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

Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure

Road traffic injuries in the province of Grosseto

Introduction. Road traffic injuries constitute a major public health issue. The Province of Grosseto is one of the territories most affected in the Region of Tuscany. The objective of the study, part of the Road Safety Provincial Council?s project, is to describe the epidemiology of the road accidents in order to contribute to the reduction of the burden of deaths and injuries. Methods. The data relative to road accidents occurring in the Province were drawn from the various sources available: Death Certificates (1991-2005), Police Reports (1991-2003), Hospital Discharge Records (1996-2005), Emergency Room visits (2004-2005). Results. On average, each year road accidents cause 30 deaths, at least 530 hospitalizations, and approximately 3,300 Emergency Room visits. The standardized mortality rate (2003-2005, males: 20.6; females: 6.0), the mortality ratio (2003: 34.6 deaths for every 1,000 accidents), and the severity ratio (2003: 1,432 injured for every 1,000 accidents) are higher than regional figures. Discussion. The greater relative number of fatalities, casualties and crashes can be explained by various physical and social environmental factors such as vast flatland, few greater urban settlements, deprived area. The territory specifically demonstrates an accentuated seasonality in August, a month in which a peak in both the number of accidents and their severity is reported, brought about by the intense volume of commuter and transit traffic, and highlighted by the fact that in that same month approximately half of Emergency Room visits concern non-residents. Conclusion. The complexity of the issue, the number of determinant factors involved, and the disproportionately greater impact on the more disadvantaged and vulnerable segments of society require the development of inter-sectoral strategies and the sharing of responsibility among individuals, groups and communities

Integrated modeling and validation for phase change with natural convection

Water-ice systems undergoing melting develop complex spatio-temporal interface dynamics and a non-trivial temperature field. In this contribution, we present computational aspects of a recently conducted validation study that aims at investigating the role of natural convection for cryo-interface dynamics of water-ice. We will present a fixed grid model known as the enthalpy porosity method. It is based on introducing a phase field and employs mixture theory. The resulting PDEs are solved using a finite volume discretization. The second part is devoted to experiments that have been conducted for model validation. The evolving water-ice interface is tracked based on optical images that shows both the water and the ice phase. To segment the phases, we use a binary Mumford Shah method, which yields a piece-wise constant approximation of the imaging data. Its jump set is the reconstruction of the measured phase interface. Our combined simulation and segmentation effort finally enables us to compare the modeled and measured phase interfaces continuously. We conclude with a discussion of our findings

Meningococcal C conjugate vaccine effectiveness before and during an outbreak of invasive meningococcal disease due to Neisseria meningitidis serogroup C/cc11, Tuscany, Italy

Introduction: In Tuscany, Italy, where a universal immunization program with monovalent meningococcal C conjugate vaccine (MCC) was introduced in 2005, an outbreak of invasive meningococcal disease (IMD) due to the hypervirulent strain of Neisseria meningitidis C/cc11 occurred in 2015–2016, leading to an immunization reactive campaign using either the tetravalent (ACWY) meningococcal conjugate or the MCC vaccine. During the outbreak, IMD serogroup C (MenC) cases were also reported among vaccinated individuals. This study aimed to characterize meningococcal C conjugate vaccines (MenC-vaccines) failures and to estimate their effectiveness since the introduction (2005–2016) and during the outbreak (2015–2016). Methods: MenC cases and related vaccine-failures were drawn from the National Surveillance System of Invasive Bacterial Disease (IBD) for the period 2006–2016. A retrospective cohort-study, including the Tuscany' population of the birth-cohorts 1994–2014, was carried out. Based on annual reports of vaccination, person-years of MenC-vaccines exposed and unexposed individuals were calculated by calendar-year, birth-cohort, and local health unit. Adjusted (by birth-cohort, local health unit, and calendar-year) risk-ratios (ARR) of MenC invasive disease for vaccinated vs unvaccinated were estimated by the Poisson model. Vaccine-effectiveness (VE) was estimated as: VE = 1-ARR. Results: In the period 2006–2016, 85 MenC-invasive disease cases were reported; 61 (71.8%) from 2015 to 2016. Twelve vaccine failures occurred, all of them during the outbreak. The time-interval from immunization to IMD onset was 20 days in one case, from 9 months to 3 years in six cases, and ≥7 years in five cases. VE was, 100% (95%CI not estimable, p = 0.03) before the outbreak (2006–2014) and 77% (95%CI 36–92, p < 0.01) during the outbreak; VE was 80% (95%CI 54–92, p < 0.01) during the overall period. Conclusions: In Tuscany, MenC-vaccine failures occurred exclusively during the 2015–2016 outbreak. Most of them occurred several years after vaccination. VE during the outbreak-period was rather high supporting an effective protection induced by MenC-vaccines

A combined nonlinear and nonlocal model for topographic evolution in channelized depositional systems

Models for the overall topographic evolution of erosional and depositional systems can be grouped into two broad classes. The first class is local models in which the sediment flux at a point is expressed as a linear or nonlinear function of local hydrogeomorphic measures (e.g., water discharge and slope). The second class is nonlocal models, where the sediment flux at a point is expressed via a weighted average (i.e., convolution integral) of measures upstream and/or downstream of the point of interest. Until now, the nonlinear and nonlocal models have been developed independently. In this study, we develop a unified model for large-scale morphological evolution that combines both nonlinear and nonlocal approaches. With this model, we show that in a depositional system, under piston-style subsidence, the topographic signatures of nonlinearity and nonlocality are identical and that in combination, their influence is additive. Furthermore, unlike either nonlinear or nonlocal models alone, the combined model fits observed fluvial profiles with parameter values that are consistent with theory and independent observations. By contrast, under conditions of steady bypass, the nonlocal and nonlinear components in the combined model have distinctly different signatures. In the absence of nonlocality, a purely nonlinear model always predicts a bypass fluvial profile with a spatially constant slope, while a nonlocal model produces a nonconstant slope, i.e., profile curvature. This result can be used as a test for inferring the presence of nonlocality and for untangling the relative roles of local and nonlocal mechanisms in shaping depositional morphology

Analysis of pre-seismic ionospheric disturbances prior to 2020 2 Croatian earthquakes

Abstract: We study the sub-ionospheric VLF transmitter signals recorded by the Austrian Graz station in the year 2020. Those radio signals are known to propagate in the Earth-ionosphere waveguide between the ground and lower ionosphere. The Austrian Graz facility (geographic coordinates: 15.46◦E, 47.03◦N) can receive such sub-ionospheric transmitter signals, particularly those propagating above earthquake (EQ) regions in the southern part of Europe. We consider in this work the transmitter amplitude variations recorded a few weeks before the occurrence of two EQs in Croatia at a distance less than 200 km from Graz VLF facility. The selected EQs happened on 22 March 2020 and 29 December 2020, with magnitudes of Mw5.4 and Mw6.4, respectively, epicenters localized close to Zagreb (16.02◦E, 45.87◦N; 16.21◦E, 45.42◦N), and with focuses of depth smaller than 10 km. In our study we emphasize the anomaly fluctuations before/after the sunrise times, sunset times, and the cross-correlation of transmitter signals. We attempt to evaluate and to estimate the latitudinal and the longitudinal expansions of the ionospheric disturbances related to the seismic preparation areas