Analytical approximations to the spectra of quark-antiquark potentials

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider the meson spectroscopy with various phenomenological potentials.Comment: 12 pages, 4 figures, 1 tabl

Quantifying the pathway and predicting spontaneous emulsification during material exchange in a two phase liquid system

Kinetic restriction of a thermodynamically favourable equilibrium is a common theme in materials processing. The interfacial instability in systems where rate of material exchange is far greater than the mass transfer through respective bulk phases is of specific interest when tracking the transient interfacial area, a parameter integral to short processing times for productivity streamlining in all manufacturing where interfacial reaction occurs. This is even more pertinent in high-temperature systems for energy and cost savings. Here the quantified physical pathway of interfacial area change due to material exchange in liquid metal-molten oxide systems is presented. In addition the predicted growth regime and emulsification behaviour in relation to interfacial tension as modelled using phase-field methodology is shown. The observed in-situ emulsification behaviour links quantitatively the geometry of perturbations as a validation method for the development of simulating the phenomena. Thus a method is presented to both predict and engineer the formation of micro emulsions to a desired specification

Centrifugal terms in the WKB approximation and semiclassical quantization of hydrogen

A systematic semiclassical expansion of the hydrogen problem about the classical Kepler problem is shown to yield remarkably accurate results. Ad hoc changes of the centrifugal term, such as the standard Langer modification where the factor l(l+1) is replaced by (l+1/2)^2, are avoided. The semiclassical energy levels are shown to be exact to first order in $\hbar$ with all higher order contributions vanishing. The wave functions and dipole matrix elements are also discussed.Comment: 5 pages, to appear in Phys. Rev.

Efficient organic-inorganic hybrid perovskite solar cells processed in air

Organic-inorganic hybrid perovskite solar cells with fluorine doped tin oxide/titanium dioxide/CH3NH3PbI3-xClx/poly(3-hexylthiophene)/silver were made in air with more than 50% humidity. The best devices showed an open circuit voltage of 640 mV, a short circuit current density of 18.85 mA cm-2, a fill factor of 0.407 and a power conversion efficiency of 5.67%. The devices showed external quantum efficiency varying from 60 to 80% over a wavelength region of 350 nm to 750 nm of the solar spectrum. The morphology of the perovskite was investigated using scanning electron microscopy and it was found to be porous in nature. This study provides insights into air-stability of perovskite solar cells

CSLM, XCT Couple interrogation of the emulsification interaction between free steel droplets suspended in steel making slags

Small Fe-based droplets have been heated to a molten phase suspended within a slag medium to replicate a partial environment within the Basic Oxygen Furnace (BOF). The confocal scanning laser microscope (CSLM) has been used as a heating platform as it offers the high heating rates necessary for slag and metal to become molten in close time proximity avoiding gradual equilibration during heating. The effect of impurities and their transfer across the metal/slag interface, on the emulsification of the droplet into the slag medium was then examined through X-ray Computer Tomography (XCT) scanning of the quenched sample. This gives the mapping of emulsion dispersion in 3D space, calculating the changing of interfacial area between the two materials, and changes of material volume due to material transfer between metal and slag. Samples were then sectioned and radial chemical analysis is used to identify component surface enrichment or lack thereof. Replication of the previously reported study by Assis et al1 has also been carried out, to show repeatability of the experimental set up and conditions through different users

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

The Roles of Transmembrane Domain Helix-III during Rhodopsin Photoactivation

Background: Rhodopsin, the prototypic member of G protein-coupled receptors (GPCRs), undergoes isomerization of 11- cis-retinal to all-trans-retinal upon photoactivation. Although the basic mechanism by which rhodopsin is activated is well understood, the roles of whole transmembrane (TM) helix-III during rhodopsin photoactivation in detail are not completely clear. Principal Findings: We herein use single-cysteine mutagenesis technique to investigate conformational changes in TM helices of rhodopsin upon photoactivation. Specifically, we study changes in accessibility and reactivity of cysteine residues introduced into the TM helix-III of rhodopsin. Twenty-eight single-cysteine mutants of rhodopsin (P107C-R135C) were prepared after substitution of all natural cysteine residues (C140/C167/C185/C222/C264/C316) by alanine. The cysteine mutants were expressed in COS-1 cells and rhodopsin was purified after regeneration with 11-cis-retinal. Cysteine accessibility in these mutants was monitored by reaction with 4, 49-dithiodipyridine (4-PDS) in the dark and after illumination. Most of the mutants except for T108C, G109C, E113C, I133C, and R135C showed no reaction in the dark. Wide variation in reactivity was observed among cysteines at different positions in the sequence 108–135 after photoactivation. In particular, cysteines at position 115, 119, 121, 129, 131, 132, and 135, facing 11-cis-retinal, reacted with 4-PDS faster than neighboring amino acids. The different reaction rates of mutants with 4-PDS after photoactivation suggest that the amino acids in different positions in helix-III are exposed to aqueous environment to varying degrees. Significance: Accessibility data indicate that an aqueous/hydrophobic boundary in helix-III is near G109 and I133. The lack of reactivity in the dark and the accessibility of cysteine after photoactivation indicate an increase of water/4-PDS accessibility for certain cysteine-mutants at Helix-III during formation of Meta II. We conclude that photoactivation resulted in water-accessible at the chromophore-facing residues of Helix-III.National Institutes of Health (U.S.) (grant GM28289)National Eye Institute (Grant Grant EY11716)National Science Foundation (U.S.) (grant EIA-0225609

From spinal central pattern generators to cortical network: integrated BCI for walking rehabilitation

Success in locomotor rehabilitation programs can be improved with the use of brain-computer interfaces (BCIs). Although a wealth of research has demonstrated that locomotion is largely controlled by spinal mechanisms, the brain is of utmost importance in monitoring locomotor patterns and therefore contains information regarding central pattern generation functioning. In addition, there is also a tight coordination between the upper and lower limbs, which can also be useful in controlling locomotion. The current paper critically investigates different approaches that are applicable to this field: the use of electroencephalogram (EEG), upper limb electromyogram (EMG), or a hybrid of the two neurophysiological signals to control assistive exoskeletons used in locomotion based on programmable central pattern generators (PCPGs) or dynamic recurrent neural networks (DRNNs). Plantar surface tactile stimulation devices combined with virtual reality may provide the sensation of walking while in a supine position for use of training brain signals generated during locomotion. These methods may exploit mechanisms of brain plasticity and assist in the neurorehabilitation of gait in a variety of clinical conditions, including stroke, spinal trauma, multiple sclerosis, and cerebral palsy

The diffusion of a new service: Combining service consideration and brand choice

We propose an individual-level model of a two-stage service diffusion process. In the first stage, customers decide whether to "consider" joining the service. This (Consideration) stage is modeled by a hazard model. Customers who decide to consider the service move on to the Choice stage, wherein they choose among the service alternatives and an outside No Choice option. This stage is modeled by a conditional Multinomial Logit model. The service provider does not observe the transition in the first stage of potential customers who have yet to choose a brand. Such potential customers may have started to consider joining the service, yet chose the outside alternative in each period thereafter. One of the main contributions of the model is its ability to distinguish between these two non-adopter types. We estimated the model using data on the adoption process of newly introduced service plans offered by a commercial bank. We employed the hierarchical Bayes Monte Carlo Markov Chain procedure to estimate individual as well as population parameters. The empirical results indicate that the model outperforms competing models in breadth of analysis, model fit, and prediction accuracy