Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod

We study waves in a rod of finite length with a viscoelastic constitutive equation of fractional distributed-order type for the special choice of weight functions. Prescribing boundary conditions on displacement, we obtain case corresponding to stress relaxation. In solving system of differential and integro-differential equations we use the Laplace transformation in the time domain

Spatially fractional-order viscoelasticity, non-locality and a new kind of anisotropy

Spatial non-locality of space-fractional viscoelastic equations of motion is studied. Relaxation effects are accounted for by replacing second-order time derivatives by lower-order fractional derivatives and their generalizations. It is shown that space-fractional equations of motion of an order strictly less than 2 allow for a new kind anisotropy, associated with angular dependence of non-local interactions between stress and strain at different material points. Constitutive equations of such viscoelastic media are determined. Explicit fundamental solutions of the Cauchy problem are constructed for some cases isotropic and anisotropic non-locality

The periodic repolarization dynamics index identifies changes in ventricular repolarization oscillations associated with music-induced emotions

The effect of music on cardiovascular dynamics may be useful in a variety of clinical settings. The aim of this study was to assess whether listening to music characterized by different emotional valence affected ventricular periodic repolarization dynamics (PRD), a recently-proposed non-invasive index of sympathetic ventricular modulation. The 12 lead ECG was recorded in 71 healthy volunteers exposed to six 90 s excerpts of pleasant music and unpleasant acoustic stimuli as well as six 90 s intervals of silence. A 20 s interval was allowed between excerpts during which the participants were asked to evaluate the previous excerpt. A simulation study was carried out to assess the capability of the algorithm of tracking fast small changes in PRD. The simulation study shows that the algorithm implemented in this study has a time-frequency resolution sufficient to capture the fast dynamics observed in this study. PRD were higher during listening to both pleasant and unpleasant music than during silence. There was a (weak) trend for the PRD to be higher during listening to pleasant than unpleasant music that may indicate the existence of a (weak) interaction between the valence of music-induced emotions and sympathetic ventricular response. The PRD significantly increased during the 20 s interval in between conditions, possibly reflecting a sympathetic response to the evaluation task and/or to the expectation of the following excerpt

Truncation effects in superdiffusive front propagation with L\'evy flights

A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a $\lambda$-truncated fractional derivative of order $\alpha$ where $1/\lambda$ is the characteristic truncation length scale. For $\lambda=0$ there is no truncation and fronts exhibit exponential acceleration and algebraic decaying tails. It is shown that for $\lambda \neq 0$ this phenomenology prevails in the intermediate asymptotic regime $(\chi t)^{1/\alpha} \ll x \ll 1/\lambda$ where $\chi$ is the diffusion constant. Outside the intermediate asymptotic regime, i.e. for $x > 1/\lambda$, the tail of the front exhibits the tempered decay $\phi \sim e^{-\lambda x}/x^{(1+\alpha)}$, the acceleration is transient, and the front velocity, $v_L$, approaches the terminal speed $v_* = (\gamma - \lambda^\alpha \chi)/\lambda$ as $t\to \infty$, where it is assumed that $\gamma > \lambda^\alpha \chi$ with $\gamma$ denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, $v_L \sim v_* - \alpha /(\lambda t)$, which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An over-truncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, $1/\nu$, is also identified. In this extreme regime, fronts exhibit exponential tails, $\phi \sim e^{-\nu x}$, and move at the constant velocity, $v=(\gamma - \lambda^\alpha \chi)/\nu$.Comment: Accepted for publication in Phys. Rev. E (Feb. 2009

Finite Larmor radius effects on non-diffusive tracer transport in a zonal flow

Finite Larmor radius (FLR) effects on non-diffusive transport in a prototypical zonal flow with drift waves are studied in the context of a simplified chaotic transport model. The model consists of a superposition of drift waves of the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. High frequency FLR effects are incorporated by gyroaveraging the ExB velocity. Transport in the direction of the density gradient is negligible and we therefore focus on transport parallel to the zonal flows. A prescribed asymmetry produces strongly asymmetric non- Gaussian PDFs of particle displacements, with L\'evy flights in one direction but not the other. For zero Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. However, FLR effects seem to eliminate this transition. The PDFs of trapping and flight events show clear evidence of algebraic scaling with decay exponents depending on the value of the Larmor radii. The shape and spatio-temporal self-similar anomalous scaling of the PDFs of particle displacements are reproduced accurately with a neutral, asymmetric effective fractional diffusion model.Comment: 14 pages, 13 figures, submitted to Physics of Plasma

Diffusion in multiscale spacetimes

We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples and the most general spectral-dimension profile of multifractional spaces is constructed.Comment: 23 pages, 5 figures. v2: discussion improved, typos corrected, references adde

Quality of Life and psychopathology in adults who underwent Hematopoietic Stem Cell Transplantation (HSCT) in childhood: a qualitative and quantitative analysis.

Background: Patients who undergo pediatric Hematopoietic Stem Cell Transplantation (HSCT) may experience long-term psychological sequelae and poor Quality of Life (QoL) in adulthood. This study aimed to investigate subjective illness experience, QoL, and psychopathology in young adults who have survived pediatric HSCT. Method: The study involved patients treated with HSCT in the Hematology-Oncology Department between 1984 and 2007. Psychopathology and QoL were investigated using the SCL-90-R and SF-36. Socio-demographic and medical information was also collected. Finally, participants were asked to write a brief composition about their experiences of illness and care. Qualitative analysis of the texts was performed using T-LAB, an instrument for text analysis that allows the user to highlight the occurrences and co-occurrences of lemma. Quantitative analyses were performed using non-parametric tests (Spearman correlations, Kruskal-Wallis and Mann-Whitney tests). Results: Twenty-one patients (9 males) participated in the study. No significant distress was found on the SCL-90 Global Severity Index, but it was found on specific scales. On the SF-36, lower scores were reported on scales referring to bodily pain, general health, and physical and social functioning. All the measures were significantly (p < 0.05) associated with specific socio-demographic and medical variables (gender, type of pathology, type of HSCT, time elapsed between communication of the need to transplant and effective transplantation, and days of hospitalization). With regard to the narrative analyses, males focused on expressions related to the body and medical therapies, while females focused on people they met during treatment, family members, and donors. Low general health and treatment with autologous HSCT were associated with memories about chemotherapy, radiotherapy, and the body parts involved, while high general health was associated with expressions focused on gratitude (V-Test \ub1 1.96). Conclusion: Pediatric HSCT survivors are more likely to experience psychological distress and low QoL in adulthood compared with the general population. These aspects, along with survivors' subjective illness experience, show differences according to specific medical and socio-demographic variables. Studies are needed in order to improve the care and long-term follow-up of these families

Levi-Civita cylinders with fractional angular deficit

The angular deficit factor in the Levi-Civita vacuum metric has been parametrized using a Riemann-Liouville fractional integral. This introduces a new parameter into the general relativistic cylinder description, the fractional index {\alpha}. When the fractional index is continued into the negative {\alpha} region, new behavior is found in the Gott-Hiscock cylinder and in an Israel shell.Comment: 5 figure

The weakly coupled fractional one-dimensional Schr\"{o}dinger operator with index 1<α≤2\bf 1<\alpha \leq 2

We study fundamental properties of the fractional, one-dimensional Weyl operator $\hat{\mathcal{P}}^{\alpha}$ densely defined on the Hilbert space $\mathcal{H}=L^2({\mathbb R},dx)$ and determine the asymptotic behaviour of both the free Green's function and its variation with respect to energy for bound states. In the sequel we specify the Birman-Schwinger representation for the Schr\"{o}dinger operator $K_{\alpha}\hat{\mathcal{P}}^{\alpha}-g|\hat{V}|$ and extract the finite-rank portion which is essential for the asymptotic expansion of the ground state. Finally, we determine necessary and sufficient conditions for there to be a bound state for small coupling constant $g$.Comment: 16 pages, 1 figur

Lebesgue regularity for differential difference equations with fractional damping

We provide necessary and sufficient conditions for the existence and unique-ness of solutions belonging to the vector-valued space of sequences �(Z, X) forequations that can be modeled in the formΔu(n)+Δu(n)=Au(n)+G(u)(n)+ (n), n ∈ Z,,>0,≥0,where X is a Banach space, ∈ �(Z, X), A is a closed linear operatorwith domain D(A) defined on X,andG is a nonlinear function. The oper-ator Δdenotes the fractional difference operator of order >0inthesense of Grünwald-Letnikov. Our class of models includes the discrete timeKlein-Gordon, telegraph, and Basset equations, among other differential differ-ence equations of interest. We prove a simple criterion that shows the existenceof solutions assuming that f is small and that G is a nonlinear term