78 research outputs found
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 EconomĂa y Competitividad MTM2010-16401Junta de AndalucĂa 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 EducaciĂłn y Ciencia MTM2010-16401Junta de AndalucĂa 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 where 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 .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
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