Work fluctuation theorem for a granular motor

We apply kinetic theory and numerical simulation to the study of the fluctuation theorem for the work performed by an asymmetric piston immersed in a bath of gas particles. The symmetry function in the Brownian limit is predicted using a Langevin approach and is shown to be consistent with the numerical simulations.     

Pyridylmagnesiates: generation by bromine–metal exchange and enantioselective addition to aldehydes

Butyl and dibutylmagnesiates incorporating chiral ligands have been prepared and their reactivity studied. The reagents were efficient to promote the clean bromine–magnesium exchange of azinyl bromides at room temperature and subsequent reaction with aldehydes affording pyridylcarbinols. (R,R)-TADDOL-based dibutylmagnesiate was the best reagent leading to acceptable to good enantioselectivities, depending on the substrate and on the aldehyde substitution. This is the first example of enantioselective addition of in situ generated pyridylmagnesiate to carbonyl electrophiles.     

Analysis and computation for nonlinear elastic surface waves of permanent form

Linear elastic surface waves are nondispersive. All wavelengths travel at the Rayleigh wave speed c _R. This absence of frequency dispersion means that nonlinear waves of permanent form cannot be determined as a small perturbation from a sinusoidal wavetrain. By representing the general Rayleigh wave of the linear theory in terms of a pair of conjugate harmonic functions, waves which propagate without distortion are characterized as those having surface elevation profiles which satisfy a certain nonlinear functional equation. In the small-strain limit, this reduces to a quadratic functional equation. Methods for the analysis of this equation are presented for both periodic and nonperiodic waveforms. For periodic waveforms, the infinite system of quadratic equations for the Fourier coefficients of the profile is solved numerically in the case of a certain harmonic elastic material. Two distinct families of profiles having phase speed differing from the linearized Rayleigh wave speed are found. Additionally, two families of exceptional waveforms are found, describing profiles which travel at the Rayleigh wave speed.     

Morse theory on timelike and causal curves

It is shown that the set of timelike curves in a globally hyperbolic space-time manifold can be given the structure of a Hubert manifold under a suitable definition of timelike. The causal curves are the topological closure of this manifold. The Lorentzian energy (corresponding to Milnor's energy, except that the Lorentzian inner product is used) is shown to be a Morse function for the space of causal curves. A fixed end point index theorem is obtained in which a lower bound for the index of the Hessian of the Lorentzian energy is given in terms of the sum of the orders of the conjugate points between the end points.     

Spherical models with a Gates-Penrose-type phase transition

Gates and Penrose have given criteria under which classical gases with weak long-range interactions fail to be described by the van der Waals equation with Maxwell's rule. Unfortunately, examples of equations of state for such systems have not yet been produced. This paper examines the Gates-Penrose class of interactions-i.e.,U (r)=q(r)+(r), in the limit0, where the Fourier transform (p) has a minimum at a nonzero value ofp-for the spherical model on a one-dimensional lattice. Free energy and magnetization isotherms are computed; it is seen that there is a phase transition, but that the zero-field spontaneous magnetization is always zero (a parahelicoidal phase). However, the pair-correlation function may exhibit either long-range order or the appearance of oscillation.     

Diminishing blocking interval in particle-conveying channel bundles

We consider a channel bundle consisting of N_c parallel channels conveying a particulate flux. Particles enter these channels according to a homogeneous Poisson process and exit after a fixed transit time, τ. An individual channel blocks if N particles are simultaneously present. When a channel is blocked the flux previously entering it is redistributed evenly over the remaining open channels. We perform event driven simulations to examine the behaviour of an initially empty channel bundle with a total entering flux of intensity Λ. The mean blockage time of the kth channel is denoted by ? t_k ? ,k = 1,...,N_c. For N = 1, as shown previously, the interval between successive blockages is constant, while for N> 1 an accelerating cascade, i.e. one in which the interval between successive blockages decreases, is observed. After an initial transient regime we observe a well-defined universal regime that is characterized by\hbox{$\Delta_k^{(N)} = (-1)^{N-1}\frac{[(N-1)!]^2}{(\Lambda\tau)^N}$}Δk(N)=(?1)N?1[(N?1)!]2(Λτ)Nwhere \hbox{$\Delta_k^{(1)}=\langle t_k \rangle-\langle t_{k-1}\rangle$}Δk(1)=?tk???tk?1? and \hbox{$\Delta_k^{(j)}=\Delta_k^{(j-1)}-\Delta_{k-1}^{(j-1)}$}Δk(j)=Δk(j?1)?Δk?1(j?1) denotes the jth order difference.     

The Largest Eigenvalue of Rank One Deformation of Large Wigner Matrices

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue for some non-necessarily Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one used by A. Soshnikov (cf. [11]) in the investigations of classical real or complex Wigner Ensembles. It is based on the computation of moments of traces of high powers of the random matrices under consideration.     

Development of SPME on-fiber derivatization for the sampling of formaldehyde and other carbonyl compounds in indoor air

Solid-phase microextraction on-fiber derivatization applied to carbonyl compounds is known, but application to indoor air is poorly developed and the methods deserve to be complemented and optimized. In this work, two derivatization reagents, pentafluorophenylhydrazine and o-2,3,4,5,6-(pentaflurobenzyl)hydroxylamine (PFBHA), and three fiber coatings were tested in order to select the best combination. As Carboxen-based coatings were proven to induce the formation of by-products during the thermal desorption step, a polydimethylsiloxane–divinylbenzene fiber in association with PFBHA was finally chosen. The study of the derivatization kinetics showed that the reaction of PFBHA with carbonyl compounds was instantaneous, except for acetone. Analyses were performed by gas chromatography coupled with flame ionization detection and mass spectrometry. For 5 min fiber exposure, the limits of detection are below 0.5 μg m^-3 in selected ion monitoring mode, the reproducibility was 15 % on average, and the linearity of the calibration curves was satisfactory. For on-site application, the influence of air humidity and the conditions in which the impregnated fibers were stored were studied. It is possible to store the fibers for 3 days before and for at least 2 days after sampling. The relative humidity of air was shown to have no influence on solid-phase microextraction sampling in the range from 0 to 70 %. For formaldehyde, the method was compared with sampling on 2,4-dinitrophenylhydrazine cartridges, and the first results showed good agreement. Finally, the method was applied to three different indoor environments to check its feasibility.     

Designing of an Intensification Process for Biosynthesis and Recovery of Menaquinone-7

A nutritional food rich in menaquinone-7 has a potential in preventing osteoporosis and cardiovascular diseases. The static fermentation of Bacillus subtilis natto is widely regarded as an optimum process for menaquinone-7 production. The major issues for the bulk production of menaquinone-7 are the low fermentation yield, biofilm formation and the use of organic solvents for the vitamin extraction. In this study, we demonstrate that the dynamic fermentation involving high stirring and aeration rates enhances the yield of fermentation process significantly compared to static system. The menaquinone-7 concentration of 226 mg/L was produced at 1,000 rpm, 5 vvm, 40 °C after 5 days of fermentation. This concentration is 70-fold higher than commercially available food products such as natto. Additionally, it was found that more than 80 % of menaquinone-7 was recovered in situ in the vegetable oil that was gradually added to the system as an anti-foaming agent. The intensification process developed in this study has a capacity to produce an oil rich in menaquinone-7 in one step and eliminate the use of organic solvents for recovery of this compound. This oil can, therefore, be used for the preparation of broad range of supplementary and dietary food products rich in menaquinone-7 to reduce the risk of osteoporotic fractures and cardiovascular diseases.