Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.Comment: 7 pages, 0 figure

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation $$-\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq \mathbb{R}^{N},\ N\geq 3,$$ where $\Omega$ is a radial domain (bounded or unbounded) and $u$ satisfies $u=0$ on $\partial \Omega$ if $\Omega \neq \mathbb{R}^{N}$ and $u\rightarrow 0$ as $\left| x\right| \rightarrow \infty$ if $\Omega$ is unbounded. The potential $V$ may be vanishing or unbounded at zero or at infinity and the nonlinearity $g$ may be superlinear or sublinear. If $g$ is sublinear, the case with $g\left( \left| \cdot \right| ,0\right) \neq 0$ is also considered.Comment: 29 pages, 8 figure

Solution of the tunneling-percolation problem in the nanocomposite regime

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolation-like and hopping-like behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter-particle electron tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any \textit{a priori} imposed cut-off in the inter-particle conductances, as usually done in the percolation-like interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary material (Appendix B

Performance Analysis of a Novel Air-based Cavity Receiver

AbstractIn this paper a new design of a novel CSP cavity receiver for parabolic trough collector is analyzed by means of an analytical Matlab model. The receiver, designed by the Swiss company Airlight Energy Manufacturing SA, is 212 m long consisting essentially of a feed pipe, a run-back pipe and 4608 helically coiled heat exchangers designed to capture the incident solar energy concentrated by a parabolic trough. The heat transfer fluid is air heated to temperatures above 600°C.The analytical Matlab model based on a pneumatic - electric circuit analogy was developed to assess the receiver performance in terms of mass flow rate distribution, pressure drop, air outlet temperature and thermal efficiency. A solution was proposed to approximately ensure the same mass flow rate for each cavity.Different skew angles for the incoming solar radiation were considered and the receiver geometry was optimized minimizing the pressure drop and the thermal losses through the runback pipe. The main requirement was to achieve, at the outlet section of the receiver, an air temperature of 650°C; therefore, the total inlet mass flow rate was tuned accordingly.The helically coiled heat exchanger and the receiver insulation sub-models were validated against accurate computational fluid dynamics simulations

Diffeomorphism-invariant properties for quasi-linear elliptic operators

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and non-degenerate coerciveness.Comment: 16 page

Non-radial sign-changing solutions for the Schroedinger-Poisson problem in the semiclassical limit

We study the existence of nonradial sign-changing solutions to the Schroedinger-Poisson system in dimension N>=3. We construct nonradial sign-changing multi-peak solutions whose peaks are displaced in suitable symmetric configurations and collapse to the same point. The proof is based on the Lyapunov-Schmidt reduction

On the stability of standing waves of Klein-Gordon equations in a semiclassical regime

We investigate the orbital stability and instability of standing waves for two classes of Klein-Gordon equations in the semi-classical regime.Comment: 9 page

Población Obrera Sociedad Explotadora de Tierra del Fuego: expresión espacial de paternalismo industrial en Punta Arenas

Vector de crecimiento económico en la Patagonia chilena, la gran industria ganadera desarrolló, a través de sus estancias, un modo particular de subdivisión del espacio rural y una estructura de apropiación singular. En contraste, y pese a la gran cantidad de mano de obra que empleó, la ganadería fue incapaz de ofrecer en las ciudades de Puerto Natales o Punta Arenas conjuntos de viviendas a gran escala para la fuerza de trabajo asociada a la diversidad de tareas del campo o de los frigoríficos. Así, la Población Obrera que aquí se analiza desde una perspectiva histórica, urbana y arquitectónica constituye una excepción que emerge tardíamente, cuando la Sociedad Explotadora de Tierra del Fuego decidió construir en la periferia de Punta Arenas un conjunto residencial en arriendo destinado a sus obreros y sus familias. Hábitat colectivo y expresión espacial de un paternalismo industrial, el conjunto de viviendas construido permitió estructurar un área de la ciudad y presentó en su arquitectura significativas innovaciones espaciales, funcionales y técnicas en el territorio de Magallanes