Weak Solutions to a Nonuniformly Elliptic PDE System in the Harmonic Regime

We study the existence of weak solutions to a nonlinear strongly coupled parabolic–elliptic PDEs arising in the heating induction-conduction process of steel hardening. In this setting, our major concern is to consider the case when the electric conductivity is nonuniformly elliptic which, together with a right hand side in L1 in the energy balance equation, yields to a difficult theoretical situation. The existence result gives a weak solution to a similar PDEs system where the energy balance equation has been perturbed by a measure term.Ministerio de Economía y Competitividad MTM2010-16401Junta de Andalucía FQM-31

Analysis and numerical simulation of an induction–conduction model arising in steel heat treating

The goal of steel heat treating is to create a hard enough part over certain critical surfaces or volumes of the workpiece and at the same time keeping its ductility properties all over the rest of the workpiece. Weconsider a mathematical model for the description of the heating–cooling industrial process of a steel workpiece. This model consists of a nonlinear coupled partial differential system of equations involving the electric potential, the magnetic vector potential, the temperature, together with a system of ordinary differential equations for the steel phase fractions. Due to the different time scales related to the electric potential and the magnetic vector potential versus the temperature, we introduce the harmonic regime, leading to a new system of nonlinear PDEs. Finally, we have carried out some 2D numerical simulations of this heating–cooling industrial process.Ministerio de Educación y Ciencia MTM2010-16401Junta de Andalucía FQM-31

Bayesian multitrait kernel methods improve multienvironment genome-based prediction

When multitrait data are available, the preferred models are those that are able to account for correlations between phenotypic traits because when the degree of correlation is moderate or large, this increases the genomic prediction accuracy. For this reason, in this article, we explore Bayesian multitrait kernel methods for genomic prediction and we illustrate the power of these models with three-real datasets. The kernels under study were the linear, Gaussian, polynomial, and sigmoid kernels; they were compared with the conventional Ridge regression and GBLUP multitrait models. The results show that, in general, the Gaussian kernel method outperformed conventional Bayesian Ridge and GBLUP multitrait linear models by 2.2–17.45% (datasets 1–3) in terms of prediction performance based on the mean square error of prediction. This improvement in terms of prediction performance of the Bayesian multitrait kernel method can be attributed to the fact that the proposed model is able to capture nonlinear patterns more efficiently than linear multitrait models. However, not all kernels perform well in the datasets used for evaluation, which is why more than one kernel should be evaluated to be able to choose the best kernel

Loop quantum gravity and light propagation

Within loop quantum gravity we construct a coarse-grained approximation for the Einstein-Maxwell theory that yields effective Maxwell equations in flat spacetime comprising Planck scale corrections. The corresponding Hamiltonian is defined as the expectation value of the electromagnetic term in the Einstein-Maxwell Hamiltonian constraint, regularized a la Thiemann, with respect to a would-be semiclassical state. The resulting energy dispersion relations entail Planck scale corrections to those in flat spacetime. Both the helicity dependent contribution of Gambini and Pullin [GP] and, for a value of a parameter of our approximation, that of Ellis et. al. [ELLISETAL] are recovered. The electric/magnetic asymmetry in the regularization procedure yields nonlinearities only in the magnetic sector which are briefly discussed. Observations of cosmological Gamma Ray Bursts might eventually lead to the needed accuracy to study some of these quantum gravity effects.Comment: Latex, 45 pages, shorter abstract, additional reference

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.Comment: 21 pages, 14 figure

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

B cell-specific conditional expression of Myd88(p.L252P) leads to the development of diffuse large B cell lymphoma in mice

The adaptor protein MYD88 is critical to relay activation of Toll-like receptor signaling to NF-{kappa}B activation.MYD88 mutations, particularly the p.L265P mutation, have been described in numerous distinct B cell malignancies, including diffuse large B cell lymphoma (DLBCL). 29% of activated B cell (ABC)-type DLBCL, which is characterized by constitutive activation of the NF-{kappa}B pathway, carry the p.L265P mutation. In addition, ABC-DLBCL frequently displays focal copy number gains affecting BCL2. Here, we generated a novel mouse model, in which Cre-mediated recombination, specifically in B cells, leads to the conditional expression of Myd88(p.L252P)(the orthologous position of the human MYD88(p.L265P) mutation) from the endogenous locus. These animals develop a lympho-proliferative disease, and occasional transformation into clonal lymphomas. The clonal disease displays morphological and immunophenotypical characteristics of ABC-DLBCL. Lymphomagenesis can be accelerated by crossing in a further novel allele, which mediates conditional overexpression ofBCL2 Cross-validation experiments in human DLBCL samples revealed that bothMYD88andCD79Bmutations are substantially enriched in ABC-DLBCL, compared to germinal center B cell DLBCL. Furthermore, analyses of human DLBCL genome sequencing data confirmed that BCL2 amplifications frequently co-occur with MYD88 mutations, further validating our approach. Lastly,in silicoexperiments revealed that particularly MYD88-mutant ABC-DLBCL cells display an actionable addiction to BCL2. Altogether, we generated a novel autochthonous mouse model of ABC-DLBCL, which could be used as a preclinical platform for the development and validation of novel therapeutic approaches for the treatment of ABC-DLBCL