Solution of the Navier-Stokes equations by the spectral-difference method

The Jacobi polynomial collocation method is extended to two and three dimensions by superimposing the individual one-dimensional expansions. Two innovative ideas are introduced in this article. The first is the cornerless/edgeless computational grid, and the second is the modified compressibility method, which is an iterative pressure solver. To evaluate the new method's applicability in solving the Navier-Stokes equation, the lid-driven cavity flow problem was solved. Two configurations were considered, the square cavity and the rectangular cavity with an aspect ratio of 2. A comparison of the center-line velocity profiles from two- and three-dimensional simulations at a Reynolds number of 1000 is provided for each of the configurations. The center-line velocity comparisons showed good quantitative agreement with previous studies. © 1994 John Wiley & Sons, Inc.     

Densities of One-Dimensional Backward SDEs

This work is devoted to the study of the existence and smoothness of the marginal densities of the solution of one-dimensional backward stochastic differential equations. Under monotonicity conditions of a function of the coefficients, we obtain that the smoothness properties of the forward process influencing the backward equation, transfer to the densities of the solution. Once established these conditions, we apply the result to study the tail behavior of the solution process. Mathematics Subject Classification (2000) 60H10.Fabio Antonelli: The first author was partially supported by the MIUR COFIN grant 2000.Arturo Kohatsu-Higa: The second author was partially supported by grants BFM2003-03324 and BFM 2003-04294. The authors wish to thank the referee for his/her comments.     

Inverse gas chromatography of poly(cyclohexyl methacrylate)

Inverse gas chromatography is applied to determine the glass transition temperature T_g of poly-(cyclohexyl methacrylate). Both good and bad solvents for the polymer are used as molecular probes. Although the transition is clearly detected by both types of probes, only the nonsolvents yield a T_g in quantitative agreement with the value determined by differential scanning calorimetry. The relative depth of penetration of the probe in the polymer phase is calculated from retention volume data. Also, the height equivalent to a theoretical plate is calculated from peak halfwidths. Both calculated magnitudes show a temperature dependence which significantly differs from good to bad solvents. Some kind of diffusion-limited penetration of the probe in the bulk of the glassy polymer may be responsible for the difference.     

Conjugate processes: Theory and application to risk forecasting

Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models – called conjugate processes – allowing the sequence of marginal distributions of a cyclic, continuous-time process to evolve stochastically in time. The connection between the two processes is given by a fundamental compatibility equation. Key results include Laws of Large Numbers in the presented framework. We provide a constructive example which illustrates the theory, and give a statistical implementation to risk forecasting in financial data.     

Existence of dicritical singularities of Levi-flat hypersurfaces and holomorphic foliations

We study holomorphic foliations tangent to singular real-analytic Levi-flat hypersurfaces in compact complex manifolds of complex dimension two. We give some hypotheses to guarantee the existence of dicritical singularities of these objects. As consequence, we give some applications to holomorphic foliations tangent to real-analytic Levi-flat hypersurfaces with singularities in \(\mathbb {P}^2\).     

Mechanistic insights into dopaminergic and serotonergic neurotransmission – concerted interactions with helices 5 and 6 drive the functional outcome

Brain functions rely on neurotransmitters that mediate communication between billions of neurons. Disruption of this communication can result in a plethora of psychiatric and neurological disorders. In this work, we combine molecular dynamics simulations, live-cell biosensor and electrophysiological assays to investigate the action of the neurotransmitter dopamine at the dopaminergic D₂ receptor (D₂R). The study of dopamine and closely related chemical probes reveals how neurotransmitter binding translates into the activation of distinct subsets of D₂R effectors (i.e.: G_i2, G_oB, G_z and β-arrestin 2). Ligand interactions with key residues in TM5 (S5.42) and TM6 (H6.55) in the D₂R binding pocket yield a dopamine-like coupling signature, whereas exclusive TM5 interaction is typically linked to preferential G protein coupling (in particular G_oB) over β-arrestin. Further experiments for serotonin receptors indicate that the reported molecular mechanism is shared by other monoaminergic neurotransmitter receptors. Ultimately, our study highlights how sequence variation in position 6.55 is used by nature to fine-tune β-arrestin recruitment and in turn receptor signaling and internalization of neurotransmitter receptors.

Neurotransmitter contacts within the receptor binding site differentially contribute to the overall functional response: transmembrane helix (TM) 5 contacts promote G protein coupling whereas concerted TM5–TM6 contacts enhance β-arrestin recruitment.     

In situ studies of the active sites for the water gas shift reaction over Cu-CeO2 catalysts: complex interaction between metallic copper and oxygen vacancies of ceria

New information about the active sites for the water gas shift (WGS) reaction over Cu-CeO2 systems was obtained using in-situ, time-resolved X-ray diffraction (TR-XRD), X-ray absorption spectroscopy (TR-XAS, Cu K and Ce L3 edges), and infrared spectroscopy (DRIFTS). Cu-CeO2 nanoparticles prepared by a novel reversed microemulsion method (doped Ce1-xCuxO2 sample) and an impregnation method (impregnated CuOx/CeO2 sample) were studied. The results from all of the samples indicate that both metallic copper and oxygen vacancies in ceria were involved in the generation of active sites for the WGS reaction. Evidence was found for a synergistic Cu-Ovacancy interaction. This interaction enhances the chemical activity of Cu, and the presence of Cu facilitates the formation of O vacancies in ceria under reaction conditions. Water dissociation occurred on the Ovacancy sites or the Cu-Ovacancy interface. No significant amounts of formate were formed on the catalysts during the WGS reaction. The presence of strongly bound carbonates is an important factor for the deactivation of the catalysts at high temperatures. This work identifies for the first time the active sites for the WGS reaction on Cu-CeO2 catalysts and illustrates the importance of in situ structural studies for heterogeneous catalytic reactions.     

Microscopic and Spectroscopic Methods Applied to the Measurements of Nanoparticles in the Environment

Abstract: Currently, thousands of commercially available products contain engineered nanoparticles (ENPs). Because numerous nanoparticles (NPs) are being used in products that will be in contact with water or directly used in water treatment processes, these materials will undoubtedly reside, at least temporarily, in bodies of water. Given the widespread use of NPs and ENPs in consumer goods, a large portion of these materials will soon go into the waste stream, potentially to soil and sediments or added directly to agricultural lands via biosolids. Possible impacts of ENPs on aquatic and terrestrial ecosystems are of great concern. Preliminary data from several research groups have shown that ENPs may have a direct impact on food safety and the food chain. However, our knowledge about detection and characterization of NPs in the environment, especially aquatic environments, is still in its infancy. This review includes the most recent literature about the methods applied to the measurement of NPs and ENPs in the environment. The review covers methods to determine size distribution, shape, structure, surface charge, chemical composition, surface area, agglomeration, surface chemistry, porosity, and solubility.     

Quasi-Static Variation of Power-Law and Log-Normal Distributions of Urban Population

We analytically derived and confirmed by empirical data the following three relations from the quasi-time-reversal symmetry, Gibrat’s law, and the non-Gibrat’s property observed in the urban population data of France. The first is the relation between the time variation of the power law and the quasi-time-reversal symmetry in the large-scale range of a system that changes quasi-statically. The second is the relation between the time variation of the log-normal distribution and the quasi-time-reversal symmetry in the mid-scale range. The third is the relation among the parameters of log-normal distribution, non-Gibrat’s property, and quasi-time-reversal symmetry.