3,064 research outputs found
Topological Constraints on the Charge Distributions for the Thomson Problem
The method of Morse theory is used to analyze the distributions of unit
charges interacting through a repulsive force and constrained to move on the
surface of a sphere -- the Thomson problem. We find that, due to topological
reasons, the system may organize itself in the form of pentagonal structures.
This gives a qualitative account for the interesting ``pentagonal buttons''
discovered in recent numerical work.Comment: 10 pages; dedicated to Rafael Sorkin on his 60th birthda
“She is the Best Female Coach”: Female Swimming Coaches’ Experiences of Sexism
Sport participation for women and girls is at an all-time high in the United States, but women are still widely underrepresented in leadership positions and coaching (Acosta & Carpenter, 2014). Women hold approximately 50% of head coaching positions of women’s teams in the National Collegiate Athletic Association, and only 18% of the head coaching positions of women’s swimming and diving teams (LaVoi & Silva-Breen, 2018). Numerous barriers have been identified through previous research on the factors that inhibit upward career mobility for female coaches. Semi-structured interviews were used to examine the career experiences of 21 current or former female swimming coaches at the NCAA Division I level. The theme of sexism in coaching was pervasive and identified in five different categories: (a) misidentification, (b) differential treatment, (c) isolation, (d) tokenism, and (e) motherhood. The sexism that female coaches experience hinders upward career mobility which can lead to career dissatisfaction and early exits from the field, contributing to the underrepresentation of women in the profession
Colour Relations in Form
The orthodox monadic determination thesis holds that we represent colour relations by virtue of representing colours. Against this orthodoxy, I argue that it is possible to represent colour relations without representing any colours. I present a model of iconic perceptual content that allows for such primitive relational colour representation, and provide four empirical arguments in its support. I close by surveying alternative views of the relationship between monadic and relational colour representation
A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments
Positive density-dependence occurs when individuals experience increased
survivorship, growth, or reproduction with increased population densities.
Mechanisms leading to these positive relationships include mate limitation,
saturating predation risk, and cooperative breeding and foraging. Individuals
within these populations may differ in age, size, or geographic location and
thereby structure these populations. Here, I study structured population models
accounting for positive density-dependence and environmental stochasticity i.e.
random fluctuations in the demographic rates of the population. Under an
accessibility assumption (roughly, stochastic fluctuations can lead to
populations getting small and large), these models are shown to exhibit a
dynamical trichotomy: (i) for all initial conditions, the population goes
asymptotically extinct with probability one, (ii) for all positive initial
conditions, the population persists and asymptotically exhibits unbounded
growth, and (iii) for all positive initial conditions, there is a positive
probability of asymptotic extinction and a complementary positive probability
of unbounded growth. The main results are illustrated with applications to
spatially structured populations with an Allee effect and age-structured
populations experiencing mate limitation
Acoustic Probing of the Jamming Transition in an Unconsolidated Granular Medium
Experiments with acoustic waves guided along the mechanically free surface of
an unconsolidated granular packed structure provide information on the
elasticity of granular media at very low pressures that are naturally
controlled by the gravitational acceleration and the depth beneath the surface.
Comparison of the determined dispersion relations for guided surface acoustic
modes with a theoretical model reveals the dependencies of the elastic moduli
of the granular medium on pressure. The experiments confirm recent theoretical
predictions that relaxation of the disordered granular packing through
non-affine motion leads to a peculiar scaling of shear rigidity with pressure
near the jamming transition corresponding to zero pressure. Unexpectedly, and
in disagreement with the most of the available theories, the bulk modulus
depends on pressure in a very similar way to the shear modulus
Characterizing kernels of operators related to thin-plate magnetizations via generalizations of Hodge decompositions
Recently developed scanning magnetic microscopes measure the magnetic field in a plane above a thin-plate magnetization distribution. These instruments have broad applications in geoscience and materials science, but are limited by the requirement that the sample magnetization must be retrieved from measured field data, which is a generically nonunique inverse problem. This problem leads to an analysis of the kernel of the related magnetization operators, which also has relevance to the 'equivalent source problem' in the case of measurements taken from just one side of the magnetization. We characterize the kernel of the operator relating planar magnetization distributions to planar magnetic field maps in various function and distribution spaces (e.g., sums of derivatives of Lp (Lebesgue spaces) or bounded mean oscillation (BMO) functions). For this purpose, we present a generalization of the Hodge decomposition in terms of Riesz transforms and utilize it to characterize sources that do not produce a magnetic field either above or below the sample, or that are magnetically silent (i.e. no magnetic field anywhere outside the sample). For example, we show that a thin-plate magnetization is silent (i.e. in the kernel) when its normal component is zero and its tangential component is divergence free. In addition, we show that compactly supported magnetizations (i.e. magnetizations that are zero outside of a bounded set in the source plane) that do not produce magnetic fields either above or below the sample are necessarily silent. In particular, neither a nontrivial planar magnetization with fixed direction (unidimensional) compact support nor a bidimensional planar magnetization (i.e. a sum of two unidimensional magnetizations) that is nontangential can be silent. We prove that any planar magnetization distribution is equivalent to a unidimensional one. We also discuss the advantages of mapping the field on both sides of a magnetization, whenever experimentally feasible. Examples of source recovery are given along with a brief discussion of the Fourier-based inversion techniques that are utilized
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