Hopf bifurcation in a size-structured population dynamic model with random growth

This paper is devoted to the study of a size-structured model with Ricker type birth function as well as random fluctuation in the growth process. The complete model takes the form of a reaction-diffusion equation with a nonlinear and nonlocal boundary condition. We study some dynamical properties of the model by using the theory of integrated semigroups. It is shown that Hopf bifurcation occurs at a positive steady state of the model. This problem is new and is related to the center manifold theory developed recently in [P. Magal, S. Ruan, Center manifold theorem for semilinear equations with non-dense domain and applications to Hopf bifurcation in age-structured models, Mem. Amer. Math. Soc., in press] for semilinear equation with non-densely defined operators.     

Existence of minimizers for Kohn–Sham models in quantum chemistry

This article is concerned with the mathematical analysis of the Kohn–Sham and extended Kohn–Sham models, in the local density approximation (LDA) and generalized gradient approximation (GGA) frameworks. After recalling the mathematical derivation of the Kohn–Sham and extended Kohn–Sham LDA and GGA models from the Schrödinger equation, we prove that the extended Kohn–Sham LDA model has a solution for neutral and positively charged systems. We then prove a similar result for the spin-unpolarized Kohn–Sham GGA model for two-electron systems, by means of a concentration-compactness argument.     

Dynamic Nuclear Polarization by Thermal Mixing Under Partial Saturation

We describe a low-temperature thermodynamic model for dynamic nuclear polarization (DNP) via continuous-wave partial saturation of electron spin resonance (ESR) lines that are both homogeneously and inhomogeneously broadened. It is a variant of a reasoning proposed by Borghini, which in turn used Redfield’s thermodynamic treatment of saturation. Our variant is furthermore based on Provotorov’s insight that under partial saturation of a coupled-spin system two distinct spin temperatures should appear in a thermodynamical theory. We apply our model to DNP results obtained at a temperature of 1.2?K and in magnetic fields of 3.35 and 5?T on 1-¹³C labeled sodium acetate dissolved in a frozen D₂O/ethanol-d₆ solution doped with the free radical TEMPO.     

Mechanism for spherical dome and microvoid formation in polycarbonate using nanojoule femtosecond laser pulses

Spherical domes are created on the surface of polycarbonate samples, and microvoids are formed within the bulk using only a femtosecond oscillator with pulse energy of just 0.47?nJ. Size of spherical domes and shape of microvoids are controlled by changing the laser focus inside the material. Their formation is explained by a combination of heat accumulation and dome formation dynamics, where the dome acts as a microlens shifting the laser focus within the sample. The technique described here provides a simple avenue for fabricating smooth microlens arrays of various sizes and opens the possibility for direct fabrication of complex three-dimensional microfluidic channels in transparent materials.     

Elaboration and characterization of magnetic nanocomposite fibers by electrospinning

We describe a simple method based on the electrospinning process to prepare heterogeneous hybrid submicronic fibers with magnetic behavior, consisting of Co nanoparticles embedded in a polyacrylonitrile (PAN) polymer. Quantity and anisotropy of magnetic nanoparticles are key parameters to improve the specific magnetic properties of fibers. We notably show that for higher Co nanoparticles concentration, their lower dispersity into the resulting fibers lead to dipolar interactions that become demagnetizing. The structural and morphological properties of Co nanodisks and of the resulting nanocomposite fibers are investigated by SEM, TEM, and EDX. The magnetic properties of the hybrid electrospun fibers have been evaluated with a SQUID magnetometer.     

Hexavalent chromium quantification in solution: Comparing direct UV–visible spectrometry with 1,5-diphenylcarbazide colorimetry

Quantification of Cr(VI) in an aqueous solution is conducted by direct UV–visible spectrophotometry based on the yellow coloring of the chromate ion. Measurements show that absorption follows the Beer–Lambert law over a wide range of concentrations. At pH below the pK_a of 6.4 (HCrO₄^?/CrO₄^?2), the absorption maximum lies at 350 nm wavelength and the linear range spans from 0.5 to 100 mg Cr(VI)/L; above the pK_a (pH 6.4), the absorption maximum is 373 nm and linearity occurs in the range of 0.5–25 mg/L. The wide range of validity of the Beer–Lambert law is advantageous for the measurement of concentrated samples. The standard method of analysis of aqueous Cr(VI) is by colorimetry with the 1,5-diphenylcarbazide (DPC)–Cr(VI) complex. This method, although very sensitive, bears a narrow range of linearity from 0 to 0.8 mg Cr(VI)/L. It is shown that when analyzing Cr(VI) solutions with concentrations in the range of 30–500 mg/L, the DPC method gives inaccurate results and relative standard deviations of 20–50%. This is due to high dilution factors. On the contrary, the direct method performs with high accuracy. Relative standard deviation is only 0.5% at 500 mg Cr(VI)/L. The direct method is fast, reliable, and nondestructive for the sample. The direct method is recommended for the quantification of Cr(VI) at concentrations greater than 1 mg/L.     

Evidence for a trianion intermediate in the metalation of 4-hydroxy-6,7-dimethoxy-8-methyl-2-naphthoic acid. Methodology and application to racemic 5,5'-didesisopropyl-5,5'-dialkylapogossypol derivatives

The metalation of 4-hydroxy-6,7-dimethoxy-8-methyl-2-naphthoic acid (8) affording trianion 6 is presented and applied to the regioselective efficient construction of a series of 5,5'-didesisopropyl-5,5'-dialkylapogossypol derivatives 3 that are potent pan-active inhibitors of antiapoptotic Bcl-2 family proteins.     

Polymorphism in micro-, submicro-, and nanocrystalline NaNbO3

NaNbO(3) powders with various particle sizes (ranging from 30 nm to several microns) and well-controlled stoichiometry were obtained through microemulsion-mediated synthesis. The effect of particle size on the phase transformation of the prepared NaNbO(3) powders was studied using X-ray powder diffraction, Raman spectroscopy, and nuclear site group analysis based on these spectroscopic data. Coarsened particles exhibit an orthorhombic Pbcm (D(2h)(11), no. 57) structure corresponding to the bulk structure, as observed for single crystals or powders prepared by conventional solid-state reaction. The crystal symmetry of submicron powders was refined with the space group Pmc2(1) (C(2v)(2), no. 26). The reduced perovskite cell volumes of these submicron powders were most expanded compared to all the other structures. Fine particles with a diameter of less than 70 nm as measured from SEM observations showed an orthorhombic Pmma (D(2h)(5), no. 51) crystal symmetry. The perovskite formula cell of this structure was pseudocubic and was the most compact one. A possible mechanism of the phase transformation is suggested.     

Microfluidic systems in proteomics

We present the state-of-the-art in miniaturized sample preparation, immunoassays, one-dimensional and multidimensional analyte separations, and coupling of microdevices with electrospray ionization-mass spectrometry. Hyphenation of these different techniques and their relevance to proteomics will be discussed. In particular, we will show that analytical performances of microfluidic analytical systems are already close to fulfill the requirements for proteomics, and that miniaturization results at the same time in a dramatic increase in analysis throughput. Throughout this review, some examples of analytical operations that cannot be achieved without microfluidics will be emphasized. Finally, conditions for the spreading of microanalytical systems in routine proteomic labs will be discussed.