A mathematical model of the ring-spinning process

This paper develops a mathematical model of the ring-spinning process that takes into account its non-stationary nature. A complex system of differential equations is obtained, which from a mathematical point of view constitutes a ‘free-boundary’ problem. Its solution involves definition of suitable boundary conditions related to the mechanical characteristics of the process and of the spinning machine itself. The boundary conditions which determine the solution are pointed out. A numerical solution of the system of differential equations can be obtained by the Finite-Segments method, as shown in an example.     

Evolution of stress and strain relaxation of Ge and SiGe alloy films on Si(0 0 1)

The growth of Ge and SiGe alloy films on Si substrates has attracted considerable interest in the last years because of their importance for optoelectronic devices as well as Si-based high speed transistors. Here we give a short overview on our recent real time stress measurements of Ge and SiGe alloy films on Si(0 0 1) performed with a sensitive cantilever beam technique and accompanied by structural investigations with atomic force microscopy. Characteristic features in the stress curves provide detailed insight into the development and relief of the misfit strain. For the Stranski–Krastanow system Ge/Si(0 0 1) as well as for SiGe films with Si contents below 20%, the strain relaxation proceeds mainly into two steps: (i) by the formation of 3D islands on top of the Ge wetting layer; (ii) via misfit dislocations in larger 3D islands and upon their percolation.     

Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer

The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.     

Analysis of saltation characteristics of bed-load transport in flowing water

The study of bed-load transport is of great significance both in theory and in practice. This paper discusses the saltation of bed-load solid grains in flowing water. Experiments and theoretic analysis have been made by means of high-speed photographing and advanced data processing technique with a combined method based on mechanical and statistical theories. It indicates that the saltation is the main form of the bed-load transport under ordinary flowing conditions. In the meantime, taking successive saltation as the model of bed-load transport, systematic analysis has been made with regard to the kinematic properties and mechanism of saltation. The statistical analysis shows that the probability density functions of the relative height and length of saltation are in conformity with Γ-type distribution, while the probability density functions of the relative velocities of saltation are in conformity with the Gaussian distribution. The project supported by National Natural Science Foundation of China     

1，4－二氟四苯基苯的合成、结构与构象

借助电子转移催化反应的方法，用电子给予体１，４－二锂四苯基丁二烯将惰性的三溴氟甲烷活化，并与之发生反应，产物１，４－二氟四苯基苯的结构经ＭＳ、ＮＭＲ和Ｘ射线单晶衍射确证，并以分子力学的方法对其进行了构象分析。     

Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Crossover from BCS-superconductivity to Bose-condensation

Starting from a model of free Fermions in two dimensions with an arbitrary strong effective interaction, we derive a Ginzburg-Landau theory describing the crossover from BCS-superconductivity to Bose-condensation. We find a smooth crossover from the standard BCS-limit to a Gross-Pitaevski type equation for the order parameter in a Bose superfluid. The mean field transition temperature exhibits a maximum at a coupling strength, where the behaviour crosses over from BCS to Bose like with corresponding values of 2 Δ₀/T_c ≈ 5 which are characteristic for high T_c superconductors.     

Self-organization in aggregating colloids

Summary The interceluster organization of a two-dimensional colloidal system undergoing diffusion-limited cluster-cluster aggregation is considered. During this process the system evolves into a stationary, scaling state. In this state the organization arises from effective intercluster repulsion due to the mutually exclusive depletion zones surrounding each cluster. It is shown that in the scaling regime the relevant size of the depletion zones is determined by the separation between clusters, rather than the cluster size. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003