Tunneling in Fractional Quantum Mechanics

We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behaviour. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by $\mathcal{T}_0 = \cos^2{\pi/\alpha}$, where $\alpha$ is the order of the derivative ($1 < \alpha \leq 2$).Comment: 21 pages, 3 figures. Revised version; accepted for publication in Journal of Physics A: Mathematical and Theoretica

A CASE STUDY OF STRIDE FREQUENCY AND SWING TIME IN ELITE ABLE-BODIED SPRINT RUNNING: IMPLICATIONS FOR AMPUTEE DEBATE

Recent research into trans-tibial double-amputee sprint performance has debated the possible inherent advantages, disadvantages and limitations to sprinting with prosthetic limbs compared to healthy limbs. Biomechanical data gathered throughout a training season from an elite able-bodied sprinter provide a new perspective on this debate. Peak stride frequency was measured at 2.62 Hz, and the corresponding swing time was estimated to be 0.287 s in the able-bodied sprinter. Published swing time and stride frequency values from the double-amputee at maximum velocity, thought to be beyond biological limits, therefore may not be so, although previously published research has provided evidence that some joint kinetic values from the double-amputee have not been shown in elite able-bodied sprinting

A CASE STUDY OF STRIDE FREQUENCY AND SWING TIME IN ELITE ABLEBODIED SPRINT RUNNING: IMPLICATIONS FOR AMPUTEE DEBATE

Recent research into trans-tibial double-amputee sprint performance has debated the possible inherent advantages, disadvantages and limitations to sprinting with prosthetic limbs compared to healthy limbs. Biomechanical data gathered throughout a training season from an elite able-bodied sprinter provide a new perspective on this debate. Peak stride frequency was measured at 2.62 Hz, and the corresponding swing time was estimated to be 0.287 s in the able-bodied sprinter. Published swing time and stride frequency values from the double-amputee at maximum velocity, thought to be beyond biological limits, therefore may not be so, although previously published research has provided evidence that some joint kinetic values from the double-amputee have not been shown in elite able-bodied sprinting

Back gating of a two-dimensional hole gas in a SiGe quantum well

A device comprising a low-resistivity, n-type, Si substrate as a back gate to a p-type (boron), remote-doped, SiGe quantum well has been fabricated and characterized. Reverse and forward voltage biasing of the gate with respect to the two-dimensional hole gas in the quantum well allows the density of holes to be varied from 8 × 1011 cm–2 down to a measurement-limited value of 4 × 1011 cm–2. This device is used to demonstrate the evolution with decreasing carrier density of a re-entrant insulator state between the integer quantum Hall effect states with filling factors 1 and 3

Kinetic pinning and biological antifreezes

Biological antifreezes protect cold-water organisms from freezing. An example are the antifreeze proteins (AFPs) that attach to the surface of ice crystals and arrest growth. The mechanism for growth arrest has not been heretofore understood in a quantitative way. We present a complete theory based on a kinetic model. We use the `stones on a pillow' picture. Our theory of the suppression of the freezing point as a function of the concentration of the AFP is quantitatively accurate. It gives a correct description of the dependence of the freezing point suppression on the geometry of the protein, and might lead to advances in design of synthetic AFPs.Comment: 4 pages, 4 figure

Effects of Short-term 3-Day Caloric Restriction on Cardiometabolic Health in Overweight and Obese Individuals

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Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

Calculation of Band Edge Eigenfunctions and Eigenvalues of Periodic Potentials through the Quantum Hamilton - Jacobi Formalism

We obtain the band edge eigenfunctions and the eigenvalues of solvable periodic potentials using the quantum Hamilton - Jacobi formalism. The potentials studied here are the Lam{\'e} and the associated Lam{\'e} which belong to the class of elliptic potentials. The formalism requires an assumption about the singularity structure of the quantum momentum function $p$, which satisfies the Riccati type quantum Hamilton - Jacobi equation, $p^{2} -i \hbar \frac{d}{dx}p = 2m(E- V(x))$ in the complex $x$ plane. Essential use is made of suitable conformal transformations, which leads to the eigenvalues and the eigenfunctions corresponding to the band edges in a simple and straightforward manner. Our study reveals interesting features about the singularity structure of $p$, responsible in yielding the band edge eigenfunctions and eigenvalues.Comment: 21 pages, 5 table

A Search for Time Variation of the Fine Structure Constant

A method offering an order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant, alpha. Applying the technique to a sample of 30 absorption systems, spanning redshifts 0.5 < z< 1.6, obtained with the Keck I telescope, we derive limits on variations in alpha over a wide range of epochs. For the whole sample Delta(alpha)/alpha = -1.1 +/- 0.4 x 10^{-5}. This deviation is dominated by measurements at z > 1, where Delta(alpha)/alpha = -1.9 +/- 0.5 x 10^{-5}. For z < 1, Delta(alpha)/alpha = -0.2 +/- 0.4 x 10^{-5}, consistent with other known constraints. Whilst these results are consistent with a time-varying alpha, further work is required to explore possible systematic errors in the data, although careful searches have so far not revealed any.Comment: 4 pages, 1 figure, accepted for publication in Physical Review Letter