The existence of ground states for fourth-order wave equations

Focusing on the fourth-order wave equation u_tt+Δ²u+f(u)=0, we prove the existence of ground state solutions u=u(x+ct) for an optimal range of speeds c∈Rⁿ and a variety of nonlinearities f.     

A lower bound for the amplitude of traveling waves of suspension bridges

We obtain a lower bound for the amplitude of nonzero homoclinic traveling wave solutions of the McKenna–Walter suspension bridge model. As a consequence of our lower bound, all nonzero homoclinic traveling waves become unbounded as their speed of propagation goes to zero (in accordance with numerical observations).     

Solitons via Lie-Bäcklund transformation for 5D low-energy string theory

We apply a non-linear matrix transformation of Lie-Bäcklund type on a seed soliton configuration in order to obtain a new solitonic solution in the framework of the 5D low-energy effective field theory of the bosonic string. The seed solution represents a stationary axisymmetric two-soliton configuration previously constructed through the inverse scattering method and consists of a massless gravitational field coupled to a non-trivial chargeless dilaton and to an axion field endowed with charge. We apply a fully parameterized non-linear matrix transformation of Ehlers type on this massless solution and get a massive rotating axisymmetric gravitational soliton coupled to charged axion and dilaton fields. We discuss on some physical properties of both the initial and the generated solitons and fully clarify the physical effect of the non-linear normalized Ehlers transformation on the seed solution.     

A tri-Hamiltonian formulation of the full Kostant-Toda lattice

We define Poisson structures which lead to a tri-Hamiltonian formulation for the full Kostant-Toda lattice. In addition, a hierarchy of vector fields called master symmetries are constructed and they are used to generate the nonlinear Poisson brackets and other invariants. Various deformation relations are investigated. The results are analogous to results for the finite nonperiodic Toda lattice.     

Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin

Received April 9, 2001 / Published online August 16, 2001     

On the asymptotic behavior of nonlinear waves in the presence of a short-range potential

Consider the nonlinear wave equation with zero mass and a time-independent potential in three space dimensions. When it comes to the associated Cauchy problem, it is already known that short-range potentials do not affect the existence of small-amplitude solutions. In this paper, we focus on the associated scattering problem and we show that the situation is quite different there. In particular, we show that even arbitrarily small and rapidly decaying potentials may affect the asymptotic behavior of solutions.     

High-Yield Synthesis of Gold Microplates Using Amphiphilic Block Copolymers: Are Lyotropic Liquid Crystals Required?

Summary : High-yield synthesis of gold microplates is achieved through autoreduction of hydrogen tetrachloroaureate (III) hydrate (HAuCl₄ · 3H₂O) in aqueous solutions of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) block copolymer (Pluronic L64, EO₁₃PO₃₀EO₁₃) at ambient conditions, in the absence of added energy, reductant, or other surfactants. The formation by the amphiphilic block copolymer of lyotropic liquid crystals (e.g., ordered cylindrical/hexagonal or lamellar phases) is not required for templating the formation of such microplates.     

Properties of the He ground state from He neutron knockout

The unbound nucleus ⁷He, produced in neutron-knockout reactions with a 240 MeV/u ⁸He beam in a liquid-hydrogen target, has been studied in an experiment at the ALADIN-LAND setup at GSI. From an R-matrix analysis the resonance parameters for ⁷He as well as the spectroscopic factor for the ⁶He(0⁺) + n configuration in its ground-state have been obtained. The spectroscopic factor is 0.61 confirming that ⁷He is not a pure single-particle state. An analysis of ⁵He data from neutron-knockout reactions of ⁶He in a carbon target reveals the presence of an s  -wave component at low energies in the α+n$\alpha +\mathrm{n}$ relative energy spectrum.     

Synthesis and size control of luminescent ZnSe nanocrystals by a microemulsion-gas contacting technique

A scalable method for controlled synthesis of luminescent compound semiconductor nanocrystals (quantum dots) using microemulsion-gas contacting at room temperature is reported. The technique exploits the dispersed phase of a microemulsion to form numerous identical nanoreactors. ZnSe quantum dots were synthesized by reacting hydrogen selenide gas with diethylzinc dissolved in the heptane nanodroplets of a microemulsion formed by self-assembly of a poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) amphiphilic block copolymer in formamide. A single nanocrystal is grown in each nanodroplet, thus allowing good control of particle size by manipulation of the initial diethylzinc concentration in the heptane. The ZnSe nanocrystals exhibit size-dependent luminescence and excellent photostability.