On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.Comment: 25 pages, published in Journal of Mathematical Physic

Approaching probabilistic truths:introduction to the Topical Collection

After Karl Popper’s original work, several approaches were developed to provide a sound explication of the notion of verisimilitude. With few exceptions, these contributions have assumed that the truth to be approximated is deterministic. This collection of ten papers addresses the more general problem of approaching probabilistic truths. They include attempts to find appropriate measures for the closeness to probabilistic truth and to evaluate claims about such distances on the basis of empirical evidence. The papers employ multiple analytical approaches, and connect the research to related issues in the philosophy of science

The Discrete Frenet Frame, Inflection Point Solitons And Curve Visualization with Applications to Folded Proteins

We develop a transfer matrix formalism to visualize the framing of discrete piecewise linear curves in three dimensional space. Our approach is based on the concept of an intrinsically discrete curve, which enables us to more effectively describe curves that in the limit where the length of line segments vanishes approach fractal structures in lieu of continuous curves. We verify that in the case of differentiable curves the continuum limit of our discrete equation does reproduce the generalized Frenet equation. As an application we consider folded proteins, their Hausdorff dimension is known to be fractal. We explain how to employ the orientation of $C_\beta$ carbons of amino acids along a protein backbone to introduce a preferred framing along the backbone. By analyzing the experimentally resolved fold geometries in the Protein Data Bank we observe that this $C_\beta$ framing relates intimately to the discrete Frenet framing. We also explain how inflection points can be located in the loops, and clarify their distinctive r\^ole in determining the loop structure of foldel proteins.Comment: 14 pages 12 figure

Semiclassical approach to the ac-conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime

DNS of gas bubbles behaviour using an improved 3D front tracking model—Model development

In recent years CFD has proven to be a valuable and powerful tool to advance our understanding of complex multiphase flow systems arising in industrial applications. However, the predictive capabilities of this tool are determined by many factors of physical and numerical origin but in particular by the quality of the closures adopted for the description of the interface forces. The objective of this study is to improve the front tracking method in order to compute such forces with sufficient accuracy. This paper describes the further development of a 3D front tracking model to achieve improved volume conservation and circumvent problems related to the representation of surface tension. First, we have included a method to handle the pressure jump at the interface. This causes the spurious currents, observed in conventional front tracking, to decrease with two orders of magnitude. Also the advection scheme has been adapted, using higher order velocity interpolation (using cubic splines), and Runge–Kutta time-stepping, in order to prevent considerable volume changes of the dispersed phase. Test simulations involving a stationary bubble, a standard advection test and an oscillating droplet, demonstrate the effect of these improvements. The implementation of these procedures enlarged the computational window and in particular enabled the simulation of very small bubbles, where large surface forces dominate, without any significant spurious currents or volume loss

Front tracking simulations on liquid-liquid systems; an investigation of the drag force on droplets

No abstract

Distinguishing step relaxation mechanisms via pair correlation functions

Theoretical predictions of coupled step motion are tested by direct STM measurement of the fluctuations of near-neighbor pairs of steps on Si(111)-root3 x root3 R30 - Al at 970K. The average magnitude of the pair-correlation function is within one standard deviation of zero, consistent with uncorrelated near-neighbor step fluctuations. The time dependence of the pair-correlation function shows no statistically significant agreement with the predicted t^1/2 growth of pair correlations via rate-limiting atomic diffusion between adjacent steps. The physical considerations governing uncorrelated step fluctuations occurring via random attachment/detachment events at the step edge are discussed.Comment: 17 pages, 4 figure

Predictors for outcome of failure of balloon dilatation in patients with achalasia

Background: Pneumatic balloon dilatation (PD) is a regular treatment modality for achalasia. The reported success rates of PD vary. Recurrent symptoms often require repeated PD or surgery. Objective: To identify predicting factors for symptom recurrence requiring repeated treatment. Methods: Between 1974 and 2006, 336 patients were treated with PD and included in this longitudinal cohort study. The median follow-up was 129 months (range 1-378). Recurrence of achalasia was defined as symptom recurrence in combination with increased lower oesophageal sphincter (LOS) pressure on manometry, requiring repeated treatment. Patient characteristics, results of timed barium oesophagram and manometry as well as baseline PD characteristics were evaluated as predictors of disease recurrence with Kaplan-Meier curves and Cox regression analysis. Results: 111 patients had symptom recurrence requiring repeated treatment. Symptoms recurred after a mean follow-up of 51 months (range 1-348). High recurrence percentages were found in patients younger than 21 years in whom the 5 and 10-year risks of recurrence were 64% and 72%, respectively. These risks were respectively 28% and 36% in patients with classic achalasia, respectively 48% and 60% in patients without complete obliteration of the balloon's waist during PD and respectively 25% and 33% in patients with a LOS pressure greater than 10 mm Hg at 3 months post-dilatation. These four predictors remained statistically significant in a multivariable Cox analysis. Conclusion: Although PD is an effective primary treatment in patients with primary achalasia, patients are at risk of recurrent disease, with this risk increasing during long-term follow-up. Young age at presentation, classic achalasia, high LOS pressure 3 months after PD and incomplete obliteration of the balloon's waist during PD are the most important predicting factors for the need for repeated treatment during follow-up. Patients who meet one or more of these characteristics may be considered earlier for alternative treatment, such as surgery

Molecular Dynamics Simulation of Solvent-Polymer Interdiffusion. I. Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t^{1/2}, which is expected for Fickian type of diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.Comment: 17 pages and 7 figure