Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.Comment: 14 pages, no figure, to appear, Acta Applicandae Mathematica

Molecular Evaluation of exons 8 and 22 of the SHANK3 gene in Autism Spectrum Disorders

Autism spectrum disorders are a group of neurodevelopmental disorders with a complex and heterogeneous etiology. Studies have shown that genetic factors play an important role in the aetiology of these diseases. Recently, de novo mutations, frameshifts and deletions have been described in the SHANK3 gene, also known as ProSAP2 gene, which encodes a synaptic scaffolding protein. All the participants of this study had normal karyotypes and underwent screening for Fragile-X syndrome. Subsequently, they were analyzed by direct sequencing of different points of exons 8 and 22 of the SHANK3 gene. None of the study participants presented with changes in these regions. These findings may be due to the fact that mutations, deletions and duplications of the SHANK3 gene are rare

A reduction of the resonant three-wave interaction to the generic sixth Painleve' equation

Among the reductions of the resonant three-wave interaction system to six-dimensional differential systems, one of them has been specifically mentioned as being linked to the generic sixth Painleve' equation P6. We derive this link explicitly, and we establish the connection to a three-degree of freedom Hamiltonian previously considered for P6.Comment: 13 pages, 0 figure, J. Phys. A Special issue "One hundred years of Painleve' VI

A quantum mechanical insight into SN2 reactions: Semiclassical initial value representation calculations of vibrational features of the Cl−^---CH3_3Cl pre-reaction complex with the VENUS suite of codes

The role of vibrational excitation of reactants in driving reactions involving polyatomic species has been often studied by means of classical or quasi-classical trajectory simulations. We propose a different approach based on investigation of vibrational features of the Cl$^-$--CH$_3$Cl pre-reaction complex for the Cl$^-$ + CH$_3$Cl SN$_2$ reaction. We present vibrational power spectra and frequency estimates for the title pre-reaction complex calculated at the level of classical, semiclassical, and second-order vibrational perturbation theory on a pre-existing analytical potential energy surface. The main goals of the paper are the study of anharmonic effects and understanding of vibrational couplings that permit energy transfer between the collisional kinetic energy and the internal vibrations of the reactants. We provide both classical and quantum pictures of intermode couplings and show that the SN2 mechanism is favored by the coupling of a C--Cl bend involving the Cl$^-$ projectile with the CH$_3$ rocking motion of the target molecule. We also illustrate how the routines needed for semiclassical vibrational spectroscopy simulations can be interfaced in a user-friendly way to pre-existing molecular dynamics software. In particular, we present an implementation of semiclassical spectroscopy into the VENUS suite of codes, thus providing a useful computational tool for users who are not experts of semiclassical dynamics

Modeling population dynamics and economic growth as competing species: An application to CO2 global emissions

Since the beginning of the last century the world is experiencing an important demographic transition, which will probably impact on economic growth. Many demographers and social scientists are trying to understand the key drivers of such transition as well as its profound implications. A correct understanding will help to predict other important trends of the world primary energy demand and the carbon emission to the atmosphere, which may be leading to an important climate change. This paper proposes a set of coupled differential equations to describe the changes of population, gross domestic product, primary energy consumption and carbon emissions, modeled as competing-species as in Lokta-Volterra prey-predator relations. The predator–prey model is well known in the biological, ecological and environmental literature and has also been applied successfully in other fields. This model proposes a new and simple conceptual explanation of the interactions and feedbacks among the principal driving forces leading to the present transition. The estimated results for the temporal evolution of world population, gross domestic product, primary energy consumption and carbon emissions are calculated from year 1850 to year 2150. The calculated scenarios are in good agreement with common world data and projections for the next 100 years.Population dynamics, economic growth, primary energy consumption, carbon emission model, Lokta-Volterra Equations, Prey-predator model.

Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation

I review recent work on the ``phase diagram'' of the one-dimensional complex Ginzburg-Landau equation for system sizes at which chaos is extensive. Particular attention is paid to a detailed description of the spatiotemporally disordered regimes encountered. The nature of the transition lines separating these phases is discussed, and preliminary results are presented which aim at evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to amoco.saclay.cea.fr in directory pub/chate, or by requesting them to [email protected]

Integrability of anisotropic and homogeneous Universes in scalar-tensor theory of gravitation

In this paper, we develop a method based on the analysis of the Kovalewski exponents to study the integrability of anisotropic and homogeneous Universes. The formalism is developed in scalar-tensor gravity, the general relativistic case appearing as a special case of this larger framework. Then, depending on the rationality of the Kovalewski exponents, the different models, both in the vacuum and in presence of a barotropic matter fluid, are classified, and their integrability is discussed.Comment: 16 pages, no figure, accepted in CQ

Hydration and water holding properties of cross-linked lignite humic acids

Lignite and lignite humic acids, which are used as soil amendments sometimes, are supposed to improve soil properties such as water holding capacity. The structure of those materials is composed of various organic molecules stabilized mostly byweak interactions. Therefore, excess ofwater causes only partial swelling, but most of the physical structure is destabilized. This accelerates the desiccation and hampers their application as natural hydrogel-like substances. In order to stabilize the structure of lignite humic acids and improve the water holding capacity, we applied formaldehyde cross-linking procedure based on covalent coupling of aromatic humic acids moieties. By combining the 1H NMR relaxometry and methods of thermal analysis, the kinetics and degree of hydration, water distribution and moisture uptake were investigated. It was found that cross-linking induced a reduction in moisture sorption capacity at lowrelative humidity and an increase at higher relative humidity,which was attributed to the separation of functional groups and decreasing of structural compactness after crosslinking. As a result, the cross-linked humic acids, exhibited faster water uptake and approximately three-fold higher water holding capacity in comparison with the parental sample. The distribution of relaxation times of water protons in swollen humic acids revealed the unification of pore size distribution upon cross-linking. Although the improved hydration of cross-linked lignite humic acids already resembles the hydration of some hydrophilic polymers, the water holding capacity is still belowthe capacity of classical hydrogels. Nevertheless, the lowprice of lignite, sorption properties and its overall positive affect on soil quality and productivity give a promise in application of this material both in agriculture and remediation technologies