Didactical reconstructions for organizing knowledge in physics teacher education

Physics teachers are in a key position to form the attitudes and conceptions of future generations toward science and technology, as well as to educate future generations of scientists. Therefore, good teacher education is one of the key areas of physics departments education program. This dissertation is a contribution to the research-based development of high quality physics teacher education, designed to meet three central challenges of good teaching. The first challenge relates to the organization of physics content knowledge. The second challenge, connected to the first one, is to understand the role of experiments and models in (re)constructing the content knowledge of physics for purposes of teaching. The third challenge is to provide for pre-service physics teachers opportunities and resources for reflecting on or assessing their knowledge and experience about physics and physics education. This dissertation demonstrates how these challenges can be met when the content knowledge of physics, the relevant epistemological aspects of physics and the pedagogical knowledge of teaching and learning physics are combined. The theoretical part of this dissertation is concerned with designing two didactical reconstructions for purposes of physics teacher education: the didactical reconstruction of processes (DRoP) and the didactical reconstruction of structures (DRoS). This part starts with taking into account the required professional competencies of physics teachers, the pedagogical aspects of teaching and learning, and the benefits of the graphical ways of representing knowledge. Then it continues with the conceptual and philosophical analysis of physics, especially with the analysis of experiments and models role in constructing knowledge. This analysis is condensed in the form of the epistemological reconstruction of knowledge justification. Finally, these two parts are combined in the designing and production of the DRoP and DRoS. The DRoP captures the knowledge formation of physical concepts and laws in concise and simplified form while still retaining authenticity from the processes of how concepts have been formed. The DRoS is used for representing the structural knowledge of physics, the connections between physical concepts, quantities and laws, to varying extents. Both DRoP and DRoS are represented in graphical form by means of flow charts consisting of nodes and directed links connecting the nodes. The empirical part discusses two case studies that show how the three challenges are met through the use of DRoP and DRoS and how the outcomes of teaching solutions based on them are evaluated. The research approach is qualitative; it aims at the in-depth evaluation and understanding about the usefulness of the didactical reconstructions. The data, which were collected from the advanced course for prospective physics teachers during 20012006, consisted of DRoP and DRoS flow charts made by students and student interviews. The first case study discusses how student teachers used DRoP flow charts to understand the process of forming knowledge about the law of electromagnetic induction. The second case study discusses how student teachers learned to understand the development of physical quantities as related to the temperature concept by using DRoS flow charts. In both studies, the attention is focused on the use of DRoP and DRoS to organize knowledge and on the role of experiments and models in this organization process. The results show that students understanding about physics knowledge production improved and their knowledge became more organized and coherent. It is shown that the flow charts and the didactical reconstructions behind them had an important role in gaining these positive learning results. On the basis of the results reported here, the designed learning tools have been adopted as a standard part of the teaching solutions used in the physics teacher education courses in the Department of Physics, University of Helsinki.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

On global solar dynamo simulations

Global dynamo simulations solving the equations of magnetohydrodynamics (MHD) have been a tool of astrophysicists who try to understand the magnetism of the Sun for several decades now. During recent years many fundamental issues in dynamo theory have been studied in detail by means of local numerical simulations that simplify the problem and allow the study of physical effects in isolation. Global simulations, however, continue to suffer from the age-old problem of too low spatial resolution, leading to much lower Reynolds numbers and scale separation than in the Sun. Reproducing the internal rotation of the Sun, which plays a crucual role in the dynamo process, has also turned out to be a very difficult problem. In the present paper the current status of global dynamo simulations of the Sun is reviewed. Emphasis is put on efforts to understand how the large-scale magnetic fields, i.e. whose length scale is greater than the scale of turbulence, are generated in the Sun. Some lessons from mean-field theory and local simulations are reviewed and their possible implications to the global models are discussed. Possible remedies to some of the current issues of the solar simulations are put forward.

Magnetorotational instability driven dynamos at low magnetic Prandtl numbers

Numerical simulations of the magnetorotational instability (MRI) with zero initial net flux in a non-stratified isothermal cubic domain are used to demonstrate the importance of magnetic boundary conditions. In fully periodic systems the level of turbulence generated by the MRI strongly decreases as the magnetic Prandtl number (Pm), which is the ratio of kinematic viscosity and magnetic diffusion, is decreased. No MRI or dynamo action below Pm=1 is found, agreeing with earlier investigations. Using vertical field conditions, which allow magnetic helicity fluxes out of the system, the MRI is found to be excited in the range 0.1

Reynolds stress and heat flux in spherical shell convection

Context. Turbulent fluxes of angular momentum and heat due to rotationally affected convection play a key role in determining differential rotation of stars. Aims. We compute turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. Methods. We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results. For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong 'banana cells'. Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance.

3D MHD simulations of subsurface convection in OB stars

During their main sequence evolution, massive stars can develop convective regions very close to their surface. These regions are caused by an opacity peak associated with iron ionization. Cantiello et al. (2009) found a possible connection between the presence of sub-photospheric convective motions and small scale stochastic velocities in the photosphere of early-type stars. This supports a physical mechanism where microturbulence is caused by waves that are triggered by subsurface convection zones. They further suggest that clumping in the inner parts of the winds of OB stars could be related to subsurface convection, and that the convective layers may also be responsible for stochastic excitation of non-radial pulsations. Furthermore, magnetic fields produced in the iron convection zone could appear at the surface of such massive stars. Therefore subsurface convection could be responsible for the occurrence of observable phenomena such as line profile variability and discrete absorption components. These phenomena have been observed for decades, but still evade a clear theoretical explanation. Here we present preliminary results from 3D MHD simulations of such subsurface convection.

Dependence of the large-scale vortex instability on latitude, stratification and domain size

In an earlier study, we reported on the excitation of large-scale vortices in Cartesian hydrodynamical convection models subject to rapid enough rotation. In that study, the conditions for the onset of the instability were investigated in terms of the Reynolds (Re) and Coriolis (Co) numbers in models located at the stellar North pole. In this study, we extend our investigation to varying domain sizes, increasing stratification, and place the box at different latitudes. The effect of the increasing box size is to increase the sizes of the generated structures, so that the principal vortex always fills roughly half of the computational domain. The instability becomes stronger in the sense that the temperature anomaly and change in the radial velocity are observed to be enhanced. The model with the smallest box size is found to be stable against the instability, suggesting that a sufficient scale separation between the convective eddies and the scale of the domain is required for the instability to work. The instability can be seen upto the colatitude of 30 degrees, above which value the flow becomes dominated by other types of mean flows. The instability can also be seen in a model with larger stratification. Unlike the weakly stratified cases, the temperature anomaly caused by the vortex structures is seen to depend on depth.

Elliptic flow of thermal photons in heavy-ion collisions at Relativistic Heavy Ion Collider and Large Hadron Collider

We calculate the thermal photon transverse momentum spectra and elliptic flow in $\sqrt{s_{NN}} = 200$ GeV Au+Au collisions at RHIC and in $\sqrt{s_{NN}} = 2.76$ TeV Pb+Pb collisions at the LHC, using an ideal-hydrodynamical framework which is constrained by the measured hadron spectra at RHIC and LHC. The sensitivity of the results to the QCD-matter equation of state and to the photon emission rates is studied, and the photon $v_2$ is discussed in the light of the photonic $p_T$ spectrum measured by the PHENIX Collaboration. In particular, we make a prediction for the thermal photon $p_T$ spectra and elliptic flow for the current LHC Pb+Pb collisions.