Spectral methods for compressible reactive flows

High order simulations are necessary in order to capture fine details in resolving supersonic reactive flows. However, high Mach number compressible flows feature sharp gradients and discontinuities, which present a challenge to successful simulations using high order methods. Spectral methods have proven a powerful tool in simulation of incompressible turbulent flows, and recent advances allow the application of spectral methods to compressible reactive flows. We review the recent advances in the theory and application of spectral methods which allow stable computations of discontinuous phenomena, and the recovery of high order information via postprocessing, and present applications of high Mach number reactive flows. To cite this article: D. Gottlieb, S. Gottlieb, C. R. Mecanique 333 (2005).     

On finite unions of ideals and cosets

Abstract

Although it is well known that the growth of Thompson's group F is exponential, the exact growth function is still unknown. Elements of its submonoid of positive words can be described using a binary rooted tree, whose norm can be computed assigning weights to each caret. Combining this fact with a combinatorial argument, the growth function of the submonoid is computed and thus providing a first step in the computation of the growth function of the group, as well as a lower bound for the growth rate for the group.     

Insights into the N-terminal Cu(II) and Cu(I) binding sites of the human copper transporter CTR1

Abstract

Copper transporter 1 (CTR1) is the main copper transporter in the eukaryotic system. CTR1 has several important roles: It binds Cu(II) ions that are present in the blood; it reduces those Cu(II) ions to Cu(I); and it subsequently transfers Cu(I) to the cytoplasmic domain, where the ion is delivered to various cellular pathways. Here, we seek to identify CTR1 binding sites for Cu(II) and Cu(I) and to shed light on the Cu(II)-to-Cu(I) reduction process. We focus on the first 14 amino acids of CTR1. This N-terminal segment is rich with histidine and methionine residues, which are known to bind Cu(II) and Cu(I), respectively; thus, this region has been suggested to have an important function in recruiting Cu(II) and reducing it to Cu(I). We utilize electron paramagnetic resonance (EPR) spectroscopy together with nuclear magnetic resonance (NMR) and UV-VIS spectroscopy and alanine substitution to reveal Cu(II) and Cu(I) binding sites in the focal 14-amino-acid segment. We show that H5 and H6 directly coordinate to Cu(II), whereas M7, M9, and M12 are involved in Cu(I) binding. This research is another step on the way to a complete understanding of the cellular copper regulation mechanism in humans.     

Atomic‐Level Alloying and De‐alloying in Doped Gold Nanoparticles

Atomically precise alloying and de‐alloying processes for the formation of Ag–Au and Cu–Au nanoparticles of 25‐metal‐atom composition (referred to as Ag_xAu_25?x(SR)₁₈ and Cu_xAu_25?x(SR)₁₈, in which R=CH₂CH₂Ph) are reported. The identities of the particles were determined by matrix‐assisted laser desorption ionization mass spectroscopy (MALDI‐MS). Their structures were probed by fragmentation analysis in MALDI‐MS and comparison with the icosahedral structure of the homogold Au₂₅(SR)₁₈ nanoparticles (an icosahedral Au₁₃ core protected by a shell of Au₁₂(SR)₁₈). The Cu and Ag atoms were found to preferentially occupy the 13‐atom icosahedral sites, instead of the exterior shell. The number of Ag atoms in Ag_xAu_25?x(SR)₁₈ (x=0–8) was dependent on the molar ratio of Ag^I/Au^III precursors in the synthesis, whereas the number of Cu atoms in Cu_xAu_25?x(SR)₁₈ (x=0–4) was independent of the molar ratio of Cu^II/Au^III precursors applied. Interestingly, the Cu_xAu_25?x(SR)₁₈ nanoparticles show a spontaneous de‐alloying process over time, and the initially formed Cu_xAu_25?x(SR)₁₈ nanoparticles were converted to pure Au₂₅(SR)₁₈. This de‐alloying process was not observed in the case of alloyed Ag_xAu_25?x(SR)₁₈ nanoparticles. This contrast can be attributed to the stability difference between Cu_xAu_25?x(SR)₁₈ and Ag_xAu_25?x(SR)₁₈ nanoparticles. These alloyed nanoparticles are promising candidates for applications such as catalysis.     

The steady shear viscosity of filled polymeric liquids described by a linear superposition of two relaxation mechanisms

Filled polymeric liquids often exhibit apparent yielding and shear thinning in steady shear flow. Yielding results from non-hydrodynamic particle—particle interactions, while shear thinning results from the non-Newtonian behavior of the polymer melt. A simple equation, based on the linear superposition of two relaxation mechanisms, is proposed to describe the viscosity of filled polymer melts over a wide range of shear rates and filler volume fraction.The viscosity is written as the sum of two generalized Newtonian liquid models. The resulting equation can describe a wide range of shear-thinning viscosity curves, and a hierarchy of equations is obtained by simplifying the general case. Some of the parameters in the equation can be related to the properties of the unfilled liquid and the solid volume fraction. One adjustable parameter, a yield stress, is necessary to describe the viscosity at low rates where non-hydrodynamic particle—particle interaction dominate. At high shear rates, where particle—particle interactions are dominated by interparticle hydrodynamics, no adjustable parameters are necessary. A single equation describes both the high and low shear rate regimes. Predictions of the equation closely fit published viscosity data of filled polymer melts. n power-law index - n ₁,n ₂ power-law index of first (second) term - shear rate - steady shear viscosity - ₀ zero-shear rate viscosity - _{0, 1}, _{0, 2} zero-shear rate viscosity of first (second) term - time constant - ₁, ₂ time constant of first (second) term - µ _r relative viscosity of filled Newtonian liquid - ₀ yield stress - ø solid volume fraction - ø _m maximum solid volume fraction     

Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy

The nonlinear equations of motion for the scan process in noncontacting atomic force microscopy are consistently derived using the extended Hamilton’s principle. A modal dynamical system obtained from the continuum model reveals that scan control appears in the form of parametric excitation. The system is analyzed asymptotically and numerically to yield escape bounds limiting the noncontacting mode of operation. Approximate stability bounds are deduced from both a global Melnikov integral and a local Moon–Chirikov overlap criterion. The Melnikov–Holmes stability curve and the overlap criterion are found to be similar for small damping. However, for very small damping, typical of ultra-high vacuum conditions, where the Melnikov bound becomes trivial, the Moon–Chirikov criterion yields an improved stability threshold.     

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