Affine connection in Hilbert space

A concise geometrodynamic approach to quantum theory is introduced, via a quo;quantum connectionQ _µ , which is the affine connection in Hilbert space. It is emphasized that this is the simplest and most natural interpretation of quantum mechanics in general relativity and yet has been largely neglected, so that much work remains to be done on it. The generalized Hilbert space has a simple Hermitian metric, but the precise form ofQ _µ remains to be determined. The quantum connection is matheamtically analogous to the spinor connection, which is discussed here for that reason, although the spinor connection arises in the first quantization, whereasQ _µ geometrizes the second quantization.     

Ferromagnetic resonance and spin wave excitations in metallic glasses: The effects of thermal ageing and long-range magnetic ordering

New ferromagnetic resonance experiments under degenerate resonance conditions are reported for FeNiPB metallic glass ribbons in annealed and polished samples. An interpretation of these experimental results in terms of established theories in Ferromagnetic and Spin Wave Resonance Spectroscopy (FSWR) is proposed. The spin-wave analysis is used to interpret the effects of magnetic anisotropy on the lineshapes of metallic glasses before and after annealing. The conclusion is reached that a model of dipolar-coupled regions which assume a common resonance frequency band is appropriate in ferromagnetic metallic glasses. The role of surface pits scattering, microheterogeneities in chemical composition, clustering processes and long-range magnetic ordering in these systems is discussed in relation to the changes of glass properties by annealing. We also conclude that FSWR techniques are more sensitive than differential scanning calorimetry, X-ray scattering and static, magnetic techniques which are currently used to study structural relaxation in glasses.     

Transfinite sequences of continuous and Baire class 1 functions

The set of continuous or Baire class 1 functions defined on a metric space is endowed with the natural pointwise partial order. We investigate how the possible lengths of well-ordered monotone sequences (with respect to this order) depend on the space .

     

Lower bounds for boundary roughness for droplets in Bernoulli percolation

We consider boundary roughness for the ``droplet' created when supercritical two-dimensional Bernoulli percolation is conditioned to have an open dual circuit surrounding the origin and enclosing an area at least l², for large l. The maximum local roughness is the maximum inward deviation of the droplet boundary from the boundary of its own convex hull; we show that for large l this maximum is at least of order l^1/3(logl)^–2/3. This complements the upper bound of order l^1/3(logl)^–2/3 proved in [Al3] for the average local roughness. The exponent 1/3 on l here is in keeping with predictions from the physics literature for interfaces in two dimensions. The research of the first author was supported by NSF grant DMS-9802368. The research of the second author was supported by NSF grants DMS-9802368 and DMS-0103790.Mathematics Subject Classification (2000): Primary 60K35; Secondary 82B20, 82B43     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Finite element modal solutions of planar photonic crystal fibers with rectangular air-holes

Modal solutions of planar photonic crystal waveguides with rectangular air-holes are presented by using a rigorous full-vectorial finite element-based approach. The effective indices, mode field profiles, spot-sizes, power confinements, modal hybridness, beat lengths and group velocity dispersions are shown for the fundamental and higher order modes of the quasi-TE and TM polarizations.     

Manipulating supercontinuum generation by minute continuous wave

We report a simple triggering mechanism that greatly enhances and stabilizes supercontinuum generation by using an extremely weak cw light (~200,000 times weaker than the pump light). Such an active manipulation scheme can be enabled by a wide range of input conditions and circumvents complex techniques such as precise time delay tuning and dedicated feedback control. It thus offers a handy and versatile approach to control and optimize supercontinuum generation, expanding its range of applications, including ultrafast all-optical signal processing, spectroscopy, and imaging. The utility of the present technique for improving signal integrity in chirped pump optical parametric amplification is also demonstrated.     

Unusual Behavior of Nanocrystalline Strontium Oxide Toward Hydrogen Sulfide

The thermodynamically favored reaction of solid strontium oxide with gaseous hydrogen sulfide is kinetically enhanced to a large degree by the use of higher surface area nanocrystalline SrO in the form of brush-like collections of metal oxide fibers. An unusual feature is that the reaction SrO + H₂S SrS + H₂O proceeds stoichiometrically at room temperature, but at higher temperatures the reaction efficiency goes down, apparently due to rapid temperature induced crystal growth of the nanocrystalline SrO. The samples studied vary in crystallite size from 20 to 27nm, while average particle size (nanocrystal aggregates) varies in the following order; aerogel prepared SrO (100nm) 相似文献   

Experimental and four‐component relativistic DFT studies of tungsten carbonyl complexes

We present a theoretical and experimental study of the structure and nuclear magnetic resonance (NMR) parameters of the pentacarbonyltungsten complexes of η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine, η²‐norbornene, and imidazolidine‐2‐thione. The three complexes have a pseudo‐octahedral molecular structure with the six ligands bonded to the tungsten atom. The η¹‐2‐(trimethylstannyl)‐4,5‐dimethylphosphinine‐pentacarbonyl tungsten complex was synthesized for the first time. For all compounds, we present four‐component relativistic calculations of the NMR parameters at the Dirac–Kohn–Sham density functional level of theory using hybrid functionals. These large‐scale relativistic calculations of NMR chemical shifts and spin–spin coupling constants were compared with available experimental data, either taken from the literature or measured in this work. The inclusion of solvent effects modeled using a conductor‐like screening model was found to improve agreement between the calculated and experimental NMR parameters, and our best estimates for the NMR parameters are generally in good agreement with available experimental results. The present work demonstrates that four‐component relativistic theory has reached a level of maturity that makes it a convenient and accurate tool for modeling and understanding chemical shifts and indirect spin–spin coupling constants of organometallic compounds containing heavy elements, for which conventional non‐relativistic theory breaks down. Copyright © 2015 John Wiley & Sons, Ltd.