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

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

Solving two-phase freezing Stefan problems: Stability and monotonicity

[EN] The two-phase Stefan problems with phase formation and depletion are special cases ofmoving boundary problemswith interest in science and industry. In this work, we study a solidification problem, introducing a front-fixing transformation. The resulting non-linear partial differential system involves singularities, both at the beginning of the freezing process and when the depletion is complete, that are treated with special attention in the numerical modelling. The problem is decomposed in three stages, in which implicit and explicit finite difference schemes are used. Numerical analysis reveals qualitative properties of the numerical solution spatial monotonicity of both solid and liquid temperatures and the evolution of the solidification front. Numerical experiments illustrate the behaviour of the temperatures profiles with time, as well as the dynamics of the solidification front.Ministerio de Ciencia, Innovacion y Universidades, Grant/Award Number: MTM2017-89664-P.Piqueras, MA.; Company Rossi, R.; Jódar Sánchez, LA. (2020). Solving two-phase freezing Stefan problems: Stability and monotonicity. Mathematical Methods in the Applied Sciences. 43(14):7948-7960. https://doi.org/10.1002/mma.5787S794879604314Schmidt, A. (1996). Computation of Three Dimensional Dendrites with Finite Elements. Journal of Computational Physics, 125(2), 293-312. doi:10.1006/jcph.1996.0095Singh, S., & Bhargava, R. (2014). Simulation of Phase Transition During Cryosurgical Treatment of a Tumor Tissue Loaded With Nanoparticles Using Meshfree Approach. Journal of Heat Transfer, 136(12). doi:10.1115/1.4028730Company, R., Egorova, V. N., & Jódar, L. (2014). Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing. Abstract and Applied Analysis, 2014, 1-9. doi:10.1155/2014/146745Griewank, P. J., & Notz, D. (2013). Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage. Journal of Geophysical Research: Oceans, 118(7), 3370-3386. doi:10.1002/jgrc.20247Javierre, E., Vuik, C., Vermolen, F. J., & van der Zwaag, S. (2006). A comparison of numerical models for one-dimensional Stefan problems. Journal of Computational and Applied Mathematics, 192(2), 445-459. doi:10.1016/j.cam.2005.04.062Briozzo, A. C., Natale, M. F., & Tarzia, D. A. (2007). Explicit solutions for a two-phase unidimensional Lamé–Clapeyron–Stefan problem with source terms in both phases. Journal of Mathematical Analysis and Applications, 329(1), 145-162. doi:10.1016/j.jmaa.2006.05.083Caldwell, J., & Chan, C.-C. (2000). Spherical solidification by the enthalpy method and the heat balance integral method. Applied Mathematical Modelling, 24(1), 45-53. doi:10.1016/s0307-904x(99)00031-1Chantasiriwan, S., Johansson, B. T., & Lesnic, D. (2009). The method of fundamental solutions for free surface Stefan problems. Engineering Analysis with Boundary Elements, 33(4), 529-538. doi:10.1016/j.enganabound.2008.08.010Hon, Y. C., & Li, M. (2008). A computational method for inverse free boundary determination problem. International Journal for Numerical Methods in Engineering, 73(9), 1291-1309. doi:10.1002/nme.2122RIZWAN-UDDIN. (1999). A Nodal Method for Phase Change Moving Boundary Problems. International Journal of Computational Fluid Dynamics, 11(3-4), 211-221. doi:10.1080/10618569908940875Caldwell, J., & Kwan, Y. Y. (2003). On the perturbation method for the Stefan problem with time-dependent boundary conditions. International Journal of Heat and Mass Transfer, 46(8), 1497-1501. doi:10.1016/s0017-9310(02)00415-5Stephan, K., & Holzknecht, B. (1976). Die asymptotischen lösungen für vorgänge des erstarrens. International Journal of Heat and Mass Transfer, 19(6), 597-602. doi:10.1016/0017-9310(76)90042-9Savović, S., & Caldwell, J. (2003). Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions. International Journal of Heat and Mass Transfer, 46(15), 2911-2916. doi:10.1016/s0017-9310(03)00050-4Kutluay, S., Bahadir, A. R., & Özdeş, A. (1997). The numerical solution of one-phase classical Stefan problem. Journal of Computational and Applied Mathematics, 81(1), 135-144. doi:10.1016/s0377-0427(97)00034-4Asaithambi, N. S. (1997). A variable time step Galerkin method for a one-dimensional Stefan problem. Applied Mathematics and Computation, 81(2-3), 189-200. doi:10.1016/0096-3003(95)00329-0Landau, H. G. (1950). Heat conduction in a melting solid. Quarterly of Applied Mathematics, 8(1), 81-94. doi:10.1090/qam/33441Churchill, S. W., & Gupta, J. P. (1977). Approximations for conduction with freezing or melting. International Journal of Heat and Mass Transfer, 20(11), 1251-1253. doi:10.1016/0017-9310(77)90134-xKutluay, S., & Esen, A. (2004). An isotherm migration formulation for one-phase Stefan problem with a time dependent Neumann condition. Applied Mathematics and Computation, 150(1), 59-67. doi:10.1016/s0096-3003(03)00197-8Esen, A., & Kutluay, S. (2004). A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method. Applied Mathematics and Computation, 148(2), 321-329. doi:10.1016/s0096-3003(02)00846-9Mitchell, S. L., & Vynnycky, M. (2016). On the accurate numerical solution of a two-phase Stefan problem with phase formation and depletion. Journal of Computational and Applied Mathematics, 300, 259-274. doi:10.1016/j.cam.2015.12.021Meek, P. C., & Norbury, J. (1984). Nonlinear Moving Boundary Problems and a Keller Box Scheme. SIAM Journal on Numerical Analysis, 21(5), 883-893. doi:10.1137/0721057Tarzia, D. (2017). Relationship between Neumann solutions for two-phase Lamé-Clapeyron-Stefan problems with convective and temperature boundary conditions. Thermal Science, 21(1 Part A), 187-197. doi:10.2298/tsci140607003tPlemmons, R. J. (1977). M-matrix characterizations.I—nonsingular M-matrices. Linear Algebra and its Applications, 18(2), 175-188. doi:10.1016/0024-3795(77)90073-8Axelsson, O. (1994). Iterative Solution Methods. doi:10.1017/cbo978051162410

Evaluation of the accuracy of surgical reconstruction of mandibular defects when using navigation templates and patient-specific titanium implants

The management of patients with post-traumatic and post-operative mandibular defects is a major challenge even for experienced surgeons. Performing traditional reconstructive interventions with the use of bone autografts is always confronted with the problem of inconsistency between the shape, architecture, a biological. An alternative to conventional bone grafting is the use of digital protocol and CAD /CAMtechnology, which allows fabricating different types of customised medical devices. All patients underwent reconstructive and restoring interventions with the use of patient-specific titanium implants guided by a full digital protocol.Patients were examined in compliance with the standard scheme. To repair the defects, PSIs were fabricated with the use of selective laser sintering of titanium.The introduction of digital technologies and computer technique of diagnosing, planning and implementation of surgical interventions has been the main direction aimed at the improving the accuracy and predictability of reconstructive restorative surgery. Among the main achievements in this direction are the improvement of software and methods of computer modeling, as well as the introduction of CAD /CAMtechnology.The use of CAD /CAMtechnologies, in particular, navigational surgical templates and patient-specific implants for the repair of mandibular defects ensures a high level of accuracy and predictability

Cyclotron production of high–specific activity 55Co and in vivo evaluation of the stability of 55Co metal-chelate-peptide complexes

This work describes the production of high–specific activity 55 Co and the evaluation of the stability of 55 Co-metal-chelate-peptide complexes in vivo. 55 Co was produced via the 58 Ni(p,α) 55 Co reaction and purified using anion exchange chromatography with an average recovery of 92% and an average specific activity of 1.96 GBq/μmol. 55 Co-DO3A and 55 Co-NO2A peptide complexes were radiolabeled at 3.7 MBq/μg and injected into HCT-116 tumor xenografted mice. Positron emission tomography (PET) and biodistribution studies were performed at 24 and 48 hours postinjection and compared to those of 55 CoCl 2 . Both 55 Co-metal-chelate complexes demonstrated good in vivo stability by reducing the radiotracers’ uptake in the liver by sixfold at 24 hours with ˜ 1% ID/g and at 48 hours with ˜ 0.5% ID/g and reducing uptake in the heart by fourfold at 24 hours with ˜ 0.7% ID/g and sevenfold at 48 hours with ˜ 0.35% ID/g. These results support the use of 55 Co as a promising new radiotracer for PET imaging of cancer and other diseases

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

Toward a Unified Science of the Earth\u27s Surface: Opportunities for Synthesis Among Hydrology, Geomorphology, Geochemistry, and Ecology

The Earth\u27s surface is shaped by the interaction of tectonics, water, sediment, solutes, and biota over a wide range of spatial and temporal scales and across diverse environments. Development of a predictive science of Earth surface dynamics integrates many disciplines and approaches, including hydrology, geomorphology, ocean and atmospheric science, sedimentary and structural geology, geochemistry, and ecology. This paper discusses challenges, opportunities, and a few example problems that can serve as pathways toward this integration

Prevalence study of mental disorders in an Italian region. Preliminary report

Background Mental disorders are a major public health problem. However, over the last few years, there have been few studies aimed at evaluating their diffusion. Therefore, this study aimed at evaluating: the prevalence of the most frequent psychiatric disorders in the general population residing in Tuscany using a clinical scale administered by trainee in psychiatry. Methods The study was carried out on a representative sample of the general population aged > 18 years, randomly extracted from the register of patients in the Tuscany region, adopting a proportional sampling method stratified by gender, age group and Local Health Units (LHU). Each person was contacted by letter followed by a phone call from an operator who makes an appointment with the trainee in psychiatry. The diagnostic interview conducted was the Mini-International Neuropsychiatric Interview (MINI). Point and lifetime prevalence by gender and age group were calculated. Differences and associations were considered statistically significant if their p-values were less than 0.05. Results Of the 408 people involved, 390 people were enrolled (of which 52.6% female). The 28.5% of the sample had been affected by a psychiatric disorder during their lifetime. In their lifetime, the most represented psychiatric disorders were major depressive episode (20.4%), major depressive disorder (17.0%) and panic disorder (10.3%), more frequent in the female than the male group. Current conditions were predominantly major depressive episode (3.1%) and agoraphobia (2.8%). A 5.9% rate of current suicidal ideation was also found. Conclusions In the general population, 28.5% of people reported a psychiatric disorder during their lifetime. This prevalence is considerably higher than that reported in a previous study carried out in central Italy

A control volume finite-element model for predicting the morphology of cohesive-frictional debris flow deposits

To predict the morphology of debris flow deposits, a control volume finite-element model (CVFEM) is proposed, balancing material fluxes over irregular control volumes. Locally, the magnitude of these fluxes is taken proportional to the difference between the surface slope and a critical slope, dependent on the thickness of the flow layer. For the critical slope, a Mohr–Coulomb (cohesive-frictional) constitutive relation is assumed, combining a yield stress with a friction angle. To verify the proposed framework, the CVFEM numerical algorithm is first applied to idealized geometries, for which analytical solutions are available. The Mohr–Coulomb constitutive relation is then checked against debris flow deposit profiles measured in the field. Finally, CVFEM simulations are compared with laboratory experiments for various complex geometries, including canyon–plain and canyon–valley transitions. The results demonstrate the capability of the proposed model and clarify the influence of friction angle and yield stress on deposit morphology. Features shared by the field, laboratory, and simulation results include the formation of steep snouts along lobe margins.</p

Hotline sessions presented at the American College of Cardiology Congress 2009

The article summarizes the results of clinical trials in the field of cardiovascular medicine, which were presented during the Hotline Sessions at the annual meeting of the American College of Cardiology in Orlando, USA, from 28th March to 31st March 2009. The data were presented by leading experts in the field with relevant positions within the trials. Unpublished reports should be considered as preliminary data as the analysis may change in the final publications. The summaries presented in the manuscript were generated from the oral presentations and provide the readers with the comprehensive information on the results of the latest clinical trials in cardiovascular medicine