72 resultados para Integrable equations in Physics
Resumo:
There is extensive uptake of ICT in the teaching of science but more evidence is needed on how ICT impacts on the learning practice and the learning outcomes at the classroom level. In this study, a physics website (Getsmart) was developed using the cognitive apprenticeship framework for students at a high school in Australia. This website was designed to enhance students’ knowledge of concepts in physics. Reflexive pedagogies were used in the delivery learning materials in a blended learning environment. The students in the treatment group accessed the website over a 10 week period. Pre and post-test results of the treatment (N= 48) and comparison group (N=32) were compared. The MANCOVA analysis showed that the web-based learning experience benefited the students in the treatment group. It not only impacted on the learning outcomes, but qualitative data from the students suggested that it had a positive impact on their attitudes towards studying physics in a blended environment.
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A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.
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In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.
Resumo:
A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.
Resumo:
The "standard" procedure for calibrating the Vesuvio eV neutron spectrometer at the ISIS neutron source, forming the basis for data analysis over at least the last decade, was recently documented in considerable detail by the instrument’s scientists. Additionally, we recently derived analytic expressions of the sensitivity of recoil peak positions with respect to fight-path parameters and presented neutron–proton scattering results that together called in to question the validity of the "standard" calibration. These investigations should contribute significantly to the assessment of the experimental results obtained with Vesuvio. Here we present new results of neutron–deuteron scattering from D2 in the backscattering angular range (theata > 90 degrees) which are accompanied by a striking energy increase that violates the Impulse Approximation, thus leading unequivocally the following dilemma: (A) either the "standard" calibration is correct and then the experimental results represent a novel quantum dynamical effect of D which stands in blatant contradiction of conventional theoretical expectations; (B) or the present "standard" calibration procedure is seriously deficient and leads to artificial outcomes. For Case(A), we allude to the topic of attosecond quantumdynamical phenomena and our recent neutron scattering experiments from H2 molecules. For Case(B),some suggestions as to how the "standard" calibration could be considerably improved are made.
Resumo:
The effects of small changes in flight-path parameters (primary and secondary flight paths, detector angles), and of displacement of the sample along the beam axis away from its ideal position, are examined for an inelastic time-of-flight (TOF) neutron spectrometer, emphasising the deep-inelastic regime. The aim was to develop a rational basis for deciding what measured shifts in the positions of spectral peaks could be regarded as reliable in the light of the uncertainties in the calibrated flight-path parameters. Uncertainty in the length of the primary or secondary flight path has the least effect on the positions of the peaks of H, D and He, which are dominated by the accuracy of the calibration of the detector angles. This aspect of the calibration of a TOF spectrometer therefore demands close attention to achieve reliable outcomes where the position of the peaks is of significant scientific interest and is discussed in detail. The corresponding sensitivities of the position of peak of the Compton profile, J(y), to flight-path parameters and sample position are also examined, focusing on the comparability across experiments of results for H, D and He. We show that positioning the sample to within a few mm of the ideal position is required to ensure good comparability between experiments if data from detectors at high forward angles are to be reliably interpreted.
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Fractional partial differential equations have been applied to many problems in physics, finance, and engineering. Numerical methods and error estimates of these equations are currently a very active area of research. In this paper we consider a fractional diffusionwave equation with damping. We derive the analytical solution for the equation using the method of separation of variables. An implicit difference approximation is constructed. Stability and convergence are proved by the energy method. Finally, two numerical examples are presented to show the effectiveness of this approximation.
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A procedure for the evaluation of multiple scattering contributions is described, for deep inelastic neutron scattering (DINS) studies using an inverse geometry time-of-flight spectrometer. The accuracy of a Monte Carlo code DINSMS, used to calculate the multiple scattering, is tested by comparison with analytic expressions and with experimental data collected from polythene, polycrystalline graphite and tin samples. It is shown that the Monte Carlo code gives an accurate representation of the measured data and can therefore be used to reliably correct DINS data.
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In this paper, the collision of a C36, with D6h symmetry, on diamond (001)-(/2×1) surface was investigated using molecular dynamics (MD) simulation based on the semi-empirical Brenner potential. The incident kinetic energy of the C36 ranges from 20 to 150 eV per cluster. The collision dynamics was investigated as a function of impact energy Ein. The C36 cluster was first impacted towards the center of two dimers with a fixed orientation. It was found that when Ein was lower than 30 eV, C36 bounces off the surface without breaking up. Increasing Ein to 30-45 eV, bonds were formed between C36 and surface dimer atoms, and the adsorbed C36 retained its original free-cluster structure. Around 50-60 eV, the C36 rebounded from the surface with cage defects. Above 70 eV, fragmentation both in the cluster and on the surface was observed. Our simulation supported the experimental findings that during low-energy cluster beam deposition small fullerenes could keep their original structure after adsorption (i.e. the memory effect), if Ein is within a certain range. Furthermore, we found that the energy threshold for chemisorption is sensitive to the orientation of the incident C36 and its impact position on the asymmetric surface.
Resumo:
Bandwidths and offsets are important components in vehicle traffic control strategies. This article proposes new methods for quantifying and selecting them. Bandwidth is the amount of green time available for vehicles to travel through adjacent intersections without the requirement to stop at the second traffic light. The offset is the difference between the starting-time of ``green'' periods at two adjacent intersections, along a given route. The core ideas in this article were developed during the 2013 Maths and Industry Study Group in Brisbane, Australia. Analytical expressions for computing bandwidth, as a function of offset, are developed. An optimisation model, for selecting offsets across an arterial, is proposed. Arterial roads were focussed upon, as bandwidth and offset have a greater impact on these types of road as opposed to a full traffic network. A generic optimisation-simulation approach is also proposed to refine an initial starting solution, according to a specified metric. A metric that reflects the number of stops, and the distance between stops, is proposed to explicitly reduce the dissatisfaction of road users, and to implicitly reduce fuel consumption and emissions. Conceptually the optimisation-simulation approach is superior as it handles real-life complexities and is a global optimisation approach. The models and equations in this article can be used in road planning and traffic control.
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The prime aim of this research project is to evaluate the performance of confined masonry walls under in-plane shear with a view to contributing to the national masonry design standard through a set of design clauses. This aim stems from the criticisms of the current provisions of the in-plane shear capacity equations in the Australian Masonry Standard AS3700 (2011) being highly non-conservative. This PhD thesis is an attempt to address this gap in the knowledge through systematic investigation of the key parameters that affects the in-plane shear strength of the masonry walls through laboratory experiments and extensive finite element analyses.
Resumo:
The unique plasma-specific features and physical phenomena in the organization of nanoscale soild-state systems in a broad range of elemental composition, structure, and dimensionality are critically reviewed. These effects lead to the possibility to localize and control energy and matter at nanoscales and to produce self-organized nano-solids with highly unusual and superior properties. A unifying conceptual framework based on the control of production, transport, and self-organization of precursor species is introduced and a variety of plasma-specific non-equilibrium and kinetics-driven phenomena across the many temporal and spatial scales is explained. When the plasma is localized to micrometer and nanometer dimensions, new emergent phenomena arise. The examples range from semiconducting quantum dots and nanowires, chirality control of single-walled carbon nanotubes, ultra-fine manipulation of graphenes, nano-diamond, and organic matter to nano-plasma effects and nano-plasmas of different states of matter. © 2013 Taylor and Francis Group, LLC.
Resumo:
In-plane shear capacity formulation of reinforced masonry is commonly conceived as the sum of the capacities of three parameters, viz, the masonry, the reinforcement, and the precompression. The term “masonry” incorporates the aspect ratio of the wall without any regard to the aspect ratio of the panels inscribed (and hence confined) by the vertical and the horizontal reinforced grout cores. This paper proposes design expressions in which the aspect ratio of such panels is explicitly included. For this purpose, the grouted confining cores are regarded as a grid of confining elements within which the panels are positioned. These confined masonry panels are then considered as building blocks for multi-bay, multi-storied confined masonry shear walls and analyzed using an experimentally validated macroscopic finite-element model. Results of the analyzes of 161 confined masonry walls containing panels of height to length ratio less than 1.0 have been regressed to formulate design expressions. These expressions have been first validated using independent test data sets and then compared with the existing equations in some selected international design standards. The concept of including the unreinforced masonry panel aspect ratio as an additional term in the design expression for partially grouted/confined masonry shear walls is recommended based on the conclusions from this paper.
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It has been well accepted that over 50% of cerebral ischemic events are the result of rupture of vulnerable carotid atheroma and subsequent thrombosis. Such strokes are potentially preventable by carotid interventions. Selection of patients for intervention is currently based on the severity of carotid luminal stenosis. It has been, however, widely accepted that luminal stenosis alone may not be an adequate predictor of risk. To evaluate the effects of degree of luminal stenosis and plaque morphology on plaque stability, we used a coupled nonlinear time-dependent model with flow-plaque interaction simulation to perform flow and stress/strain analysis for stenotic artery with a plaque. The Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian (ALE) formulation were used as the governing equations for the fluid. The Ogden strain energy function was used for both the fibrous cap and the lipid pool. The plaque Principal stresses and flow conditions were calculated for every case when varying the fibrous cap thickness from 0.1 to 2mm and the degree of luminal stenosis from 10% to 90%. Severe stenosis led to high flow velocities and high shear stresses, but a low or even negative pressure at the throat of the stenosis. Higher degree of stenosis and thinner fibrous cap led to larger plaque stresses, and a 50% decrease of fibrous cap thickness resulted in a 200% increase of maximum stress. This model suggests that fibrous cap thickness is critically related to plaque vulnerability and that, even within presence of moderate stenosis, may play an important role in the future risk stratification of those patients when identified in vivo using high resolution MR imaging.
Resumo:
This paper reports and discusses findings from a recent study which explored the science enrolment decisions of high achieving, or ‘science proficient’ secondary level students in Australia (Lyons 2003). The research was prompted by the increasing reluctance of such students to enrol in postcompulsory science courses, particularly in physics and chemistry. The study investigated the influences on students’ deliberations about taking a range of science courses. However, this report confines itself to decisions about enrolling in the physical sciences. The paper summarises the students’ experiences and conceptions of school science, as well as the characteristics of their ‘family worlds’ found to be influential in their decisions1. The paper discusses the important roles of cultural and social capital in these decisions, and concludes that enrolment in physical science courses was associated with congruence between the students’ conceptions of school science, and characteristics of their family backgrounds.