An improved k-epsilon model for near wall turbulence

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence

Unveiling the Molecular Mechanisms Regulating the Activation of the ErbB Family Receptors at Atomic Resolution through Molecular Modeling and Simulations

The EGFR/ErbB/HER family of kinases contains four homologous receptor tyrosine kinases that are important regulatory elements in key signaling pathways. To elucidate the atomistic mechanisms of dimerization-dependent activation in the ErbB family, we have performed molecular dynamics simulations of the intracellular kinase domains of the four members of the ErbB family (those with known kinase activity), namely EGFR, ErbB2 (HER2) and ErbB4 (HER4) as well as ErbB3 (HER3), an assumed pseudokinase, in different molecular contexts: monomer vs. dimer, wildtype vs. mutant. Using bioinformatics and fluctuation analyses of the molecular dynamics trajectories, we relate sequence similarities to correspondence of specific bond-interaction networks and collective dynamical modes. We find that in the active conformation of the ErbB kinases (except ErbB3), key subdomain motions are coordinated through conserved hydrophilic interactions: activating bond-networks consisting of hydrogen bonds and salt bridges. The inactive conformations also demonstrate conserved bonding patterns (albeit less extensive) that sequester key residues and disrupt the activating bond network. Both conformational states have distinct hydrophobic advantages through context-specific hydrophobic interactions. The inactive ErbB3 kinase domain also shows coordinated motions similar to the active conformations, in line with recent evidence that ErbB3 is a weakly active kinase, though the coordination seems to arise from hydrophobic interactions rather than hydrophilic ones. We show that the functional (activating) asymmetric kinase dimer interface forces a corresponding change in the hydrophobic and hydrophilic interactions that characterize the inactivating interaction network, resulting in motion of the αC-helix through allostery. Several of the clinically identified activating kinase mutations of EGFR act in a similar fashion to disrupt the inactivating interaction network. Our molecular dynamics study reveals the asymmetric dimer interface helps progress the ErbB family through the activation pathway using both hydrophilic and hydrophobic interaction. There is a fundamental difference in the sequence of events in EGFR activation compared with that described for the Src kinase Hck

A Search for Moderate-Redshift Survivors from the Population of Luminous Compact Passive Galaxies at High Redshift

From a search of a ~ 2400 square degree region covered by both the SDSS and UKIDSS databases, we have attempted to identify galaxies at z ~ 0.5 that are consistent with their being essentially unmodified examples of the luminous passive compact galaxies found at z ~ 2.5. After isolating good candidates via deeper imaging, we further refine the sample with Keck moderate-resolution spectroscopy and laser-guide-star adaptive-optics imaging. For 4 of the 5 galaxies that so far remain after passing through this sieve, we analyze plausible star-formation histories based on our spectra in order to identify galaxies that may have survived with little modification from the population formed at high redshift. We find 2 galaxies that are consistent with having formed > 95% of their mass at z > 5. We attempt to estimate masses both from our stellar population determinations and from velocity dispersions. Given the high frequency of small axial ratios, both in our small sample and among samples found at high redshifts, we tentatively suggest that some of the more extreme examples of passive compact galaxies may have prolate morphologies.Comment: 9 pages, 5 figures, ApJ in press; error in Table 1 corrected, some new references adde

Optimal quantum algorithm for polynomial interpolation

We consider the number of quantum queries required to determine the coefficients of a degree-d polynomial over GF(q). A lower bound shown independently by Kane and Kutin and by Meyer and Pommersheim shows that d/2+1/2 quantum queries are needed to solve this problem with bounded error, whereas an algorithm of Boneh and Zhandry shows that d quantum queries are sufficient. We show that the lower bound is achievable: d/2+1/2 quantum queries suffice to determine the polynomial with bounded error. Furthermore, we show that d/2+1 queries suffice to achieve probability approaching 1 for large q. These upper bounds improve results of Boneh and Zhandry on the insecurity of cryptographic protocols against quantum attacks. We also show that our algorithm's success probability as a function of the number of queries is precisely optimal. Furthermore, the algorithm can be implemented with gate complexity poly(log q) with negligible decrease in the success probability. We end with a conjecture about the quantum query complexity of multivariate polynomial interpolation.Comment: 17 pages, minor improvements, added conjecture about multivariate interpolatio

Recounting Dyons in N=4 String Theory

A recently discovered relation between 4D and 5D black holes is used to derive weighted BPS black hole degeneracies for 4D N=4 string theory from the well-known 5D degeneracies. They are found to be given by the Fourier coefficients of the unique weight 10 automorphic form of the modular group Sp(2,Z). This result agrees exactly with a conjecture made some years ago by Dijkgraaf, Verlinde and Verlinde.Comment: 5 page

Counting Dyons in N=8 String Theory

A recently discovered relation between 4D and 5D black holes is used to derive exact (weighted) BPS black hole degeneracies for 4D N=8 string theory from the exactly known 5D degeneracies. A direct 4D microscopic derivation in terms of weighted 4D D-brane bound state degeneracies is sketched and found to agree.Comment: 10 page

Molecular Systems Biology of ErbB1 Signaling: Bridging the Gap through Multiscale Modeling and High-Performance Computing

The complexity in intracellular signaling mechanisms relevant for the conquest of many diseases resides at different levels of organization with scales ranging from the subatomic realm relevant to catalytic functions of enzymes to the mesoscopic realm relevant to the cooperative association of molecular assemblies and membrane processes. Consequently, the challenge of representing and quantifying functional or dysfunctional modules within the networks remains due to the current limitations in our understanding of mesoscopic biology, i.e., how the components assemble into functional molecular ensembles. A multiscale approach is necessary to treat a hierarchy of interactions ranging from molecular (nm, ns) to signaling (μm, ms) length and time scales, which necessitates the development and application of specialized modeling tools. Complementary to multiscale experimentation (encompassing structural biology, mechanistic enzymology, cell biology, and single molecule studies) multiscale modeling offers a powerful and quantitative alternative for the study of functional intracellular signaling modules. Here, we describe the application of a multiscale approach to signaling mediated by the ErbB1 receptor which constitutes a network hub for the cell’s proliferative, migratory, and survival programs. Through our multiscale model, we mechanistically describe how point-mutations in the ErbB1 receptor can profoundly alter signaling characteristics leading to the onset of oncogenic transformations. Specifically, we describe how the point mutations induce cascading fragility mechanisms at the molecular scale as well as at the scale of the signaling network to preferentially activate the survival factor Akt. We provide a quantitative explanation for how the hallmark of preferential Akt activation in cell-lines harboring the constitutively active mutant ErbB1 receptors causes these cell-lines to be addicted to ErbB1-mediated generation of survival signals. Consequently, inhibition of ErbB1 activity leads to a remarkable therapeutic response in the addicted cell lines