Inversion of Gamow's Formula and Inverse Scattering

We present a pedagogical description of the inversion of Gamow's tunnelling formula and we compare it with the corresponding classical problem. We also discuss the issue of uniqueness in the solution and the result is compared with that obtained by the method of Gel'fand and Levitan. We hope that the article will be a valuable source to students who have studied classical mechanics and have some familiarity with quantum mechanics.Comment: LaTeX, 6 figurs in eps format. New abstract; notation in last equation has been correcte

A statistical model for the prediction of wind-speed probabilities in the atmospheric surface layer

Wind fields in the atmospheric surface layer (ASL) are highly three-dimensional and characterized by strong spatial and temporal variability. For various applications such as wind comfort assessments and structural design, an understanding of potentially hazardous wind extremes is important. Statistical models are designed to facilitate conclusions about the occurrence probability of wind speeds based on the knowledge of low-order flow statistics. Being particularly interested in the upper tail regions we show that the statistical behavior of near-surface wind speeds is adequately represented by the Beta distribution. By using the properties of the Beta probability density function in combination with a model for estimating extreme values based on readily available turbulence statistics, it is demonstrated that this novel modelling approach reliably predicts the upper margins of encountered wind speeds. The model’s basic parameter is derived from three substantially different calibrating datasets of flow in the ASL originating from boundary-layer wind-tunnel measurements and direct numerical simulation. Evaluating the model based on independent field observations of near-surface wind speeds showed a high level of agreement between the statistically modelled horizontal wind speeds and measurements. The results show that, based on the knowledge of only a few simple flow statistics (mean wind speed, wind speed fluctuations and integral time scales), the occurrence probability of velocity magnitudes at arbitrary flow locations in the ASL can be estimated with a high degree of confidence

MODELLING THE CONCENTRATION FLUCTUATION AND INDIVIDUAL EXPOSURE IN COMPLEX URBAN ENVIRONMENTS

The concentrations fluctuations of a dispersing hazardous gaseous pollutant in the atmospheric boundary layer, and the hazard associated with short-term concentration levels, demonstrate the necessity of estimating the magnitude of these fluctuations using predicting models. Moreover the computation of concentration fluctuations and individual exposure in case of dispersion in realistic situations, such as built-up areas or street canyons, is of special practical interest for hazard assessment purposes. In order to predict or/and estimate the maximum expected dosage and the exposure time within which the dosage exceeds certain health limits, the knowledge of the behaviour of concentration fluctuations at the point under consideration is needed. In this study the whole effort is based on the ‘Mock Urban Setting Test – MUST’, an extensive field test carried out on a test site of the US Army in the Great Basin Desert in 2001 (Biltoft, 2001; Yee, 2004). The experimental data that was used for the model evaluation concerned the dispersion of a passive gas between street canyons which have been created by 120 standard size shipping containers. The computational simulations have been performed using the laboratory CFD code ADREA, which has been developed for simulating the dispersion and exposure of pollutants over complex geometries. The ADREA model is evaluated by comparing the model’s predictions with the observations utilizing statistical metrics and scatter plots. The present study has been performed in the frame of the Action COST 732 “Quality Assurance and Improvement of Micro-Scale Meteorological Models”

Modelling short-term maximum individual exposure from airborne hazardous releases in urban environments. Part ΙI: Validation of a deterministic model with wind tunnel experimental data

The capability to predict short-term maximum individual exposure is very important for several applications including, for example, deliberate/accidental release of hazardous substances, odour fluctuations or material flammability level exceedance. Recently, authors have proposed a simple approach relating maximum individual exposure to parameters such as the fluctuation intensity and the concentration integral time scale. In the first part of this study (Part I), the methodology was validated against field measurements, which are governed by the natural variability of atmospheric boundary conditions. In Part II of this study, an in-depth validation of the approach is performed using reference data recorded under truly stationary and well documented flow conditions. For this reason, a boundary-layer wind-tunnel experiment was used. The experimental dataset includes 196 time-resolved concentration measurements which detect the dispersion from a continuous point source within an urban model of semi-idealized complexity. The data analysis allowed the improvement of an important model parameter. The model performed very well in predicting the maximum individual exposure, presenting a factor of two of observations equal to 95%. For large time intervals, an exponential correction term has been introduced in the model based on the experimental observations. The new model is capable of predicting all time intervals giving an overall factor of two of observations equal to 100%

Applications of Partial Supersymmetry

I examine quantum mechanical Hamiltonians with partial supersymmetry, and explore two main applications. First, I analyze a theory with a logarithmic spectrum, and show how to use partial supersymmetry to reveal the underlying structure of this theory. This method reveals an intriguing equivalence between two formulations of this theory, one of which is one-dimensional, and the other of which is infinite-dimensional. Second, I demonstrate the use of partial supersymmetry as a tool to obtain the asymptotic energy levels in non-relativistic quantum mechanics in an exceptionally easy way. In the end, I discuss possible extensions of this work, including the possible connections between partial supersymmetry and renormalization group arguments.Comment: 11 pages, harvmac, no figures; typo corrected in identifying info on title pag

Greybody factors in a rotating black-hole background-II : fermions and gauge bosons

We study the emission of fermion and gauge boson degrees of freedom on the brane by a rotating higher-dimensional black hole. Using matching techniques, for the near-horizon and far-field regime solutions, we solve analytically the corresponding field equations of motion. From this, we derive analytical results for the absorption probabilities and Hawking radiation emission rates, in the low-energy and low-rotation case, for both species of fields. We produce plots of these, comparing them to existing exact numerical results with very good agreement. We also study the total absorption cross-section and demonstrate that, as in the non-rotating case, it has a different behaviour for fermions and gauge bosons in the low-energy limit, while it follows a universal behaviour -- reaching a constant, spin-independent, asymptotic value -- in the high-energy regime.Comment: 22 pages, 8 figures, added reference

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

Shape Invariance in the Calogero and Calogero-Sutherland Models

We show that the Calogero and Calogero-Sutherland models possess an N-body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymmetric generalizations of these models, which are interesting both in their own right and for the insights they offer in connection with the exact solubility of these models.Comment: Latex file, 23 pages, no picture

A review of methods for addressing components of interventions in meta-analysis

Many healthcare interventions are complex, consisting of multiple, possibly interacting, components. Several methodological articles addressing complex interventions in the metaanalytical context have been published. We hereby provide an overview of methods used to evaluate the effects of complex interventions with meta-analytical models. We summarized the methodology, highlighted new developments, and described the benefits, drawbacks, and potential challenges of each identified method. We expect meta-analytical methods focusing on components of several multicomponent interventions to become increasingly popular due to recently developed, easy-to-use, software tools that can be used to conduct the relevant analyses. The different meta-analytical methods are illustrated through two examples comparing psychotherapies for panic disorder. Copyright