Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

Metal-insulator transition and charge ordering in the extended Hubbard model at one-quarter filling

We study, with exact diagonalization, the zero temperature properties of the quarter-filled extended Hubbard model on a square lattice. We find that increasing the ratio of the intersite Coulomb repulsion, V, to the bandwidth drives the system from a metal to a charge ordered insulator. The evolution of the optical conductivity spectrum with increasing V is in agreement with the observed optical conductivity of several layered molecular crystals with the theta and beta crystal structures.

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Computation of the linear elastic properties of random porous materials with a wide variety of microstructure

A finite-element method is used to study the elastic properties of random three-dimensional porous materials with highly interconnected pores. We show that Young's modulus, E, is practically independent of Poisson's ratio of the solid phase, nu(s), over the entire solid fraction range, and Poisson's ratio, nu, becomes independent of nu(s) as the percolation threshold is approached. We represent this behaviour of nu in a flow diagram. This interesting but approximate behaviour is very similar to the exactly known behaviour in two-dimensional porous materials. In addition, the behaviour of nu versus nu(s) appears to imply that information in the dilute porosity limit can affect behaviour in the percolation threshold limit. We summarize the finite-element results in terms of simple structure-property relations, instead of tables of data, to make it easier to apply the computational results. Without using accurate numerical computations, one is limited to various effective medium theories and rigorous approximations like bounds and expansions. The accuracy of these equations is unknown for general porous media. To verify a particular theory it is important to check that it predicts both isotropic elastic moduli, i.e. prediction of Young's modulus alone is necessary but not sufficient. The subtleties of Poisson's ratio behaviour actually provide a very effective method for showing differences between the theories and demonstrating their ranges of validity. We find that for moderate- to high-porosity materials, none of the analytical theories is accurate and, at present, numerical techniques must be relied upon.

A hedging point strategy - balancing effluent quality, economy and robustness in the control of wastewater treatment plants

An operational space map is an efficient tool to compare a large number of operational strategies to find an optimal choice of setpoints based on a multicriterion. Typically, such a multicriterion includes a weighted sum of cost of operation and effluent quality. Due to the relative high cost of aeration such a definition of optimality result in a relatively high fraction of the effluent total nitrogen in the form of ammonium. Such a strategy may however introduce a risk into operation because a low degree of ammonium removal leads to a low amount of nitrifiers. This in turn leads to a reduced ability to reject event disturbances, such as large variations in the ammonium load, drop in temperature, the presence of toxic/inhibitory compounds in the influent etc. Hedging is a risk minimisation tool, with the aim to "reduce one's risk of loss on a bet or speculation by compensating transactions on the other side" (The Concise Oxford Dictionary (1995)). In wastewater treatment plant operation hedging can be applied by choosing a higher level of ammonium removal to increase the amount of nitrifiers. This is a sensible way to introduce disturbance rejection ability into the multi criterion. In practice, this is done by deciding upon an internal effluent ammonium criterion. In some countries such as Germany, a separate criterion already applies to the level of ammonium in the effluent. However, in most countries the effluent criterion applies to total nitrogen only. In these cases, an internal effluent ammonium criterion should be selected in order to secure proper disturbance rejection ability.

Callus induction and plant regeneration from broccoli (Brassica oleracea var. italica) for transformation

We evaluated the efficiency of callus induction and plantlet regeneration from hypocotyl explants of broccoli (Brassica oleracea var. italica). The cultivars were ‘Marathon’, ‘Greenbelt’, and ‘Shogun’. Transformation success was not affected by the presence of tobacco feeder-cell layers on the culture media. The frequency of shoot regeneration was greater from 10-d-old hypocotyls than from 14-d-old hypocotyls. Both ‘Marathon’ and ‘Greenbelt’ had higher potentials for tissue regeneration than did ‘Shogun’. We found that for transformation selection, the optimum concentration was either 50 mg/L kanamycin or 100 mg/L genetkin.

Welding and rheomorphism of phonolitic fallout deposits from the Las Canadas caldera, Tenerife, Canary Islands

The Las Canadas caldera is a nested collapse caldera formed by the successive migration and collapse of shallow magmatic chambers. Among the pyroclastic products of this caldera are phonolitic fallout deposits that crop out in the caldera wall and on the extracaldera slopes. These deposits exhibit an uninterrupted facies gradation from nonwelded to lava-like and record continuous volcanic deposition. Densely welded and lava-like facies result from the extreme attenuation and complete homogenization of juvenile clasts that destroy original clast outlines and any evidence of fallout deposition. Agglutination contributes significantly to the final degree of flattening observed in the welded facies. After deposition, rheomorphic flowage occurs. Emplacement temperatures for one of the welding sequences are calculated from magmatic temperatures and a model of tephra cooling during fallout. Results are 486 degreesC for the nonwelded facies and 740 degreesC for the moderately welded facies. For the same welding sequence, a cooling time between 25 and 54 days is estimated from published experimental and computational data as the possible duration of welding and rheomorphism. Following deposition and agglutination, the lava-like pyroclastic facies had the rheological properties of viscous lavas and flowed down the outer slopes away from the caldera. Some lava-like masses detached from proximal areas to more distal regions. During deposition, the eruptive style evolved from Plinian fallout to fountain-fed spatter deposition. This evolution was accompanied by a decrease in explosive power and a lower height of the eruptive column, which produce higher emplacement temperatures and more effective heat retention of pyroclasts.

Transformation processes, pathways, and possible sources of distinctive polychlorinated dibenzo-p-dioxin signatures in sink environments

In recent years, studies on environmental samples with unusual dibenzo-p-dioxin (PCDD) congener profiles were reported from a range of countries. These profiles, characterized by a dominance of octachlorinated dibenzodioxin (OCDD) and relatively low in dibenzofuran (PCDF) concentrations, could not be attributed to known sources or formation processes. In the present study, the processes that result in these unusual profiles were assessed using the concentrations and isomer signatures of PCDDs from dated estuarine sediment cores in Queensland, Australia. Increases in relative concentrations of lower chlorinated PODS and a relative decrease of OCDD were correlated with time of sediment deposition. Preferred lateral, anaerobic dechlorination of OCDD represents a likely pathway for these changes. In Queensland sediments, these transformations result in a distinct dominance of isomers fully chlorinated in the 1,4,6,9-positions (1,4-patterns), and similar 1,4-patterns were observed in sediments from elsewhere. Consequently, these environmental samples may not reflect the signatures of the original source, and a reevaluation of source inputs was undertaken. Natural formation of PCDDs, which has previously been suggested, is discussed; however, based on the present results and literature comparisons, we propose an alternative scenario. This scenario hypothesizes that an anthropogenic PCDD precursor input (e.g. pentachlorophenol) results in the contamination. These results and hypothesis imply further investigations are warrented into possible anthropogenic sources in areas where natural PCDD formation has been suggested.

The martensitic transformation in ceramics - its role in transformation toughening

This paper reviews the current knowledge and understanding of martensitic transformations in ceramics - the tetragonal to monoclinic transformation in zirconia in particular. This martensitic transformation is the key to transformation toughening in zirconia ceramics. A very considerable body of experimental data on the characteristics of this transformation is now available. In addition, theoretical predictions can be made using the phenomenological theory of martensitic transformations. As the paper will illustrate, the phenomenological theory is capable of explaining all the reported microstructural and crystallographic features of the transformation in zirconia and in some other ceramic systems. Hence the theory, supported by experiment, can be used with considerable confidence to provide the quantitative data that is essential for developing a credible, comprehensive understanding of the transformation toughening process. A critical feature in transformation toughening is the shape strain that accompanies the transformation. This shape strain, or nucleation strain, determines whether or not the stress-induced martensitic transformation can occur at the tip of a potentially dangerous crack. If transformation does take place, then it is the net transformation strain left behind in the transformed region that provides toughening by hindering crack growth. The fracture mechanics based models for transformation toughening, therefore, depend on having a full understanding of the characteristics of the martensitic transformation and, in particular, on being able to specify both these strains. A review of the development of the models for transformation toughening shows that their refinement and improvement over the last couple of decades has been largely a result of the inclusion of more of the characteristics of the stress-induced martensitic transformation. The paper advances an improved model for the stress-induced martensitic transformation and the strains resulting from the transformation. This model, which separates the nucleation strain from the subsequent net transformation strain, is shown to be superior to any of the constitutive models currently available. (C) 2002 Elsevier Science Ltd. All rights reserved.

Relationship between stress-induced martensitic transformation and impact toughness in low carbon austenitic steels

The effect of test temperature, which controls the stability of austenite, on the impact toughness of a low carbon Fe-Ni-Mn-C austenitic steel and 304 stainless steel, has been investigated. Under impact conditions, stress-induced martensitic transformation occurred, in a region near the fracture surface, at test temperatures below 80degreesC for the Fe-Ni-Mn-C steel and below -25degreesC for 304 stainless steel. The former shows significant transformation toughening and the highest impact toughness was obtained at 10degreesC, which corresponds to the maximum amount of martensite formed by stress-induced transformation above the Ms temperature. The stress-induced martensitic transformation contributes negatively to the impact toughness in the 304 stainless steel. Increasing the amount of stress-induced transformation to martensite, lowered the impact toughness. The experimental results can be well explained by the Antolovich theory through the analysis of metallography and fractography. The different effect of stress-induced transformation on the impact toughness in Fe-Ni-Mn-C steel and 304 stainless steel has been further understood by applying the crystallographic model for stress-induced martensitic transformation to these two steels. (C) 2002 Kluwer Academic Publishers.