Non-gaussian diffusion modeling in composite porous media by homogenization: Tail effect

In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The long-tail effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O( ²), where is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of tail-effect. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the long-tail effect in two particular cases.Notations c _i the concentration of chemical species in water within the medium i - D _i the effective diffusion coefficient for the medium i - D _ij ^eff the macroscopic (or effective) diffusion tensor in the composite - ERV the elementary representative volume - h the thickness of the period - l a chracteristic length of the ERV or the periodic cell - L a characteristic macroscopic length - n the volumetric fraction of the material 2 - 1–n the volumetric fraction of the material 1 - N the unit vector normal to - t the time variable - x the macroscopic (or slow) space variable - y the microscopic (or fast) space variable - c _1c ,C _2c ,D _1c ,D _2c the characteristic quantities - T,T _1L ,T _2L ,T _1l ,T _2l the characteristic times - c ₁ ^* ,c ₂ ^* ,D ₁ ^* ,D ₂ ^* ,t ^* the non-dimensional variables - the homogenization parameter - ₁ the domain occupied by the material 1 - ₂ the domain occupied by the material 2 - the interface between the domains 1 and 2 - the total volume of the periodic cell - /x_i the gradient operator - the gradient operator     

Signal modelization for improved precision of assessment of minimum and mean telomere lengths

Telomere length is an important measure of cell and tissue regenerative capacities. The mean telomere length is classically used as global indicator of a tissue telomere length. In skeletal muscle, which is made of postmitotic myonuclei and satellite cells (muscle stem cells), minimum telomere length is also used to assess the telomere length of satellite cells and newly incorporated myonuclei. At present, the estimation of the method reproducibility during the assessment of mean and minimum telomere length using Southern blot analysis has never been documented. The aim of this report is to describe a signal modelization for improved precision of assessment of minimum and mean telomere lengths and to document the method reproducibility. Telomeres are assessed using a Southern technique where the gel is directly hybridized with the specific probe without the membrane-transferring step in order to prevent telomeric low signal loss. We found that the improved signal analysis for determination of telomere length is associated with coefficients of variation ranging from 1.37 to 4.29% for the mean telomeric restriction fragment (TRF) length and from 2.04 to 4.95% for the minimum TRF length. Improved method reproducibility would allow saving time and biological material as duplicate and triplicate measurement of the same sample is no longer required.     

Fresnel-based analysis of Kasprzak's crystalline model: statistical results and individual predictions

We present a new modelization technique of the human eye based on the calculation of light distributions inside the eye. The method is applied to the study of the crystalline model proposed by Kasprzak and Popiolek. We obtain corneal surface data and axial lengths for two groups of real eyes. With these data, we construct a diffractive model of a human eye, which permits calculation of propagated light distributions at any distance inside the eye. The real crystalline lens is substituted by Kasprzak's model, thus obtaining a realistic model eye. From calculated patterns, we obtain the Strehl ratio and the modulation transfer functions of 44 eyes, divided in two groups according to the age. We compare our results with those in the bibliography. Finally, we check the performance of the method through individual comparison of the calculated image positions with respect to the retina with the refractive data for the each subject. We have observed good agreement between our method and results from other authors. We also find reasonable correlation between calculated refraction and subjective exams.