates for the first pp-Laplacian eigenvalue and for the pp-torsional rigidity on convex sets with holes

We study, in dimension $n\geq2$, the eigenvalue problem and the torsional rigidity for the $p$-Laplacian on convex sets with holes, with external Robin boundary conditions and internal Neumann boundary conditions. We prove that the annulus maximizes the first eigenvalue and minimizes the torsional rigidity when the measure and the external perimeter are fixed.Comment: 17 page