Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits

We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant bubble characteristics are the Plateau border radius and a new variable, the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau borders interfaces. The resulting prediction is successfully tested, without adjustable parameter, using extensive bidimensional Potts model simulations. Simulations also show that a selfsimilar growth regime is observed at any liquid fraction and determine how the average size growth exponent, side number distribution and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals and other domains with coarsening driven by curvature

USING ALGORITHMS TO ANALYSE THE VISUAL PROPERTIES OF A BUILDING’S STYLE

Residential development within heritage conservation areas is regulated by Development Control Plans (DCP) that provide guidelines about the shape and form that new houses, alterations and additions should take (DIPNR 2004). By understanding that the visual amenity of streets within a city plays an important role in creating a sense of place and community for its citizens (Lynch 1960) they attempt to sustain, through regulation, an urban pattern that has become valued by the community. The visual character of a building within a streetscape is often associated with the style of its construction - a set of visual characteristics that a group of buildings might share. These characteristics include the relationship of the parts of the building to each other, and to the building as a whole, the use of ornament and visible textures, and the scale of elements within the composition. Using algorithms developed within robotic research that enable a computer to interpret a visual environment (similar to those used in medicine and facial recognition for instance), this paper outlines how algorithms can be used to study the visual properties of the built environment. One of the methodological qualities of computer visualisation that makes it so useful for a comparative visual analysis of buildings is that the representational and symbolic meanings of a buildings style play no part. The organisation of the elements can be analysed without having to interpret their possible meaning at the beginning of the process. This paper builds on an established interdisciplinary approach, utilising architectural knowledge and computer visualisation to evaluate the visual character of detached housing within a heritage conservation area. The visual environment is analysed using computer software developed to locate the visual boundaries within a view of a streetscape both as an elevation and aerial view

MEASURING ARCHITECTURE: QUESTIONING THE APPLICATION OF NON-LINEAR MATHEMATICS IN THE ANALYSIS OF HISTORIC BUILDINGS

In the late 1970s the mathematician Benoit Mandelbrot argued that natural systems frequently possess characteristic geometric or visual complexity over multiple scales of observation. This proposition suggests that systems which have evolved over time may exhibit certain local visual qualities that also possess deep structural resonance. In mathematics this observation lead to the formulation of fractal geometry and was central to the rise of the sciences of non-linearity and complexity. During the 1990s a number of researchers developed this concept in relation to architectural design and urban planning and more recently architectural scholars have suggested that such approaches might be used in the analysis of historic buildings. At the heart of this approach, in both its theoretical and computational forms, is a set of processes initially developed by Carl Bovill for analyzing buildings. However, the assumptions implicit in Bovill’s method (itself an extrapolation of an approach proposed by Mandelbrot) have never been adequately questioned. The present paper returns to the origins of Bovill’s analytical method to reconsider his original investigation of key works of 20th century architecture and the way in which Bovill frames images for analysis. The aim of this analysis is to question several assumptions present in Bovill’s method about the way in which computer technology is used to understand the visual qualities of historic buildings

Non-equilibrium Anisotropic Phases, Nucleation and Critical Behavior in a Driven Lennard-Jones Fluid

We describe short-time kinetic and steady-state properties of the non--equilibrium phases, namely, solid, liquid and gas anisotropic phases in a driven Lennard-Jones fluid. This is a computationally-convenient two-dimensional model which exhibits a net current and striped structures at low temperature, thus resembling many situations in nature. We here focus on both critical behavior and details of the nucleation process. In spite of the anisotropy of the late--time spinodal decomposition process, earlier nucleation seems to proceed by Smoluchowski coagulation and Ostwald ripening, which are known to account for nucleation in equilibrium, isotropic lattice systems and actual fluids. On the other hand, a detailed analysis of the system critical behavior rises some intriguing questions on the role of symmetries; this concerns the computer and field-theoretical modeling of non-equilibrium fluids.Comment: 7 pages, 9 ps figures, to appear in PR

Polydispersity Effects in Colloid-Polymer Mixtures

We study phase separation and transient gelation in a mixture consisting of polydisperse colloids and non-adsorbing polymers, where the ratio of the average size of the polymer to that of the colloid is approximately 0.063. Unlike what has been reported previously for mixtures with somewhat lower colloid polydispersity, the addition of polymers does not expand the fluid-solid coexistence region. Instead, we find a region of fluid-solid coexistence which has an approximately constant width but an unexpected re-entrant shape. We detect the presence of a metastable gas-liquid binodal, which gives rise to two-stepped crystallization kinetics that can be rationalized as the effect of fractionation. Finally, we find that the separation into multiple coexisting solid phases at high colloid volume fractions predicted by equilibrium statistical mechanics is kinetically suppressed before the system reaches dynamical arrest.Comment: 11 pages, 5 figure

Utilizing Surface Area to Volume ratios and Thermal Tolerance of Various Bee Species to Predict their Performance under Rising Global Temperatures

The purpose of this research project is to investigate how rising temperatures, for instance climate change, can affect bees of various body sizes given their essential role in the global food supply through pollination of agricultural crops. To achieve this I utilized 3D imaging and 3D modeling techniques to calculate surface area-to-volume (SA/V) ratios of the bees that otherwise cannot be obtained using conventional methods. SA/V ratios were calculated for 4 different families (Halictidae, Colletidae, Apidae, and Megachilidae) in the order Hymenoptera and were analyzed alongside the bee’s Critical Thermal Maximum (CT Max) data, the maximum heat a bee can withstand before losing mobility, to gain insight on the bee's ability to survive in extreme hot temperatures. It is evident from the data that larger bees, characterized by smaller SA/V ratios, presented a higher CT Max suggesting their greater chance of survival in higher temperatures than smaller bees due to less heat exchange relative to their body size. This data implies that with earth’s rising global temperatures larger bees will likely perform better than smaller bees.This poster was presented at the UCSB Center for Science and Engineering Partnerships (CSEP) summer colloquium in 2023

A Mean-Field Theory for Coarsening Faceted Surfaces

A mean-field theory is developed for the scale-invariant length distributions observed during the coarsening of one-dimensional faceted surfaces. This theory closely follows the Lifshitz-Slyozov-Wagner theory of Ostwald ripening in two-phase systems [1-3], but the mechanism of coarsening in faceted surfaces requires the addition of convolution terms recalling the work of Smoluchowski [4] and Schumann [5] on coalescence. The model is solved by the exponential distribution, but agreement with experiment is limited by the assumption that neighboring facet lengths are uncorrelated. However, the method concisely describes the essential processes operating in the scaling state, illuminates a clear path for future refinement, and offers a framework for the investigation of faceted surfaces evolving under arbitrary dynamics. [1] I. Lifshitz, V. Slezov, Soviet Physics JETP 38 (1959) 331-339. [2] I. Lifshitz, V. Slyozov, J. Phys. Chem. Solids 19 (1961) 35-50. [3] C. Wagner, Elektrochemie 65 (1961) 581-591. [4] M. von Smoluchowski, Physikalische Zeitschrift 17 (1916) 557-571. [5] T. Schumann, J. Roy. Met. Soc. 66 (1940) 195-207

Variation in Bee Body Size Due to Anthropogenic Land Use

This study investigates the impact of anthropogenic land use on the body size of bees across 18 different species. Adult bee body size, primarily influenced by developmental nutrition, is significantly affected by the availability of floral resources. Developed land often has reduced floral diversity and density is hypothesized to produce smaller bees due to limited food resources. Specimens from the UCSB Invertebrate Zoology Collection were categorized based on their collection sites into three land use types: developed, agricultural, and forest using USGS National Land Cover Database. Measurements of head width, intertegular distance (ITD), and dry mass were taken to assess body size. A body size index was calculated as the average of these measurements. Analysis of Variance (ANOVA) were done in Python version 3.12.4. Results indicate that bees from agricultural habitats are significantly larger than those from developed and forest habitats across all metrics (head width, ITD, dry mass, and body size index). These findings highlight the influence of landscape changes on bee functional traits, providing essential insights into the ecological consequences of land use on bee health.This poster was presented at the UCSB CSEP summer colloquium 2024

On the action potential as a propagating density pulse and the role of anesthetics

The Hodgkin-Huxley model of nerve pulse propagation relies on ion currents through specific resistors called ion channels. We discuss a number of classical thermodynamic findings on nerves that are not contained in this classical theory. Particularly striking is the finding of reversible heat changes, thickness and phase changes of the membrane during the action potential. Data on various nerves rather suggest that a reversible density pulse accompanies the action potential of nerves. Here, we attempted to explain these phenomena by propagating solitons that depend on the presence of cooperative phase transitions in the nerve membrane. These transitions are, however, strongly influenced by the presence of anesthetics. Therefore, the thermodynamic theory of nerve pulses suggests a explanation for the famous Meyer-Overton rule that states that the critical anesthetic dose is linearly related to the solubility of the drug in the membranes.Comment: 13 pages, 8 figure

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio