A Gradient-Type Optimization Technique for the Optimal Control for Schrodinger Equations

In this paper, we are considered with the optimal control of a schrodinger equation. Based on the formulation for the variation of the cost functional, a gradient-type optimization technique utilizing the finite difference method is then developed to solve the constrained optimization problem. Finally, a numerical example is given and the results show that the method of solution is robust.

Impact of third-order dispersion on the evolution of parabolic pulses

We present a perturbation analysis that describes the effect of third-order dispersion on the similariton pulse solution of the nonlinear Schrödinger equation in a fibre gain medium. The theoretical model predicts with sufficient accuracy the pulse structural changes induced, which are observed through direct numerical simulations.

The impact of coordination on the effectiveness of last mile relief distribution

Last mile relief distribution is the final stage of humanitarian logistics. It refers to the supply of relief items from local distribution centers to the disaster affected people (Balcik et al., 2008). In the last mile relief distribution literature, researchers have focused on the use of optimisation techniques for determining the exact optimal solution (Liberatore et al., 2014), but there is a need to include behavioural factors with those optimisation techniques in order to obtain better predictive results. This paper will explain how improving the coordination factor increases the effectiveness of the last mile relief distribution process. There are two stages of methodology used to achieve the goal: Interviews: The authors conducted interviews with the Indian Government and with South Asian NGOs to identify the critical factors for final relief distribution. After thematic and content analysis of the interviews and the reports, the authors found some behavioural factors which affect the final relief distribution. Model building: Last mile relief distribution in India follows a specific framework described in the Indian Government disaster management handbook. We modelled this framework using agent based simulation and investigated the impact of coordination on effectiveness. We define effectiveness as the speed and accuracy with which aid is delivered to affected people. We tested through simulation modelling whether coordination improves effectiveness.

Generalised Riccati solution and pinning control of complex stochastic networks

This paper considers the global synchronisation of a stochastic version of coupled map lattices networks through an innovative stochastic adaptive linear quadratic pinning control methodology. In a stochastic network, each state receives only noisy measurement of its neighbours' states. For such networks we derive a generalised Riccati solution that quantifies and incorporates uncertainty of the forward dynamics and inverse controller in the derivation of the stochastic optimal control law. The generalised Riccati solution is derived using the Lyapunov approach. A probabilistic approximation type algorithm is employed to estimate the conditional distributions of the state and inverse controller from historical data and quantifying model uncertainties. The theoretical derivation is complemented by its validation on a set of representative examples.

Singular Solutions with Exponential Growth for the (3+1)-D Wave Equation

Недю И. Попиванов, Тодор П. Попов, Рудолф Шерер - Разглеждат се четиримерни гранични задачи за нехомогенното вълново уравнение. Те са предложени от М. Протер като многомерни аналози на задачата на Дарбу в равнината. Известно е, че единственото обобщено решение може да има силна степенна особеност само в една гранична точка. Тази сингулярност е изолирана във върха на характеристичния конус и не се разпространява по конуса. Друг аспект на проблема е, че задачата не е фредхолмова, тъй като има безкрайномерно коядро. Предишни резултати сочат, че решението може да има най-много експоненциален ръст, но оставят открит въпроса дали наистина съществуват такива решения. Показваме, че отговора на този въпрос е положителен и строим обобщено решение на задачата на Протер с експоноциална особеност.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

Maximizing the Efficiency of Greenhouse Gas Related Consumer Policy

Consumer policy approaches regarding green products and solutions can be differentiated by their main focus. “Green positioning” is basically targeted at environmentally aware consumers, while “efficiency-focused positioning” concentrates on the efficiency gain of the product or solution, targeting the whole society, regardless of consumers' environmental awareness. The paper argues that the scope and total environmental benefit can be increased if green products or solutions are promoted in different ways, not only as “green” but also based on other arguments (like cost-efficiency, return on investment, etc.). The paper suggests a model for improving the efficiency of greenhouse gas (GHG)-related consumer policy. Based on the marginal social cost curve and the marginal private cost curve, different (green, yellow, and red) zones of action are identified. GHG mitigation options chosen from those zones are then evaluated with the help of profiling method, addressing the barriers to implementation. Profiling may help design an implementation strategy for the selected options and make consumer policy more effective and acceptable for mass market. Case study results show three different ways of positioning of GHG-related consumer policy in Hungary from 2000 and give practical examples of profiling, based on the latest marginal social cost curve and the contemporary energy saving policy of the state regarding the residential sector.

Maximizing the Efficiency of Greenhouse Gas Related Consumer Policy

Consumer policy approaches regarding green products and solutions can be differentiated by their main focus. “Green positioning” is basically targeted at environmentally aware consumers, while “efficiency-focused positioning” concentrates on the efficiency gain of the product or solution, targeting the whole society, regardless of consumers' environmental awareness. The paper argues that the scope and total environmental benefit can be increased if green products or solutions are promoted in different ways, not only as “green” but also based on other arguments (like cost-efficiency, return on investment, etc.). The paper suggests a model for improving the efficiency of greenhouse gas (GHG)-related consumer policy. Based on the marginal social cost curve and the marginal private cost curve, different (green, yellow, and red) zones of action are identified. GHG mitigation options chosen from those zones are then evaluated with the help of profiling method, addressing the barriers to implementation. Profiling may help design an implementation strategy for the selected options and make consumer policy more effective and acceptable for mass market. Case study results show three different ways of positioning of GHG-related consumer policy in Hungary from 2000 and give practical examples of profiling, based on the latest marginal social cost curve and the contemporary energy saving policy of the state regarding the residential sector.

The Shapley value for airport and irrigation games

In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. We first show that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games by providing alternative solutions that satisfy these axioms. However, when considering an assignment game as a communication graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph buyers are connected with sellers only, we show that Myerson's component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.

Capillary siphons and their application in the fuel delivery system of direct methanol fuel cells

The objective of the work is to develop a fuel delivery system for potable direct methanol fuel cell. Currently, one of the most fundamental limitations of direct methanol fuel cells is that the fuel supplied to the anode of the DMFC must be a very dilute aqueous methanol solution (usually 0.5∼1.5 M). If a DMFC is filled with a dilute aqueous methanol solution, the fuel cell operation time per refuel would be very short, which would considerably diminish the advantage of a DMFC over a conventional battery. To overcome this difficulty, a complex fuel delivery system based on the modern micro system technology was proposed by the author. The proposed fuel delivery system would include micro-pumps, a methanol sensor, and a control unit. The fuel delivery system adds considerable costs to the fuel cell system and consume considerable amount of electricity from the fuel cell, which in turn significantly reduces the net power output of the fuel cell. As a result, the DMFC would have tremendous difficulty to compete with the conventional battery technology in terms of costs and power output. ^ This work presents a novel passive fuel delivery system for direct methanol fuel cells. In this particular system, a methanol fuel and an aqueous methanol solution are stored separately in two containers and a wick is disposed between the two containers in a siphon fashion, with the container of the aqueous methanol solution communicating with the anode of the DMFC. Methanol is siphoned from the methanol container to the aqueous solution container in-situ when the methanol in the aqueous methanol solution is consumed during the operation of the fuel cell. Through a proper selection of the wick and the containers, the methanol concentration near the anode of the DMFC could be maintained within a preferable range. ^

Hydrogeophysical characterization of anisotropy in the Biscayne Aquifer using geophysical methods

The anisotropy of the Biscayne Aquifer which serves as the source of potable water for Miami-Dade County was investigated by applying geophysical methods. Electrical resistivity imaging, self potential and ground penetration radar techniques were employed in both regional and site specific studies. In the regional study, electrical anisotropy and resistivity variation with depth were investigated with azimuthal square array measurements at 13 sites. The observed coefficient of electrical anisotropy ranged from 1.01 to 1.36. The general direction of measured anisotropy is uniform for most sites and trends W-E or SE-NW irrespective of depth. Measured electrical properties were used to estimate anisotropic component of the secondary porosity and hydraulic anisotropy which ranged from 1 to 11% and 1.18 to 2.83 respectively. 1-D sounding analysis was used to models the variation of formation resistivity with depth. Resistivities decreased from NW (close to the margins of the everglades) to SE on the shores of Biscayne Bay. Porosity calculated from Archie's law, ranged from 18 to 61% with higher values found along the ridge. Higher anisotropy, porosities and hydraulic conductivities were on the Atlantic Coastal Ridge and lower values at low lying areas west of the ridge. The cause of higher anisotropy and porosity is attributed to higher dissolution rates of the oolitic facies of the Miami Formation composing the ridge. The direction of minimum resistivity from this study is similar to the predevelopment groundwater flow direction indicated in published modeling studies. Detailed investigations were carried out to evaluate higher anisotropy at West Perrine Park located on the ridge and Snapper Creek Municipal well field where the anisotropy trend changes with depth. The higher anisotropy is attributed to the presence of solution cavities oriented in the E-SE direction on the ridge. Similarly, the change in hydraulic anisotropy at the well field might be related to solution cavities, the surface canal and groundwater extraction wells.^

Orbitally tuned time scale and astronomical forcing in the middle Eocene to early Oligocene determined on ODP and IODP sediment cores

Deciphering the driving mechanisms of Earth system processes, including the climate dynamics expressed as paleoceanographic events, requires a complete, continuous, and high-resolution stratigraphy that is very accurately dated. In this study, we construct a robust astronomically calibrated age model for the middle Eocene to early Oligocene interval (31-43 Ma) in order to permit more detailed study of the exceptional climatic events that occurred during this time, including the Middle Eocene Climate Optimum and the Eocene/Oligocene transition. A goal of this effort is to accurately date the middle Eocene to early Oligocene composite section cored during the Pacific Equatorial Age Transect (PEAT, IODP Exp. 320/321). The stratigraphic framework for the new time scale is based on the identification of the stable long eccentricity cycle in published and new high-resolution records encompassing bulk and benthic stable isotope, calibrated XRF core scanning, and magnetostratigraphic data from ODP Sites 171B-1052, 189-1172, 199-1218, and 207-1260 as well as IODP Sites 320-U1333, and -U1334 spanning magnetic polarity Chrons C12n to C20n. Subsequently we applied orbital tuning of the records to the La2011 orbital solution. The resulting new time scale revises and refines the existing orbitally tuned age model and the Geomagnetic Polarity Time Scale from 31 to 43 Ma. Our newly defined absolute age for the Eocene/Oligocene boundary validates the astronomical tuned age of 33.89 Ma identified at the Massignano (Italy) global stratotype section and point. Our compilation of geochemical records of climate-controlled variability in sedimentation through the middle-to-late Eocene and early Oligocene demonstrates strong power in the eccentricity band that is readily tuned to the latest astronomical solution. Obliquity driven cyclicity is only apparent during very long eccentricity cycle minima around 35.5 Ma, 38.3 Ma and 40.1 Ma.

COGNITIVE AND LINGUISTIC FACTORS OF READING ARABIC: THE ROLE OF MORPHOLOGICAL AWARENESS IN READING

Scientific reading research has produced substantial evidence linking specific reading components to a range of constructs including phonological awareness (PA), morphological awareness, orthographic processing (OP), rapid automatized naming, working memory and vocabulary. There is a paucity of research on Arabic, although 420 million people around the world (Gordon, 2005) speak Arabic. As a Semitic language, Arabic differs in many ways from Indo-European languages. Over the past three decades, literacy research has begun to elucidate the importance of morphological awareness (MA) in reading. Morphology is a salient aspect of Arabic word structure. This study was designed to (a) examine the dimensions underlying MA in Arabic; (b) determine how well MA predicts reading; (c) investigate the role of the standard predictors in different reading outcomes; and (d) investigate the construct of reading in Arabic. This study was undertaken in two phases. In Phase I, 10 MA measures and two reading measures were developed, and tested in a sample of 102 Grade 3 Arabic-speaking children. Factor analysis of the 10 MA tasks yielded one predominant factor supporting the construct validity of MA in Arabic. Hierarchical regression analyses, controlling for age and gender, indicated that the MA factor solution accounted for 41– 43% of the variance in reading. In Phase II, the widely studied predictor measures were developed for PA and OP in addition to one additional measure of MA (root awareness), and three reading measures In Phase II, all measures were administered to another sample of 201 Grade 3 Arabic-speaking children. The construct of reading in Arabic was examined using factor analysis. The joint and unique effects of all standard predictors were examined using different sets of hierarchical regression analyses. Results of Phase II showed that: (a) all five reading measures loaded on one factor; (b) MA consistently accounted for unique variance in reading, particularly in comprehension, above and beyond the standard predictors; and (c) the standard predictors had differential contributions. These findings underscore the contribution of MA to all components of Arabic reading. The need for more emphasis on including morphology in Arabic reading instruction and assessment is discussed.

Tracing the Chromospheric and Coronal Magnetic Field with AIA, IRIS, IBIS, and ROSA Data

The aim of this study is to explore the suitability of chromospheric images for magnetic modeling of active regions. We use high-resolutionimages (≈0.2"-0.3"), from the Interferometric Bidimensional Spectrometer in the Ca II 8542 Å line, the Rapid Oscillations in the Solar Atmosphere instrument in the Hα 6563Å line, the Interface Region Imaging Spectrograph in the 2796Å line, and compare non-potential magnetic field models obtainedfrom those chromospheric images with those obtained from images of the Atmospheric Imaging Assembly in coronal (171 Å, etc.) and inchromospheric (304 Å) wavelengths. Curvi-linear structures are automatically traced in those images with the OCCULT-2 code, to which we forward-fitted magnetic field lines computed with the Vertical-current Approximation Nonlinear Force Free Field code. We find that the chromospheric images: (1) reveal crisp curvi-linear structures (fibrils, loop segments, spicules) that are extremely well-suited for constraining magnetic modeling; (2) that these curvi-linear structures arefield-aligned with the best-fit solution by a median misalignment angle of μ2 ≈ 4°–7° (3) the free energy computed from coronal data may underestimate that obtained from chromospheric data by a factor of ≈2–4, (4) the height range of chromospheric features is confined to h≲4000 km, while coronal features are detected up to h = 35,000 km; and (5) the plasma-β parameter is β ≈ 10^-5 - 10^-1 for all traced features. We conclude that chromospheric images reveal important magnetic structures that are complementary to coronal images and need to be included in comprehensive magnetic field models, something that is currently not accomodated in standard NLFFF codes.