Fractional Generalization of Kac Integral

Generalization of the Kac integral and Kac method for paths measure based on the Levy distribution has been used to derive fractional diffusion equation. Application to nonlinear fractional Ginzburg-Landau equation is discussed.Comment: 16 pages, LaTe

Algebraic damping in the one-dimensional Vlasov equation

We investigate the asymptotic behavior of a perturbation around a spatially non homogeneous stable stationary state of a one-dimensional Vlasov equation. Under general hypotheses, after transient exponential Landau damping, a perturbation evolving according to the linearized Vlasov equation decays algebraically with the exponent -2 and a well defined frequency. The theoretical results are successfully tested against numerical $N$-body simulations, corresponding to the full Vlasov dynamics in the large $N$ limit, in the case of the Hamiltonian mean-field model. For this purpose, we use a weighted particles code, which allows us to reduce finite size fluctuations and to observe the asymptotic decay in the $N$-body simulations.Comment: 26 pages, 8 figures; text slightly modified, references added, typos correcte

Convergent Validity of a Single Question with Multiple Classification Options for Depression Screening in Medical Settings

The purpose of this study was to assess the convergent validity of a single depression question with multiple classification options for depression screening. Participants were 40 medical inpatients. The age range of our sample was 18 to 85 years (M = 56.15, SD = 17.66). A clinical interview and the BDI-II were administered. The correlation between patients’ self-rating classification of depression and their BDI-II classification was significant, rs(38) = .90, p < .01. Follow-up repeated-measures chi-square revealed a statistically significant association between BDI-II classification and patients’ self-rating classification, χ2(9, N = 40) = 47.79, p < .005. Significant positive standardized residuals revealed a clear linear relationship between BDI-II and patient self-rating classifications. Our data support the use of a single depression question with multiple classification options as a useful and valid means of quickly screening for the presence of depression by frontline health care professionals

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure

Coupled oscillators with power-law interaction and their fractional dynamics analogues

The one-dimensional chain of coupled oscillators with long-range power-law interaction is considered. The equation of motion in the infrared limit are mapped onto the continuum equation with the Riesz fractional derivative of order $\alpha$, when $0<\alpha<2$. The evolution of soliton-like and breather-like structures are obtained numerically and compared for both types of simulations: using the chain of oscillators and using the continuous medium equation with the fractional derivative.Comment: 16 pages, 5 figure

Patient-reported outcome measures for cancer caregivers: a systematic review

Purpose Informal caregivers provide invaluable help and support to people with cancer. As treatments extend survival and the potential burdens on carers increase, there is a need to assess the impact of the role. This systematic review identified instruments that measure the impact of caregiving, evaluated their psychometric performance specifically in cancer and appraised the content. Methods A 2-stage search strategy was employed to: 1. identify instruments that measure the impact of caregiving, 2. run individual searches on each measure to identify publications evaluating psychometric performance in the target population. Searches were conducted in Medline, Embase, CINAHL and Psychinfo and restricted to English for instrument used and article language. Psychometric performance was evaluated for content and construct validity, internal consistency, test-retest reliability, precision, responsiveness and acceptability. Individual scale items were extracted and systematically categorised into conceptual domains. Results 10 papers were included reporting on the psychometric properties of 8 measures. Although construct validity and internal consistency were most frequently evaluated, no study comprehensively evaluated all relevant properties. Few studies met our inclusion criteria so it was not possible to consider the psychometric performance of the measures across a group of studies. Content analysis resulted in 16 domains with 5 overarching themes: lifestyle disruption; wellbeing; health of the caregiver; managing the situation and relationships. Conclusions Few measures of caregiver impact have been subject to psychometric evaluation in cancer caregivers. Those that have do not capture well changes in roles and responsibilities within the family and career, indicating the need for a new instrument

Dynamics with Low-Level Fractionality

The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and field theory. For the fractional linear oscillator the physical meaning of the derivative of order $\alpha<2$ is dissipation. In systems with many spacially coupled elements (oscillators) the fractional derivative, along the space coordinate, corresponds to a long range interaction. We discuss a method of constructing a solution using an expansion in $\epsilon=n-\alpha$ with small $\epsilon$ and positive integer $n$. The method is applied to the fractional linear and nonlinear oscillators and to fractional Ginzburg-Landau or parabolic equations.Comment: LaTeX, 24 pages, to be published in Physica

Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches

Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are obtained by fractional variation of Lagrangian and Hamiltonian that have only integer derivatives.Comment: 21 pages, LaTe

Toward a first-principles integrated simulation of tokamak edge plasmas

Performance of the ITER is anticipated to be highly sensitive to the edge plasma condition. The edge pedestal in ITER needs to be predicted from an integrated simulation of the necessary first-principles, multi-scale physics codes. The mission of the SciDAC Fusion Simulation Project (FSP) Prototype Center for Plasma Edge Simulation (CPES) is to deliver such a code integration framework by (1) building new kinetic codes XGC0 and XGC1, which can simulate the edge pedestal buildup; (2) using and improving the existing MHD codes ELITE, M3D-OMP, M3D-MPP and NIMROD, for study of large-scale edge instabilities called Edge Localized Modes (ELMs); and (3) integrating the codes into a framework using cutting-edge computer science technology. Collaborative effort among physics, computer science, and applied mathematics within CPES has created the first working version of the End-to-end Framework for Fusion Integrated Simulation (EFFIS), which can be used to study the pedestal-ELM cycles