Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic

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

Completeness of the cubic and quartic H\'enon-Heiles Hamiltonians

The quartic H\'enon-Heiles Hamiltonian $H = (P_1^2+P_2^2)/2+(\Omega_1 Q_1^2+\Omega_2 Q_2^2)/2 +C Q_1^4+ B Q_1^2 Q_2^2 + A Q_2^4 +(1/2)(\alpha/Q_1^2+\beta/Q_2^2) - \gamma Q_1$ passes the Painlev\'e test for only four sets of values of the constants. Only one of these, identical to the traveling wave reduction of the Manakov system, has been explicitly integrated (Wojciechowski, 1985), while the three others are not yet integrated in the generic case $(\alpha,\beta,\gamma)\not=(0,0,0)$. We integrate them by building a birational transformation to two fourth order first degree equations in the classification (Cosgrove, 2000) of such polynomial equations which possess the Painlev\'e property. This transformation involves the stationary reduction of various partial differential equations (PDEs). The result is the same as for the three cubic H\'enon-Heiles Hamiltonians, namely, in all four quartic cases, a general solution which is meromorphic and hyperelliptic with genus two. As a consequence, no additional autonomous term can be added to either the cubic or the quartic Hamiltonians without destroying the Painlev\'e integrability (completeness property).Comment: 10 pages, To appear, Theor.Math.Phys. Gallipoli, 34 June--3 July 200

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

Correspondence Model Of Occupational Accidents

We present a new generalized model for the diagnosis and prediction of accidents among the Spanish workforce. Based on observational data of the accident rate in all Spanish companies over eleven years (7,519,732 accidents), we classified them in a new risk-injury contingency table (19x19). Through correspondence analysis, we obtained a structure composed of three axes whose combination identifies three separate risk and injury groups, which we used as a general Spanish pattern. The most likely or frequent relationships between the risk and injuries identified in the pattern facilitated the decision-making process in companies at an early stage of risk assessment. Each risk-injury group has its own characteristics, which are understandable within the phenomenological framework of the accident. The main advantages of this model are its potential application to any other country and the feasibility of contrasting different country results. One limiting factor, however, is the need to set a common classification framework for risks and injuries to enhance comparison, a framework that does not exist today. The model aims to manage work-related accidents automatically at any level

Metastable hydrogels from aromatic dipeptides

We demonstrate that the well-known self-assembling dipeptide diphenylalanine (FF) and its amidated derivative (FF-NH2) can form metastable hydrogels upon sonication of the dipeptide solutions. The hydrogels show instantaneous syneresis upon mechanical contact resulting in rapid expulsion of water and collapse into a semi-solid gel

On elliptic solutions of the cubic complex one-dimensional Ginzburg-Landau equation

The cubic complex one-dimensional Ginzburg-Landau equation is considered. Using the Hone's method, based on the use of the Laurent-series solutions and the residue theorem, we have proved that this equation has neither elliptic standing wave nor elliptic travelling wave solutions. This result amplifies the Hone's result, that this equation has no elliptic travelling wave solutions.Comment: LaTeX, 12 page

Spin-orbit torques for current parallel and perpendicular to a domain wall

We report field- and current-induced domain wall (DW) depinning experiments in Ta/Co20Fe60B20/MgO nanowires through a Hall cross geometry. While purely field-induced depinning shows no angular dependence on in-plane fields, the effect of the current depends crucially on the internal DW structure, which we manipulate by an external magnetic in-plane field. We show for the first time depinning measurements for a current sent parallel to the DW and compare its depinning efficiency with the conventional case of current flowing perpendicularly to the DW. We find that the maximum efficiency is similar for both current directions within the error bars, which is in line with a dominating damping-like spin-orbit torque (SOT) and indicates that no large additional torques arise for currents parallel to the DW. Finally, we find a varying dependence of the maximum depinning efficiency angle for different DWs and pinning levels. This emphasizes the importance of our full angular scans compared to previously used measurements for just two field directions (parallel and perpendicular to the DW) and shows the sensitivity of the spin-orbit torque to the precise DW structure and pinning sites.Comment: 11 pages, 3 figure

Polycyclic aromatic hydrocarbons in some Nigerian rasted plant foods

Thirteen polycyclic aromatic hydrocarbons (PAHs) were identified and quantified in three different roasted plant foods (Zea mays, Dioscorea rotundata and Musa paradisiaca) using a rapid method involving microwave assisted saponification and simultaneous extraction followed by solid-phase extraction (SPE), high-performance liquid chromatography (HPLC) separation and spectrofluorometric detection. The method applied had good recovery and repeatability characteristcs. With respect to raw samples, roasted samples had higher contamination levels with a maximum benzo[a]pyrene (BaP) content of 0.6 \u3bcg kg-1 dry weight. Roasted Zea mays had the highest low molecular weight- polycyclic aromatic hydrocarbons (LMW-PAH) load of 31.2 \u3bcg kg-1 dry weight, which may be due to the fact that the charred portions after roasting are not usually subjected to scrapping, an exercise which is usually carried out on other roasted plant foods. Anyways, PAHs exposure due to the consumption of roasted plant foods may not pose serious concerns for human health, especially as they are low in heavy molecular weight polycyclic aromatic hydrocarbons (HMW-PAHs)