Integral transform solution of random coupled parabolic partial differential models

[EN] Random coupled parabolic partial differential models are solved numerically using random cosine Fourier transform together with non-Gaussian random numerical integration that captures the highly oscillatory behaviour of the involved integrands. Sufficient condition of spectral type imposed on the random matrices of the system is given so that the approximated stochastic process solution and its statistical moments are numerically convergent. Numerical experiments illustrate the results.Spanish Ministerio de Economia, Industria y Competitividad (MINECO); Agencia Estatal de Investigacion (AEI); Fondo Europeo de Desarrollo Regional (FEDER UE), Grant/Award Number: MTM2017-89664-PCasabán Bartual, MC.; Company Rossi, R.; Egorova, VN.; Jódar Sánchez, LA. (2020). Integral transform solution of random coupled parabolic partial differential models. Mathematical Methods in the Applied Sciences. 43(14):8223-8236. https://doi.org/10.1002/mma.6492S822382364314Bäck, J., Nobile, F., Tamellini, L., & Tempone, R. (2010). Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison. Spectral and High Order Methods for Partial Differential Equations, 43-62. doi:10.1007/978-3-642-15337-2_3Bachmayr, M., Cohen, A., & Migliorati, G. (2016). Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, 51(1), 321-339. doi:10.1051/m2an/2016045Ernst, O. G., Sprungk, B., & Tamellini, L. (2018). Convergence of Sparse Collocation for Functions of Countably Many Gaussian Random Variables (with Application to Elliptic PDEs). SIAM Journal on Numerical Analysis, 56(2), 877-905. doi:10.1137/17m1123079Sheng, D., & Axelsson, K. (1995). Uncoupling of coupled flows in soil—a finite element method. International Journal for Numerical and Analytical Methods in Geomechanics, 19(8), 537-553. doi:10.1002/nag.1610190804Mitchell, J. K. (1991). Conduction phenomena: from theory to geotechnical practice. Géotechnique, 41(3), 299-340. doi:10.1680/geot.1991.41.3.299Das, P. K. (1991). Optical Signal Processing. doi:10.1007/978-3-642-74962-9Ashkenazy, Y. (2017). Energy transfer of surface wind-induced currents to the deep ocean via resonance with the Coriolis force. Journal of Marine Systems, 167, 93-104. doi:10.1016/j.jmarsys.2016.11.019Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544. doi:10.1113/jphysiol.1952.sp004764Galiano, G. (2012). On a cross-diffusion population model deduced from mutation and splitting of a single species. Computers & Mathematics with Applications, 64(6), 1927-1936. doi:10.1016/j.camwa.2012.03.045Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical solutions of random mean square Fisher‐KPP models with advection. Mathematical Methods in the Applied Sciences, 43(14), 8015-8031. doi:10.1002/mma.5942Casabán, M. C., Company, R., & Jódar, L. (2019). Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness. Mathematics, 7(9), 853. doi:10.3390/math7090853Shampine, L. F. (2008). Vectorized adaptive quadrature in MATLAB. Journal of Computational and Applied Mathematics, 211(2), 131-140. doi:10.1016/j.cam.2006.11.021Iserles, A. (2004). On the numerical quadrature of highly-oscillating integrals I: Fourier transforms. IMA Journal of Numerical Analysis, 24(3), 365-391. doi:10.1093/imanum/24.3.365Ma, J., & Liu, H. (2018). On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels. Symmetry, 10(7), 239. doi:10.3390/sym10070239Jódar, L., & Goberna, D. (1996). Exact and analytic numerical solution of coupled diffusion problems in a semi-infinite medium. Computers & Mathematics with Applications, 31(9), 17-24. doi:10.1016/0898-1221(96)00038-7Jódar, L., & Goberna, D. (1998). A matrix D’Alembert formula for coupled wave initial value problems. Computers & Mathematics with Applications, 35(9), 1-15. doi:10.1016/s0898-1221(98)00052-2Ostrowski, A. M. (1959). A QUANTITATIVE FORMULATION OF SYLVESTER’S LAW OF INERTIA. Proceedings of the National Academy of Sciences, 45(5), 740-744. doi:10.1073/pnas.45.5.740Ashkenazy, Y., Gildor, H., & Bel, G. (2015). The effect of stochastic wind on the infinite depth Ekman layer model. EPL (Europhysics Letters), 111(3), 39001. doi:10.1209/0295-5075/111/3900

A Variational Method in Out of Equilibrium Physical Systems

A variational principle is further developed for out of equilibrium dynamical systems by using the concept of maximum entropy. With this new formulation it is obtained a set of two first-order differential equations, revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. In particular, it is obtained an extended equation of motion for a rotating dynamical system, from where it emerges a kind of topological torsion current of the form $\epsilon_{ijk} A_j \omega_k$, with $A_j$ and $\omega_k$ denoting components of the vector potential (gravitational or/and electromagnetic) and $\omega$ is the angular velocity of the accelerated frame. In addition, it is derived a special form of Umov-Poynting's theorem for rotating gravito-electromagnetic systems, and obtained a general condition of equilibrium for a rotating plasma. The variational method is then applied to clarify the working mechanism of some particular devices, such as the Bennett pinch and vacuum arcs, to calculate the power extraction from an hurricane, and to discuss the effect of transport angular momentum on the radiactive heating of planetary atmospheres. This development is seen to be advantageous and opens options for systematic improvements.Comment: 22 pages, 1 figure, submitted to review, added one referenc

Comparing etoricoxib and celecoxib for preemptive analgesia for acute postoperative pain in patients undergoing arthroscopic anterior cruciate ligament reconstruction: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>The efficacy of selective cox-2 inhibitors in postoperative pain reduction were usually compared with conventional non-selective conventional NSAIDs or other types of medicine. Previous studies also used selective cox-2 inhibitors as single postoperative dose, in continued mode, or in combination with other modalities. The purpose of this study was to compare analgesic efficacy of single preoperative administration of etoricoxib versus celecoxib for post-operative pain relief after arthroscopic anterior cruciate ligament reconstruction.</p> <p>Methods</p> <p>One hundred and two patients diagnosed as anterior cruciate ligament injury were randomized into 3 groups using opaque envelope. Both patients and surgeon were blinded to the allocation. All of the patients were operated by one orthopaedic surgeon under regional anesthesia. Each group was given either etoricoxib 120 mg., celecoxib 400 mg., or placebo 1 hour prior to operative incision. Post-operative pain intensity, time to first dose of analgesic requirement and numbers of analgesic used for pain control and adverse events were recorded periodically to 48 hours after surgery. We analyzed the data according to intention to treat principle.</p> <p>Results</p> <p>Among 102 patients, 35 were in etoricoxib, 35 in celecoxib and 32 in placebo group. The mean age of the patients was 30 years and most of the injury came from sports injury. There were no significant differences in all demographic characteristics among groups. The etoricoxib group had significantly less pain intensity than the other two groups at recovery room and up to 8 hours period but no significance difference in all other evaluation point, while celecoxib showed no significantly difference from placebo at any time points. The time to first dose of analgesic medication, amount of analgesic used, patient's satisfaction with pain control and incidence of adverse events were also no significantly difference among three groups.</p> <p>Conclusions</p> <p>Etoricoxib is more effective than celecoxib and placebo for using as preemptive analgesia for acute postoperative pain control in patients underwent arthroscopic anterior cruciate ligament reconstruction.</p> <p>Trial registration number</p> <p>NCT01017380</p

Swimming obstructed by dead-water

In nautical literature, 'dead-water' refers to the obstructive effect encountered by ships moving in stratified water due to the ship generating waves on an interface that separates different water masses. To investigate the hypothesis that open water swimming may also be obstructed by an encounter of dead-water, possibly causing drowning, we performed two experiments that assess the impact of stratified water on swimming. In the first experiment, subjects made a single front-crawl stroke while lying on a carriage that was rolling just above the water surface. The gain in kinetic energy, as a result of the stroke, was far less in stratified than in homogeneous water. In the second experiment, four subjects swam a short distance (5 m) in homogeneous and in two different settings of stratified water. At the same stroke frequency, swimming in stratified conditions was slower by 15%, implying a loss in propulsive power by 40%. Although in nature stratification will be less strong, extrapolation of the results suggests that dead-water might indeed obstruct swimming in open water as well. This effect will be most pronounced during fair weather, when stratification of a shallow surface layer is most easily established. Our findings indicate that swimmers' anecdotal evidence on 'water behaving strangely' may have to be taken more seriously than previously thought. © 2008 Springer-Verlag

The Generation R Study: design and cohort update 2010

The Generation R Study is a population-based prospective cohort study from fetal life until young adulthood. The study is designed to identify early environmental and genetic causes of normal and abnormal growth, development and health during fetal life, childhood and adulthood. The study focuses on four primary areas of research: (1) growth and physical development; (2) behavioural and cognitive development; (3) diseases in childhood; and (4) health and healthcare for pregnant women and children. In total, 9,778 mothers with a delivery date from April 2002 until January 2006 were enrolled in the study. General follow-up rates until the age of 4 years exceed 75%. Data collection in mothers, fathers and preschool children included questionnaires, detailed physical and ultrasound examinations, behavioural observations, and biological samples. A genome wide association screen is available in the participating children. Regular detailed hands on assessment are performed from the age of 5 years onwards. Eventually, results forthcoming from the Generation R Study have to contribute to the development of strategies for optimizing health and healthcare for pregnant women and children

Contributions of Albert Einstein to Earth Sciences: A review in Commemoration of the World Year of Physics

The World Year of Physics (2005) is an international celebration to commemorate the one hundredth anniversary of Einstein's "Annus Mirabilis". The United Nations has officially declared 2005 the International Year of Physics. However, the impact of Einstein's ideas was not restricted to physics. Among numerous other disciplines, Einstein also made significant and specific contributions to Earth Sciences. His geosciences-related letters, comments, and scientific articles, are dispersed, not easily accesible and are poorly known. The present review attempts to integrate them, as a tribute to Einstein in commemoration of this centenary. These contributions can be classified into three basic areas: geodynamics, geological (planetary) catastrophism and fluvial geomorphology.Comment: 17 pages, no figures, to be published in Naturwissenschafte

Phosphoinositide-binding interface proteins involved in shaping cell membranes

The mechanism by which cell and cell membrane shapes are created has long been a subject of great interest. Among the phosphoinositide-binding proteins, a group of proteins that can change the shape of membranes, in addition to the phosphoinositide-binding ability, has been found. These proteins, which contain membrane-deforming domains such as the BAR, EFC/F-BAR, and the IMD/I-BAR domains, led to inward-invaginated tubes or outward protrusions of the membrane, resulting in a variety of membrane shapes. Furthermore, these proteins not only bind to phosphoinositide, but also to the N-WASP/WAVE complex and the actin polymerization machinery, which generates a driving force to shape the membranes