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

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

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

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

Fractional dynamics of systems with long-range interaction

We consider one-dimensional chain of coupled linear and nonlinear oscillators with long-range power wise interaction defined by a term proportional to 1/|n-m|^{\alpha+1}. Continuous medium equation for this system can be obtained in the so-called infrared limit when the wave number tends to zero. We construct a transform operator that maps the system of large number of ordinary differential equations of motion of the particles into a partial differential equation with the Riesz fractional derivative of order \alpha, when 0<\alpha<2. Few models of coupled oscillators are considered and their synchronized states and localized structures are discussed in details. Particularly, we discuss some solutions of time-dependent fractional Ginzburg-Landau (or nonlinear Schrodinger) equation.Comment: arXiv admin note: substantial overlap with arXiv:nlin/051201

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

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

Small BGK waves and nonlinear Landau damping

Consider 1D Vlasov-poisson system with a fixed ion background and periodic condition on the space variable. First, we show that for general homogeneous equilibria, within any small neighborhood in the Sobolev space W^{s,p} (p>1,s<1+(1/p)) of the steady distribution function, there exist nontrivial travelling wave solutions (BGK waves) with arbitrary minimal period and traveling speed. This implies that nonlinear Landau damping is not true in W^{s,p}(s<1+(1/p)) space for any homogeneous equilibria and any spatial period. Indeed, in W^{s,p} (s<1+(1/p)) neighborhood of any homogeneous state, the long time dynamics is very rich, including travelling BGK waves, unstable homogeneous states and their possible invariant manifolds. Second, it is shown that for homogeneous equilibria satisfying Penrose's linear stability condition, there exist no nontrivial travelling BGK waves and unstable homogeneous states in some W^{s,p} (p>1,s>1+(1/p)) neighborhood. Furthermore, when p=2,we prove that there exist no nontrivial invariant structures in the H^{s} (s>(3/2)) neighborhood of stable homogeneous states. These results suggest the long time dynamics in the W^{s,p} (s>1+(1/p)) and particularly, in the H^{s} (s>(3/2)) neighborhoods of a stable homogeneous state might be relatively simple. We also demonstrate that linear damping holds for initial perturbations in very rough spaces, for linearly stable homogeneous state. This suggests that the contrasting dynamics in W^{s,p} spaces with the critical power s=1+(1/p) is a trully nonlinear phenomena which can not be traced back to the linear level

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

Interacting with eHealth - Towards grand challenges for HCI

While health records are increasingly stored electronically, we, as citizens, have little access to this data about ourselves. We are not used to thinking of these official records either as ours or as useful to us. We increasingly turn to the Web, however, to query any ache, pain or health goal we may have before consulting with health care professionals. Likewise, for proactive health care such as nutrition or fitness, or to find fellow-sufferers for post diagnosis support, we turn to online resources. There is a potential disconnect between points at which professional and lay eHealth data and resources intersect for preventative or proactive health care. Such gaps in information sharing may have direct impact on practices we decide to take up, the care we seek, or the support professionals offer. In this panel, we consider several places within proactive, preventative health care in particular HCI has a role towards enhancing health knowledge discovery and health support interaction. Our goal is to demonstrate how now is the time for eHealth to come to the forefront of the HCI research agenda