Dynamics of Conformal Maps for a Class of Non-Laplacian Growth Phenomena

Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are described by generalizing conformal-mapping techniques for viscous fingering and diffusion-limited aggregation, respectively. A general notion of time in stochastic growth is also introduced. The theory is applied to simulations of advection-diffusion-limited aggregation in a background potential flow. A universal crossover in morphology is observed from diffusion-limited to advection-limited fractal patterns with an associated crossover in the growth rate, controlled by a time-dependent effective Peclet number. Remarkably, the fractal dimension is not affected by advection, in spite of dramatic increases in anisotropy and growth rate, due to the persistence of diffusion limitation at small scales.Comment: 4 pages, 2 figures (six color plates

Using ordinary multiplication to do relativistic velocity addition

Relativistic addition of velocities in one dimension, though a mainstay of introductory physics, contributes much less physical insight than it could. For such calculations, we propose the use of velocity factors (two-way doppler factors). Velocities can easily, often by inspection, be turned into velocity factors, and vice versa. Velocity factors compose by ordinary multiplication. This simple device considerably extends the kinds of questions that can be asked and answered in an introductory course.Comment: 6 page

The initial development of a jet caused by fluid, body and free surface interaction with a uniformly accelerated advancing or retreating plate. Part 1. The principal flow

The free surface and flow field structure generated by the uniform acceleration (with dimensionless acceleration σ) of a rigid plate, inclined at an angle α ∈ (0, π/2) to the exterior horizontal, as it advances (σ > 0) or retreats (σ < 0) from an initially stationary and horizontal strip of inviscid, incompressible fluid under gravity, are studied in the small-time limit via the method of matched asymptotic expansions. This work generalises the case of a uniformly accelerating plate advancing into a fluid as studied in Needham et al. (2008). Particular attention is paid to the innermost asymptotic regions encompassing the initial interaction between the plate and the free surface. We find that the structure of the solution to the governing initial boundary value problem is characterised in terms of the parameters α and μ (where μ = 1+σ tan α), with a bifurcation in structure as μ changes sign. This bifurcation in structure leads us to question the well-posedness and stability of the governing initial boundary value problem with respect to small perturbations in initial data in the innermost asymptotic regions, the discussion of which will be presented in the companion paper Gallagher et al. (2016) . In particular, when (α, μ) ∈ (0, π/2) × R+, the free surface close to the initial contact point remains monotone, and encompasses a swelling jet when (α, μ) ∈ (0, π/2)×[1,∞), or a collapsing jet when (α, μ) ∈ (0, π/2) × (0, 1). However, when (α, μ) ∈ (0, π/2) × R−, the collapsing jet develops a more complex structure, with the free surface close to the initial contact point now developing a finite number of local oscillations, with near resonance type behaviour occurring close to a countable set of critical plate angles α = α∗n ∈ (0, π/2) (n = 1, 2, . . .)

Attacking Group Protocols by Refuting Incorrect Inductive Conjectures

Automated tools for finding attacks on flawed security protocols often fail to deal adequately with group protocols. This is because the abstractions made to improve performance on fixed 2 or 3 party protocols either preclude the modelling of group protocols all together, or permit modelling only in a fixed scenario, which can prevent attacks from being discovered. This paper describes Coral, a tool for finding counterexamples to incorrect inductive conjectures, which we have used to model protocols for both group key agreement and group key management, without any restrictions on the scenario. We will show how we used Coral to discover 6 previously unknown attacks on 3 group protocols

Diffusion-Limited Aggregation on Curved Surfaces

We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic projections to simulate diffusion-limited-aggregation (DLA) on surfaces of constant Gaussian curvature, including the sphere ($K>0$) and pseudo-sphere ($K<0$), which approximate "bumps" and "saddles" in smooth surfaces, respectively. Although curvature affects the global morphology of the aggregates, the fractal dimension (in the curved metric) is remarkably insensitive to curvature, as long as the particle size is much smaller than the radius of curvature. We conjecture that all aggregates grown by conformally invariant transport on curved surfaces have the same fractal dimension as DLA in the plane. Our simulations suggest, however, that the multifractal dimensions increase from hyperbolic ($K0$) geometry, which we attribute to curvature-dependent screening of tip branching.Comment: 4 pages, 3 fig

Overcharging a Black Hole and Cosmic Censorship

We show that, contrary to a widespread belief, one can overcharge a near extremal Reissner-Nordstrom black hole by throwing in a charged particle, as long as the backreaction effects may be considered negligible. Furthermore, we find that we can make the particle's classical radius, mass, and charge, as well as the relative size of the backreaction terms arbitrarily small, by adjusting the parameters corresponding to the particle appropriately. This suggests that the question of cosmic censorship is still not wholly resolved even in this simple scenario. We contrast this with attempting to overcharge a black hole with a charged imploding shell, where we find that cosmic censorship is upheld. We also briefly comment on a number of possible extensions.Comment: 26 pages, 3 figures, LaTe

A phenomenological approach to the simulation of metabolism and proliferation dynamics of large tumour cell populations

A major goal of modern computational biology is to simulate the collective behaviour of large cell populations starting from the intricate web of molecular interactions occurring at the microscopic level. In this paper we describe a simplified model of cell metabolism, growth and proliferation, suitable for inclusion in a multicell simulator, now under development (Chignola R and Milotti E 2004 Physica A 338 261-6). Nutrients regulate the proliferation dynamics of tumor cells which adapt their behaviour to respond to changes in the biochemical composition of the environment. This modeling of nutrient metabolism and cell cycle at a mesoscopic scale level leads to a continuous flow of information between the two disparate spatiotemporal scales of molecular and cellular dynamics that can be simulated with modern computers and tested experimentally.Comment: 58 pages, 7 figures, 3 tables, pdf onl

Characterisation of the Temperature-dependent Dark Rate of Hamamatsu R7081-100 10" Photomultiplier Tubes

Dark noise is a dominant background in photomultiplier tubes (PMTs), which are commonly used in liquid-filled particle detectors for single-photon detection to see the results of particle interactions. A major contribution to dark noise is thermionic emission from the photocathode. The dark noise of Hamamatsu R7081-100 PMTs is characterised in a temperature and purity controlled water tank, with the thermionic emission contribution isolated. The results suggest that the intrinsic dark rate of PMTs does not depend on the medium, but does follow Richardson's law of thermionic emission. There are external contributions to the overall observed PMT count rate identified, but the intrinsic PMT dark rate in water matches that measured in air.Comment: 11 pages, 7 figures, 2 tables, prepared for submission to J. Instru

Artemis Curation: Preparing for Sample Return from the Lunar South Pole

Space Policy Directive-1 mandates that the United States will lead the return of humans to the Moon for long-term exploration and utilization, followed by human missions to Mars and other destinations. In addition, the Vice President stated that It is the stated policy of this administration and the United States of America to return American astronauts to the Moon within the next five years, that is, by 2024. These efforts, under the umbrella of the recently formed Artemis Program, include such historic goals as the flight of the first woman to the Moon and the exploration of the lunar south-polar region. Among the top priorities of the Artemis Program is the return of a suite of geologic samples, providing new and significant opportunities for progressing lunar science and human exploration. In particular, successful sample return is necessary for understanding the history of volatiles in the Solar System and the evolution of the Earth-Moon system, fully constraining the hazards of the lunar polar environment for astronauts, and providing the necessary data for constraining the abundance and distribution of resources for in-situ resource utilization (ISRU). Here we summarize the ef-forts of the Astromaterials Acquisition and Curation Office (hereafter referred to as the Curation Office) to ensure the success of Artemis sample return (per NASA Policy Directive (NPD) 7100.10E)

Inductive learning spatial attention

This paper investigates the automatic induction of spatial attention from the visual observation of objects manipulated on a table top. In this work, space is represented in terms of a novel observer-object relative reference system, named Local Cardinal System, defined upon the local neighbourhood of objects on the table. We present results of applying the proposed methodology on five distinct scenarios involving the construction of spatial patterns of coloured blocks