NUMERICAL DISSIPATION FOR THREE-POINT DIFFERENCE SCHEMES TO HYPERBOLIC EQUATIONS WITH UNEVEN MESHES

The widely used locally adaptive Cartesian grid methods involve a series of abruptly refined interfaces. The numerical dissipation due to these interfaces is studied here for three-point difference approximations of a hyperbolic equation. It will be shown that if the wave moves in the fine-to-coarse direction then the dissipation is positive (stabilizing),and if the wave moves in the coarse-to-fine direction then the dissipation is negative (de-stabilizing).     

Ordering at Solid-Liquid Interfaces Between Dissimilar Materials

In an earlier report we explored structural correlations at a liquid-solid interface with molecular dynamics simulations of a model aluminium system using the Ercolessi-Adams potential and up to 4320 atoms. Substrate atoms were pinned to their equilibrium fcc crystalline positions while liquid atoms were free to move. A direct correlation between the amount of ordering in the liquid phase and the underlying substrate orientation was found. In the present paper we extend this study to the case of a fixed bcc substrate in contact with liquid aluminium. We find surprisingly similar results for the density profiles of both (100) and (110) substrates. However, there is a far greater in-plane ordering in the (100) than for the (110) system. For the (100) substrates we observe adsorption of liquid atoms into the terminating plane of the bcc (100) substrate, effectively transforming the bcc (100) plane into an fcc (100) plane.     

Thermal Effects of Interfacial Dynamics

Dynamical Ginzburg-Landau theory is applied to the study of thermal effects of motion of interfaces that appear after different phase transitions. These effects stem from the existence of the surface internal energy, entropy and temperature gradients in the interfacial transition region. Evolution equations for the interfacial motion are derived. For the experimental verification of the thermal effects the expression is derived for the amplitude of temperature waves during continuous ordering.     

Electrostatically induced undulations of lamellar DNA-lipid complexes

We consider DNA-cationic lipid complexes that form lamellar stacks of lipid bilayers with parallel DNA strands intercalated in between. We calculate the electrostatically induced elastic deformations of the lipid bilayers. It is found that the membranes undulate with a periodicity that is set by the DNA interaxial distance. As a consequence the lamellar repeat distance changes resulting in a swelling or compression of the lamellar stack. Such undulations may be responsible for the intermembrane coupling between DNA strands in different layers as it is observed experimentally. Received 2 March 2001     

Hydrodynamic interactions in the structural fluctuation of a ternary amphiphilic system C12E5/water/ n-octane

Dynamical fluctuations of microemulsion and lamellar structures in a ternary amphiphilic system C₁₂E ₅/water/n-octane are studied by means of neutron spin echo spectrometry. The decay rate of the time correlation of the concentration was analyzed in terms of a theory (M. Nonomura, T. Ohta, J. Chem. Phys. 110, 7516 (1999)), in which both van Hove and hydrodynamic interactions are considered. The result shows that the time correlation function is expressed mostly by a single exponential determined exclusively by hydrodynamic interactions. Received 1 December 1999 and Received in final form 12 March 2001     

Growth and shapes of a cubic lyotropic liquid crystal

Monocrystals of the cubic lyotropic liquid crystal phase V₁ are studied in droplets of the mixture C ₁₂ EO ₆/water surrounded by water vapor of controlled pressure p. Shapes of monocrystals are found to depend on the conditions of growth from the lamellar phase and on the nature of the substrate. After the growth, when the lamellar phase is exhausted and crystals are in equilibrium with water vapors, their shapes are shown to depend on the pressure p. Thermodynamic aspects of these phenomena are discussed. Received 22 November 2000     

Spectral patterns and ultrafast dynamics in planar acetylene

A diabatic correlation diagram procedure is used to classify energy and intensity patterns in a planar model for coupled stretches and bends of acetylene using an effective spectroscopic fitting Hamiltonian. Analysis with polyad phase spheres accounts for the observed patterns in terms of classical phase space structure and bifurcations of the normal modes. Received 29 August 2000 and Received in final form 14 September 2000     

Correlation functions for a Bose-Einstein condensate in the Bogoliubov approximation

In this article we introduce a differential equation for the first order correlation function G ⁽¹⁾ of a Bose-Einstein condensate at T = 0. The Bogoliubov approximation is used. Our approach points out directly the dependence on the physical parameters. Furthermore it suggests a numerical method to calculate G ⁽¹⁾ without solving an eigenvector problem. The G ⁽¹⁾ equation is generalized to the case of non zero temperature. Received 20 September 2000     

Nanostructures of gold coated iron core-shell nanoparticles and the nanobands assembled under magnetic field

Pure metal iron nanoparticles are unstable in the air. By a coating iron on nanoparticle surface with a stable noble metal, these air-stable nanoparticles are protected from the oxidation and retain most of the favorable magnetic properties, which possess the potential application in high density memory device by forming self-assembling nanoarrays. Gold-coated iron core-shell structure nanoparticles (Fe/Au) synthesized using reverse micelles were characterized by transmission electron microscopy (TEM). The average nanoparticle size of the core-shell structure is about 8 nm, with about 6 nm diameter core and 1∼2 nm shell. Since the gold shell is not epitaxial growth related to the iron core, the morié pattern can be seen from the overlapping of iron core and gold shell. However, the gold shell lattice can be seen by changing the defocus of TEM. An energy dispersive X-ray spectrum (EDS) also shows the nanoparticles are air-stable. The magnetic measurement of the nanoparticles also proved successful synthesis of gold coated iron core-shell structure. The nanoparticles were then assembled under 0.5 T magnetic field and formed parallel nanobands with about 10 μm long. Assembling two dimensional ordered nanoarrays are still under going. Received 29 November 2000     

Preparation and decoherence of superpositions of electromagnetic field states

In a recent experiment the progressive decoherence of a mesoscopic superposition of two coherent field states in a high-Q cavity, known as Schr?dinger cat state, has been measured for the first time [Brune et al., Phys. Rev. Lett. 77, 4887 (1996)]. Here, the full master equation governing the coupled dissipative dynamics of the atom-field system studied in the experiment is formulated and solved numerically for the experimental parameters. The model simulated avoids the approximations underlying an analytically solvable model which is based on a harmonic expansion of the energies of the dressed atomic states and on a treatment of their dynamics within the adiabatic approximation. In particular, the numerical simulations reveal that the coupling of the cavity field mode to its environment causes important decoherence effects already during the initial preparation phase of the Schr?dinger cat state. This phenomenon is investigated in detail with the help of a measure for the purity of states. Moreover, the Hilbert-Schmidt distance of the intended target state, the Schr?dinger cat, to the state that is actually prepared in the experiment is determined. Received 13 September 2000 and Received in final form 22 December 2000