Darrell Velegol’s research while affiliated with William Penn University and other places

The purpose of this article is to analyze a sequence of independent bets by modeling it with a convective-diffusion equation (CDE). The approach follows the derivation of the Kelly Criterion (i.e., with a binomial distribution for the numbers of wins and losses in a sequence of bets) and reframes it as a CDE in the limit of many bets. The use of the CDE clarifies the role of steady growth (characterized by a velocity U) and random fluctuations (characterized by a diffusion coefficient D) to predict a probability distribution for the remaining bankroll as a function of time. Whereas the Kelly Criterion selects the investment fraction that maximizes the median bankroll (0.50 quantile), we show that the CDE formulation can readily find an optimum betting fraction f for any quantile. We also consider the effects of “ruin” using an absorbing boundary condition, which describes the termination of the betting sequence when the bankroll becomes too small. We show that the probability of ruin can be expressed by a dimensionless Péclet number characterizing the relative rates of convection and diffusion. Finally, the fractional Kelly heuristic is analyzed to show how it impacts returns and ruin. The reframing of the Kelly approach with the CDE opens new possibilities to use known results from the chemico-physical literature to address sequential betting problems.

Accurate prediction of molecular properties is essential in the screening and development of drug molecules and other functional materials. Traditionally, property-specific molecular descriptors are used in machine learning models. This in turn requires the identification and development of target or problem-specific descriptors. Additionally, an increase in the prediction accuracy of the model is not always feasible from the standpoint of targeted descriptor usage. We explored the accuracy and generalizability issues using a framework of Shannon entropies, based on SMILES, SMARTS and/or InChiKey strings of respective molecules. Using various public databases of molecules, we showed that the accuracy of the prediction of machine learning models could be significantly enhanced simply by using Shannon entropy-based descriptors evaluated directly from SMILES. Analogous to partial pressures and total pressure of gases in a mixture, we used atom-wise fractional Shannon entropy in combination with total Shannon entropy from respective tokens of the string representation to model the molecule efficiently. The proposed descriptor was competitive in performance with standard descriptors such as Morgan fingerprints and SHED in regression models. Additionally, we found that either a hybrid descriptor set containing the Shannon entropy-based descriptors or an optimized, ensemble architecture of multilayer perceptrons and graph neural networks using the Shannon entropies was synergistic to improve the prediction accuracy. This simple approach of coupling the Shannon entropy framework to other standard descriptors and/or using it in ensemble models could find applications in boosting the performance of molecular property predictions in chemistry and material science.

Solubilizing, self-propelling droplets have emerged as a rich chemical platform for the exploration of active matter, but isotropic droplets rely on spontaneous symmetry breaking to sustain motion. The introduction of permanent asymmetry, e.g., in the form of a biphasic Janus droplet, has not been explored as a comprehensive design strategy for active droplets, despite the widespread use of Janus structures in motile solid particles. Here, we uncover the chemomechanical framework underlying the self-propulsion of biphasic Janus oil droplets solubilizing in aqueous surfactant. We elucidate how droplet propulsion is influenced by the degree of oil mixing, droplet shape, and oil solubilization rates for a range of oil combinations. In addition, spatiotemporal control over droplet swimming speed and orientation is demonstrated through the application of thermal gradients applied via joule heating and laser illumination. We also explore the interactions between collections of Janus droplets, including the spontaneous formation of spinning multi-droplet clusters.

The study of active colloidal microswimmers with tunable phoretic and self-organizational behaviors is important for understanding out-of-equilibrium systems and the design of functional, adaptive matter. Solubilizing, self-propelling droplets have emerged as a rich chemical platform for exploration of active behaviors, but isotropic droplets rely on spontaneous symmetry breaking to sustain motion. The introduction of permanent asymmetry, e.g. in the form of a biphasic Janus droplet, has not been explored previously as a comprehensive design strategy for active droplets, despite the widespread use of Janus structures in motile solid particles. Here, we uncover the chemomechanical framework underlying the self-propulsion of biphasic Janus oil droplets solubilizing in aqueous surfactant. We elucidate how droplet propulsion is influenced by the degree of oil mixing, droplet shape, and oil solubilization rates for a range of oil combinations. A key finding is that for droplets containing both a mobile (solubilizing) and non-mobile oil, the degree of partitioning of the mobile oil across the Janus droplets’ oil-oil interface plays a pivotal role in determining the droplet speed and swimming direction. In addition, spatiotemporal control over droplet swimming speed and orientation is demonstrated through the application of local thermal gradients applied via joule heating and laser illumination. We also explore the interactions between collections of Janus droplets including the spontaneous formation of multi-droplet clusters that spin predictably based on symmetry. Our findings provide insights as to how the chemistry and structure of multiphase fluids can be harnessed to design microswimmers with programmable active and collective behaviors.

The study of active colloidal microswimmers with tunable phoretic and self-organizational behaviors is important for understanding out-of-equilibrium systems and the design of functional, adaptive matter. Solubilizing, self-propelling droplets have emerged as a rich chemical platform for exploration of active behaviors, but isotropic droplets rely on spontaneous symmetry breaking to sustain motion. The introduction of permanent asymmetry, e.g. in the form of a biphasic Janus droplet, has not been explored previously as a comprehensive design strategy for active droplets, despite the widespread use of Janus structures in motile solid particles. Here, we uncover the chemomechanical framework underlying the self-propulsion of biphasic Janus oil droplets solubilizing in aqueous surfactant. We elucidate how droplet propulsion is influenced by the degree of oil mixing, droplet shape, and oil solubilization rates for a range of oil combinations. A key finding is that for droplets containing both a mobile (solubilizing) and non-mobile oil, the degree of partitioning of the mobile oil across the Janus droplets’ oil-oil interface plays a pivotal role in determining the droplet speed and swimming direction. In addition, spatiotemporal control over droplet swimming speed and orientation is demonstrated through the application of local thermal gradients applied via joule heating and laser illumination. We also explore the interactions between collections of Janus droplets including the spontaneous formation of multi-droplet clusters that spin predictably based on symmetry. Our findings provide insights as to how the chemistry and structure of multiphase fluids can be harnessed to design microswimmers with programmable active and collective behaviors.

p>The study of active colloidal microswimmers with tunable phoretic and self-organizational behaviors is important for understanding out-of-equilibrium systems and the design of functional, adaptive matter. Solubilizing, self-propelling droplets have emerged as a rich chemical platform for exploration of active behaviors, but isotropic droplets rely on spontaneous symmetry breaking to sustain motion. The introduction of permanent asymmetry, e.g. in the form of a biphasic Janus droplet, has not been explored previously as a comprehensive design strategy for active droplets, despite the widespread use of Janus structures in motile solid particles. Here, we uncover the chemomechanical framework underlying the self-propulsion of active, biphasic Janus oil droplets solubilizing in aqueous surfactant. We elucidate how droplet propulsion is influenced by the degree of oil mixing, droplet shape, and oil solubilization rates for a range of oil combinations. A key finding is that for droplets containing both a mobile (solubilizing) and non-mobile oil, the degree of partitioning of the mobile oil across the Janus droplets’ oil-oil interface plays a pivotal role in determining the droplet speed and swimming direction. As a result, we observe propulsion speeds of Janus droplets more than an order-of-magnitude faster than chasing pairs of single emulsion droplets which lack an oil-oil interface. In addition, spatiotemporal control over droplet swimming speed and orientation is demonstrated through the application of local thermal gradients applied via induced via joule heading and laser spot illumination. We also explore the interactions between collections of Janus droplets including the spontaneous formation of multi-droplet spinning clusters that rotate predictably based on symmetry. Our findings provide key insights as to how the chemistry and structure of multiphase fluids can be harnessed to design microswimmers with programmable active and collective behaviors. <br

Climate change is a critical 21st century challenge. Major initiatives are underway across the globe but the key metric of success the reduction of greenhouse gas concentration (GHG) in the atmosphere is not improving. A new model for engaging, educating, and securing support from the world community is needed. We propose the formation of a new Sustainable Energy Corps, designed to engage students, communities, professionals, universities, companies, government, and other stakeholders. The focus is on measurement and reduction of GHG concentration in the atmosphere. Translating the “adopt-a-highway” model the world would be divided into local regions connected globally using contemporary data and content platforms. A proposed approach for building a global integrated approach is presented.