A Study of Drop Size Distribution in Multistage Bubble Extractor

Results obtained in determining experimentally the mean volume-surface drop diameter of the dispersed phase in a multistage bubble extractor are presented.     

Magnetic field penetration into half-space for type-II superconductors of the second kind

Equations that simulate the magnetic induction and current density distributions in half-space in view of the power I-V characteristic are derived. The magnetization front velocity is determined for a given mean rate of external magnetic field variation at the boundary of the sample. An integral condition for the electrical resistance (nonlinearly depending on the magnetic field) under which the magnetic flux penetrates into the sample with a finite rate is found. An analytical solution that simulates the power variation of the magnetic field at the boundary is given. The Bean generalized model describing the current density distribution near the critical current is considered. It is shown that solutions like shock waves may arise beyond the applicability domain of the Bean model.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

Modification of GaAs by medium-energy N<Stack><Subscript>2</Subscript><Superscript>+</Superscript></Stack> ions

The modification of GaAs with a 2500-eV beam containing N ₂ ⁺ and Ar⁺ ions is examined with Auger electron spectroscopy. Most implanted nitrogen atoms are found to react with the matrix, substituting arsenic atoms to produce a several-nanometer-thick layer of the single-phase GaAs_1−x N_x (x=6%) solid solution. The GaN phase is absent. Displaced arsenic atoms and nitrogen atoms unreacted with the matrix are present in the layer and on its surface. The former segregate, whereas the latter form molecules.     

IR-induced nonlinear optics in Ge-doped Bi12TiO20 large-sized nanocrystallites

Photoinduced non-linear optical effects in large-sized (up to 25 nm) nanocrystallites (NC) of Ge-doped Bi₁₂TiO₂₀ (BTO:Ge) incorporated within olygoether photopolymer matrix have been studied. Photoinduced second harmonic generation (PISHG) was measured. Nd:YAG pulsed laser (λ=1.06 μm) was used as a source of photoinducing light. As a fundamental light source for the SHG and two-photon absorption, Er:LiYF₄ laser (λ=2.065 μm) was used. We have found that with increasing IR pump power density, the output doubled frequency SHG signal (λ=1.03 μm) increases and achieves its maximum value at the pump power density about 0.45 GW/cm² and NC size about 12 nm.The values of second-order optical susceptibilities were almost 20% larger than for the pure BTO NC single crystals. With decreasing temperature below 60 K, the SHG signal increases achieving maximal value at LHeT.     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

Wiener path integrals and the fundamental solution for the Heisenberg Laplacian

In this paper, we present an explicit calculation of the heat kernel, fundamental solution and Schwartz kernel of the resolvent for the Heisenberg Laplacian using Wiener path integrals and their realizations via the Trotter product formula. This also gives another derivation of mehler’s formula.