Ambient noise cross correlation in free space: theoretical approach

It has been experimentally demonstrated that the Green's function between two points could be recovered using the cross-correlation function of the ambient noise measured at these two points. This paper investigates the theory behind this result in the simple case of a homogeneous medium with attenuation.     

Magnetically driven ferroelectric order in Ni3V2O8

We show that long-range ferroelectric and incommensurate magnetic order appear simultaneously in a single phase transition in Ni3V2O8. The temperature and magnetic-field dependence of the spontaneous polarization show a strong coupling between magnetic and ferroelectric orders. We determine the magnetic symmetry using Landau theory for continuous phase transitions, which shows that the spin structure alone can break spatial inversion symmetry leading to ferroelectric order. This phenomenological theory explains our experimental observation that the spontaneous polarization is restricted to lie along the crystal b axis and predicts that the magnitude should be proportional to a magnetic order parameter.     

Dynamics and bistability in a reduced model of the lac operon

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and beta-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on beta-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.     

On quadratic fields with large 3-rank

Davenport and Heilbronn defined a bijection between classes of binary cubic forms and classes of cubic fields, which has been used to tabulate the latter. We give a simpler proof of their theorem then analyze and improve the table-building algorithm. It computes the multiplicities of the general cubic discriminants (real or imaginary) up to in time and space , or more generally in time and space for a freely chosen positive . A variant computes the -ranks of all quadratic fields of discriminant up to with the same time complexity, but using only units of storage. As an application we obtain the first real quadratic fields with , and prove that is the smallest imaginary quadratic field with -rank equal to .

     

A generalization of a theorem on biseparating maps

In J. Math. Anal. Appl. 12 (1995) 258–265, Araujo et al. proved that for any linear biseparating map  from C(X) onto C(Y), where X and Y are completely regular, there exist ω in C(Y) and an homeomorphism h from the realcompactification vX of X onto vY, such that

The compact version of this result was proved before by Jarosz in Bull. Canad. Math. Soc. 33 (1990) 139–144. In Contemp. Math., Vol. 253, 2000, pp. 125–144, Henriksen and Smith asked to what extent the result above can be generalized to a larger class of algebras. In the present paper, we give an answer to that question as follows. Let A and B be uniformly closed Φ-algebras. We first prove that every order bounded linear biseparating map from A onto B is automatically a weighted isomorphism, that is, there exist ω in B and a lattice and algebra isomorphism ψ between A and B such that

(a)=ωψ(a) for all aA.

We then assume that every universally σ-complete projection band in A is essentially one-dimensional. Under this extra condition and according to a result from Mem. Amer. Math. Soc. 143 (2000) 679 by Abramovich and Kitover, any linear biseparating map from A onto B is automatically order bounded and, by the above, a weighted isomorphism. It turns out that, indeed, the latter result is a generalization of the aforementioned theorem by Araujo et al. since we also prove that every universally σ-complete projection band in the uniformly closed Φ-algebra C(X) is essentially one-dimensional.     

Role of interfacial chemistry on the rheology and thermo-mechanical properties of clay-polymer nanocomposites for building applications

This study is directed towards investigating the role of the surface treatment of clay particles on the rheological and thermomechanical behaviour of clay-epoxy blends. Nanocomposites were prepared by mixing small amounts (5–10 mass %) of commercial organoclays or raw clays with an epoxy system commonly used in civil engineering. Rheological characterisations in the liquid state revealed a pronounced thixotropic character of the organoclay-based systems, which all exhibited a shear-thinning behaviour above a critical stress threshold (yield stress), depending on both the intensity of interfacial interactions and the degree of filler dispersion. On the other hand, systems based on raw clay particles behaved like Newtonian fluids, in the same way as the unreinforced polymer matrix. Complementary dynamic mechanical analyses (DMA) performed on the cured cross-linked nanocomposites also showed significant changes in the viscoelastic behaviour of the epoxy matrix due to the introduction of organoclays, whereas only minor variations were observed following the introduction of raw fillers. These results were consistent with nanoscale morphological characterisations performed by conventional X-ray diffraction (XRD) on the various hybrid systems. In this context, rheology and DMA appear as attractive alternative methods for assessing the filler dispersion at a macroscopic (and possibly more relevant) scale. This research is of practical interest for civil engineers, since clay reinforced-epoxies could in the future be used as coating materials with enhanced barrier performances, in order to protect infrastructures against environmental ageing or corrosion.     

Varying Track Etch Rates along the Fission Fragments＇ Trajectories in CR-39 Detectors

We determine the behavior of track etch rate VT along the tracks in CR-39 detectors exposed to fission fragments from ^252Cf source. CR-39 detectors are etched at 70℃ in different concentrations of Na2COa-mixed 6M NaOH solutions for different etching time intervals of 5-10min starting from 15 min up to 210min. Two values of track etch rate are determined along the fission fragment trajectories. The variation in VT is correlated with the energy loss rate of the fission fragment in the detector material.     

Two local search approaches for solving real-life car sequencing problems

The NP-hard problem of car sequencing appears as the heart of the logistic process of many car manufacturers. The subject of the ROADEF’2005 challenge addressed a car sequencing problem proposed by the car manufacturer RENAULT, more complex than the academic problem generally addressed in the literature. This paper describes two local search approaches for this problem. In the first part, a new approach by very large-scale neighborhood search is presented. This approach, designed during the qualification stage preceding the final, is based on an original integer linear programming formulation. The second part is dedicated to the approach which enabled us to win the ROADEF’2005 challenge. Inspired by the latest works on the subject, this one is based on very fast explorations of small neighborhoods. Our contribution here is mainly algorithmic, in particular by showing how much exploiting invariants speeds up the neighborhood evaluation and contributes to the diversification of the search. Finally, the two approaches are compared and discussed through an extensive computational study on RENAULT’s benchmarks. The main conclusion drawn at this point is that sophisticated metaheuristics are useless to solve car sequencing problems. More generally, our victory on ROADEF’2005 challenge demonstrates that algorithmic aspects, sometimes neglected, remain the key ingredients for designing and engineering high-performance local search heuristics.     

General properties of Bertrand curves in Riemann–Otsuki space

In this paper we studied the general properties of Bertrand curves and their characterizations in Riemann–Otsuki space.