Elliptic operators with unbounded drift coefficients and Neumann boundary condition

We study the realization A_N of the operator in L2(Ω,μ) with Neumann boundary condition, where Ω is a possibly unbounded convex open set in , U is a convex unbounded function, DU(x) is the element with minimal norm in the subdifferential of U at x, and is a probability measure, infinitesimally invariant for . We show that A_N is a dissipative self-adjoint operator in L2(Ω,μ). Log-Sobolev and Poincaré inequalities allow then to study smoothing properties and asymptotic behavior of the semigroup generated by A_N.     

High performance liquid chromatography of aromatic carboxylic acids on p-tert-butyl-calix[8]arene-bonded silica gel stationary phase

A new p-tert-butyl-calix[8]arene-bonded silica gel stationary phase (CABS) was used for the separation of some aromatic carboxylic acids by HPLC. The chromatographic behaviour of the solutes on CABS was studied in comparison with conventional ODS. The results show that the calix[8]arene-bonded phase exhibits a stronger retention and better selectivity than ODS for the aromatic carboxylic acids. The different elution order of the analytes was also observed on both packings, which show the existence of distinct retention mechanisms. According to chromatographic data, it can be concluded that the high selectivity of CABS for aromatic carboxylic acids ascribes to various interactions between CABS and the analytes, such as hydrophobic interaction, hydrogen bonding interaction, π-π interaction and inclusion interaction.     

A stochastic model in liquid penetration through fibrous media

The statistical genesis of the process of liquid penetration through fibrous media can be regarded as the interaction and the resulting balance among media and liquid cells that comprise the ensemble. A stochastic method, Ising's model, combined with Monte Carlo simulation, can therefore be employed in the study of liquid penetration through fibrous media. This process is driven by the difference of energy of the system after and before a liquid moves from one cell to the other. The energy of the system comprises the internal energy, work done by external force to the system, and the mechanical energy. For experimental verification, the process of water penetration through isotropic fiber mats, both spontaneously and under pressure, is examined. Simulation results are in good agreement with the experiments, indicating a good prospect of the method to be applied in this area.     

Nonlinear Internal Damping of Wave Equations with Variable Coefficients

For wave equations with variable coefficients on regions which are not necessarily smooth, we study the energy decay rate when a nonlinear damping is applied on a suitable subrigion.     

High resolution miniaturized stepper ultrasonic motor using differential composite motion

Experiments show that there is a limited minimum stepped angle in ultrasonic motors (USM). The research on the minimum angle of stepper USM with 15 mm in diameter and wobbling mode is being carried out. This paper presents a novel way to decrease the minimum stepped angle of USM based on the principle of differential composite motion (DCM), i.e. clockwise and counterclockwise rotation. The prototype was fabricated and experiments proved that this method is useful and also keeps a high torque for a large stepped angle. The stator of the prototype is steel, and rotor is fiberglass, antifriction material or steel. The prototype can operate well over 150 h with a 5 kHz wide frequency band. The minimum stepped angle is 46" using a coventional method while 12" using DCM method proposed in this paper.     

Quantum interference in carbon-nanotube electron resonators

A new mechanism is proposed to explain the slow conductance fluctuations in the conductance-gate voltage plot observed in the nanotube electron resonators. It is found that the slow conductance fluctuation is an intrinsic quantum interference phenomenon and exists in all metallic nanotube resonators except zigzag ones. Analytical expressions for both slow and rapid oscillation periods of the conductance fluctuations have been derived, which are well consistent with the existing experiments. It is predicted that the ratio of the slow oscillation period to the rapid one is independent of the gate-voltage efficiency, and determined only by the nanotube length used in experiments.     

Silicon nanowires grown from Au-coated Si substrate

Amorphous Si nanowires were grown on an Au-coated Si substrate by heat treatment at 1000 °C under an H₂ atmosphere. The nanowires have a length of several tens of a micron and a diameter of 10–20 nm. The growth mechanism of the nanowires was investigated and explained with a solid–liquid–solid model. Received: 11 July 2002 / Accepted: 7 July 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +86/10-62751615, E-mail: yudp@pku.edu.cn     

The structure of a self-assembled calixarene aqua-channel system

The crystal structure of the complex 12.calix-[4]-arene dihydroxyphosphonic acid, 12.propane diammonium, 12.ethanol and 40.water molecules is based on dimeric units of the calix, assembled via trigonal units into a hexameric tube of 15 A radius and 16 A depth, further assemby via spanning propane diammonium cations and ethanol molecules forms a channel (40 A), selectively containing all the water molecules.