Do different subjective evaluation criteria reflect distinct constructs?

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A scanning drift tube apparatus for spatio-temporal mapping of electron swarms

A "scanning" drift tube apparatus, capable of mapping of the spatio-temporal evolution of electron swarms, developing between two plane electrodes under the effect of a homogeneous electric field, is presented. The electron swarms are initiated by photoelectron pulses and the temporal distributions of the electron flux are recorded while the electrode gap length (at a fixed electric field strength) is varied. Operation of the system is tested and verified with argon gas, the measured data are used for the evaluation of the electron bulk drift velocity. The experimental results for the space-time maps of the electron swarms - presented here for the first time - also allow clear observation of deviations from hydrodynamic transport. The swarm maps are also reproduced by particle simulations

Drying and cracking mechanisms in a starch slurry

Starch-water slurries are commonly used to study fracture dynamics. Drying starch-cakes benefit from being simple, economical, and reproducible systems, and have been used to model desiccation fracture in soils, thin film fracture in paint, and columnar joints in lava. In this paper, the physical properties of starch-water mixtures are studied, and used to interpret and develop a multiphase transport model of drying. Starch-cakes are observed to have a nonlinear elastic modulus, and a desiccation strain that is comparable to that generated by their maximum achievable capillary pressure. It is shown that a large material porosity is divided between pore spaces between starch grains, and pores within starch grains. This division of pore space leads to two distinct drying regimes, controlled by liquid and vapor transport of water, respectively. The relatively unique ability for drying starch to generate columnar fracture patterns is shown to be linked to the unusually strong separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments

Drying and cracking mechanisms in a starch slurry

Starch-water slurries are commonly used to study fracture dynamics. Drying starch-cakes benefit from being simple, economical, and reproducible systems, and have been used to model desiccation fracture in soils, thin film fracture in paint, and columnar joints in lava. In this paper, the physical properties of starch-water mixtures are studied, and used to interpret and develop a multiphase transport model of drying. Starch-cakes are observed to have a nonlinear elastic modulus, and a desiccation strain that is comparable to that generated by their maximum achievable capillary pressure. It is shown that a large material porosity is divided between pore spaces between starch grains, and pores within starch grains. This division of pore space leads to two distinct drying regimes, controlled by liquid and vapor transport of water, respectively. The relatively unique ability for drying starch to generate columnar fracture patterns is shown to be linked to the unusually strong separation of these two transport mechanisms.Comment: 9 pages, 8 figures [revised in response to reviewer comments

An Experimental Investigation of the Scaling of Columnar Joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.Comment: 12 pages, 11 figures, for supporting online movies, go to http://www.physics.utoronto.ca/nonlinear/movies/starch_movies.htm

Coexistence of ferromagnetism and superconductivity

A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the paramagnetic one. The resulting phase diagram is compared with the experimental observations in UGe_2 and ZrZn_2.Comment: 16 pp., REVTeX, 6 eps figs; final version as publishe

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is >= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field.Comment: The paper has 17 pages, including 15 figures and 3 table

Analytic solution of the fractional advection diffusion equation for the time-of-flight experiment in a finite geometry

A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast into a simple closed form expression in Laplace space using the Poisson summation theorem. An analytic expression for the current measured in a time-of-flight experiment is derived, and the sum of the slopes of the two respective time regimes on logarithmic axes is demonstrated to be -2, in agreement with the well known result for a continuous time random walk model. The sensitivity of current and particle number density to variation of experimentally controlled parameters is investigated in general, and the results applied to analyze selected experimental data.Comment: 10 pages, 6 figure

Nodal domains of Maass forms I

This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the $L^2$-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.Comment: To appear in GAF

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure