H2 molecule in strong magnetic fields

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions given by one-dimensional \delta-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity

Using asteroseismology to determine membership of stellar clusters observed by the Kepler Mission

Abstract If we can measure the speed of sound in a gas, we have information about the pressure and density of that gas. From the equation of state, we can constrain the temperature and chemical composition. Therefore, by measuring the sound speed in stars we can deduce these same characteristics of the star being measured. The goal of asteroseismology is to use oscillations to measure this sound speed throughout the star to determine these fundamental stellar parameters. Asteroseismology accomplishes this by extracting the oscillation frequencies of the sound at the stellar surface, and combining this with models to infer the sound speed and density inside the star. The Kepler space telescope has initiated a revolution in asteroseismology. The Kepler mission is a NASA space-based photometric telescope, designed to detect Earth-size planets around Sun-like stars. Kepler has observed one patch of sky for a continuous four year period. The high photometric precision of the data in conjunction with the long time span also makes it ideal for measuring the frequencies of the sound-wave induced by oscillations at the stellar surface. I use a new technique to determine the cluster membership of red giant stars in two open clusters using asteroseismology. By determining the oscillation frequencies of a number of red giants in the region of two clusters in the Kepler field, I can determine whether they are consistent with membership of the cluster or are field stars in the foreground or background. This thesis focuses on the evolved stars, which have left the hydrogen-core burning phase on the main sequence to become hydrogen shell-burning subgiants, or red giants. I was able to use the Kepler long-cadence (29.4 min) data to measure the oscillation frequencies of the red giants, and thus infer their fundamental stellar parameters. Stars in a cluster are believed to share a common age and initial composition, being formed from the same interstellar cloud. This allows for membership to be inferred from photometric studies by using models of isochrones in a color-magnitude diagram. As a result, this technique is dependent on knowing distance and interstellar extinction. Alternatively, the common space velocity can also be used to determine membership status, however, this relies on the field stars not randomly aligning with the cluster motion. Recently, Stello et al. (2010b) introduced a new technique based on asteroseismology to determine cluster membership that is dependent only on the internal properties of the stars. I detect the oscillation frequencies to measure the frequency of maximum oscillation power, vmax and the large frequency separation, ∆v. These parameters are related to surface gravity and the mean density of the star respectively, and are therefore known to scale with the M, L and Teff (where M is the mass, L is the luminosity and Teff is the surface temperature) of the star (Ulrich 1986; Kjeldsen & Bedding 1995). The common initial conditions of the cluster allow us to compare the parameters of individual stars in the vicinity of the cluster with the mean of the cluster. A ratio of 1.0 for the measured to scaled parameter indicates a likely member of the cluster independent of distance or interstellar absorption. I analysed over 400 red giant stars in the vicinity of two clusters in the Kepler field of view, NGC 6791 and NGC 6819. By measuring the asteroseismic parameters of each star and comparing them with the solar scaled values, I was able to confirm the members of Stello et al. (2011b) and to identify 45 new red giant members distributed over the two clusters. This has increased the red giant population by almost 40% for NGC 6791 and almost 10% for NGC 6819, which will allow stellar evolution models to be constrained

Using asteroseismology to determine membership of stellar clusters observed by the Kepler Mission

Abstract If we can measure the speed of sound in a gas, we have information about the pressure and density of that gas. From the equation of state, we can constrain the temperature and chemical composition. Therefore, by measuring the sound speed in stars we can deduce these same characteristics of the star being measured. The goal of asteroseismology is to use oscillations to measure this sound speed throughout the star to determine these fundamental stellar parameters. Asteroseismology accomplishes this by extracting the oscillation frequencies of the sound at the stellar surface, and combining this with models to infer the sound speed and density inside the star. The Kepler space telescope has initiated a revolution in asteroseismology. The Kepler mission is a NASA space-based photometric telescope, designed to detect Earth-size planets around Sun-like stars. Kepler has observed one patch of sky for a continuous four year period. The high photometric precision of the data in conjunction with the long time span also makes it ideal for measuring the frequencies of the sound-wave induced by oscillations at the stellar surface. I use a new technique to determine the cluster membership of red giant stars in two open clusters using asteroseismology. By determining the oscillation frequencies of a number of red giants in the region of two clusters in the Kepler field, I can determine whether they are consistent with membership of the cluster or are field stars in the foreground or background. This thesis focuses on the evolved stars, which have left the hydrogen-core burning phase on the main sequence to become hydrogen shell-burning subgiants, or red giants. I was able to use the Kepler long-cadence (29.4 min) data to measure the oscillation frequencies of the red giants, and thus infer their fundamental stellar parameters. Stars in a cluster are believed to share a common age and initial composition, being formed from the same interstellar cloud. This allows for membership to be inferred from photometric studies by using models of isochrones in a color-magnitude diagram. As a result, this technique is dependent on knowing distance and interstellar extinction. Alternatively, the common space velocity can also be used to determine membership status, however, this relies on the field stars not randomly aligning with the cluster motion. Recently, Stello et al. (2010b) introduced a new technique based on asteroseismology to determine cluster membership that is dependent only on the internal properties of the stars. I detect the oscillation frequencies to measure the frequency of maximum oscillation power, vmax and the large frequency separation, ∆v. These parameters are related to surface gravity and the mean density of the star respectively, and are therefore known to scale with the M, L and Teff (where M is the mass, L is the luminosity and Teff is the surface temperature) of the star (Ulrich 1986; Kjeldsen & Bedding 1995). The common initial conditions of the cluster allow us to compare the parameters of individual stars in the vicinity of the cluster with the mean of the cluster. A ratio of 1.0 for the measured to scaled parameter indicates a likely member of the cluster independent of distance or interstellar absorption. I analysed over 400 red giant stars in the vicinity of two clusters in the Kepler field of view, NGC 6791 and NGC 6819. By measuring the asteroseismic parameters of each star and comparing them with the solar scaled values, I was able to confirm the members of Stello et al. (2011b) and to identify 45 new red giant members distributed over the two clusters. This has increased the red giant population by almost 40% for NGC 6791 and almost 10% for NGC 6819, which will allow stellar evolution models to be constrained

A search for factors controlling the formation and maintenance of connections between the thelamus and cortex in vitro

Although the development of the nervous system is continuous, the neurones that constitute the nervous system proceed through specific developmental stages. Such stages included: birth, differentiation, migration, the formation of efferent and afferent connections, and the organisation of these connections based on exogenous and endogenous cues. Alternatively, a neuron may undergo "natural occurring" cell death at various points during development.When considering the complexity of the nervous system, it is not surprising that our knowledge, as to the factors that control these development stages, is limited One significant obstacle for experimentally addressing these questions, for practical and/or ethical reasons, has been the animal itself. Thus, the advent of tissue culture techniques has greatly facilitated research in this area.In addition to in vivo Dil tract-tracing experiments, I have used three different in vitro techniques: (i) co-cultures of organotypic explants on a two-dimensional collagen substrate, (ii) organotypic explants co-cultured within a three-dimensional collagen gel, and (iii) co-cultures of dissociated cells. Because serum is known to contain many trophic factors, only serum-free medium was used for all of these experiments. Using the above in vitro techniques, I investigated questions concerning the development of connections between the thalamus and cortex.These experiments yielded the following results, (i) When thalamocortical and corticothalamic efferent fibres began to grow in vivo at embryonic day 15 (El5), conserved diffusible target-derived factors enhanced their neurite elongation in vitro, (ii) The survival of El 5 thalamic and cortical neurones was independent from target-derived iii trophic support, since both the thalamus and cortex promoted their own survival in vitro. possibly through the production of endogenous trophic factors. However (iii), between E17 and postnatal day 2, a time coincident with the arrival of their fibres to their target, the survival of thalamocortical and corticothalamic neurones was dependent on factors released from their target, (iv) The production of growth promoting factors within the cortex increased with postnatal age and was at least partially regulated by afferent activity. And finally (v), it seems that the recognition/stop-signalling molecules expressed within these targets are also highly conserved since they were recognised in inter-species co-culture experiments. Thus, in general, the development of both thalamocortical and corticothalamic efferents are highly influenced by factors produced by their target cells in vitro. In vivo, these factors may play various roles during the different developmental stages from promoting neurite outgrowth and cell survival, to regulating the reorganisation of connection

Aristotle and Game Theory on Human Nature and Ethics

This paper considers whether Aristotle’s ethics is consistent with one modern scientific view of humans. The modern scientific view discussed is based on Nancy Cartwright’s argument that game theory uncovers something akin to the Aristotelian natures of humans. Following Martha Nussbaum, this paper focuses on the role of human nature in Aristotle’s ethics. Specifically, it focuses on two kinds of ethical conclusions Aristotle grounds in claims about human nature: one about what can be coherently desired for a human being, one about the social arrangements appropriate to human beings. This paper considers Nussbaum’s interpretation that Aristotle’s claims about human nature are dependent upon common beliefs and values. This paper argues that game theory’s application to Aristotle’s ethics is limited because of differences between Aristotle and Cartwright’s natures. Specifically, game theory’s account of humans cannot ground Aristotle’s conclusions about what can be coherently desired for a human being. However, game theory does allow a relatively value-free grounding of Aristotle’s conclusions about social arrangements. Further, this paper argues, on the latter, the game theoretic account is preferable not only because it is relatively value-free, but also because it can account for more of the diversity of human social arrangements than Aristotle’s can. Thus, this paper concludes that the game theoretic account’s advantages perhaps compensate for its inability to ground Aristotle’s first kind of conclusion. Further research can explore similarities between game theory’s and Aristotle’s accounts, perhaps leading to a way that game theory can ground the first kind of conclusion

Density Matrix Renormalization Group study of superconducting pairing near the quarter-filled Wigner crystal

Charge ordering is often found in the phase diagram of unconventional superconductors in close proximity to the superconducting state. This has led to the suggestion that fluctuations of charge order can mediate superconducting pairing. While several mechanisms can lead to charge order, one common mechanism is the long-range Coulomb interaction, resulting in a Wigner crystal charge ordered state. We investigate using exact diagonalization and the density matrix renormalization group the properties of superconducting pair-pair correlations near a Wigner crystal as a function of $V$, the nearest neighbor Coulomb interaction. We consider several different lattice boundary conditions for an electron density of 0.5 per site, the quarter-filled band. Our results show that the strength of pairing decreases with $V$ and remains weaker than the tendency of pairing for non-interacting electrons.Comment: 7 pages, 9 figure

What Are Lightness Illusions and Why Do We See Them?

Lightness illusions are fundamental to human perception, and yet why we see them is still the focus of much research. Here we address the question by modelling not human physiology or perception directly as is typically the case but our natural visual world and the need for robust behaviour. Artificial neural networks were trained to predict the reflectance of surfaces in a synthetic ecology consisting of 3-D “dead-leaves” scenes under non-uniform illumination. The networks learned to solve this task accurately and robustly given only ambiguous sense data. In addition—and as a direct consequence of their experience—the networks also made systematic “errors” in their behaviour commensurate with human illusions, which includes brightness contrast and assimilation—although assimilation (specifically White's illusion) only emerged when the virtual ecology included 3-D, as opposed to 2-D scenes. Subtle variations in these illusions, also found in human perception, were observed, such as the asymmetry of brightness contrast. These data suggest that “illusions” arise in humans because (i) natural stimuli are ambiguous, and (ii) this ambiguity is resolved empirically by encoding the statistical relationship between images and scenes in past visual experience. Since resolving stimulus ambiguity is a challenge faced by all visual systems, a corollary of these findings is that human illusions must be experienced by all visual animals regardless of their particular neural machinery. The data also provide a more formal definition of illusion: the condition in which the true source of a stimulus differs from what is its most likely (and thus perceived) source. As such, illusions are not fundamentally different from non-illusory percepts, all being direct manifestations of the statistical relationship between images and scenes

Effects of water availability on the germination of native and exotic forbs

Native and Exotic Forbes Germination Response to Drought Stress Beau R. Jennings, Mandy L. Slate, Dean E. Pearson Abstract The shifting climate of the western North American grasslands is forecasted to continue the trend of decreased annual rainfall and longer phases of rain-free windows in times where rainfall has been previously abundant. This understanding has inspired many studies on how ecosystems will respond to these changes. One of the key factors in the shaping of the ecosystem is the availability of precipitation in the spring, which will limit plant recruitment and seedling survival for the dryland ecosystem. Furthermore, seedling’s ability to establish themselves prior to hot dry summers is a key attribute to ensuring success in survival and reproduction. Yet, the expansion of exotic over native species in dryland ecosystems suggests that some exotic plants have traits that allow them to succeed at a higher success rate than native plants. Specifically, understanding the germination tendencies of exotic and native forbes will allow better predictions to be made on the future shaping of these ecosystems. We conducted an experiment in a lab comparing germination percentages and rates of germination for multiple species of native and exotic grassland forbs under different levels of water availability. The experiment was conducted in a growth chamber where temperature, lighting, and humidity were kept as constant variables. The specimens were placed in petri dishes on top of filter paper, and each petri dish lid had three ⅛” holes to allow some evaporation. We hydrated seeds with either 2ml and 3ml daily or every other day. Specimens were examined daily in order to record germination promptly. We will present a comparison of Germination synchrony, germinability, time to germination, germination t50, and germination range between native and exotic forbes species, and discuss how these findings may be used to better understand the processes in which exotic plants are able to overtake plants in their native habitats