Prophet inequalities for averages of independent non-negative random variables

Mathematische Zeitschrift -     

Carrier hopping in InAs/AlyGa1−yAs quantum dot heterostructures: effects on optical and laser properties

The optical properties of InAs/Al_yGa_1−yAs self-assembled quantum dots are studied as a function of temperature from 10 K to room temperature. The temperature dependence of carrier hopping between dots is discussed in terms of the depth of the dot confinement potential and the dispersion in dot size and composition. We show that carrier hopping between dots influences both the electrical and optical properties of laser devices having dots as active medium.     

Ligand and base additive effects on the reversibility of nucleophilic addition in palladium-catalyzed allylic aminations monitored by nucleophile crossover

A nucleophile crossover experiment was used to monitor the reversibility of nucleophilic addition of benzylamine to π-allylpalladium complexes. Dppe, dppp, dppb, and PHOX showed more crossover than PPh₃ and dppm in both DMF and dichloromethane. Crossover was inhibited by the addition of DBU or Cs₂CO₃, but much less elimination to diene side products was observed with Cs₂CO₃. Analysis of percent crossover vs. percent reaction completion using the PHOX ligand revealed that with added DBU or Cs₂CO₃ crossover only began occurring after 100% completion had been reached.     

Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link

We have created a long-lived (≈40 s) persistent current in a toroidal Bose-Einstein condensate held in an all-optical trap. A repulsive optical barrier across one side of the torus creates a tunable weak link in the condensate circuit, which can affect the current around the loop. Superflow stops abruptly at a barrier strength such that the local flow velocity at the barrier exceeds a critical velocity. The measured critical velocity is consistent with dissipation due to the creation of vortex-antivortex pairs. This system is the first realization of an elementary closed-loop atom circuit.     

Phase transitions in shear-induced segregation of granular materials

We computationally study shear-induced segregation of different-sized particles in vertical chute flow. We find that, for low solid fractions, large particles segregate toward regions of low shear rates where the granular temperature (velocity variance) is low. As the solid fraction increases, this trend reverses, and large particles segregate toward regions of high shear rates and temperatures. We find that this is a global phenomenon: local segregation trends reverse at high system solid fractions even where local solid fractions are small. The reversal corresponds to the growth of a single enduring cluster of 30%-60% of the particles that we propose changes the segregation dynamics.     

Packing configurations for methane storage in carbon nanotubes

In this paper we investigate methane packing in single-walled carbon nanotubes. We employ classical applied mathematical modelling using the basic principles of mechanics to exploit the Lennard-Jones potential function and the continuous approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider both zigzag and spiral configurations formed by packing methane molecules into (9, 5), (8, 8) and (10, 10) carbon nanotubes, and we derive analytical expressions for the interaction potential energy of these configurations. Our findings indicate that for the zigzag configuration for a (9, 5) tube, the potential energy of the system is minimized when the methane molecules simply form a linear chain along the tube axis, but genuine zigzag patterns are found as the tube size increases such as for the (8, 8) and (10, 10) tubes. For the spiral configuration, the potential energy of the system is minimized when the angular spacing is approximately equal to π for the (9, 5) and (8, 8) tubes, and π/2 for the (10, 10) tube. Overall, our results are in good agreement with molecular dynamics simulations in the literature and show that the most energetically efficient packing configuration of the three tubes studied, occurs for a (10, 10) tube with a zigzag packing, while a (10, 10) tube with a spiral packing configuration has the largest free-cavity volume for methane adsorption at higher temperatures.     

Encapsulation of methane molecules into carbon nanotubes

Methane gas (CH₄) is a chemical compound comprising a carbon atom surrounded by four hydrogen atoms, and carbon nanotubes have been proposed as possible molecular containers for the storage of such gases. In this paper, we investigate the interaction energy between a CH₄ molecule and a carbon nanotube using two different models for the CH₄ molecule, the first discrete and the second continuous. In the first model, we consider the total interaction as the sum of the individual interactions between each atom of the molecule and the nanotube. We first determine the interaction energy by assuming that the carbon atom and one of the hydrogen atoms lie on the axis of the tube with the other three hydrogen atoms offset from the axis. Symmetry is assumed with regard to the arrangement of the three hydrogen atoms surrounding the carbon atom on the axis. We then rotate the atomic position into 100 discrete orientations and determine the average interaction energy from all orientations. In the second model, we approximate the CH₄ molecule by assuming that the four hydrogen atoms are smeared over a spherical surface of a certain radius with the carbon atom located at the center of the sphere. The total interaction energy between the CH₄ molecule and the carbon nanotube for this model is calculated as the sum of the individual interaction energies between both the carbon atom and the spherical surface and the carbon nanotube. These models are analyzed to determine the dimensions of the particular nanotubes which will readily suck-up CH₄ molecules. Our results determine the minimum and maximum interaction energies required for CH₄ encapsulation in different tube sizes, and establish the second model of the CH₄ molecule as a simple and elegant model which might be exploited for other problems.     

High sensitivity (1 ppm) hydrogen detection using an unconventional Pd/n-InP Schottky device

Hydrogen is detected using a Pd/n-InP Schottky diode in which the elongated, very thin Pd electrode is of greater resistance than the underlying semiconductor substrate. Four-probe measurements of the device resistance, as a function of hydrogen concentration, are made by contacting only the Pd electrode, with a sensitivity of 1 ppm being achieved. On hydrogen exposure the device resistance drops from an initial high value, characteristic of the Pd electrode alone, to a lower value due to a hydrogen-induced lowering of the Schottky barrier that opens up the InP substrate as a parallel current carrying channel.     

An Analogy Principle in Inductive Logic

We propose an Analogy Principle in the context of Unary Inductive Logic and characterize the probability functions which satisfy it. In particular in the case of a language with just two predicates the probability functions satisfying this principle correspond to solutions of Skyrms? ‘Wheel of Fortune’.