24 research outputs found
Cosmic ray modulation with a Fisk-type heliospheric magnetic field and a latitude-dependent solar wind speed
No full textThe effect of a latitude-dependent solar wind speed on a Fisk heliospheric magnetic field [Fisk, L. A. Motion of the footpoints of heliospheric magnetic field lines at the Sun: implications for recurrent energetic particle events at high heliographic latitudes. J. Geophys. Res. 101, 15547–15553, 1996] was first discussed by Schwadron and Schwadron and McComas [Schwadron, N.A. An explanation for strongly underwound magnetic field in co-rotating rarefaction regions and its relationship to footpoint motion on the the sun. Geophys. Res. Lett. 29, 1–8, 2002. and Schwadron, N.A., McComas, D.J. Heliospheric “FALTS”: favored acceleration locations at the termination shock. Geophys. Res. Lett. 30, 41–1, 2003]. Burger and Sello [Burger, R.A., Sello, P.C. The effect on cosmic ray modulation of a Parker field modified by a latitudinal-dependent solar wind speed. Adv. Space Res. 35, 643–646, 2005] found a significant effect for a simplified 2D version of a latitude-dependent Fisk-type field while Miyake and Yanagita [Miyake, S., Yanagita, S. The effect of a modified Parker field on the modulation of the galactic cosmic rays. In: Proceedings of 30th International Cosmic Ray Conference. Merida, Mexico, vol. 1, 445–448, 2007] found a smaller effect. The current report improves on a previous attempt Hitge and Burger [Hitge, M., Burger, R.A. The effect of a latitude-dependent solar wind speed on cosmic-ray modulation in a Fisk-type heliospheric magnetic field. In: Proceedings of 30th International Cosmic Ray Conference. Merida, Mexico, vol. 1, pp. 449–450, 2007] where the global change in the solar wind speed and not the local speed gradient was emphasized. The sheared Fisk field of Schwadron and McComas [Schwadron, N.A., McComas, D.J. Heliospheric “FALTS”: Favored acceleration locations at the termination shock. Geophys. Res. Lett. 30, 41–1, 2003.) is similar to the current Schwadron–Parker hybrid field. Little difference is found between the effects of a Parker field and a Schwadron–Parker hybrid field on cosmic-ray modulation, in contrast to the results of Burger and Sello and Miyake and Yanagita [Burger, R.A., Sello, P.C. The effect on cosmic ray modulation of a Parker field modified by a latitudinal-dependent solar wind speed. Adv. Space Res. 35, 643–646, 2005 and Miyake, S., Yanagita, S. The effect of a modified Parker field on the modulation of the galactic cosmic rays. In: Proceedings of 30th International Cosmic Ray Conference. Merida, Mexico, vol. 1, pp. 445–448, 2007]. The two-dimensional approximation used by these authors is therefore inadequate to model the complexities of the actual three-dimensional field. We also show that a Fisk-type field with a latitude-dependent solar wind speed (Schwadron–Parker hybrid field) decreases both the relative amplitude of recurrent cosmic ray intensity variations and latitude gradients and yields similar constants of proportionality for these quantities as for the constant solar wind speed case
A Fisk‐Parker Hybrid Heliospheric Magnetic Field with a Solar‐Cycle Dependence
No full textWe present a refinement of the Fisk-Parker hybrid field of Burger and Hitge which now includes a region bordering the solar rotational equator where magnetic field footpoint motion occurs only through diffusive reconnection. The hybrid field, therefore, only occurs above a certain latitude in a given hemisphere, and in the equatorial region the field is a pure Parker field. We also propose a simple qualitative model for the solar cycle dependence of the hybrid field, taking into account changes in the tilt angle of the heliospheric current sheet and the latitudinal extend of the polar coronal hole on the photosphere and on the source surface over the course of a solar activity cycle. We find that the amplitude of magnetic field fluctuations for assumed solar minimum parameters would not be observable above the background noise (see Roberts and coworkers). We also show that for these parameters, periodicities associated with differential footpoint motion would be barely distinguishable from rigid rotation at the solar equatorial rate. We point out that the question of periodicities in magnetic field data is perhaps more complicated than previously thought. We confirm the result of Burger and Hitge that a Fisk-type heliospheric magnetic field provides a natural explanation for the observed linear relationship between the amplitude of the recurrent cosmic-ray variations and the global latitude gradient (see Zhang). We show that this relationship holds for helium, protons, and electrons. Moreover, we show that the constant of proportionality is larger when qA > 0 than when qA < 0, as inferred from observations by Richardson and coworker
The influence of student engagement on the performance of first-year mathematics students
No full textMSc (Science Education), North-West University, Potchefstroom Campus, 2017Student engagement, specifically in higher education, is an important field of research, which can help to improve the learning of students, as well as other anticipated outcomes. Student engagement is a complex concept and according to different researchers, consists of different components.
In this study, several facets of student engagement were explored, and the aim of this two-phase sequential, mixed method research is to determine the influence, which student engagement has on the performance of first-year mathematics students in their first semester at the North-West University, Potchefstroom Campus. The National Survey of Student Engagement (NSSE) divides student engagement into five facets: level of academic challenge, active and collaborative learning, supportive campus environment, enriching educational experiences and student-staff interaction.
A pilot study was done by administering a modified National Survey of Student Engagement (NSSE) to ascertain whether the adjusted questions in the questionnaire, specifically for mathematics students, were correctly formulated.
An explanatory sequential design mixed method research was used. The quantitative research was conducted during the first phase. The target population was 712 first-year Mathematics students and data were collected from a study population of 304 students who voluntarily completed a questionnaire. The second phase was the qualitative research where data were generated by means of individual, semi-structured interviews to explain the quantitative data further. The selection of the interviewees was done by the researcher.
Descriptive statistics, confirmatory factor analyses and linear regressions were done to analyse the quantitative data. The analysis of the qualitative data was done with the digital analysis software programme Atlas.ti.
The most significant results of this study are as follows: The Grade 12 Mathematics mark was the most noteworthy predictor for the Mathematics first-year module mark. Revision of class notes and assignments, perseverance to solve mathematics problems and academic help from tutors influenced mathematics performance. However, class preparation, the amount of hours studied, academic help from lecturers and peers and visiting the Mathematics centre did not have a significant effect on Mathematics performance. The Mathematics module mark of students who were involved in too many social activities tended to be low and most of the participants experienced the Mathematics module as difficult.
Results from this research indicate that Level of academic challenge emerged as the most prominent facet of student engagement. This is meaningful in the area of mathematics education at tertiary level since it illustrates that the complexity of mathematics directly impacts the students‘ engagement on a multitude of levels. This facet, in turn, influences the other four facets of student engagement and ultimately the student‘s overall performance in Mathematics.Master
Cosmic ray modulation processes in the heliosphere
No full textThesis (M.Sc. (Physics))--North-West University, Potchefstroom Campus, 2012.The solar minimum of 2009 has been identified as an exceptional event with regard to
cosmic ray (CR)modulation, since conditions in the heliosphere have reached unprecedented
quiet levels. This unique minimum has been observed by the Earth–orbiting
satellite, PAMELA, launched in June, 2006, from which vast sets of accurate proton
and electron preliminary observations have been made available. These simultaneous
measurements from PAMELA provide the ideal opportunity to conduct an in–depth
study of CR modulation, in particular charge–sign dependent modulation. In utilizing
this opportunity, a three–dimensional, steady–state modulation model was used to reproduce
a selection of consecutive PAMELA proton and electron spectra from 2006 to
2009. Thiswas done by assuming full drifts and simplified diffusion coefficients, where
the rigidity dependence and absolute value of themean free paths for protons and electrons
were sequentially adjusted below 3 GV and 300 MV, respectively. Care has
been taken in calculating yearly–averaged current–sheet tilt angle and magnetic field
values that correspond to the PAMELA spectra. Following this study where the numerical
model was used to investigate the individual effects resulting from changes in
the tilt angle, diffusion coefficients, and global drifts, it was found that all these modulation
processes played significant roles in contributing to the total increase in CR
intensities from 2006 to 2009, as was observed by PAMELA. Furthermore, the effect
that drifts has on oppositely charged particles was also evident from the difference
between the peak–shaped time profiles of protons and the flatter time profiles of electrons,
as is expected for an A < 0 polarity cycle. Since protons, which drift into the
heliosphere along the heliospheric current–sheet, haven’t yet reached maximum intensity
levels by 2008, their intensities increased notably more than electrons toward the
end of 2009. The time and energy dependence of the electron to proton ratios were
also studied in order to further illustrate and quantify the effect of drifts during this
remarkable solar minimum period.Master
The transition from secondary to tertiary mathematics : exploring means to assist students and lecturers
No full textThesis (Ph.D. (Natural Sciences Education))--North-West University, Potchefstroom Campus, 2013Early in 2009 it became apparent from articles in the newspapers that first year mathematics students were not performing as well as the students of previous years. There was great concern regarding the insufficient transition from secondary to tertiary mathematics, as well as the preparedness of first year students for university studies. This research focuses on the different factors that are potential causes of the underachievement of first year mathematics students. Students‟ and lecturers‟ beliefs are shaped by their experiences, the impact of continuous perceptions from the world around them, the present dominant paradigm, as well as the beliefs of their teachers. The different views of the nature of school mathematics show how a worldview has an effect on these views and the implications of this on the teaching of mathematics in secondary, as well as tertiary institutions. The paradigm shift from the modern era to the post-modern era caused an awareness of and interest in the construction of meaningful mathematical understanding. The gap between first year students‟ and lecturers‟ beliefs regarding the nature of mathematics and how mathematics is learned became apparent. The changes in the thoughts about the structure of mathematics were investigated and a better understanding of the processes through which mathematical understanding develops emerged. This brought insight into the gap between the reasoning abilities of incoming students from secondary schools and the reasoning needed to succeed in university mathematics. The theoretical study of the global theories of Piaget and Van Hiele gave insight into conceptual development through different stages and that a person should be on an appropriate conceptual level to make sense of what they learn. If not, then rote learning is likely to occur. The local theory of Tall implies that to facilitate understanding of a concept in mathematics, one should go through three worlds of mathematics: the embodied world, symbolic world and the formal world. The embodied view helps someone to give deep meaning to a page iv concept, otherwise one can be trapped in the symbolic world and not be able to move on to the formal world of mathematical thinking. The theoretical investigations led to an empirical study in three phases. Phase 1 was an investigation into the views of mathematics held by the students and the lecturers. In phase 2 an investigation was done to establish the students‟ preferences on how they learn mathematics and how mathematics should be taught, using the Index of Learning Styles (ILS) questionnaire of Felder and Silverman. The results were compared with the way lecturers want their students to learn and how they themselves prefer to teach. Phase 3 included a classification of the questions in the first mathematics test written at tertiary level and subsequent analysis of the answers of students to obtain information on the type of reasoning required from students at tertiary level, as well as the reasoning abilities of the students. The empirical study assisted in understanding the problematic transition from secondary to tertiary mathematics with regard to the nature of mathematics, the beliefs on teaching and learning of mathematics, as well as the reasoning skills that the students possess when entering universityDoctora
The survivability of cycling in a co-evolutionary agent-based model
No full textDATA AVAILABILITY : The datasets generated and analysed during the current study are not publicly available because they constitute an excerpt of research in progress but are available from the corresponding author upon reasonable request.Many cities plan to grow cycling as a prominent mode to improve accessibility and environmental and financial sustainability. However, relatively few cities have made meaningful headway in this direction. Policymakers would be more inclined to implement the necessary interventions when they have certainty about potential demand, especially knowing where it is located in space. This paper introduces an approach to estimating potential cycling demand using agent-based modelling to determine who may benefit from switching from their current modes to cycling. People benefit when they obtain a similar or higher travel utility score when cycling between their daily activities than when using their existing modes. The model is based on individual mode selection, that all activities in the trip chain are included and can include detailed road and cycle network elements. The co-evolutionary mechanisms within the agent-based simulation allow us to test the potential for cycling relative to the performance of other modes on the network. The case for Cape Town, South Africa, shows that about 32% of those that travel would benefit from cycling based on their utility score. Understanding that travel time benefits are not the only criteria for mode selection, we apply a rejection sampling algorithm based on demographic factors to demonstrate that a more realistic, or pragmatic, cycling potential for Cape Town is in the region of 8%. The results also show that more than 46% of the observed pragmatic demand for cycling is concentrated in an area covering less than 7% of the study area. This has practical implications for policymakers to target interventions both in space and towards specific demographic market segments.https://link.springer.com/journal/11116hj2024Industrial and Systems EngineeringSDG-09: Industry, innovation and infrastructureSDG-11:Sustainable cities and communitie
On the development and applications of a three–dimensional ab initio cosmic–ray modulation model
No full textThesis (PhD (Physics))--North-West University, Potchefstroom Campus, 2013A proper understanding of the effects of turbulence on the diffusion and drift of cosmic-rays in the heliosphere is imperative for a better understanding of cosmic-ray modulation. This study
presents an ab initio model for cosmic-ray modulation, incorporating for the first time the results yielded by a two-component turbulence transport model. The latter model is solved for solar minimum heliospheric conditions, utilizing boundary values chosen in such a way that the results of this model are in fair to good agreement with spacecraft observations of turbulence quantities, not only in the ecliptic plane, but also along the out-of-ecliptic trajectory of the
Ulysses spacecraft. These results are employed as inputs for modelled slab and 2D turbulence energy spectra, which in turn are used as inputs for parallel mean free paths based on those derived from quasi-linear theory, and perpendicularmean free paths from extended nonlinear guiding center theory. The modelled 2D spectrum is chosen based on physical considerations,
with a drop-off at the very lowest wavenumbers commencing at the 2D outerscale. There currently exist no models or observations for this quantity, and it is the only free parameter in this
study. The use of such a spectrum yields a non-divergent 2D ultrascale, which is used as an input for the reduction terms proposed to model the effects of turbulence on cosmic-ray drifts. The resulting diffusion and drift coefficients are applied to the study of galactic cosmic-ray protons, electrons, antiprotons, and positrons using a three-dimensional, steady-state numerical
cosmic-ray modulation code. The magnitude and spatial dependence of the 2D outerscale is demonstrated to have a significant effect on computed cosmic-ray intensities. A form for the 2D outerscale was found that resulted in computed cosmic-ray intensities, for all species considered, in reasonable agreement with multiple spacecraft observations. Computed galactic electron intensities are shown to be particularly sensitive to choices of parameters pertaining
to the dissipation range of the slab turbulence spectrum, and certain models for the onset wavenumber of the dissipation range could be eliminated in this study.Doctora
Effect of Fisk-type heliospheric magnetic fields on the latitudinal transport of cosmic rays
No full textABSTRACT The Fisk model of the heliospheric magnetic field (HMF) has proved to be quite difficult to implement in three-dimensional numerical modulation codes. We have developed a divergence-free Fisk-Parker hybrid HMF that is easier to implement and that should be a reasonable approximation for the case when field lines open into the heliosphere both in the polar coronal holes and at low latitudes. To study the effects of this hybrid field on galactic cosmic rays, we solve the three-dimensional steady state Parker transport equation numerically, covering the entire model heliosphere. We find that latitudinal cosmic-ray gradients are reduced as expected, but only during epochs when particles are drifting from the polar regions of the heliosphere toward the ecliptic plane. We investigate 26 day recurrent variations of both protons and electrons and find that the amplitude of these variations are directly proportional to the latitudinal intensity gradient, independent of species, in agreement with observational studies. In the absence of drifts in the code, electrons and protons obey different but still linear relationships
