An approach to anomalous diffusion in the n-dimensional space generated by a self-similar Laplacian

We analyze a quasi-continuous linear chain with self-similar distribution of harmonic interparticle springs as recently introduced for one dimension (Michelitsch et al., Phys. Rev. E 80, 011135 (2009)). We define a continuum limit for one dimension and generalize it to $n=1,2,3,..$ dimensions of the physical space. Application of Hamilton's (variational) principle defines then a self-similar and as consequence non-local Laplacian operator for the $n$-dimensional space where we proof its ellipticity and its accordance (up to a strictly positive prefactor) with the fractional Laplacian $-(-\Delta)^\frac{\alpha}{2}$. By employing this Laplacian we establish a Fokker Planck diffusion equation: We show that this Laplacian generates spatially isotropic L\'evi stable distributions which correspond to L\'evi flights in $n$-dimensions. In the limit of large scaled times $\sim t/r^{\alpha} >>1$ the obtained distributions exhibit an algebraic decay $\sim t^{-\frac{n}{\alpha}} \rightarrow 0$ independent from the initial distribution and spacepoint. This universal scaling depends only on the ratio $n/\alpha$ of the dimension $n$ of the physical space and the L\'evi parameter $\alpha$.Comment: Submitted manuscrip

Generalized space-time fractional dynamics in networks and lattices

International audienceWe analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the time-fractional Poisson renewal process. This process introduces a non-Markovian walk with long-time memory effects and fat-tailed characteristics in the waiting time density. We analyze `generalized space-time fractional diffusion' in the infinite $\it d$-dimensional integer lattice $\it \mathbb{Z}^d$. We obtain in the diffusion limit a `macroscopic' space-time fractional diffusion equation. Classical CTRW models such as with Laskin's fractional Poisson process and standard Poisson process which occur as special cases are also analyzed. The developed generalized space-time fractional CTRW model contains a four-dimensional parameter space and offers therefore a great flexibility to describe real-world situations in complex systems

Analysis of the vibrational mode spectrum of a linear chain with spatially exponential properties

We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the continuous limiting case which represents an elastic I D exponentially graded material. The discrete model yields closed form expressions for the N x N Green's function for an arbitrary number N = 2,...,infinity of particles of the chain. Utilizing this Green's function yields an explicit expression for the vibrational mode density. Despite of its simplicity the model reflects some characteristics of the dynamics of a I D exponentially graded elastic material. As a special case the well-known expressions for the Green's function and oscillator density of the homogeneous linear chain are contained in the model. The width of the frequency band is determined by the grading parameter which characterizes the exponential spatial dependence of the properties. In the limiting case of large grading parameter, the frequency band is localized around a single finite frequency where the band width tends to zero inversely with the grading parameter. In the continuum limit the discrete Green's function recovers the Green's function of the continuous equation of motion which takes in the time domain the form of a Klein-Gordon equation. (C) 2008 Elsevier Ltd. All rights reserved

External audit of providers of the Cervical Cancer Prevention Programme in Poland in 2016/2017

Introduction. The Cervical Cancer (CC) Prevention Programme includes 3 phases: basic (Pap smear collection), diagnostic (Pap smear evaluation) and in-depth (colposcopy/biopsy in case of abnormal smear test findings). The Programme service providers are subject to an external audit and this publication’s objective is to analyse its results from 2016 and the first half of 2017. Materials and methods. The audit of the Programme performance in the period 01.01.2016–30.06.2017 was carried out by external auditors by way of personal visits to the offices of the service providers and by way of direct data retrieval. The audit covered 12% (198) of the basic phase, 100% (66) of the diagnostic phase and 100% (62) of the in-depth phase facilities. The Polish National Health Fund (NHF) did not make available the routinely collected data for the purpose of audit. Audit data collected in the developed protocols were analysed. Results. The number of Pap smears (2,028,988) and the number of colposcopies (13,636) outside the Programme was, respectively, more than two and three times higher than in the Programme (cytology — 801,640, colposcopy — 3929). The performance of the procedures (Programme vs outside the Programme) was highly variable depending on the provider. The percentage of Pap smears unsuitable for evaluation did not differ significantly between gynaecologists and midwives. All audited cytological laboratories carried out rescreening of samples. Biopsy was not performed in 11% (2016) and 15% (2017) of colposcopy laboratories. Inaccuracies were found in 19% (61) of the audit protocols. Discussion. Significantly higher number of procedures performed outside the Programme results from lower renu­meration of procedures within the Programme. Variable provider's preferences in the mode of procedures execution indicates that with the use of appropriate organisational solutions it would be possible to reduce opportunistic screening, which is of unknown quality. The quality of Pap smear sample collection in the case of gynaecologists and midwives is the same, but the number of primary care provider (PCP) facilities where midwives collect smears is very limited. The inaccuracies noted in the audit protocols indicate that the lack of access to data collected by the National Health Fund decreased the quality of the audit carried out and the reliability of the data obtained. Conclusions. Restoring full access to data collected by the NHF is crucial for the Programme audit quality. Measures should be implemented to reduce opportunistic screening and shift the stream of tests to the Programme (both at the basic and at the in-depth phase), and to increase the availability of tests in PCP facilities through training for midwives.

Sur une généralisation de l'opérateur fractionnaire

Les matériaux dont la microstructure est invariante par changement d'échelle est peu abordée par la mécanique, faute d'approches réellement satisfaisantes. On propose ici une approche à partir des « fonctions auto-similaires » (Michelitsch, Maugin et al. PRE 80, 011135, 2009) en introduisant la notion de « dérivée généralisée ».On définit la « dérivée généralisée » résultant d'un processus (h vers 0) d'une fonction opérateur A(T(h)-1)/A(h) appliquée à f(x) avec l'opérateur de translation T(h) (T(h)f(x)=f(x+h)). Quelques exemples dynamiques en mécanique des matériaux seront discutés

Modified shear stress transport model with curvature correction for the prediction of swirling flow in a cyclone separator

The paper investigates the confined swirling flow in a cyclone. The numerical simulations are performed using a proposed eddy viscosity turbulence model, which accounts for the effects of the streamline curvature and rotation. This distinguishes the current model from the conventional Eddy Viscosity Models (EVMs) that are known to fail to predict the Rankine vortex in swirling flows. Although computationally more expensive approaches, the Reynolds Stress Model (RSM) and Large Eddy Simulation (LES), have demonstrated a high capability of dealing with such flows, these techniques are often unsuited for use in complex design studies where computational speed and robustness are key factors. In the present approach, the Shear Stress Transport with Curvature Correction (SSTCC) turbulence model is modified by the introduction of the Richardson number to account for the rotation and curvature effects. The numerical predictions were validated using experimental results and also compared to the data obtained using the RSM model and various EVMs without the proposed modifications. The investigations started with a benchmark case of a flow through a channel duct with a U-turn, after which more challenging simulations of a high swirling flow within a cyclone separator device were performed. The results show that the proposed model is competitive in terms of accuracy when compared to RSM and proves to be superior to the RSM model in terms of computational cost. Furthermore, it is found that the proposed model preserves the ability to represent the Rankine vortex profile at different longitudinal levels of the cyclone. It is also more efficient in terms of the computational cost than the SSTCC model without the introduced modifications

Grand unified theory constrained supersymmetry and neutrinoless double beta decay

We analyze the contributions to the neutrinoless double $\beta$ decay ($0\nu\beta\beta$-decay) coming from the Grand Unified Theory (GUT) constrained Minimal Supersymmetric Standard Model (MSSM) with trilinear R-parity breaking. We discuss the importance of two-nucleon and pion-exchange realizations of the quark-level $0\nu\beta\beta$-decay transitions. In this context, the questions of reliability of the calculated relevant nuclear matrix elements within the Renormalized Quasiparticle Random Phase Approximation (pn-RQRPA) for several medium and heavy open-shell nuclei are addressed. The importance of gluino and neutralino contributions to $0\nu\beta\beta$-decay is also analyzed. We review the present experiments and deduce limits on the trilinear R-parity breaking parameter $\lambda_{111}'$ from the non-observability of $0\nu\beta\beta$-decay for different GUT constrained SUSY scenarios. In addition, a detailed study of limits on the MSSM parameter space coming from the $B \to X_s \gamma$ processes by using the recent CLEO and OPAL results is performed. Some studies in respect to the future $0\nu\beta\beta$-decay project GENIUS are also presented.Comment: 29 pages, 8 figure