Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries

The numerical analysis of spectral methods when non-constant coefficients appear in the equation, either due to the original statement of the equations or to take into account the deformed geometry, is presented. Particular attention is devoted to the optimality of the discretization even for low values of the discretization parameter. The effect of some overintegration is also addressed, in order to possibly improve the accuracy of the discretization

Analysis of Iterative Methods for the Steady and Unsteady Stokes Problem: Application to Spectral Element Discretizations

A new and detailed analysis of the basic Uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady Stokes operator is presented. The paper focuses on the following new aspects: explicit construction of the Uzawa pressure-operator spectrum for a semiperiodic model problem; general relationship of the convergence rate of the Uzawa procedure to classical inf-sup discretization analysis; and application of the method to high-order variational discretization

Parallelization in time through tensor-product space-time solvers

In this note, we extend the fast tensor-product algorithm for the simulation of time-dependent partial differential equations. We use the natural tensorization of the space-time domain to propose, after discretization, a set of independent problems, each one with the complexity of a single steady problem. This allows for an efficient parallel implementation that is already interesting on small architectures, but that can also be combined with standard domain-decomposition-based algorithms providing a further direction of parallelism on large computer platforms. Preliminary numerical simulations are presented for a one-dimensional unsteady heat equation

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

We present a parareal in time algorithm for the simulation of neutron diffusion transient model. The method is made efficient by means of a coarse solver defined with large time steps and steady control rods model. Using finite element for the space discretization, our implementation provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch-Maurer-Werner (LMW) benchmark [1]

Prospects for Dark Energy Evolution: a Frequentist Multi-Probe Approach

A major quest in cosmology is the understanding of the nature of dark energy. It is now well known that a combination of cosmological probes is required to break the underlying degeneracies on cosmological parameters. In this paper, we present a method, based on a frequentist approach, to combine probes without any prior constraints, taking full account of the correlations in the parameters. As an application, a combination of current SNIa and CMB data with an evolving dark energy component is first compared to other analyses. We emphasise the consequences of the implementation of the dark energy perturbations on the result for a time varying equation of state. The impact of future weak lensing surveys on the measurement of dark energy evolution is then studied in combination with future measurements of the cosmic microwave background and type Ia supernovae. We present the combined results for future mid-term and long-term surveys and confirm that the combination with weak lensing is very powerful in breaking parameter degeneracies. A second generation of experiment is however required to achieve a 0.1 error on the parameters describing the evolution of dark energy.Comment: Submitted to Astronomy & Astrophysics 14 pages, 8 figure

Tyrosine phosphorylation controls brassinosteroid receptor activation by triggering membrane release of its kinase inhibitor

Receptor tyrosine kinases control many critical processes in metazoans, but these enzymes appear to be absent in plants. Recently, two Arabidopsis receptor kinases-BRASSINOSTEROID INSENSITIVE 1 (BRI1) and BRI1-ASSOCIATED KINASE1 (BAK1), the receptor and coreceptor for brassinosteroids-were shown to autophosphorylate on tyrosines. However, the cellular roles for tyrosine phosphorylation in plants remain poorly understood. Here, we report that the BRI1 KINASE INHIBITOR 1 (BKI1) is tyrosine phosphorylated in response to brassinosteroid perception. Phosphorylation occurs within a reiterated [KR][KR] membrane targeting motif, releasing BKI1 into the cytosol and enabling formation of an active signaling complex. Our work reveals that tyrosine phosphorylation is a conserved mechanism controlling protein localization in all higher organisms

lHuman cytotoxic T lymphocytes with reduced sensitivity to Fas-induced apoptosis

Effector-memory T cells expressing Fas (Apo-1/CD95) are switched to an apoptotic program by cross-linking with Fas-ligand (FasL). Consequently, tumors that express FasL can induce apoptosis of infiltrating Fas-positive T lymphocytes and subdue any antitumor host immune response. Since Epstein-Barr virus (EBV)-associated tumors such as Hodgkin lymphoma (HL) and nasopharyngeal carcinoma (NPC) express FasL, we determined whether EBV-specific cytotoxic T lymphocytes (EBV-CTLs) could be modified to resist this evasion strategy. We show that long-term down-modulation of Fas can be achieved in EBV-CTLs by transduction with small interfering RNA (siRNA) encoded in a retrovirus. Modified T cells resisted Fas/FasL-mediated apoptosis compared with control cells and showed minimal cleavage of the caspase3 substrate poly(ADP-ribose) polymerase (PARP) protein after Fas engagement. Prolonged Fas stimulation selected a uniformly Fas(low) and FasL resistant population. Removal of responsiveness to this single death signal had no other discernible effects on EBV-CTLs. In particular, it did not lead to their autonomous growth since the modified EBV-CTLs remained polyclonal, and their survival and proliferation retained dependence on antigen-specific stimulation and on the presence of other physiologic growth signals. EBV-CTLs with knocked down Fas should have a selective functional and survival advantage over unmodified EBV-CTLs in the presence of tumors expressing FasL and may be of value for adoptive cellular therapy. (c) 2005 by The American Society of Hematology