Global wellposedness for a certain class of large initial data for the 3D Navier-Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier-Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier-Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm $B^{-1}_{\infty,\infty}$ that satisfies the conditions that we considered.Comment: 13 pages, updated references for v

Solar Flux Emergence Simulations

We simulate the rise through the upper convection zone and emergence through the solar surface of initially uniform, untwisted, horizontal magnetic flux with the same entropy as the non-magnetic plasma that is advected into a domain 48 Mm wide from from 20 Mm deep. The magnetic field is advected upward by the diverging upflows and pulled down in the downdrafts, which produces a hierarchy of loop like structures of increasingly smaller scale as the surface is approached. There are significant differences between the behavior of fields of 10 kG and 20 or 40 kG strength at 20 Mm depth. The 10 kG fields have little effect on the convective flows and show little magnetic buoyancy effects, reaching the surface in the typical fluid rise time from 20 Mm depth of 32 hours. 20 and 40 kG fields significantly modify the convective flows, leading to long thin cells of ascending fluid aligned with the magnetic field and their magnetic buoyancy makes them rise to the surface faster than the fluid rise time. The 20 kG field produces a large scale magnetic loop that as it emerges through the surface leads to the formation of a bipolar pore-like structure.Comment: Solar Physics (in press), 12 pages, 13 figur

Non-perturbative flow equations from continuous unitary transformations

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving one flow parameter and two system specific auxiliary variables. The implementation is non-perturbative as the partial differential equation involves a systematic expansion in fluctuations, controlled by the size of the system, rather than the coupling constant. The method is applied to the Lipkin model to construct a mapping which maps the non-interacting spectrum onto the interacting spectrum to a very high accuracy. This function is universal in the sense that the full spectrum for any (large) number of particles can be obtained from it. In a similar way expectation values for a large class of operators can be obtained, which also makes it possible to probe the stucture of the eigenstates.Comment: 24 pages, 13 figure

Research review: young people leaving care

This paper reviews the international research on young people leaving care. Set in the context of a social exclusion framework, it explores young people's accelerated and compressed transitions to adulthood, and discusses the development and classification of leaving care services in responding to their needs. It then considers the evidence from outcome studies and argues that adopting a resilience framework suggests that young people leaving care may fall into three groups: young people 'moving on', 'survivors' and 'victims'. In concluding, it argues that these three pathways are associated with the quality of care young people receive, their transitions from care and the support they receive after care

On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces

In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in \cite{Chae1}.Comment: 16page

Synthesis and electrochemical characterization of bimetallic ruthenium complexes with the bridging eta2(s,s)-1,3-butadiyne-1,4-diyl ligand

The bis(ruthenium)alkyne complex [cis-{RuCl (bpy)2(mu-CºC-)}]2 (1) was obtained by treatment of 1 equiv of either 1,4-bis(trimethylsilyl)-1,3-butadiyne or bis(trimetylsilyl)acetylene with 2 equiv of cis-[RuCl2(bpy)2].2H2O, NaF and NaBF4 salts in methanol/CH2Cl2 mixture (10/1) in 52% and 35% yields, respectively. ¹H, 13C{H} NMR and principally electrochemical analyses confirmed that the same product was obtained from the two reactions. Cyclic voltammetric analyses of (1) from 0 to 1.20 V displays two one-electron quasi-reversible oxidation peaks attributed to the Ru(II)/Ru(III) couple. The redox processes are separated by 520 mV, indicating a significant electronic communication between the two metallic centers.O complexo [cis-{RuCl(bpy)2(mi-CºC-)}] 2 (1) foi obtido pelo tratamento de 1 equive de 1,4-bis(trimetilsilil)-1,3-butadiino ou bis(trimetilsilil)acetileno com 2 equiv do complexo cis-[RuCl2(bpy)2].2H2O, NaF e NaBF4na mistura de solventes metanol/CH2Cl2 (10/1) com rendimentos de 52% e 35%, respectivamente. Análises de RMN de ¹H, 13C{H} e principalmente eletroquímica, confirmaram que o mesmo produto foi obtido dos dois métodos. Análise de (1) através de voltametria cíclica, no intervalo de potencial de 0 a 1,20 V mostrou dois picos de oxidação quasi-reversíveis referentes ao par redox Ru(II)/Ru(III). Os dois processos redox são separados por 520 V, indicando comunicação eletrônica significante entre os dois centros metálicos252256Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Bayesian Network Structure Learning with Permutation Tests

In literature there are several studies on the performance of Bayesian network structure learning algorithms. The focus of these studies is almost always the heuristics the learning algorithms are based on, i.e. the maximisation algorithms (in score-based algorithms) or the techniques for learning the dependencies of each variable (in constraint-based algorithms). In this paper we investigate how the use of permutation tests instead of parametric ones affects the performance of Bayesian network structure learning from discrete data. Shrinkage tests are also covered to provide a broad overview of the techniques developed in current literature.Comment: 13 pages, 4 figures. Presented at the Conference 'Statistics for Complex Problems', Padova, June 15, 201

Making a home, finding a job: investigating early housing and employment outcomes for young people leaving care

This paper presents findings from a new study of outcomes for young people leaving care funded by the Department for Education and Skills. It reports findings for a sample of 106 young people in relation to progress made in housing and employment some 12-15 months after leaving care. The generally poor employment outcomes of care leavers are acknowledged, but ingredients that make for success are also highlighted, including the value of settled care and post-care careers, sound career planning and, significantly, the value of delaying young people's transitions from care. Early career paths also interconnect with how young people fare in housing, in developing life skills and with other problems in their lives after leaving care. Housing outcomes were more encouraging and predominantly shaped by events after leaving care, and faring well in housing was the factor most closely associated with positive mental well-being in young people. Some groups that are at risk of faring badly are identified, including young people with mental-health problems, young people with persistent offending or substance misuse problems and, in some respects, young disabled people. The implications of these findings for leaving care services are considered

Spin Susceptibility of a 2D Electron System in GaAs towards the Weak Interaction Region

We determine the spin susceptibility $\chi$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a GaAs/AlGaAs heterostructure. The band structure effects, modifying mass and g-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime. When properly normalized, $\chi$ decreases monotonically from 3 to 1.1 with increasing density over our experimental range from 0.1 to $4\times10^{11} cm^{-2}$. In the high density limit, $\chi$ tends correctly towards $\chi\to 1$ and compare well with recent theory.Comment: Submitted to Physical Review