A numerical method to solve higher-order fractional differential equations

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order derivatives only. With this, we can rewrite FDEs in terms of a classical one and then apply any known technique. With some examples, we show the accuracy of the method.

Higher-Order Functions for Parsing

In combinator parsing, the text of parsers resembles BNF notation. We present the basic method, and a number of extensions. We address the special problems presented by white-space, and parsers with separate lexical and syntactic phases. In particular, a combining form for handling the offside rule is given. Other extensions to the basic method include an $quot;into$quot; combining form with many useful applications, and a simple means by which combinator parsers can produce more informative error messages.

Ordinal Arithmetic: A Case Study for Rippling in a Higher Order Domain

This paper reports a case study in the use of proof planning in the context of higher order syntax. Rippling is a heuristic for guiding rewriting steps in induction that has been used successfully in proof planning inductive proofs using first order representations. Ordinal arithmetic provides a natural set of higher order examples on which transfinite induction may be attempted using rippling. Previously Boyer-Moore style automation could not be applied to such domains. We demonstrate that a higher-order extension of the rippling heuristic is sufficient to plan such proofs automatically. Accordingly, ordinal arithmetic has been implemented in lambda-clam, a higher order proof planning system for induction, and standard undergraduate text book problems have been successfully planned. We show the synthesis of a fixpoint for normal ordinal functions which demonstrates how our automation could be extended to produce more interesting results than the textbook examples tried so far.

Airframe sound simulation based on staggered-grid higher order schemes and finite volume CFD methods

Abstract not available

Reverse-flow integral methods for second-order supersonic flow theory,

"CM-1033."

Higher-order variational problems of Herglotz type

We obtain a generalized Euler–Lagrange differential equation and transversality optimality conditions for Herglotz-type higher-order variational problems. Illustrative examples of the new results are given.

TRANSFORMATIONS OF TASK-DEPENDENT PLASTICITY FROM A1 TO HIGHER-ORDER AUDITORY CORTEX

Everyday, humans and animals navigate complex acoustic environments, where multiple sound sources overlap. Somehow, they effortlessly perform an acoustic scene analysis and extract relevant signals from background noise. Constant updating of the behavioral relevance of ambient sounds requires the representation and integration of incoming acoustical information with internal representations such as behavioral goals, expectations and memories of previous sound-meaning associations. Rapid plasticity of auditory representations may contribute to our ability to attend and focus on relevant sounds. In order to better understand how auditory representations are transformed in the brain to incorporate behavioral contextual information, we explored task-dependent plasticity in neural responses recorded at four levels of the auditory cortical processing hierarchy of ferrets: the primary auditory cortex (A1), two higher-order auditory areas (dorsal PEG and ventral-anterior PEG) and dorso-lateral frontal cortex. In one study we explored the laminar profile of rapid-task related plasticity in A1 and found that plasticity occurred at all depths, but was greatest in supragranular layers. This result suggests that rapid task-related plasticity in A1 derives primarily from intracortical modulation of neural selectivity. In two other studies we explored task-dependent plasticity in two higher-order areas of the ferret auditory cortex that may correspond to belt (secondary) and parabelt (tertiary) auditory areas. We found that representations of behaviorally-relevant sounds are progressively enhanced during performance of auditory tasks. These selective enhancement effects became progressively larger as you ascend the auditory cortical hierarchy. We also observed neuronal responses to non-auditory, task-related information (reward timing, expectations) in the parabelt area that were very similar to responses previously described in frontal cortex. These results suggests that auditory representations in the brain are transformed from the more veridical spectrotemporal information encoded in earlier auditory stages to a more abstract representation encoding sound behavioral meaning in higher-order auditory areas and dorso-lateral frontal cortex.

The role of information literacy competence and higher order thinking skills to develop academic writing in science and engineering students

This article discusses a study organized to develop academic writing skills in undergraduate students pursuing engineering courses. The target group consisted of 30 students pursuing a Bachelor of Technology in their third year. The classroom observations regarding teaching writing revealed that writing proficiency for most of the students was at a very low level. Followed by this, an intervention program was organized in one college, where the researcher taught academic writing to the students. Units comprising tasks that focused on raising awareness of the academic texts and involving the students in the cognitive processes of writing were designed. The study focused on raising student awareness regarding the nature and characteristics of academic texts in order to develop academic writing skills. The study also emphasized that involving the students in the cognitive processes of writing (e.g., defining the rhetorical problem, identifying the rhetorical situation, determining the audience, setting goals for writing, planning for the text by generating, and organizing ideas) is necessary. The study further suggests that discussions between students and teachers regarding the construction of a text and the way language works in various text types facilitates better writing.

Collaborative technologies, higher order thinking and self-sufficient learning: A case study of adult learners

The inclusion of online elements in learning environments is becoming commonplace in Post Compulsory Education. A variety of research into the value of such elements is available, and this study aims to add further evidence by looking specifically at the use of collaborative technologies such as online discussion forums and wikis to encourage higher order thinking and self-sufficient learning. In particular, the research examines existing pedagogical models including Salmon’s five-stage model, along with other relevant literature. A case study of adult learners in community-based learning centres forms the basis of the research, and as a result of the findings, an arrow model is suggested as a framework for online collaboration that emphasises the learner, mentions pre-course preparation and then includes three main phases of activity: post, interact and critique. This builds on Salmon’s five-stage model and has the benefit of being flexible and responsive, as well as allowing for further development beyond the model, particularly in a blended learning environment.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

The role of a transcrustal shear zone in orogenic gold mineralization at the Aijanahalli Mine, Dharwar Craton, South India

The Ajjanahalli gold mine is spatially associated with a Late Archean craton-scale shear zone in the eastern Chitradurga greenstone belt of the Dharwar craton, India. Gold mineralization is hosted by an similar to100-m-wide antiform in a banded iron formation. Original magnetite and siderite are replaced by a peak metamorphic alteration assemblage of chlorite, stilpnomelane, minnesotaite, sericite, ankerite, arsenopyrite, pyrite, pyrrhotite, and gold at ca. 300degrees to 350degreesC. Elements enriched in the banded iron formation include Ca, Mg, C, S, An, As, Bi. Cu, Sb, Zn, Pb, Se, Ag, and Te, whereas in the wall rocks As, Cu, Zn, Bi, Ag, and An are only slightly enriched. Strontium correlates with CaO, MgO, CO2, and As, which indicates cogenetic formation of arsenopyrite and Mg-Ca carbonates. The greater extent of alteration in the Fe-rich banded iron formation layers than in the wall rock reflects the greater reactivity of the banded iron formation layers. The ore fluids, as interpreted from their isotopic composition (delta(18)O = 6.5-8.5parts per thousand; initial Sr-87/Sr-86 = 0.7068-0.7078), formed by metamorphic devolatilization of deeper levels of the Chitradurga greenstone belt. Arsenopyrite, chalcopyrite, and pyrrhotite have delta(34)S values within a narrow range between 2.1 and 2.7 per mil, consistent with a sulfur source in Chitradurga greenstone belt lithologies. Based on spatial and temporal relationships between mineralization, local structure development, and sinistral strike-slip deformation in the shear zone at the eastern contact of the Chitradurga greenstone belt, we suggest that the Ajjanahalli gold mineralization formed by fluid infiltration into a low strain area within the first-order structure. The ore fluids were transported along this shear zone into relatively shallow crustal levels during lateral terrane accretion and a change from thrust to transcurrent tectonics. Based on this model of fluid flow, exploration should focus on similar low strain areas or potentially connected higher order splays of the first-order shear zone.

Second order gauge theory

A gauge theory of second order in the derivatives of the auxiliary field is constructed following Utiyama's program. A novel field strength G = partial derivative F + fAF arises besides the one of the first order treatment, F = partial derivative A - partial derivative A + fAA. The associated conserved current is obtained. It has a new feature: topological terms are determined from local invariance requirements. Podolsky Generalized Eletrodynamics is derived as a particular case in which the Lagrangian of the gauge field is L-P alpha G(2). In this application the photon mass is estimated. The SU(N) infrared regime is analysed by means of Alekseev-Arbuzov-Baikov's Lagrangian. (c) 2006 Elsevier B.V. All rights reserved.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Apparent strain localization and shear wave dispersion in elastic fault gouge with microrotations

Shear deformation of fault gouge or other particulate materials often results in observed strain localization, or more precisely, the localization of measured deformation gradients. In conventional elastic materials the strain localization cannot take place therefore this phenomenon is attributed to special types of non-elastic constitutive behaviour. For particulate materials however the Cosserat continuum which takes care of microrotations independent of displacements is a more appropriate model. In elastic Cosserat continuum the localization in displacement gradients is possible under some combinations of the generalized Cosserat elastic moduli. The same combinations of parameters also correspond to a considerable dispersion in shear wave propagation which can be used for independent experimental verification of the proposed mechanism of apparent strain localization in fault gouge.