The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

The validity of the vanishing viscosity limit, that is, whether solutions of the Navier-Stokes equations modeling viscous incompressible flows converge to solutions of the Euler equations modeling inviscid incompressible flows as viscosity approaches zero, is one of the most fundamental issues in mathematical fluid mechanics. The problem is classified into two categories: the case when the physical boundary is absent, and the case when the physical boundary is present and the effect of the boundary layer becomes significant. The aim of this article is to review recent progress on the mathematical analysis of this problem in each category.Comment: To appear in "Handbook of Mathematical Analysis in Mechanics of Viscous Fluids", Y. Giga and A. Novotn\'y Ed., Springer. The final publication is available at http://www.springerlink.co

RICK/Rip2/CARDIAK mediates signalling for receptors of the innate and adaptive immune systems

The immune system consists of two evolutionarily different but closely related responses, innate immunity and adaptive immunity. Each of these responses has characteristic receptors-Toll-like receptors (TLRs) for innate immunity and antigen-specific receptors for adaptive immunity. Here we show that the caspase recruitment domain (CARD)-containing serine/threonine kinase Rip2 (also known as RICK, CARDIAK, CCK and Ripk2)(1-4) transduces signals from receptors of both immune responses. Rip2 was recruited to TLR2 signalling complexes after ligand stimulation. Moreover, cytokine production in Rip2-deficient cells was reduced on stimulation of TLRs with lipopolysaccharide, peptidoglycan and double-stranded RNA, but not with bacterial DNA, indicating that Rip2 is downstream of TLR2/3/4 but not TLR9. Rip2-deficient cells were also hyporesponsive to signalling through interleukin (IL)-1 and IL-18 receptors, and deficient for signalling through Nod proteins-molecules also implicated in the innate immune response. Furthermore, Rip2-deficient T cells showed severely reduced NF-kappaB activation, IL-2 production and proliferation on T-cell-receptor (TCR) engagement, and impaired differentiation to T-helper subtype 1 (T(H)1) cells, indicating that Rip2 is required for optimal TCR signalling and T-cell differentiation. Rip2 is therefore a signal transducer and integrator of signals for both the innate and adaptive immune systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62842/1/416194a.pd

Identification of tetrahydrocarbazoles as novel multifactorial drug candidates for treatment of Alzheimer's disease

Alzheimer's disease (AD) is a progressive neurodegenerative brain disorder and the most frequent cause of dementia. To date, there are only a few approved drugs for AD, which show little or no effect on disease progression. Impaired intracellular calcium homeostasis is believed to occur early in the cascade of events leading to AD. Here, we examined the possibility of normalizing the disrupted calcium homeostasis in the endoplasmic reticulum (ER) store as an innovative approach for AD drug discovery. High-throughput screening of a small-molecule compound library led to the identification of tetrahydrocarbazoles, a novel multifactorial class of compounds that can normalize the impaired ER calcium homeostasis. We found that the tetrahydrocarbazole lead structure, first, dampens the enhanced calcium release from ER in HEK293 cells expressing familial Alzheimer's disease (FAD)-linked presenilin 1 mutations. Second, the lead structure also improves mitochondrial function, measured by increased mitochondrial membrane potential. Third, the same lead structure also attenuates the production of amyloid-beta (A beta) peptides by decreasing the cleavage of amyloid precursor protein (APP) by beta-secretase, without notably affecting alpha- and gamma-secretase cleavage activities. Considering the beneficial effects of tetrahydrocarbazoles addressing three key pathological aspects of AD, these compounds hold promise for the development of potentially effective AD drug candidates

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field

Genomic-based-breeding tools for tropical maize improvement

Maize has traditionally been the main staple diet in the Southern Asia and Sub-Saharan Africa and widely grown by millions of resource poor small scale farmers. Approximately, 35.4 million hectares are sown to tropical maize, constituting around 59% of the developing worlds. Tropical maize encounters tremendous challenges besides poor agro-climatic situations with average yields recorded <3 tones/hectare that is far less than the average of developed countries. On the contrary to poor yields, the demand for maize as food, feed, and fuel is continuously increasing in these regions. Heterosis breeding introduced in early 90 s improved maize yields significantly, but genetic gains is still a mirage, particularly for crop growing under marginal environments. Application of molecular markers has accelerated the pace of maize breeding to some extent. The availability of array of sequencing and genotyping technologies offers unrivalled service to improve precision in maize-breeding programs through modern approaches such as genomic selection, genome-wide association studies, bulk segregant analysis-based sequencing approaches, etc. Superior alleles underlying complex traits can easily be identified and introgressed efficiently using these sequence-based approaches. Integration of genomic tools and techniques with advanced genetic resources such as nested association mapping and backcross nested association mapping could certainly address the genetic issues in maize improvement programs in developing countries. Huge diversity in tropical maize and its inherent capacity for doubled haploid technology offers advantage to apply the next generation genomic tools for accelerating production in marginal environments of tropical and subtropical world. Precision in phenotyping is the key for success of any molecular-breeding approach. This article reviews genomic technologies and their application to improve agronomic traits in tropical maize breeding has been reviewed in detail

An Extrapolated Crank Nicholson VMS-POD Methodfor Darcy Brinkman Equations.

This study presents a variational multiscale (VMS) reduced order model (ROM) based on proper orthogonal decomposition (POD) for the Darcy Brinkman equations. The idea of POD consists of extracting the dominant features of a data set, which are naturally assumed to represent Galerkin finite element solution of a partial differential equation. In this way, POD reduces the complexity of systems. Despite the widespread use of POD, it can perform quite poorly without any numerical stabilization. In this work, to obtain POD solution of the Darcy Brinkman system with double convection, we consider a projection-based VMS method as a numerical stabilization. The proposed scheme uses VMS type stabilization in POD for the velocity, temperature and concentration. For the fully discretization of the system, the finite element method is utilized for space variables and Crank Nicholson time discretization for time variables. The nonlinear term is treated with an extrapolated Crank Nicholson method. The numerical analysis for the VMS-POD is carried out and optimal error estimates are proved for each fluid variable. Numerical studies are performed to verify the theoretical findings

Enriched Finite Volume Approximations of the Plane-Parallel Flow at a Small Viscosity

We investigate viscous boundary layers of the plane-parallel flow, governed by the stationary Navier-Stokes equations under a certain symmetry. Following the analysis in Gie et al. (Annales de l&apos;Institut Henri Poincare C. Analyse Non Lineaire, 2018), we first construct the so-called corrector, which is an analytic approximation of the velocity vector field near the boundary. Then, by embedding the corrector function into the classical Finite Volume schemes, we construct the semi-analytic enriched Finite Volume schemes for the plane-parallel flow, and numerically verify that our new enriched schemes reduce significantly the computational error of classical schemes especially near the boundary, and hence produce more accurate approximations without introducing any finer mesh near the boundary