Newton's method for nonlinear ordinary and partial differential equations

A unified approach is presented for proving the local, uniform and quadratic convergence of the approximate solutions and a-posteriori error bounds obtained by Newton's method for systems of nonlinear ordinary or partial differential equations satisfying an inverse-positive property. An important step is to show that, at each iteration, the linearized problem is inverse-positive. Many classes of problems are shown to satisfy this property. The convergence proofs depend crucially on an error bound derived previously by Rosen and the author for quasilinear elliptic, parabolic and hyperbolic problems.     

Studies of the quantum Hall to quantum Hall insulator transition in InSb-based 2DESs

The temperature dependence of ρ_xx is studied in the vicinity of the quantum Hall to quantum Hall insulator transition (ν=1→0) in InSb/InAlSb based 2DESs. ρ_xx displays a symmetric temperature dependence about the transition with on the QH side and on the insulating side. A plot of 1/T₀ for successive ν displays power-law divergence with 1/T₀∝|ν−ν_c|^−γ,² with γ=2.2±0.3. This critical behavior in addition to the behavior expected of the quantum transport regime confirms that the QH/QHI transition is indeed a good quantum phase transition.     

Phase shift analysis and extraction of structure functions for Coulomb distortion on (e, e'p) reactions at high electron energies

New results for the double beta decay of ⁷⁶ Ge are presented. They are extracted from data obtained with the HEIDELBERG-MOSCOW experiment, which operates five enriched ⁷⁶ Ge detectors in an extreme low-level environment in the Gran Sasso underground laboratory. The two-neutrino-accompanied double beta decay is evaluated for the first time for all five detectors with a statistical significance of 47.7 kg y resulting in a half-life of T _1/2 ^2ν = [1.55±0.01(stat)^+0.19 _-0.15(syst)]×10²¹ y. The lower limit on the half-life of the 0νββ decay obtained with pulse shape analysis is T _1/2 ^0ν > 1.9×10²⁵(3.1×10²⁵) y with 90% C.L. (68% C.L.) (with 35.5 kg y). This results in an upper limit of the effective Majorana-neutrino mass of 0.35 eV (0.27 eV) using the matrix elements of A. Staudt et al.'s work (Europhys. Lett. 13, 31 (1990)). This is the most stringent limit at present from double beta decay. No evidence for a majoron-emitting decay mode is observed. Received: 22 August 2001 / Accepted: 18 October 2001     

Nuclear matter properties and relativistic mean-field theory

Nuclear matter properties are calculated in the relativistic mean-field theory by using a number of different parameter sets. The result shows that the volume energy a₁ and the symmetry energy J are around the acceptable values 16MeV and 30MeV, respectively; the incompressibility K₀ is unacceptably high in the linear model, but assumes reasonable value if nonlinear terms are included; the density symmetry L is around 100MeV for most parameter sets, and the symmetry incompressibility K _s has positive sign which is opposite to expectations based on the nonrelativistic model. In almost all parameter sets there exists a critical point (,), where the minimum and the maximum of the equation of state are coincident and the incompressibility equals zero, falling into ranges 0.014fm^-3 < < 0.039fm^-3 and 0.74 < ≤0.95; for a few parameter sets there is no critical point and the pure neutron matter is predicted to be bound. The maximum mass M _NS of neutron stars is predicted in the range 2.45M ?M _NS? 3.26M , the corresponding neutron star radius R _NS is in the range 12.2km ?R _NS? 15.1km. Received: 5 May 2000 / Accepted: 28 November 2000     

Some new domains with complete Kähler metrics of negative curvature

We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?ⁿ, intersections of complex-ellipsoidal domains in ?², and intersections of fractional linear transforms of the unit ball in ?². In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?², the sum of the Bergman metrics is a Kähler metric with negative curvature operator.     

Two-machine flow shop scheduling problem with an outsourcing option

We consider a two-machine flow shop problem in which each job is processed through an in-house system or outsourced to a subcontractor. A schedule is established for the in-house jobs, and performance is measured by the makespan. Jobs processed by subcontractors require paying an outsourcing cost. The objective is to minimize the sum of the makespan and total outsourcing costs. We show that the problem is NP-hard in the ordinary sense. We consider a special case in which each job has a processing requirement, and each machine a characteristic value. In this case, the time a job occupies a machine is equal to the job’s processing requirement plus a setup time equal to the characteristic value of that machine. We introduce some optimality conditions and present a polynomial-time algorithm to solve the special case.     

Acoustic vibration of the amphibian eardrum studied by white noise analysis and holographic interferometry

The motion of the amphibian eardrum under free-field acoustic stimulation was investigated using time-averaged holography. We show that the amplitude is linearly related to sound pressure up to +/- 1000 nm. The frequency response of the eardrum shows broad resonance characteristics with a main peak between 1200-2200 Hz. The velocity of the tympanic membrane's motion at its resonance frequency matches the acoustic velocity of air particles. The resonance characteristics of the eardrum are also revealed by white noise stimulation. The power spectrum obtained by Fourier transformation of the autocorrelation of the response to noise resembles closely that obtained by holography.     

Design of a circular Dammann grating

A novel circular Dammann grating is proposed to generate uniform-intensity impulse rings corresponding to different diffraction orders in the far field. The intensities of the rings are determined by the coefficients of the circular sine series decomposition of the grating function. The definition of diffraction efficiency and uniformity for this novel device are described. Numerical solutions of binary phase circular Dammann gratings are presented. A binary phase three-order circular Dammann grating of pi phase depth is fabricated by an e-beam direct writing technique and is experimentally demonstrated.     

Absorption of short laser pulses on solid targets in the ultrarelativistic regime

We report the first direct measurements of total absorption of short laser pulses on solid targets in the ultrarelativistic regime. The data show an enhanced absorption at intensities above 10(20) W/cm(2), reaching 60% for near-normal incidence and 80%-90% for 45 degrees incidence. Two-dimensional particle-in-cell simulations demonstrate that such high absorption is consistent with both interaction with preplasma and hole boring by the intense laser pulse. A large redshift in the second harmonic indicates a surface recession velocity of 0.035c.     

Strategies Towards Capturing Nitrogenase Substrates and Intermediates via Controlled Alteration of Electron Fluxes

Nitrogenase utilizes an ATP-dependent reductase to deliver electrons to its catalytic component to enable two important reactions: the reduction of N₂ to NH₄⁺, and the reduction of CO to hydrocarbons. The two nitrogenase-based reactions parallel the industrial Haber–Bosch and Fischer–Tropsch processes, yet they occur under ambient conditions. As such, understanding the enzymatic mechanism of nitrogenase is crucial for the future development of biomimetic strategies for energy-efficient production of valuable chemical commodities. Mechanistic investigations of nitrogenase has long been hampered by the difficulty to trap substrates and intermediates relevant to the nitrogenase reactions. Recently, we have successfully captured CO on the Azotobacter vinelandii V-nitrogenase via two approaches that alter the electron fluxes in a controlled manner: one approach utilizes an artificial electron donor to trap CO on the catalytic component of V-nitrogenase in the resting state; whereas the other employs a mismatched reductase component to reduce the electron flux through the system and consequently accumulate CO on the catalytic component of V-nitrogenase. Here we summarize the major outcome of these recent studies, which not only clarified the catalytic relevance of the one-CO (lo-CO) and multi-CO (hi-CO) bound states of nitrogenase, but also pointed to a potential competition between N₂ and CO for binding to the same pair of reactive Fe sites across the sulfur belt of the cofactor. Together, these results highlight the utility of these strategies in poising the cofactor at a well-defined state for substrate- or intermediate-trapping via controlled alteration of electron fluxes, which could prove beneficial for further elucidation of the mechanistic details of nitrogenase-catalyzed reactions.