In this study we are interested in how learners of geometrical optics express disciplinary relevant aspects multimodally in an inquiry-based learning with support of a computer simulation. Students' discussions and work with the simulation were filmed, transcribed, and we analysed some parts of the transcript where the students show signs of disciplinary relevant aspects by a method based in conversation analysis. We found evidence that the students use multiple semiotic resources for expressing disciplinary relevant aspects about the tasks, especially gestures. The letter are by their visual nature well suited for communication in physics, and are used by the students to transduct semiotic information.
As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.
We propose a statistical method for analyzing key comparisons with two transfer standards measured in two petals. The new approach is based on an extension of the established random effects model. A full Bayesian analysis based on the reference prior is developed and analytic expressions for the results are derived. One benefit of the suggested approach is that it provides a comprehensive assessment of the laboratory biases in terms of their posterior distributions. Another advantage is that it can easily be applied in practice. The approach is illustrated for the CCM.M-K7 key comparison data.
Weighted least-squares estimation is commonly applied in metrology to fit models to measurements that are accompanied with quoted uncertainties. The weights are chosen in dependence on the quoted uncertainties. However, when data and model are inconsistent in view of the quoted uncertainties, this procedure does not yield adequate results.
When it can be assumed that all uncertainties ought to be rescaled by a common factor, weighted least-squares estimation may still be used, provided that a simple correction of the uncertainty obtained for the estimated model is applied. We show that these uncertainties and credible intervals are robust, as they do not rely on the assumption of a Gaussian distribution of the data. Hence, common software for weighted least-squares estimation may still safely be employed in such a case, followed by a simple modification of the uncertainties obtained by that software. We also provide means of checking the assumptions of such an approach.
The Bayesian regression procedure is applied to analyze the CODATA values for the Planck constant published over the past decades in terms of three different models: a constant model, a straight line model and a spline model. Our results indicate that the CODATA values may not have yet stabilized
The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty.
This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand.
The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists.
We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.
To develop an equation of state with simple structure and reasonable accuracy for engineering application, Redlich-Kwong equation of state was modified for gaseous CO2 and CO2-H2O mixtures. In the new modification, parameter a of gaseous CO2 was regressed as a function of temperature and pressure from recent reliable experimental data in the range: 220-750 K and 0.1-400 MPa. Moreover, a new mixing rule was proposed for gaseous CO2-H2O mixtures. To verify the accuracy of the new modification, densities were calculated and compared with experimental data. The average error is 1.68% for gaseous CO2 and 0.93% for gaseous mixtures of CO2 and H2O. Other thermodynamic properties, such as enthalpy and heat capacities of CO2 and excess enthalpy of gaseous CO2-H2O mixtures, were also calculated; results fit experimental data well, except for the critical region.
This article reports progress on homogeneous isotropic tensor random fields (TRFs) for continuum mechanics. The basic thrust is on determinin most general representations of the correlation functions as well as their spectral expansions. Once this is accomplished, the second step is finding the restrictionsdictated by a particular physical application. Thus, in the case of fields of material properties (like conductivity and stiffness), the restriction resides in the positive-definiteness, whereby a connection to experiments and/or computational micromechanics can be established. On the other hand, in the case of fields of dependent properties (e.g., stress, strain and displacement), restrictions are due to the respective field equations.
Scattering theory has had a major roll in twentieth century mathematical physics. Mathematical modeling and algorithms of direct,- and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are acknowledged.
The results established in contemporary statistical physics indicating that, on very small space and time scales, the entropy production rate may be negative, motivate a generalization of continuum mechanics. On account of the fluctuation theorem, it is recognized that the evolution of entropy at a material point is stochastically (not deterministically) conditioned by the past history, with an increasing trend of average entropy production. Hence, the axiom of Clausius-Duhem inequality is replaced by a submartingale model, which, by the Doob decomposition theorem, allows classification of thermomechanical processes into four types depending on whether they are conservative or not and/or conventional continuum mechanical or not. Stochastic generalizations of thermomechanics are given in the vein of either thermodynamic orthogonality or primitive thermodynamics, with explicit models formulated for Newtonian fluids with, respectively, parabolic or hyperbolic heat conduction. Several random field models of the martingale component, possibly including spatial fractal and Hurst effects, are proposed. The violations of the second law are relevant in those situations in continuum mechanics where very small spatial and temporal scales are involved. As an example, we study an acceleration wavefront of nanoscale thickness which randomly encounters regions in the medium characterized by a negative viscosity coefficient.
Creative learning is discussed with respect to a specific physics topic. A teaching example, based on an apparatus that demonstrates the standard dynamo model of geomagnetism, is presented. It features many of the basic physics concepts within the syllabus of electromagnetism at high-school and university.
To stimulate conceptual learning and to invite student explorations, the apparatus is designed to exhibit simplicity and transparency. Due to the connection to natural phenomena and to engineering applications it promotes a holistic view of physics. The apparatus is therefore useful for practising creative learning.
An alternative way of introducing magnetism at all levels of education isproposed. It is stressed that magnetism can be introduced through theinteraction between current-carrying conductors giving the students, at thesame time, the possibility to measure the magnetic permeability μo. Focusingon currents instead of permanent magnets provides a pathway to explore thefull dynamics between the basic constituents, i.e. the elementary charges. Italso connects better to some modern applications of magnetism such as thedefinition of mass, which utilizes a current balance and the link betweenmagnetism and special relativity
In order to increase understanding of the cochlea and to illustrate its connection to basic physics, a functional model was developed. It was found to be useful in exploring the basic dynamics of the basilar membrane and its role in the frequency mapping of the cochlea.
This article presents an evaluation of the environmental impact of forestry based on landscape theory. It has been argued that this type of forestry offers a positive impact on the climate because there is a balance between the amount of greenhouse gas emissions and the absorption of these gases within an entire forested area. However, this analysis will demonstrate that the arrangement and composition of managed forests are linked to a significant carbon debt. This debt represents the disparity between the carbon that would typically be stored in a natural forest and the actual amount of carbon stored in the managed forest. While this excess carbon remains in the atmosphere rather than being sequestered, it contributes to the greenhouse effect. Using Swedish forestry as an example, the carbon debt is estimated to be comparable in scale to the total accumulated fossil fuel emissions of the country.
The need and benefits of new universal mathematical and especially algebraic and operator structures and methods in all branches and levels of modem physics from experiments to fundamentals is nowdays widely recognized. The far reaching pioneering discoveries of R. M. Santilli extend significantly the Lie analysis and operator methods and models of modem physics opening new areas of applications with possible essential improvements and revisions in models in particle physics and cosmology. In this article, some fundamental aspects of Lie-Santilli isotopic theory and relevant references are presented.