The shallow water approximation applied to the aluminium electrolysis process

The industrial production of aluminium is an electrolysis process where two superposed horizontal liquid layers are subjected to a mainly vertical electric current supplied by carbon electrodes. The lower layer consists of molten aluminium and lies on the cathode. The upper layer is the electrolyte and is covered by the anode. The interface between the two layers is often perturbed, leading to oscillations, or waves, similar to the waves on the surface of seas or lakes. The presence of electric currents and the resulting magnetic field are responsible for electromagnetic (Lorentz) forces within the fluid, which can amplify these oscillations and have an adverse influence on the process. The electrolytic bath vertical to horizontal aspect ratio is such, that it is advantageous to use the shallow water equations to model the interface motion. These are the depth-averaging the Navier-Stokes equations so that nonlinear and dispersion terms may be taken into account. Although these terms are essential to the prediction of wave dynamics, they are neglected in most of the literature on interface instabilities in aluminium reduction cells where only the linear theory is usually considered. The unknown variables are the two horizontal components of the fluid velocity, the height of the interface and the electric potential. In this application, a finite volume resolution of the double-layer shallow water equations including the electromagnetic sources has been developed, for incorporation into a generic three-dimensional computational fluid dynamics code that also deals with heat transfer within the cell.

A finite-volume shallow layer method for the MHD instabilities in an aluminium production cell

An electrolytic cell for Aluminium production contains molten metal and molten electrolyte, which are subject to high dc-currents and magnetic fields. Lorentz forces arising from the cross product of current and magnetic field may amplify natural gravity waves at the interface between the two fluids, leading to short circuits in extreme cases. The external magnetic field and current distribution in the production cell is computed through a detailed finite element analysis at Torino Polytechnic. The results are then used to compute the magnetohydrodynamic and thermal effects in the aluminium/electrolyte bath. Each cell has lateral dimensions of 6m x 2m, whilst the bath depth is only 30cm. the electrically resistive electrolyte path, which is critical in the operation of the cell, has layer depth of only a few centimetres below each carbon anode. Because the shallow dimensions of the liquid layer a finite-volume shallow-layer technique has been used at Greenwich to compute the resulting flow-field and interface perturbations. The information obtained from this method, i.e. depth averaged velocities and aluminium/electrolyte interface position is then embedded in the three-dimensional finite volume code PHYSICA and will be used to compute the heat transfer and phase change in the cell.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.

Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0Lorentz-type spaces.

Railgun

Com a presente evolução das railguns na Marinha dos Estados Unidos da América e possível instalação em seus navios num futuro muito próximo, outras marinhas se seguirão. Creio que será do interesse da Marinha Portuguesa acompanhar esta evolução tecnológica, considerando as vantagens que advém da adoção deste tipo de armamento. Neste documento são abordados os princípios básicos subjacentes ao funcionamento da railgun, com principal foco nas questões eletrodinâmicas. Pretende-se adquirir familiaridade com este novo tipo de armamento através do estudo crítico dos seus princípios de funcionamento. O princípio básico de funcionamento de uma railgun, à primeira vista, parece bastante simples, à luz da aplicação imediata da expressão da força de Lorentz sobre um condutor percorrido por corrente elétrica. No entanto, tudo se torna mais complicado no caso de uma variação rápida dos parâmetros envolvidos (regime transitório), que exige uma análise mais aprofundada do comportamento da corrente, campos elétrico e magnético, e todos os materiais envolvidos neste sistema. Este trabalho envolveu ainda a construção de duas railguns, uma primeira de dimensões mais pequenas para ganhar familiaridade com o sistema, e uma última de dimensões de laboratório na qual foram feitos vários disparos para testar diferentes tipos de material e dimensões de projétil. Em suma, é demonstrado neste documento uma análise, no domínio do tempo, da distribuição espacial do campo eletromagnético, corrente elétrica e consequente fluxo de energia, complementados por uma parte experimental.

Measurement of the inclusive and differential t/t cross sections at 13 TeV in the all-jets boosted regime with CMS

The t/t production cross section is measured with the CMS detector in the all-jets channel in $pp$ collisions at the centre-of-mass energy of 13 TeV. The analysis is based on the study of t/t events in the boosted topology, namely events in which decay products of the quark top have a high Lorentz boost and are thus reconstructed in the detector as a single, wide jet. The data sample used in this analysis corresponds to an integrated luminosity of 2.53 fb-1. The inclusive cross section is found to be sigma(t/t) = 727 +- 46 (stat.) +115-112 (sys.) +- 20~(lumi.) pb, a value which is consistent with the theoretical predictions. The differential, detector-level cross section is measured as a function of the transverse momentum of the leading jet and compared to the QCD theoretical predictions. Finally, the differential, parton-level cross section is reported, measured as a function of the transverse momentum of the leading parton, extrapolated to the full phase space and compared to the QCD predictions.

Search for ultrarelativistic magnetic monopoles with the Pierre Auger observatory

We present a search for ultrarelativistic magnetic monopoles with the Pierre Auger observatory. Such particles, possibly a relic of phase transitions in the early Universe, would deposit a large amount of energy along their path through the atmosphere, comparable to that of ultrahigh-energy cosmic rays (UHECRs). The air-shower profile of a magnetic monopole can be effectively distinguished by the fluorescence detector from that of standard UHECRs. No candidate was found in the data collected between 2004 and 2012, with an expected background of less than 0.1 event from UHECRs. The corresponding 90% confidence level (C.L.) upper limits on the flux of ultrarelativistic magnetic monopoles range from 10(-1)9 (cm(2) sr s)(-1) for a Lorentz factor gamma = 10(9) to 2.5 x 10(-21) (cm(2) sr s)(-1) for gamma = 10(12). These results-the first obtained with a UHECR detector-improve previously published limits by up to an order of magnitude.

Covariant Spectator Theory and Hadron Structure

We present the first results of a study on meson spectroscopy using a covariant formalism based on the Covariant Spectator Theory. Our approach is derived directly in Minkowski space and it approximates the Bethe–Salpeter equation by taking effectively into account the contributions from both ladder and crossed ladder diagrams in the $q\bar{q}$ interaction kernel. A general Lorentz structure of the kernel is tested and chiral constraints on the kernel are discussed. Results for the pion form factor are also presented.

Covariant Spectator Theory of heavy–light and heavy mesons and the predictive power of covariant interaction kernels

The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy–light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin–orbit and tensor forces and do not allow to separate the spin–spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark–antiquark interactions.