Geometric gradient-flow dynamics with singular solutions

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.     

Characteristics of adsorption phase with water/organic mixtures at a surface of activated carbons possessing intraparticle and textural porosities

The behaviour of water and water/organic mixtures adsorbed onto activated microporous carbons or a carbon adsorbent with narrow intraparticle micropores and broad mesopores and macropores between nanoparticles was studied using low-temperature adsorption method and ¹H NMR spectroscopy with layer-by-layer freezing-out of liquids at 190-273 K. These investigations revealed concentration-dependent effects of benzene, DMSO, acetone, chloroform, methane and acetonitrile on the characteristics of adsorbed water and the influence of this water on the interfacial behaviour of adsorbed organics. The influence of organics causes the structural and energetic differentiations of adsorbed water. The latter can be displaced by organics from micropores into broader pores and/or form mixture with polar solvents in meso and macropores. Freezing of adsorbed water can affect the adsorbent structure because ice crystallites have a larger size than that of liquid water droplets that lead to changes in the behaviour of adsorbed water/organic mixtures observed by the ¹H NMR and adsorption methods.     

Transport Characteristics of Mesoscopic Radio-Frequency Single Electron Transistor

The transport property of a quantum dot under the influence of external time-dependent field is investigated. The mesoscopic device is modelled as semiconductor quantum dot coupled weakly to superconducting leads via asymmetric double tunnel barriers of different heights. An expression for the current is deduced by using the Landauer-Buttiker formula, taking into consideration of both the Coulomb blockade effect and the magnetic field. It is found that the periodic oscillation of the current with the magnetic field is controlled by the ratio of the frequency of the applied ac-field to the electron cyclotron frequency. Our results show that the present device operates as a radio-frequency single electron transistor.     

Kinetics of Liquid Structure Transition of Sn-（40wt%）Bi Melt

The kinetics of temperature-induced liquid-liquid structure transition （TI-LLST） process in Sn-（40wt%）Bi melt is investigated in isothermal and continuous heating experiments with electrical resistivity method. The time evolution pattern of the electrical resistivity suggested the transition mechanism of TI-LLST for Sn-（40wt%）Bi melt in accordance with the autocatalytic reaction model, which is an indication of nucleation-growth type. With the calculated reaction rate constant KT and apparent activation energy Δ E, we deduce the reason for the characteristics of TI-LLST. The present result may be beneficial for further understanding of the nature of TI-LLST.     

Truncated States Obtained by Iteration

We introduce the concept of truncated states obtained via iterative processes （TSI） and study its statistical features, making an analogy with dynamical systems theory （DST）. As a specific example, we have studied TSI for the doubling and the logistic functions, which are standard functions in studying chaos. TSI for both the doubling and logistic functions exhibit certain similar patterns when their statistical features are compared from the point of view of DST.     

Influence of Different Substrates on Laser Induced Damage Thresholds at 1064nm of Ta2O5 Films

Ta2O5 films are prepared on Si, BK7, fused silica, antireflection （AR） and high reflector （HR） substrates by electron beam evaporation method, respectively. Both the optical property and laser induced damage thresholds （LIDTs） at 1064 nm of Ta2O5 films on different substrates are investigated before and after annealing at 673 K for 12 h. It is shown that annealing increases the refractive index and decreases the extinction index, and improves the O/Ta ratio of the Ta2O5 films from 2.42 to 2.50. Moreover, the results show that the LIDTs of the Ta2O5 films are mainly correlated with three parameters： substrate property, substoichiometry defect in the films and impurity defect at the interface between the substrate and the films. Details of the laser induced damage models in different cases are discussed.     

Determination of Thickness of an Inaccessible Thin Film under a Multilayered System from Natural Frequencies

We investigate the relationship between natural frequencies of a multilayered system of different elastic materials and the thickness of the undermost thin film. The natural frequencies are numerically calculated from the reflection coefficient of a sample system of ＂steel-epoxy resin-aluminium-thin polymer＂ with normal incidence. Strain energy ratio is defined and calculated to give the physics explanation why some frequencies are sensitive to thickness of the thin film in certain range. Experiments of three specimens indicate that the measured natural frequencies agree well with the theoretical ones. It is found in our experiments that the ratio of the lowest film thickness to wavelength is about 1/5. The average relative errors for the inverted polymer film thicknesses are found to be 11.8%, -4.8% and -1.3%, respectively.     

Property of Image-Object Using TE/TM-polarized Wave in the Near-Field Optics with CCGM-FFT

Discretization of the Lippmann-Schwinger integral equation with complex conjugate gradient method and fast Fourier transform （CCGM-FFT） is solved, which can reduce the memory storage and the CPU time compared with the traditional method, MOM. Thus objects with large size and multiple scattering objects could be simulated with CCGM-FFT. The total intensity and the distribution of each field component of the dielectric and metallic objects under the excitation of the TE//TM-polarized wave are calculated with photon scanning tunnelling microscopy （PSTM） at the constant height. The simulating results are analysed and explained reasonably. The results show that the polarization plays an important role for imaging of PSTM.     

Bi- and Au-Induced Reconstructions on GaAs（001）-2 × 4 Surface

Submonolayer Bi and Au adsorptions on the GaAs（001）-2× 4 surface are investigated by scanning tunnelling microscopy, low energy electron diffraction and first-principles calculations. The 1 ×4 and 3 × 4 reconstructed surface induced by Bi and Au, respectively, are revealed and their structural models are proposed based on experiments and first-principles calculations. Moreover, the validity of the recently proposed generalized electron counting （GEC） model [Phys. Rev. Lett. 97 （2006） 126103] is examined in detail by using the two surfaces. The GEC model perfectly explains the structural features, such Bi-1 × 4 surface and the 3x arrangement of four-atom Au as the characteristic short double-line structure in the clusters.     

Accurate One-Centre Method for Hydrogen Molecule Ions in Strong Magnetic Field

An accurate one-centre method for the hydrogen molecule ion is tested. The slow convergence and singularities at the nuclear positions that are problems in the general one-centre method axe solved well by employing the optimal radial and angular B-spline basis. Therefore, the accuracy of the one-centre method is improved observably. For the ground state of the H2^＋ in the free field, 7 ×10^-8 accuracy is obtained, which rivals the best one-centre calculation before. As a test, the nuclear distances and the total energies of the 1σ g,u, 1πu, 1δ9,u and 2σg states of the H2^＋ for the magnetic field strength B = 1 a.u. are also obtained. Compared to other results, five-digit accuracy at least can be arrived even for the antibonding states 1σu and 1σu, whose equilibrium distances R is very large.