Modelling the Evaporation of a Binary Droplet in a Well

While the drying behaviour of sessile droplets has been extensively studied over the last 25 years, the evaporation of droplets from wells (DiWs) has largely been neglected, especially from a mathematical modelling standpoint. Understanding a drying DiW is both important for industrial processes (such as inkjet printing and, increasingly, the manufacture of organic displays) and an interesting problem in its own right as a natural progression from sessile droplets, and we still do not have a thorough theoretical description of their evaporation. The main aim of this project was to build an understanding of pure and binary DiWs under the lubrication approximation by constructing a simple mathematical model for the evolution of their shape. We solved the resulting partial differential equations for droplet height and composition profile numerically using the Method of Lines. In the case of a pure droplet, we found that we could control the interface shape using a single parameter (C) based on the capillary number; the more complex binary system required two new parameters governing evaporation and surface tension differences. Comparison to experimental data was improved with the inclusion of a dynamic evaporative flux for each component that depended on the their volume fraction distribution. These simulations offer insight into the deposit that evaporating DiWs leave behind. We have shown that the smaller C, the more likely the DiW will cause an undesirable ring stain, but this is suppressed in binary droplets in which the more volatile component has the lower surface tension

MEASURING GLUTAMATE AND OXYGEN IN BRAIN REWARD CIRCUITS IN ANIMAL MODELS OF COCAINE ABUSE AND DECISION-MAKING

Drug-specific reward and associated effects on neural signaling are often studied between subjects, where one group self-administers drug and a separate group self-administers a natural reinforcer. However, exposure to drugs of abuse can cause long-term neural adaptations that can affect how an organism responds to drug reward, natural reward, and their reward-associated stimuli. Thus, to isolate drug-specific effects it is important to use models that expose the same organism to all of the aforementioned. Multiple schedules provide a means of dissociating the rewarding effects of a drug from the rewarding effects of food within a single animal. Further, drug users do not take drugs in isolation; rather, they are often faced with several concurrently available commodities (e.g. monetary goods, social relationships). Thus, using choice measures to assess the relative subjective value of drug reinforcers in both humans and animals promotes a translational understanding of mechanisms that govern drug-associated decision-making. Thus, in order to gain a more translational view of the neurobehavioral mechanisms that underlie drug-associated behavior, in the first study, glutamate was measured in the nucleus accumbens core (NAcC) and prefrontal cortex (PrL) in freely-moving rats as they behaved in a cocaine-food multiple schedule procedure. In the second study, oxygen dynamics were measured in the orbitofrontal cortex (OFC) of freely-moving rats as they behaved in a cocaine/food choice procedure. The results from the first study showed that, in the NAc and PrL, there was an increase in glutamate release when animals earned cocaine. Further, the number of glutamate peaks that occurred per cocaine lever press and per cocaine reinforcer was increased compared to food. In the second study, OFC oxygen dynamics were positively correlated with cocaine/food choice and generally tracked preference. Further, OFC oxygen dynamics were greater to cocaine related events. Taken together, these results showed the feasibility of combining electrochemical measurements with complex drug-related behavioral procedures. These results also highlight the importance of the PrL, NAcC, and OFC in the valuation of drug and non-drug commodities. Overall, these results add to our understanding of the neurobehavioral mechanisms that guide drug-associated behavior and create more precise experimental avenues to research potential treatments

On the t-Term Rank of a Matrix

For t a positive integer, the t-term rank of a (0,1)-matrix A is defined to be the largest number of 1s in A with at most one 1 in each column and at most t 1s in each row. Thus the 1-term rank is the ordinary term rank. We generalize some basic results for the term rank to the t-term rank, including a formula for the maximum term rank over a nonempty class of (0,1)-matrices with the the same row sum and column sum vectors. We also show the surprising result that in such a class there exists a matrix which realizes all of the maximum terms ranks between 1 and t.Comment: 18 page

Cyclic Matching Sequencibility of Graphs

We define the cyclic matching sequencibility of a graph to be the largest integer $d$ such that there exists a cyclic ordering of its edges so that every $d$ consecutive edges in the cyclic ordering form a matching. We show that the cyclic matching sequencibility of $K_{2m}$ and $K_{2m+1}$ equal $m-1$

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin

The Power Control Rack: A Modular Solution for Building Power Systems

LDRD proposal presentation to ETA ALD at LBNL. Proposing use of SST to create a modular efficient single point of common coupling for buildings

Detection of Enhanced Central Mass-to-Light Ratios in Low-Mass Early-Type Galaxies: Evidence for Black Holes?

We present dynamical measurements of the central mass-to-light ratio ($M/L$) of a sample of 27 low-mass early-type ATLAS$^{3D}$ galaxies. We consider all ATLAS$^{3D}$ galaxies with 9.7$<$log(M$_\star/$M$_\odot)$$<$10.5 in our analysis, selecting out galaxies with available high-resolution Hubble Space Telescope (HST) data, and eliminating galaxies with significant central color gradients or obvious dust features. We use the HST images to derive mass models for these galaxies and combine these with the central velocity dispersion values from ATLAS$^{3D}$ data to obtain a central dynamical $M/L$ estimate. These central dynamical $M/L$s are higher than dynamical $M/L$s derived at larger radii and stellar population estimates of the galaxy centers in $\sim$80\% of galaxies, with a median enhancement of $\sim$14\% and a statistical significance of 3.3$\sigma$. We show that the enhancement in the central $M/L$ is best described either by the presence of black holes in these galaxies or by radial IMF variations. Assuming a black hole model, we derive black hole masses for the sample of galaxies. In two galaxies, NGC 4458 and NGC 4660, the data suggests significantly over-massive BHs, while in most others only upper limits are obtained. We also show that the level of $M/L$ enhancements we see in these early-type galaxy nuclei are consistent with the larger enhancements seen in ultracompact dwarf galaxies (UCDs), supporting the scenario where massive UCDs are created by stripping galaxies of these masses.Comment: Accepted to ApJ, 17 pages, 13 figure