Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+: Y3Al5O12 using density matrix theory

The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in cm(4)s Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 x 10(-50) cm(4)s which is very close to the previous experimental value 4 x 10(-50) cm(4) s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Theory of Handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height, either through altering the frequency or altering the acceleration amplitude. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape, and such changes can be effected through modifying the horizontal oscillation amplitude and phase. Changing the slope at this zero crossing controls writing slant; this slope depends on the horizontal and vertical velocity zero amplitudes and on the relative phase difference. Letter height modulation is also best applied at the vertical velocity zero crossing to preserve an even baseline. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. Under these constraints interletter separation is not an independent parameter. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal, rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical sources; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory. It is shown that the minimum energy movement for the spring muscle is bang-coast-bang. For certain parameter values a singular arc solution can be shown to be minimizing. Experimental measurements however indicate that handwriting is not a minimum energy movement.

Theory of World Security

Booth, Ken, Theory of World Security (Cambridge: Cambridge University Press, 2008), pp.xviii+489 RAE2008

One Order, Two Laws: Recovering the 'Normative' in English School Theory

Bain, William, 'One Order, Two Laws: Recovering the 'Normative' in English School Theory', Review of International Studies, (2007) 33(4) pp.557-575 RAE2008

Kappa calculus and evidential strength: A note on Åqvist's logical theory of legal evidence

Lennart Åqvist (1992) proposed a logical theory of legal evidence, based on the Bolding-Ekelöf of degrees of evidential strength. This paper reformulates Åqvist's model in terms of the probabilistic version of the kappa calculus. Proving its acceptability in the legal context is beyond the present scope, but the epistemological debate about Bayesian Law isclearly relevant. While the present model is a possible link to that lineof inquiry, we offer some considerations about the broader picture of thepotential of AI & Law in the evidentiary context. Whereas probabilisticreasoning is well-researched in AI, calculations about the threshold ofpersuasion in litigation, whatever their value, are just the tip of theiceberg. The bulk of the modeling desiderata is arguably elsewhere, if one isto ideally make the most of AI's distinctive contribution as envisaged forlegal evidence research.

Environmental selection and resource allocation determine spatial patterns in picophytoplankton cell size

Here we describe a new trait-based model for cellular resource allocation that we use to investigate the relative importance of different drivers for small cell size in phytoplankton. Using the model, we show that increased investment in nonscalable structural components with decreasing cell size leads to a trade-off between cell size, nutrient and light affinity, and growth rate. Within the most extreme nutrient-limited, stratified environments, resource competition theory then predicts a trend toward larger minimum cell size with increasing depth. We demonstrate that this explains observed trends using a marine ecosystem model that represents selection and adaptation of a diverse community defined by traits for cell size and subcellular resource allocation. This framework for linking cellular physiology to environmental selection can be used to investigate the adaptive response of the marine microbial community to environmental conditions and the adaptive value of variations in cellular physiology.

Analogies between linguistics and information theory

An analogy is established between the syntagm and paradigm from Saussurean linguistics and the message and messages for selection from the information theory initiated by Claude Shannon. The analogy is pursued both as an end itself and for its analytic value in understanding patterns of retrieval from full text systems. The multivalency of individual words when isolated from their syntagm is contrasted with the relative stability of meaning of multi-word sequences, when searching ordinary written discourse. The syntagm is understood as the linear sequence of oral and written language. Saussureâ??s understanding of the word, as a unit which compels recognition by the mind, is endorsed, although not regarded as final. The lesser multivalency of multi-word sequences is understood as the greater determination of signification by the extended syntagm. The paradigm is primarily understood as the network of associations a word acquires when considered apart from the syntagm. The restriction of information theory to expression or signals, and its focus on the combinatorial aspects of the message, is sustained. The message in the model of communication in information theory can include sequences of written language. Shannonâ??s understanding of the written word, as a cohesive group of letters, with strong internal statistical influences, is added to the Saussurean conception. Sequences of more than one word are regarded as weakly correlated concatenations of cohesive units.

Fe XIII emission lines in active region spectra obtained with the Solar Extreme-Ultraviolet Research Telescope and Spectrograph

Recent fully relativistic calculations of radiative rates and electron impact excitation cross-sections for FeXIII are used to generate emission-line ratios involving 3s23p2-3s3p3 and 3s23p2-3s23p3d transitions in the 170-225 and 235-450 Å wavelength ranges covered by the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS). A comparison of these line ratios with SERTS active region observations from rocket flights in 1989 and 1995 reveals generally very good agreement between theory and experiment. Several new FeXIII emission features are identified, at wavelengths of 203.79, 259.94, 288.56 and 290.81 Å. However, major discrepancies between theory and observation remain for several FeXIII transitions, as previously found by Landi and others, which cannot be explained by blending. Errors in the adopted atomic data appear to be the most likely explanation, in particular for transitions which have 3s23p3d1D2 as their upper level. The most useful FeXIII electron-density diagnostics in the SERTS spectral regions are assessed, in terms of the line pairs involved being (i) apparently free of atomic physics problems and blends, (ii) close in wavelength to reduce the effects of possible errors in the instrumental intensity calibration, and (iii) very sensitive to changes in Ne over the range 108-1011cm-3. It is concluded that the ratios which best satisfy these conditions are 200.03/202.04 and 203.17/202.04 for the 170-225 Å wavelength region, and 348.18/320.80, 348.18/368.16, 359.64/348.18 and 359.83/368.16 for 235-450 Å.

Extreme ultraviolet transitions of Fe XXI in solar, stellar and laboratory spectra

Recent R-matrix calculations of electron impact excitation rates for transitions among the 2s(2)2p(2), 2s2p(3) and 2p(4) levels of Fe XXI are used to derive theoretical electron density (N-e) sensitive emission-line ratios involving 2S2(2)p(2)-2s2p(3) transitions in the similar to 98-146 Angstrom wavelength range. A comparison of these with observations from the PLT tokamak plasma, for which the electron density has been independently determined, reveals generally very good agreement between theory and experiment, and in some instances removes discrepancies found previously. The observed Fe XXI ratios for a solar flare, obtained with the OSO-5 satellite, imply electron densities which are consistent, with discrepancies that do not exceed 0.2 dex. In addition, the derived values of N-e are similar to those estimated for the high-temperature regions of other solar flares. The good agreement between theory and observation, in particular for the tokamak spectra, provides experimental support for the accuracy of the present line-ratio calculations, and hence for the atomic data on which they are based.

A comparison of theoretical line intensity ratios for Ni XII with extreme ultraviolet observations from the JET tokamak

Recent R-matrix calculations of electron impact excitation rates in Ni XII are used to derive the emission line ratios R-1 = I(154.17 Angstrom)/I(152.15 Angstrom), R-2 = I(152.95 Angstrom)/I(152.15 Angstrom) and R-3 = 1(160.55 Angstrom)/I(152.15 Angstrom). This is the first time (to our knowledge) that theoretical emission line ratios have been calculated for this ion. The ratios are found to be insensitive to changes in the adopted electron density (N-e) when N-e greater than or equal to 5 x 10(11) cm(-3), typical of laboratory plasmas. However, they do vary with electron temperature (T-e), with for example R-1 and R-3 changing by factors of 1.3 and 1.8, respectively, between T-e = 10(5) and 10(6) K. A comparison of the theoretical line ratios with measurements from the Joint European Tents (JET) tokamak reveals very good agreement between theory and observation for R-1, with an average discrepancy of only 7%. Agreement between the calculated and experimental ratios for R-2 and R-3 is less satisfactory, with average differences of 30 and 33%, respectively. These probably arise from errors in the JET instrument calibration curve. However, the discrepancies are smaller than the uncertainties in the R-2 and R-3 measurements. Our results, in particular for R-1, provide experimental support for the accuracy of the Ni XIII line ratio calculations, and hence for the atomic data adopted in their derivation.

Simplified theory of wideband spectra of liquid H2O and D2O (from 0 to 1000 cm(-1)) due to reorienting polar and vibrating H-bonded water molecules

A semi-phenomenological molecular model is presented, which is capable of describing with the use of analytical formulae, the wideband dielectric(1) and far-infrared spectra of ordinary and heavy water. In the model the vector of a dipole moment is presented as a sum of two components. The absolute value of the first one is constant; the second one changes harmonically with time. The key aspect of this work is consideration of FIR spectra due to the second component. In the context of the modified hybrid model presented in the work, reorientation of the dipoles in the rectangular potential well is considered, as a result of which the librational (near 700 cm (-1)) and translational (near 200 cm (-1)) absorption bands and the microwave Debye relaxation spectrum arise. It is shown that the time-dependent part of a dipole moment contributes most to the translational band, the relevant mechanism is taken to be stretching vibration of the H-bonded molecules. Previous linear-response molecular models were unsuccessful in describing this band (in heavy water) in terms of the complex dielectric permittivity. The spatial and time scales characteristic of water are estimated. (C) 2002 Elsevier Science B.V. All rights reserved.

An investigation of Fe XVI emission lines in solar and stellar extreme-ultraviolet and soft X-ray spectra

New fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe XVI are used to determine theoretical emission-line ratios applicable to the 251-361 and 32-77 angstrom portions of the extreme-ultraviolet (EUV) and soft X-ray spectral regions, respectively. A comparison of the EUV results with observations from the Solar Extreme-Ultraviolet Research Telescope and Spectrograph (SERTS) reveals excellent agreement between theory and experiment. However, for emission lines in the 32-49 angstrom portion of the soft X-ray spectral region, there are large discrepancies between theory and measurement for both a solar flare spectrum obtained with the X-Ray Spectrometer/Spectrograph Telescope (XSST) and for observations of Capella from the Low- Energy Transmission Grating Spectrometer (LETGS) on the Chandra X-ray Observatory. These are probably due to blending in the solar flare and Capella data from both first-order lines and from shorter wavelength transitions detected in second and third order. By contrast, there is very good agreement between our theoretical results and the XSST and LETGS observations in the 50-77 angstrom wavelength range, contrary to previous results. In particular, there is no evidence that the Fe XVI emission from the XSST flare arises from plasma at a much higher temperature than that expected for Fe XVI in ionization equilibrium, as suggested by earlier work.

A density functional theory study of carbon monoxide oxidation on the Cu3Pt(111) alloy surface: Comparison with the reactions on Pt(111) and Cu(111)

Alloying metals is often used as an effective way to enhance the reactivity of surfaces. Aiming to shed light on the effect of alloying on reaction mechanisms, we carry out a comparative study of CO oxidation on Cu3Pt(111), Pt(111), and Cu(111) by means of density functional theory calculations. Alloying effects on the bonding sites and bonding energies of adsorbates, and the reaction pathways are investigated. It is shown that CO preferentially adsorbs on an atop site of Pt and O preferentially adsorbs on a fcc hollow site of three Cu atoms on Cu3Pt(111). It is also found that the adsorption energies of CO (or O-a) decreases on Pt (or Cu) on the alloy surface with respect to those on pure metals. More importantly, having identified the transition states for CO oxidation on those three surfaces, we found an interesting trend for the reaction barrier on the three surfaces. Similar to the adsorption energies, the reaction barrier on Cu3Pt possesses an intermediate value of those on pure Pt and Cu metals. The physical origin of these results has been analyzed in detail. (C) 2001 American Institute of Physics.

Emission lines of Fe X in active region spectra obtained with the Solar Extreme-ultraviolet Research Telescope and Spectrograph

Fully relativistic calculations of radiative rates and electron impact excitation cross-sections for Fe X are used to derive theoretical emission-line ratios involving transitions in the 174-366 angstrom wavelength range. A comparison of these with solar active region observations obtained during the 1989 and 1995 flights of the Solar Extreme-ultraviolet Research Telescope and Spectrograph (SERTS) reveals generally very good agreement between theory and experiment. Several Fe X emission features are detected for the first time in SERTS spectra, while the 3s(2)3p(5) P-2(3/2)-3s(2)3p(4)(S-1)3d D-2(3/2) transition at 195.32 angstrom is identified for the first time (to our knowledge) in an astronomical source. The most useful Fe X electron density (N-e) diagnostic line ratios are assessed to be 175.27/174.53 and 175.27/177.24, which both involve lines close in wavelength and free from blends, vary by factors of 13 between N-e = 10(8) and 10(11) cm(-3), and yet show little temperature sensitivity. Should these lines not be available, then the 257.25/345.74 ratio may be employed to determine N-e, although this requires an accurate evaluation of the instrument intensity calibration over a relatively large wavelength range. However, if the weak 324.73 angstrom line of Fe X is reliably detected, the use of 324.73/345.74 or 257.25/324.73 is recommended over 257.25/345.74. Electron densities deduced from 175.27/174.53 and 175.27/177.24 for the stars Procyon and alpha Cen, using observations from the Extreme-Ultraviolet Explorer (EUVE) satellite, are found to be consistent and in agreement with the values of N-e determined from other diagnostic ratios in the EUVE spectra. A comparison of several theoretical extreme-ultraviolet Fe X line ratios with experimental values for a theta-pinch, for which the plasma parameters have been independently determined, reveals reasonable agreement between theory and observation, providing some independent support for the accuracy of the adopted atomic data.

Bio-folio: applying portfolio theory to biodiversity

Genes, species and ecosystems are often considered to be assets. The need to ensure a sufficient diversity of this asset is being increasingly recognised today. Asset managers in banks and insurance companies face a similar challenge. They are asked to manage the assets of their investors by constructing efficient portfolios. They deliberately make use of a phenomenon observed in the formation of portfolios: returns are additive, while risks diversify. This phenomenon and its implications are at the heart of portfolio theory. Portfolio theory, like few other economic theories, has dramatically transformed the practical work of banks and insurance companies. Before portfolio theory was developed about 50 years ago, asset managers were confronted with a situation similar to the situation the research on biodiversity faces today. While the need for diversification was generally accepted, a concept that linked risk and return on a portfolio level and showed the value of diversification was missing. Portfolio theory has closed this gap. This article first explains the fundamentals of portfolio theory and transfers it to biodiversity. A large part of this article is then dedicated to some of the implications portfolio theory has for the valuation and management of biodiversity. The last section introduces three development openings for further research.