Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Quadratic distances for capacity and bi-capacity approximation and identification

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. The proposed approach, consisting in solving a strictly convex quadratic program, has been implemented within the GNU R kappalab package for capacity and nonadditive integral manipulation. Its application is illustrated on two examples.      

Characterisation of the photocatalyst Pilkington Activ™: a reference film photocatalyst?

Pilkington Glass Activ™ represents a possible suitable successor to P25 TiO₂, especially as a benchmark photocatalyst film for comparing other photocatalyst or PSH self-cleaning films. Activ™ is a glass product with a clear, colourless, effectively invisible, photocatalytic coating of titania that also exhibits PSH. Although not as active as a film of P25 TiO₂, Activ™ vastly superior mechanical stability, very reproducible activity and widespread commercial availability makes it highly attractive as a reference photocatalytic film. The photocatalytic and photo-induced superhydrophilitic (PSH) properties of Activ™ are studied in some detail and the results reported. Thus, the kinetics of stearic acid destruction (a 10⁴ electron process) are zero order over the stearic acid range 4–129 monolayers and exhibit formal quantum efficiencies (FQE) of 0.7×10⁻⁵ and 10.2×10⁻⁵ molecules per photon when irradiated with light of 365±20 and 254 nm, respectively; the latter appears also to be the quantum yield for Activ™ at 254 nm. The kinetics of stearic acid destruction exhibit Langmuir–Hinshelwood-like saturation type kinetics as a function of oxygen partial pressure, with no destruction occurring in the absence of oxygen and the rate of destruction appearing the same in air and oxygen atmospheres. Further kinetic work revealed a Langmuir adsorption type constant for oxygen of 0.45±0.16 kPa⁻¹ and an activation energy of 19±1 kJ mol⁻¹. A study of the PSH properties of Activ™ reveals a high water contact angle (67°) before ultra-bandgap irradiation reduced to 0° after prolonged irradiation. The kinetics of PSH are similar to those reported by others for sol–gel films using a low level of UV light. The kinetics of contact angle recovery in the dark appear monophasic and different to the biphasic kinetics reported recently by others for sol–gel films [J. Phys. Chem. B 107 (2003) 1028]. Overall, Activ™ appears a very suitable reference material for semiconductor film photocatalysis.     

Self-consistent modelling of argon microwave discharge sustained by electromagnetic wave in dipole mode

Microwave discharges produced by travelling/standing electromagnetic waves have drawn considerable attention in recent years due to their wide application in microelectronic industry. Here are presented the axial distributions of the electrons and ions as well as those of excited atoms in an argon microwave discharge at a low gas pressure (400 mTorr) sustained by a 2.45 GHz travelling dipolar electromagnetic wave. The numerical calculations are based on a self-consistent kinetic-electrodynamic model and the results obtained are in a good agreement with the experimental data. The model yields also the magnitude of the wave power sustaining the discharge and the axial profiles of all electromagnetic-wave characteristics and the axial distribution of the neutral gas temperature.     

The branching graphs of polyhexes: Some elementary theorems,conjectures and open questions

This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex.     

Limited resolution in complex network community detection with Potts model approach

According to Fortunato and Barthélemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.     

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

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.