Analytic characterization of conditional gaugeability for non-local Feynman-Kac transforms

An analytic characterization of gaugeability and conditional gaugeability is given for non-local (or discontinuous) Feynman-Kac transforms of general symmetric Markov processes. This analytic characterization is very useful in determining whether a process perturbed by a potential is gaugeable or conditionally gaugeable in concrete cases.     

Telltale Signs: What Common Explanatory Strategies in Chemistry Reveal about Explanation Itself

This essay addresses issues concerningexplanation by exploring how explanatorystructures function within contemporarychemistry. Three examples are discussed:explanations of the behavior of gases using theideal gas law, explanations of trends inchemical properties using the periodic table,and explanations of molecular geometry usingdiagrammatic orbital schemes. In each case,the general explanatory structure, rather thanparticular explanations, occupies center stagein the analysis. It is argued that thisquasi-empirical investigation may be morefruitful than previous analyses that attempt toisolate the essential features of individualexplanations. There are two reasons for thisconclusion, each discussed in some detail. First, the traditional analyses rely on highlyprecarious reasoning. Second, empiricallygrounded investigations provide a more naturalconnection to the core aim of analyses ofexplanation, namely to provide a rationale forthe widely expressed preference for explanatorytheories in science.     

Dynamics and stability of a new class of periodic solutions of the optical parametric oscillator

The stability and dynamics of a new class of periodic solutions is investigated when a degenerate optical parametric oscillator system is forced by an external pumping field with a periodic spatial profile modeled by Jacobi elliptic functions. Both sinusoidal behavior as well as localized hyperbolic (front and pulse) behavior can be considered in this model. The stability and bifurcation behaviors of these transverse electromagnetic structures are studied numerically. The periodic solutions are shown to be stabilized by the nonlinear parametric interaction between the pump and signal fields interacting with the cavity diffraction, attenuation, and periodic external pumping. Specifically, sinusoidal solutions result in robust and stable configurations while well-separated and more localized field structures often undergo bifurcation to new steady-state solutions having the same period as the external forcing. Extensive numerical simulations and studies of the solutions are provided.     

Optimization techniques for Available Transfer Capability (ATC) and market calculations

The recent movement towards an open, competitive market environmentintroduced new optimization problems such as market clearingmechanism, bidding decision and Available Transfer Capability(ATC) calculation. These optimization problems are characterizedby the complexity of power systems and the uncertainties inthe electricity market. Accurate evaluation of the transfercapability of a transmission system is required to maximizethe utilization of the existing transmission systems in a competitivemarket environment. The transfer capability of the transmissionnetworks can be limited by various system constraints such asthermal, voltage and stability limits. The ability to incorporatesuch limits into the optimization problem is a challenge inthe ATC calculation from an engineering point of view. In thecompetitive market environment, a power supplier needs to findan optimal strategy that maximizes its own profits under variousuncertainties such as electricity prices and load. On the otherhand, an efficient market clearing mechanism is needed to increasethe social welfare, i.e. the sum of the consumers’ andproducers’ surplus. The need to maximize the social welfaresubject to system operational constraints is also a major challengefrom a societal point of view. This paper presents new optimizationtechniques motivated by the competitive electricity market environment.Numerical simulation results are presented to demonstrate theperformance of the proposed optimization techniques.     

Influence of Polymer Specimen Structure on The Reproducibility of Micro-thermomechanical Transitions

Glass transitions of amorphous polystyrenes with low polydispersity were evaluated using the modulated Local Thermal Analysis mode of the TA Instruments 2990 μ TA and evaluating the thermomechanical signal. Transition temperature variance and fraction of transitions measured were compared for high molecular mass thermosetting materials and the melt of Nylon 6.6. The transition reproducibility was found to decrease as the molecular size of the polymer samples increased. Reproducibility also decreased for thermosetting materials when the experimental ramp rate was decreased. Heat transfer within the specimen was evaluated using finite element analysis, allowing scaling of microscale experimental results for comparison to bulk transitions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effective-range corrections to the proton-proton fusion rate

Proton-proton fusion is considered in the effective field theory of Kaplan, Savage and Wise. Coulomb effects are included systematically in a non-perturbative way. Including the dimension-eight derivative coupling which determines the effective ranges of the scattering amplitudes, next-to-leading order corrections to the fusion rate are calculated. When the renormalization mass is well above the characteristic energies of the system, this contribution gives a rate which is eight percent below the standard value. The difference can be due to an unknown counterterm which comes in at this order.     

Isomorphism rigidity in entropy rank two

We study the rigidity properties of a class of algebraic ℤ³-actions with entropy rank two. For this class, conditions are found which force an invariant measure to be the Haar measure on an affine subset. This is applied to show isomorphism rigidity for such actions, and to provide examples of non-isomorphic ℤ³-actions with all their ℤ²-sub-actions isomorphic. The proofs use lexicographic half-space entropies and total ergodicity along critical directions. The second-named author thanks the University of Washington for their hospitality and the support of NSF grant DMS 0222452.     

Phase diagrams in the proton conductor systems Sr6Ta2O11 × nH2O and Sr5.92Ta2.08O11.12 × nH2O

The systems Sr₆Ta₂O₁₁–H₂O and Sr_5.92Ta_2.08O_11.12–H₂O were investigated. At high temperatures, both compounds are normal proton conductors but at lower temperatures show the formation of hydrate phases (here labelled β-phases). The latter are deleterious if the above compounds were to be used in fuel cells, sensors and pumping devices. The phase diagrams of the 2 systems were determined using thermogravimetry. The solubilities of water vapor in the α-phases were measured. Considering 2-phase mixtures of α and β, the plateau vapor pressures were determined as well as the pertinent thermodynamic parameters. The α→α + β solvus was also investigated. The present study complements recent work [I. Animitsa, A. Nieman, A. Sharafutdinov, S. Nochrin, Solid State Ionics 136–137 (2000) 265; I. Animitsa, A. Nieman, S. Titova, N. Kochetova, E. Isaeva, A. Sharafutdinov, N. Timofeeva, Ph. Colomban, Solid State Ionics 156 (2003) 95].     

Advances in nanomagnetism via X-ray techniques

This report examines the current status and the future directions of the field of nanomagnetism and assesses the ability of hard X-ray synchrotron facilities to provide new capabilities for making advances in this field. The report first identifies major research challenges that lie ahead in three broadly defined subfields of nanomagnetism: confined systems, clusters and complex oxides. It then examines the relevant experimental capabilities that are currently available at hard X-ray synchrotron light sources, using the Advanced Photon Source (APS) at Argonne as an example. Finally, recommendations are made for future development in X-ray facilities that will enhance the study of nanomagnetism, including new experimental directions, modifications that would enable in situ sample preparation, and measurements at high magnetic fields and/or low temperatures. In particular, in situ sample preparation is of high priority in many experiments, especially those in the area of surface magnetism.     

Shy couplings

A pair (X, Y) of Markov processes on a metric space is called a Markov coupling if X and Y have the same transition probabilities and (X, Y) is a Markov process. We say that a coupling is “shy” if inf _{t ≥ 0} dist(X _t , Y _t ) >  0 with positive probability. We investigate whether shy couplings exist for several classes of Markov processes.