Scaling dependence on time and distance in nonlinear fractional diffusion equations and possible applications to the water transport in soils

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different physical systems like: amorphous semicondutors, polymers, composite heterogeneous films and porous media. They have also been used to calculate the heat load intensity change in blast furnace walls, to solve problems of control theory \ and dynamic problems of linear and nonlinear hereditary mechanics of solids. In this work, we investigate the scaling properties related to the nonlinear fractional diffusion equations and indicate the possibilities to the applications of these equations to simulate the water transport in unsaturated soils. Usually, the water transport in soils with anomalous diffusion, the dependence of concentration on time and distance may be expressed in term of a single variable given by $\lambda _{q}=x/t^{q}.$ In particular, for $q=1/2$ the systems obey Fick's law and Richards' equation for water transport. We show that a generalization of Richards' equation via fractional approach can incorporate the above property.Comment: 9 page

Integro-differential diffusion equation for continuous time random walk

In this paper we present an integro-differential diffusion equation for continuous time random walk that is valid for a generic waiting time probability density function. Using this equation we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential, and a combination of power law and generalized Mittag-Leffler function. We show that for the case of the exponential waiting time probability density function a normal diffusion is generated and the probability density function is Gaussian distribution. In the case of the combination of a power-law and generalized Mittag-Leffler waiting probability density function we obtain the subdiffusive behavior for all the time regions from small to large times, and probability density function is non-Gaussian distribution.Comment: 12 page

Tsallis distribution and luminescence decays

Usually, the Kohlrausch (stretched exponential) function is employed to fit the luminescence decays. In this work we propose to use the Tsallis distribution as an alternative to describe them. We show that the curves of the luminescence decay obtained from the Tsallis distribution are close to those ones obtained from the stretched exponential. Further, we show that our result can fit well the data of porous silicon at low temperature and simulation result of the trapping controlled luminescence model.Comment: 8 pages and 4 figure

Fokker-Planck equation with variable diffusion coefficient in the Stratonovich approach

We consider the Langevin equation with multiplicative noise term which depends on time and space. The corresponding Fokker-Planck equation in Stratonovich approach is investigated. Its formal solution is obtained for an arbitrary multiplicative noise term given by $g(x,t)=D(x)T(t)$, and the behaviors of probability distributions, for some specific functions of $D(x)$% , are analyzed. In particular, for $D(x)\sim | x| ^{-\theta /2}$, the physical solutions for the probability distribution in the Ito, Stratonovich and postpoint discretization approaches can be obtained and analyzed.Comment: 6 pages in LATEX cod

Pooled analysis of WHO Surgical Safety Checklist use and mortality after emergency laparotomy

Background The World Health Organization (WHO) Surgical Safety Checklist has fostered safe practice for 10 years, yet its place in emergency surgery has not been assessed on a global scale. The aim of this study was to evaluate reported checklist use in emergency settings and examine the relationship with perioperative mortality in patients who had emergency laparotomy. Methods In two multinational cohort studies, adults undergoing emergency laparotomy were compared with those having elective gastrointestinal surgery. Relationships between reported checklist use and mortality were determined using multivariable logistic regression and bootstrapped simulation. Results Of 12 296 patients included from 76 countries, 4843 underwent emergency laparotomy. After adjusting for patient and disease factors, checklist use before emergency laparotomy was more common in countries with a high Human Development Index (HDI) (2455 of 2741, 89.6 per cent) compared with that in countries with a middle (753 of 1242, 60.6 per cent; odds ratio (OR) 0.17, 95 per cent c.i. 0.14 to 0.21, P <0001) or low (363 of 860, 422 per cent; OR 008, 007 to 010, P <0.001) HDI. Checklist use was less common in elective surgery than for emergency laparotomy in high-HDI countries (risk difference -94 (95 per cent c.i. -11.9 to -6.9) per cent; P <0001), but the relationship was reversed in low-HDI countries (+121 (+7.0 to +173) per cent; P <0001). In multivariable models, checklist use was associated with a lower 30-day perioperative mortality (OR 0.60, 0.50 to 073; P <0.001). The greatest absolute benefit was seen for emergency surgery in low- and middle-HDI countries. Conclusion Checklist use in emergency laparotomy was associated with a significantly lower perioperative mortality rate. Checklist use in low-HDI countries was half that in high-HDI countries.Peer reviewe

Search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks in proton-proton collisions at root s=13TeV

A search for dark matter produced in association with a Higgs boson decaying to a pair of bottom quarks is performed in proton-proton collisions at a center-of-mass energy of 13 TeV collected with the CMS detector at the LHC. The analyzed data sample corresponds to an integrated luminosity of 35.9 fb(-1). The signal is characterized by a large missing transverse momentum recoiling against a bottom quark-antiquark system that has a large Lorentz boost. The number of events observed in the data is consistent with the standard model background prediction. Results are interpreted in terms of limits both on parameters of the type-2 two-Higgs doublet model extended by an additional light pseudoscalar boson a (2HDM+a) and on parameters of a baryonic Z simplified model. The 2HDM+a model is tested experimentally for the first time. For the baryonic Z model, the presented results constitute the most stringent constraints to date.Peer reviewe