A kinematically coupled time-splitting scheme for fluid–structure interaction in blood flow

We present a new time-splitting scheme for the numerical simulation of fluid–structure interaction between blood flow and vascular walls. This scheme deals in a successful way with the problem of the added mass effect. The scheme is modular and it embodies the stability properties of implicit schemes at the low computational cost of loosely coupled ones.     

On ordered categories as a framework for fuzzification of algebraic and topological structures

Using the framework of ordered categories, the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by Rosenfeld as well as provides a new approach to fuzzification of topological structures, which amounts to fuzzifying the underlying “set” of a structure in a suitably compatible way, leaving the structure itself crisp. The latter machinery allows the so-called “double fuzzification”, i.e., a fuzzification of something that is already fuzzified.     

A non-autonomous flow system with Plykin type attractor

A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a two-dimensional sphere, consisting of four stages of continuous geometrically evident transformations. The computations indicate that in a certain parameter range the map has a uniformly hyperbolic attractor. It may be represented on a plane by means of a stereographic projection. Accounting structural stability, a modification of the model is undertaken to obtain a set of two non-autonomous differential equations of the first order with smooth coefficients. As follows from computations, it has the Plykin type attractor in the Poincaré cross-section.     

On the isoperimetric constants for product measures

Isoperimetric constants of product probability measures are known to have an almost dimension-free character. We propose a new proof based on certain Sobolev-type inequalities of additive type (introduced by the author in connection with the isoperimetric problem in Gauss space). Bibliography: 18 titles. Dedicated to Nina Nikolaevna Uraltseva Translated from Problemy Matematicheskogo Analiza, 40, May 2009, pp. 49–56.     

Functional a posteriori error estimates for incremental models in elasto-plasticity

We consider incremental problem arising in elasto-plastic models with isotropic hardening. Our goal is to derive computable and guaranteed bounds of the difference between the exact solution and any function in the admissible (energy) class of the problem considered. Such estimates are obtained by an advanced version of the variational approach earlier used for linear boundary-value problems and nonlinear variational problems with convex functionals [24, 30]. They do no contain mesh-dependent constants and are valid for any conforming approximations regardless of the method used for their derivation. It is shown that the structure of error majorant reflects properties of the exact solution so that the majorant vanishes only if an approximate solution coincides with the exact one. Moreover, it possesses necessary continuity properties, so that any sequence of approximations converging to the exact solution in the energy space generates a sequence of positive numbers (explicitly computable by the majorant functional) that tends to zero.      

Photoconvertible fluorescent protein EosFP: biophysical properties and cell biology applications

EosFP is a fluorescent protein from the coral Lobophyllia hemprichii that changes its fluorescence emission from green to red upon irradiation with near-UV light. Here we present the spectroscopic properties of wild-type EosFP and a variety of monomeric and dimeric mutants and provide a structural interpretation of its oligomerization and photoconversion, which is based on X-ray structure analysis of the green and red species that we reported recently. Because functional expression of the monomeric EosFP variant is limited to temperatures of 30 degrees C, we have developed a tandem dimer. This construct, in which two EosFP subunits are connected by a flexible 12 amino acid linker, expresses well after fusion with the androgen and endothelin A receptors at 37 degrees C. A variety of applications in cellular imaging, developmental biology and automated high-content screening applications are presented, which demonstrate that EosFP is a powerful tool for in vivo monitoring of cellular processes.     

Single-file diffusion near channel boundaries

Molecular transport under the conditions of single-file diffusion was investigated near the channel boundaries by using dynamic Monte Carlo and molecular dynamics simulations of tracer exchange between single-file channels and their surroundings. The boundary effect reported in our recent papers (Vasenkov S.; K?rger, J. Phys. Rev. E 2002, 66, 052601. Schüring, A.; Vasenkov S.; Fritzsche, S. J. Phys. Chem. B 2005, 109, 16711) was studied in detail. This boundary effect is characterized by deviations of the intrachannel concentration profiles of tracer molecules observed in the case of single-file diffusion near the channel boundaries from the corresponding profiles typical for normal diffusion. It has been shown in our previous studies that these deviations occur under the conditions when the potential-energy difference inside and outside of single-file channels was both comparable and much larger than the activation energy of intrachannel diffusion. Here, we report a quantitative model describing the boundary effect. According to this model, an occurrence of the boundary effect is related to a complex character of diffusion in finite single-file systems. Such diffusion can be described by the following two types of movements occurring in parallel: (i) correlated displacements of all molecules in any particular channel and (ii) fast displacements of single molecules, which are uncorrelated with the displacements of all other molecules in the same channel. The latter displacements are restricted to a certain length interval that depends on the channel length and the channel occupancy. This length interval is shown to determine the extensions of the channel margins where the boundary effect is observed.     

Mössbauer investigation of the photoexcited spin states and crystal structure analysis of the spin-crossover dinuclear complex [{Fe(bt)(NCS)(2)}(2)bpym] (bt=2,2'-bithiazoline, bpym=2,2'-bipyrimidine)

The crystal structure of the complex [{Fe(bt)(NCS)(2)}(2)bpym] (1) (bt=2,2'-bithiazoline, bpym=2,2'-bipyrimidine) has been solved at 293, 240, 175 and 30 K. At all four temperatures the crystal remains in the P space group with a=8.7601(17), b=9.450(2), c=12.089(3) A, alpha=72.77(2), beta=79.150(19), gamma=66.392(18) degrees , V=873.1(4) Angstrom(3) (data for 293 K structure). The structure consists of centrosymmetric dinuclear units in which each iron(II) atom is coordinated by two NCS(-) ions in the cis position and two nitrogen atoms of the bridging bpym ligand, with the remaining positions occupied by the peripheral bt ligand. The iron atom is in a severely distorted octahedral FeN(6) environment. The average Fe--N bond length of 2.15(9) Angstrom indicates that compound 1 is in the high-spin state (HS-HS) at 293 K. Crystal structure determinations at 240, 175 and 30 K gave a cell comparable to that seen at 293 K, but reduced in volume. At 30 K, the average Fe--N distance is 1.958(4) Angstrom, showing that the structure is clearly low spin (LS-LS). At 175 K the average Fe--N bond length of 2.052(11) Angstrom suggests that there is an intermediate phase. M?ssbauer investigations of the light-induced excited spin state trapping (LIESST) effect (lambda=514 nm, 25 mW cm(-2)) in 1 (4.2 K, H(ext)=50 kOe) show that the excited spin states correspond to the HS-HS and HS-LS pairs. The dynamics of the relaxation of the photoexcited states studied at 4.2 K and H(ext)=50 kOe demonstrate that HS-HS pairs revert with time to both HS-LS and LS-LS configurations. The HS-LS photoexcited pairs relax with time back to the ground LS-LS configuration. Complex [{Fe(0.15)Zn(0.85)(bt)(NCS)(2)}(2)bpym] (2) exhibits a continuous spin transition centred around 158 K in contrast to the two-step transition observed for 1. The different spin-crossover behaviour observed for 2 is due to the decrease of cooperativity (intermolecular interactions) imposed by the matrix of Zn(II) ions. This clearly demonstrates the role of the intermolecular interactions in the stabilization of the HS-LS intermediate state in 1.     

Thioether sulfur oxygenation from O2 or H2O2 reactivity of copper complexes with tridentate N2Sthioether ligands

To model thioether-copper coordination chemistry including oxidative reactivity, such as occurs in the copper monooxygenases peptidylglycine -hydroxylating monooxygenase (PHM) and dopamine beta-hydroxylase (DbetaH), we have synthesized new tridentate N2S ligands LSEP and LSBz [LSEP = methyl(2-phenethylsulfanylpropyl)(2-pyridin-2-ylethyl)amine; LSBz = (2-benzylsulfanylpropyl)methyl(2-pyridin-2-ylethyl)amine)]. Both copper(I) and copper(II) complexes have been prepared, and their respective O2 and H2O2 chemistry has been studied. Under mild conditions, oxygenation of [(LSEP)CuI]+ (1a) and [(LSBz)CuI]+ (2a) leads to ligand sulfoxidation, thus exhibiting copper monooxygenase activity. A copper(II) complex of this sulfoxide ligand product, [(LSOEP)CuII(CH3OH)(OClO3)2], has been structurally characterized, demonstrating Cu-Osulfoxide ligation. The X-ray structure of [(LSEP)CuII(H2O)(OClO3)]+ (1b) and its solution UV-visible spectral properties [S-CuII LMCT band at 365 nm (MeCN solvent); epsilon = 4285 M-1 cm-1] indicate the thioether sulfur atom is bound to the cupric ion in both the solid (CuII-S distance: 2.31 A) and solution states. Reaction of 1b with H2O2 leads to sulfonation via the sulfoxide; excess hydrogen peroxide gives mostly sulfone product. These results may provide some insight into recent reports concerning protein methionine oxidation, showing the potential importance of copper-mediated oxidation processes in certain biological settings.