Modeling anomalous heat diffusion: Comparing fractional derivative and non-linear diffusivity treatments

In the Fourier heat conduction equation, when the flux definition is expressed as the product of a constant diffusivity and the temperature gradient, the characteristic length scale evolves as the square root of time. However, if we replace the 1 st order transient and gradient terms in the Fourier equation with fractional derivatives and/or define a non-linear spatially dependent diffusivity, it is possible to generate an anomalous space-time scaling, i.e., a scaling where the time exponent differs from the expected value of 1/2 . To compare and contrast the possible consequences of using fractional calculus along with a non-linear flux, we investigate a space-time fractional heat diffusion equation that involves a non-linear diffusivity. Following presentation of the governing non-linear fractional equation, we arrive at a space-time scaling that accounts for the combined anomalous contributions of memory (fractional derivative in time), non-locality (fractional derivative in space), and a non-linear diffusivity. We demonstrate how this scaling can manifest in a physical setting by considering the analytical solution of a non-linear fractional space-time diffusion equation, a limit case Stefan problem related to moisture infiltration into a porous media. A direct physically realizable simulation of this process shows how the anomalous space-time scaling is explicitly related to measures of both the memory and non-linearity in the system. Overall, the findings from this work clearly show how the definition of a non-linear diffusivity might contribute to anomalous diffusion behavior and suggests that, in modeling a particular observation, the roles of fractional derivatives and a suitably defined non-linear diffusivity are interchangeable.SEV-2013-0323 BERC.2014–201

A generalized Stefan model accounting for system memory and non-locality

The Stefan problem, involving the tracking of an evolving phase-change front, is the prototypical example of a moving boundary problem. In basic one- dimensional problems it is well known that the front advances as the square root of time. When memory or non-locality are introduced into the system however, this classic signal may be anomalous; replaced by a power-law advance with a time exponent that differs from n = 1/2. Up to now memory treatments in Stefan problem models have only been able to reproduce sub-diffusive front movements with exponents n 1/2. In the present paper, using a generalized Caputo fractional derivative operator, we introduce new memory and non-local treatment for Stefan problems. On considering a limit case Stefan problem, related to the melting problem, we are able to show that, this gen- eral treatment can not only produce arbitrary power-law in time predictions for the front movement but, in the case of memory treatments, can also produce non-power-law anomalous behaviors. Further, also in the context of the limit problem, we are able to establish an equivalence between non-locality and a space varying conductivity and memory and a time varying conductivity

Sustained improvement of a girl affected with Devic's disease over 2 years of mycophenolate mofetil treatment

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Bone mass and quality in patients with juvenile idiopathic arthritis: longitudinal evaluation of bone mass determinants using dual energy X-ray absorptiometry, peripheral quantitative computed tomography, and quantitative ultrasonography.

INTRODUCTION: Our objective was to evaluate longitudinally the main bone-mass and quality predictors in young juvenile idiopathic arthritis (JIA) patients by using lumbar spine dual-energy X-ray absorptiometry (DXA) scan, radius peripheral quantitative computed tomography (pQCT), and phalangeal quantitative ultrasonography (QUS) at the same time. METHODS: In total, 245 patients (172 females, 73 males; median age, 15.6 years: 148 oligoarticular, 55 polyarticular, 20 systemic, and 22 enthesitis-related-arthritis (ERA) onset) entered the study. Of these, 166 patients were evaluated longitudinally. Data were compared with two age- and sex-matched control groups. RESULTS: In comparison with controls, JIA patients, but not with ERA, had a reduced spine bone-mineral apparent density (BMAD) standard deviation score (P < 0.001) and musculoskeletal deficits, with significantly lower levels of trabecular bone mineral density (TrabBMD) (P < 0.0001), muscle cross-sectional area (CSA) (P < 0.005), and density-weighted polar section modulus (SSIp) (P < 0.05). In contrast, JIA showed fat CSA significantly higher than controls (P < 0.0001). Finally, JIA patients had a significant reduced amplitude-dependent speed of sound (AD-SoS) (P < 0.001), and QUS z score (P < 0.005). Longitudinally, we did not find any difference in all JIA patients in comparison with baseline, except for the SSIp value that normalized. Analyzing the treatments, a significant negative correlation among spine BMAD values, TrabBMD, AD-SoS, and systemic and/or intraarticular corticosteroids, and a positive correlation among TNF-α-blocking agents and spine BMAD, TrabBMD, and AD-SoS were observed. CONCLUSIONS: JIA patients have a low bone mass that, after a first increase due to the therapy, does not reach the normal condition over time. The pronounced bone deficits in JIA are greater than would be expected because of reduction in muscle cross-sectional area. Thus, bone alterations in JIA likely represent a mixed defect of bone accrual and lower muscle forces

GIANO-TNG spectroscopy of red supergiants in the young star cluster RSGC2

The inner disk of the Galaxy has a number of young star clusters dominated by red supergiants that are heavily obscured by dust extinction and observable only at infrared wavelengths. These clusters are important tracers of the recent star formation and chemical enrichment history in the inner Galaxy. During the technical commissioning and as a first science verification of the GIANO spectrograph at the Telescopio Nazionale Galileo, we secured high-resolution (R~50,000) near-infrared spectra of three red supergiants in the young Scutum cluster RSGC2. Taking advantage of the full YJHK spectral coverage of GIANO in a single exposure, we were able to identify several tens of atomic and molecular lines suitable for chemical abundance determinations. By means of spectral synthesis and line equivalent width measurements, we obtained abundances of Fe and other iron-peak elements such as V, Cr, Ni, of alpha (O, Mg, Si, Ca and Ti) and other light elements (C, N, Na, Al, K, Sc), and of some s-process elements (Y, Sr). We found iron abundances between half and one third solar and solar-scaled [X/Fe] abundance patterns of iron-peak, alpha and most of the light elements, consistent with a thin-disk chemistry. We found a depletion of [C/Fe] and enhancement of [N/Fe], consistent with CN burning, and low 12C/13C abundance ratios (between 9 and 11), requiring extra-mixing processes in the stellar interiors during the post-main sequence evolution. Finally, we found a slight [Sr/Fe] enhancement and a slight [Y/Fe] depletion (by a factor of <=2), with respect to solar.Comment: Paper accepted on A&

GIANO-TNG spectroscopy of red supergiants in the young star cluster RSGC3

The Scutum complex in the inner disk of the Galaxy has a number of young star clusters dominated by red supergiants that are heavily obscured by dust extinction and observable only at infrared wavelengths. These clusters are important tracers of the recent star formation and chemical enrichment history in the inner Galaxy. During the technical commissioning and as a first science verification of the GIANO spectrograph at the Telescopio Nazionale Galileo, we secured high-resolution (R=50,000) near-infrared spectra of five red supergiants in the young Scutum cluster RSGC3. Taking advantage of the full YJHK spectral coverage of GIANO in a single exposure, we were able to measure several tens of atomic and molecular lines that were suitable for determining chemical abundances. By means of spectral synthesis and line equivalent width measurements, we obtained abundances of Fe and iron-peak elements such as Ni, Cr, and Cu, alpha (O, Mg, Si, Ca, Ti), other light elements (C, N, F, Na, Al, and Sc), and some s-process elements (Y, Sr). We found average half-solar iron abundances and solar-scaled [X/Fe] abundance patterns for most of the elements, consistent with a thin-disk chemistry. We found depletion of [C/Fe] and enhancement of [N/Fe], consistent with standard CN burning, and low 12C/13C abundance ratios (between 9 and 11), which require extra-mixing processes in the stellar interiors during the post-main sequence evolution. We also found local standard of rest V(LSR)=106 km/s and heliocentric V(HEL)=90 km/s radial velocities with a dispersion of 2.3 km/s. The inferred radial velocities, abundances, and abundance patterns of RSGC3 are very similar to those previously measured in the other two young clusters of the Scutum complex, RSGC1 and RSGC2, suggesting a common kinematics and chemistry within the Scutum complex