Embedding and splitting ordinary differential equations in normal form

We introduce an embedding of real or complex n-dimensional space Kⁿ as an algebraic variety V which is determined by the action of a linear one-parameter group. Every analytic vector field on Kⁿ corresponds to some embedded vector field on V. For a symmetric vector field this embedded vector field splits into a reduced system and a direct sum of non-autonomous linear systems. Examples and applications are mostly concerned with Poincaré-Dulac normal forms. Embeddings provide a natural setting for perturbations of symmetric systems, in particular of systems in normal form up to some degree.     

Collapse and stability of necklace beams in Kerr media

We investigate the spatial dynamics of optical necklace beams in Kerr media. For powers corresponding to less than the critical power for self-focusing per bead, we experimentally confirm the confinement of these necklace beams as proposed in [Phys. Rev. Lett. 81, 4851 (1998)10.1103/PhysRevLett.81.4851]. At higher powers, we observe a transition from collective necklace behavior to one in which the beads of the necklace collapse independently. We observe that, below the transition power, the perturbed necklace still behaves in a collective manner with coupling between individual beads but that, at higher powers, it undergoes a similar transition to a decoupled state of the necklace.     

Path integral synthesis of lyapunov functionals for partial differential equations

A method is given for constructing Lyapunov Functionals for dynamical systems governed by partial differential equations. The functionals are obtained as path integrals in a suitably chosen state space of a generalized gradient operator, and the method may be viewed as an extension to infinite dimensional systems of the variable gradient technique. Some of the fundamental concepts underlying the formalism are reviewed, and examples of applications to some linear, non-linear and hybrid systems are given.     

Material electromagnetic fields and material forces

Electromagnetic fields address configurational forces in a natural way through an energy–stress tensor, which reduces to the Maxwell tensor in the simplest case. This tensor is related to physical forces and to the Cauchy traction in a continuum. Material forces, as opposed to physical forces, are of a different nature as they act upon a site of a continuum where the possible material inhomogeneity is located. A material energy–stress tensor, which is reminiscent of the Maxwell stress, is associated with these forces. Through appropriate balance laws, a material momentum is also associated with material forces. The material momentum is of particular interest in electromagnetic materials as it is intimately related to the pseudomomentum of light [Peierls in Highlights of Condensed Matter Physics, pp. 237–255 (1985) and in Surprises in Theoretical Physics, pp. 91–99 (1979); Thellung in Ann. Phys. 127, 289–301 (1980)]. The balance law for the material momentum can be derived either from the classical physical laws or independently of them. This derivation, which is based on the material electromagnetic potentials and the related gauge transformations, is discussed and commented on for an electromagnetic body.     

A preconditioning approach to the pagerank computation problem

Some spectral properties of the transition matrix of an oriented graph indicate the preconditioning of Euler-Richardson (ER) iterative scheme as a good way to compute efficiently the vertexrank vector associated with such graph. We choose the preconditioner from an algebra U of matrices, thereby obtaining an ER_U method, and we observe that ER_U can outperform ER in terms of rate of convergence. The proposed preconditioner can be updated at a very low cost whenever the graph changes, as is the case when it represents a generic set of information. The particular U utilized requires a surplus of operations per step and memory allocations, which make ER_U superior to ER for not too wide graphs. However, the observed high improvement in convergence rate obtained by preconditioning and the general theory developed, are a reason for investigating different choices of U, more efficient for huge graphs.     

Kinetics and equilibria associated with the absorption and desorption of water and lithium chloride in an ethylene—vinyl alcohol copolymer

Sorption and desorption equilibria and kinetics for LiCl and H₂O in an ethylene—vinyl alcohol copolymer film containing 70 mole percent vinyl alcohol were investigated at 25°C. The swelling behavior of water in the polymer was characterized by vapor and liquid sorption experiments over a range of water activities. p]The effects of LiCl content on the water sorption kinetics and equilibria in the films are presented and discussed. The kinetics and mechanism of LiCl sorption have also been studied. The amount of salt sorbed into the polymeric films increases linearly with the salt concentration in the external aqueous solutions. Both the rate and the amount of sorbed water increase significantly as the LiCl content increases. p]The desorption of LiCl, previously sorbed into the polymer, was characterized for different salt loadings. The rate of fractional salt release is independent of LiCl concentration in the film. Initially, the salt release is controlled by the nearly constant-rate absorption of water. The salt release, at long times, lags behind the swelling-controlled water uptake, indicating that the salt release is not completely controlled by the water sorption and that diffusion in the swollen polymer matrix contributes significantly to the long term elution of LiCl. Independent thermal analysis experiments suggest the formation of a metal salt—poly(ethylene—vinyl alcohol) complex.     

Characterization of macromolecules in liquid solutions by thermal diffusion. I. Dependence of the soret coefficient on the nature of the dispersing medium

Experiments have been carried out on thermal diffusion of macromolecular particles dispersed in various liquids, with the object of checking some predictions of the radiation-pressure theory of Soret effect in liquids and of establishing a method of physical characterization of macromolecules in liquid solutions. The experimental results confirm the importance of the ratio G between thermal conductivity K and (phase) velocity v of high-frequency elastic waves of the materials composing the mixture in determining the thermodiffusive behavior of a liquid solution. We have shown that the migration of the macromolecular component takes place in the same direction in which thermal energy is flowing or opposite to it, depending on whether G of the dispersed particles is smaller or larger relative to the G of the liquid. Another aspect of the same phenomenon may be observed when macroscopic pieces of nonmetallic materials are suspended in a liquid, and heat is made to flow through this solid plunger and the surrounding liquid. The experiments performed with molecular solutions and with macroscopic plungers mutually complement and confirm each other. Anomalous results obtained in the case of solutions of polyvinylpyrrolidone in methanol are also discussed, and the possibility that this might be the consequence of the existence of a marked velocity dispersion in the high-frequency region of the spectrum of thermal waves in both water and methyl alcohol is indicated. Finally the possibility is hinted that thermal diffusion might have been responsible for the phenomena of molecular selection and evolution which ultimately led to the origin of life on our planet.     

I–V characteristics and critical currents in superconducting/ferromagnetic bilayers

Current–voltage (I–V) characteristics and critical current density, J_c, for the onset of vortex motion were measured at different magnetic fields, H, and temperatures, T, in a superconducting (S)/ferromagnetic (F) bilayer and in a single Nb film. We choose Nb as a superconductor and a weak ferromagnetic alloy, Pd_1−xNi_x with x = 16, as F. We found that J_c was smaller for the S/F bilayer with respect to the single Nb film. The result was related to the reduced value of the superconducting order parameter in the bilayer.     

Dynamic response of converse magnetoelectric effect in a PMN-PT-based multiferroic heterostructure

A multiferroic heterostructure, consisting of a 25 μm thick Metglas® ribbon affixed to a lead magnesium niobate–lead titanate (PMN-PT) crystal, was systemically studied to investigate the time response of converse magnetoelectric coupling under the application of electric fields at low frequencies (0.05<f<10 Hz). This multiferroic heterostructure exhibits a considerably strong converse magnetoelectric effect, CME=?80%, where CME=[M(E)?M(0)]/M(0), and a converse ME coupling constant, A=22.5 Oe-cm/kV, at frequencies below 1 Hz and near saturation electric polarization. A switching time (t _s), representing the response time of the CME coupling, is measured to be 0.6 seconds for this heterostructure under the application of instantaneous electric fields. The switching time results in significant influences on the magnetoelectric effect especially at frequencies higher than 2 Hz. The dynamic response of CME coupling is predominantly determined by ferroelectric relaxation within the PMN-PT crystal, as opposed to the magnetic relaxation of the Metglas® ribbon. A model was used to describe the dynamic behavior of CME coupling in disordered systems such as PMN-PT.