Novel Wronskian Condition and New Exact Solutions to a （3＋1）-Dimensional Generalized KP Equation

Utilizing the Wronskian technique, a combined Wronskian condition is established for a （3＋1）-dimensional generalized KP equation. The generating functions for matrix entries satisfy a linear system of new partial differential equations. Moreover, as applications, examples of Wronskian determinant solutions, including N-soliton solutions, periodic solutions and rational solutions, are computed.     

Synergistic effects in mixed wormlike micelles of dimeric and single-chain cationic surfactants at high ionic strength

The mixed micellization between the cationic gemini surfactant [ C₁₂H₂₅( CH₃)₂N⁺( C₂H₄) N⁺( CH₃)₂ C₁₂H₂₅•2Br^-] and the cationic cetyltrimethylammonium bromide (CTAB) in 150 mM KBr solutions has been investigated. The variation of the cmc of the mixtures, measured by surface tension experiments, with composition revealed synergism in micelle formation. T-Jump and light scattering experiments performed in the vicinity of the crossover volume fraction showed the existence of two micellar populations, possibly linear and toroidal micelles. Rheological and dynamic light scattering experiments allowed to fully characterize the linear viscoelasticity of the mixtures. These measurements revealed synergistic gains in viscoelastic properties with a maximum of the stress-relaxation time around the equimolar composition. These effects are ascribed to a progressive intermicellar crosslinking resulting from a continuous increase of the end-cap energy with the 12-2-12 content in the mixture. Received: 18 November 2002 / Accepted: 8 April 2003 / Published online: 27 May 2003 RID="a" ID="a"e-mail: candau@fresnel.u-strasbg.fr     

Self-healing slip pulses and the friction of gelatin gels

We present an extensive experimental study and scaling analysis of friction of gelatin gels on glass. At low driving velocities, sliding occurs via propagation of periodic self-healing slip pulses whose velocity is limited by collective diffusion of the gel network. Healing can be attributed to a frictional instability occurring at the slip velocity V = V _c. For V > V _c, sliding is homogeneous and friction is ruled by the shear-thinning rheology of an interfacial layer of thickness of order the (nanometric) mesh size, containing a solution of polymer chain ends hanging from the network. In spite of its high degree of confinement, the rheology of this system does not differ qualitatively from known bulk ones. The observed ageing of the static friction threshold reveals the slow increase of adhesive bonding between chain ends and glass. Such structural ageing is compatible with the existence of a velocity-weakening regime at velocities smaller than V _c, hence with the existence of the healing instability. Received: 7 March 2003 / Accepted: 2 May 2003 / Published online: 11 June 2003 RID="b" ID="b"e-mail: ronsin@gps.jussieu.fr     

Influence of the Type of a Ligand on the Intensity of Luminescence of Ln3+ Ions in Aqueous Solutions

The luminescence characteristics of hydrated Ln³⁺ ions and their complexes with some acidic ligands have been investigated. The possibility of determining the stability of the complexes of lanthanides in solutions from the intensity of luminescence bands is shown. The influence of the characteristic features of the f-electron shell of Ln³⁺ on the formation of the spectrochemical series is discussed.     

Equilibrium points of the tilted perfect fluid Bianchi VI<Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> state space

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI_h filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VI_h.     

Fermi, Majorana and the Statistical Model of Atoms

We give an account of the appearance and first developments of the statistical model of atoms proposed by Thomas and Fermi, focusing on the main results achieved by Fermi and his group in Rome. Particular attention is addressed to the unknown contribution to this subject by Majorana, anticipating some important results reached later by leading physicists.     

Vortex structures with complex points singularities in two-dimensional Euler equations. New exact solutions

In this work we present a new class of exact stationary solutions for two-dimensional (2D) Euler equations. Unlike already known solutions, the new ones contain complex singularities. We consider point singularities which have a vector field index greater than 1 as complex. For example, the dipole singularity is complex because its index is equal to 2. We present in explicit form a large class of exact localized stationary solutions for 2D Euler equations with a singularity whose index is equal to 3. The solutions obtained are expressed in terms of elementary functions. These solutions represent a complex singularity point surrounded by a vortex satellite structure. We also discuss the motion equation of singularities and conditions for singularity point stationarity which provide the stationarity of the complex vortex configuration.     

A geometric characterisation of resonance in Hopf bifurcation from relative equilibria

We give a new characterisation of resonance in Hopf bifurcation from relative equilibria in systems with compact symmetry group. This characterisation provides a full geometric explanation of the resonance phenomenon. In addition, we develop techniques based on normal form theory to give a complete solution to the associated bifurcation problem.     

Analytic solutions of the susceptibility for Doppler-broadened two-level atoms

We derive the rigorous analytic solutions for the susceptibility of Doppler-broadened two-level atoms, valid for arbitrary laser intensities. As is usually the case with real atoms, we observe that, when the homogeneous linewidth is much narrower than the Doppler width, the real part of the susceptibility is given by the product of an imaginary error function and a Gaussian, whereas the imaginary part consists simply of a Gaussian function. By employing the analytic results, in particular, we study the effects of optical pumping and saturation on the atomic susceptibility. We also find that the real (imaginary) part of the susceptibility is weakly (strongly) dependent on such parameters as the laser intensity or the optical pumping rate. The availability of analytic solutions for the simple laser-atom interaction may provide convenient tools for its understanding as well as application to more general and realistic situations.