Minimization- and Saddle-Point-Based Modeling of Diffusion-Deformation-Processes in Hydrogels

Hydrogels have gained importance during the last years due to their wide range of synthetically fabricable elastic properties as well their increasing meaning in biomedical applications. Future exploitation of the vast prospects of hydrogels is however only feasible by establishing reliable material models that precisely capture their behavior in different environments. To this end, we propose a consistent variational framework for deformation-diffusion processes, offering a canonically compact approach to the chemo-mechanical coupling of hydrogels via a saddle-point as well as a new minimization formulation. The work depicts the construction of rate-type potentials for the chemo-mechanical evolution problem and their transformation into time-discrete incremental potentials. In terms of spatial discretization, the finite element method is employed, benefiting from the intrinsic symmetric structure of the variational foundation. While the saddle-point formulation yields the well-known LBB condition as a constraint for finite element interpolations, on the part of its minimizing counterpart H(Div, ℬ︁)-conforming elements have to be chosen. We illustrate appropriate solutions to both challenges, using mixed Taylor-Hood for the saddle-point and Raviart-Thomas elements for the minimization formulation and discuss advantages of the new approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of “Racemic Compound-Like” Behavior of Diastereomeric Mixture of Pinanyl Sulfoxides by X-Ray Diffraction,IR Spectroscopy,and DFT Calculations

Abstract

The oxidation of a β-hydroxysulfide in the pinane series by use of m-chloroperbenzoic acid resulted in the formation of the corresponding β-hydroxysulfoxide as a mixture of two diastereomers in 4:5 ratio. According to single-crystal X-ray diffraction (XRD) results, it is established that the diastereomeric mixture of sulfoxides crystallizes in the “racemic compound-like” manner under formation of asymmetric dimers through S=O··H–O interactions. This asymmetric dimer formed from diastereomeric molecules is a structural unit in both crystal modifications, the triclinic and the monoclinic one. The behavior of the diastereomeric mixture of pinane derived sulfoxides in crystals, melts and in tetrachloromethane solutions was studied by IR spectroscopy. The density functional theory (DFT) method with 6-31G (d, p) basis set was used to calculate the optimized geometrical parameters and vibrational frequencies of different associates in solutions. The calculated vibrational frequencies are compared with experimental IR spectra.     

A Review in Linear Alkylbenzene (LAB) Production Processes in the Petrochemical Industry

Russian Journal of Applied Chemistry - Linear alkylbenzene (LAB) is a cost-effective and biodegradable intermediate in the production of detergents and surfactants. Recently, due to the spread of...     

Sensitive Biosensor Based on Urease/In2O5Sn Nano-Coated Fluorinated SnO2 for Urea Detection in Blood Serum

Journal of Analytical Chemistry - A sensitive electrochemical matrix based on In2O5Sn nanoparticles modified fluorinated tin oxide (SnO2:F) conducting glass was reported. Besides, urease (Urs) was...     

Spatial and temporal resolution effects on dynamic contrast-enhanced magnetic resonance mammography

We tested the hypothesis that partial volume effects due to poor in-plane resolution and/or low temporal resolution used in clinical dynamic contrast-enhanced magnetic resonance imaging results in erroneous diagnostic information based on inaccurate estimates of tumor contrast agent extravasation and tested whether reduced encoding techniques can correct for dynamic data volume averaging. Image spatial resolution was reduced from 469 x 469 microm2 to those reported below by selecting a subset of k-space data. We then compared the top five K(trans)/V(T) "hot spots" obtained from the original data set, 469 x 469-microm in-plane spatial resolution and an 18-s temporal resolution processed by fast Fourier transform (FFT), with values obtained from data sets having in-plane spatial resolutions of 938 x 938, 1875 x 1875 and 2500 x 2500 microm2 and a temporal resolution of 18 s, or data sets with temporal resolutions of 36, 54 and 72 and a spatial resolution of 469 x 469 microm2, and found them to statistically differ from the parent data sets. We then tested four different post processing methods for improving the spatial resolution without sacrificing temporal resolution: zero-filled FFT, keyhole, reduced-encoding imaging by generalized-series reconstruction (RIGR) and two-reference RIGR (TRIGR). The top five values of K(trans)/V(T) obtained from data sets, the in-plane spatial resolutions of which were improved to 469 x 469 microm2 by zero-filling FFT, Keyhole and RIGR, statistically differed from those obtained from the original 469 x 469 microm2 FFT parent image data set. Only the 938 x 938 and 1875 x 1875 microm2 data sets reconstructed to 469 x 469 microm2 with TRIGR reconstruction method yielded values of the top five K(trans)/V(T) hot spots statistically the same as the original parent data set, 469 x 469 microm2 in-plane spatial and 18-s temporal-resolution FFT. That is, partial volume effects from data sets of different in-plane spatial resolution resulted in statistically different values of the top five K(trans)/V(T) hot spots relative to a high spatial and temporal resolution data set, and TRIGR reconstruction of these low resolution data sets to high resolution images provided statistically similar values with a savings in temporal resolution of 2 to 4 times.     

Finding the buckling load of non-uniform columns using the iteration perturbation method

The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called “perfectibility” parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.     

The role of mercury in the processes of vital activity of the human and mammalian organisms

Mercury belongs to one of the most common heavy metals that have high biological activity in relation to human and animal cells. However, the physiological role of mercury in the metabolism of eukaryotic cells is still unclear. The given review provides current information on certain properties of mercury, the mechanisms of penetration of Hg (II) inside cells, its genotoxic and cytotoxic effects, as well as the role of mercury in the induction of autoimmune processes involving production of autoantibodies to the nucleolar protein fibrillarin.     

On copositive approximation in some classical spaces of sequences

In this paper the author writes a simple characterization for the best copositive approximation in c; the space of convergent sequences, by elements of finite dimensional Chebyshev subspaces, and shows that it is unique.     

On Schnabl solutions of string field equations

We clarify the relationship between Schnabl’s solution and pure gauge configurations. Both Schnabl’s and pure gauge solutions are obtained by means of an iterative procedure. We show that the pure gauge string field configuration that is used in the construction of a perturbation series for Schnabl’s solution diverges on a large subspace of string configurations, but it can be rendered convergent by adding a compensating term. The additional term ensures the fulfillment of the equations of motion in a weak sense. This compensating term coincides with the term necessary for obtaining an action consistent with Sen’s first conjecture.     

Cauchy problem on non-globally hyperbolic space-times

We consider solutions of the Cauchy problem for hyperbolic equations on non-globally hyperbolic space-times containing closed timelike curves (time machines). We prove that for the wave equation on such space-times, there exists a solution of the Cauchy problem that is discontinuous and in some sense unique for arbitrary initial conditions given on a hypersurface at a time preceding the formation of closed timelike curves. If the hypersurface of initial conditions intersects the region containing closed timelike curves, then the solution of the Cauchy problem exists only for initial conditions satisfying a certain self-consistency requirement. To Vasilii Sergeevich Vladimirov with best wishes on his 85th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 334–344, December, 2008.