Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Light guiding light: Nonlinear refraction in rubidium vapor

Recently there has been experimental and theoretical interest in cross-dispersion effects in rubidium vapor, which allows one beam of light to be guided by another. We present theoretical results which account for the complications created by the D line hyperfine structure of rubidium as well as the presence of the two major isotopes of rubidium. This allows the complex frequency dependence of the effects observed in our experiments to be understood and lays the foundation for future studies of nonlinear propagation.

Active site heterogeneity in dimethyl sulfoxide reductase from Rhodobacter capsulatus revealed by raman spectroscopy

Raman spectroscopy has been used to investigate the structure of the molybdenum cofactor in DMSO reductase from Rhodobacter capsulatus. Three oxidized forms of the enzyme, designated 'redox cycled', 'as prepared', and DMSORmodD, have been studied using 752 nm laser excitation. In addition, two reduced forms of DMSO reductase, prepared either anaerobically using DMS or using dithionite, have been characterized. The 'redox cycled' form has a single band in the Mo=O stretching region at 865 cm(-1) consistent with other studies. This oxo ligand is found to be exchangeable directly with (DMSO)-O-18 or by redox cycling. Furthermore, deuteration experiments demonstrate that the oxo ligand in the oxidized enzyme has some hydroxo character, which is ascribed to a hydrogen bonding interaction with Trp 116. There is also evidence from the labeling studies for a modified dithiolene sulfur atom, which could be present as a sulfoxide. In addition to the 865 cm(-1) band, an extra band at 818 cm(-1) is observed in the Mo=O stretching region of the 'as prepared' enzyme which is not present in the 'redox cycled' enzyme. Based on the spectra of unlabeled and labeled DMS reduced enzyme, the band at 818 cm(-1) is assigned to the S=O stretch of a coordinated DMSO molecule. The DMSORmodD form, identified by its characteristic Raman spectrum, is also present in the 'as prepared' enzyme preparation but not after redox cycling. The complex mixture of forms identified in the 'as prepared' enzyme reveals a substantial degree of active site heterogeneity in DMSO reductase.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

The radiation chemistry of ultem at 77 K as revealed by ESR spectroscopy

Radical formation in ultem following gamma-radiolysis has been reassessed, and the G(R*) values at different temperatures have been determined by ESR spectroscopy. The radical assignment and radical reactivity have been re-examined by photobleaching and thermal annealing studies. Photobleachable radical anions were found to comprise approximate to40% of the total number of radicals formed on radiolysis at 77 K. Spectral subtraction methods, ESR spectral simulations, measurement of g-values and the hyperfine splitting constants were used to identify the other radical intermediates. The principal chain scission radicals are formed due to scission of the main-chain at (i) the ether linkage, (ii) the isopropylidene group and (iii) the imide ring in the main chain. The side chain methyl groups of the isopropylidine units also lose hydrogen to form methylene radicals. The five-line spectrum observed to decay in the temperature range 370-430 K, which has not been assigned previously, has been identified as being characteristic of a di-substituted benzyl radical. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Probing the time course of nonlinear discriminations during human electrodermal conditioning

Animal-based theories of Pavlovian conditioning propose that patterning discriminations are solved using unique cues or immediate configuring. Recent studies with humans, however, provided evidence that in positive and negative patterning two different rules are utilized. The present experiment was designed to provide further support for this proposal by tracking the time course of the allocation of cognitive resources. One group was trained in a positive patterning; schedule (A-, B-, AB+) and a second in a negative patterning schedule (A+, B+, AB-). Electrodermal responses and secondary task probe reaction time were measured. In negative patterning, reaction times were slower during reinforced stimuli than during non-reinforced stimuli at both probe positions while there were no differences in positive patterning. These results support the assumption that negative patterning is solved using a rule that is more complex and requires more resources than does the rule employed to solve positive patterning. (C) 2001 Elsevier Science (USA).

Nitrate in soil humic acids revealed by N-14 nuclear magnetic resonance spectroscopy

Ecosystem management such as plant residue retention and prescribed burning can significantly affect soil organic matter (SOM) composition and, thereby, the closely associated carbon (C) and nitrogen (N) cycling processes, which underpin terrestrial ecosystem productivity and sustainability. Humic acid (HA) is an important SOM component and its chemical composition has attracted much attention. Here we report the first application of N-14 nuclear magnetic resonance (NMR) spectroscopy to soil HA study, revealing the surprising existence of nitrate-N and ammonia-N in the HAs. This newly discovered HA nitrate-N, though in a relatively low concentrations, is closely related to soil N availability and responsive to plant residue management regimes in contrasting forest ecosystems. The HA nitrate-N may be a useful and sensitive biochemical indicator of SOM quality in response to different ecosystem management regimes.

Impact of land-use on soil organic matter quality in south-western Australia - characterization with C-13 CP/MAS NMR spectroscopy

The influence of change in land-use from native vegetation to pasture (20-71 yr after conversion), and subsequent change from pasture to eucalypt plantation (7-10 yr after conversion) on soil organic matter quality was investigated using C-13 CP/MAS NMR spectroscopy. We studied surface soil (0-10 cm) from six sites representing a range of soil, and climate types from south-western Australia. Total C in the samples ranged from 1.6 to 5.5%, but the relative proportions of the four primary spectral regions (alkyl, O-alkyl, aromatic and carboxylic) were similar across the sites, and changes due to land-use at each site were relatively minor. Main impacts of changed land-use were higher O-alkyl (carbohydrate) material under pasture than under native vegetation and plantation (P = 0.048), and lower aromatic C under pasture than under native vegetation (P = 0.027). The decrease in aromatic C in pasture soils was related to time since clearing. (C) 2002 Elsevier Science Ltd. All rights reserved.