On uniform propagation of chaos

In this paper we obtain a time-uniform propagation estimate for a system of interacting diffusion processes. Using a well defined metric function h , our result guarantees a time-uniform estimate for the convergence of a class of interacting stochastic differential equations towards their mean field limit, under conditions that ensure that the decay associated to the internal dynamics term dominates the interaction and noise terms. Our result should have diverse applications, particularly in neuroscience, and allows for models more elaborate than the one of Wilson and Cowan. In particular, the internal dynamics need not be that of linear decay.     

Treatment by serum up-conversion nanoparticles in the fluoride matrix changes the mechanism of cell death and the elasticity of the membrane

Nanoparticles are increasingly being used for treatment and diagnostic purposes, but their effects on cells is not fully understood. Here, the interaction of fluorescent up-conversion nanoparticles (UpC-NPs) with neutrophils was investigated by imaging and measurement of membrane-cytosceletal elasticity by atomic force microscopy. It was found that UpC-NPs induce the death of neutrophils mainly by necrosis, and to a smaller extent by a novel process called ‘mummification'. Necrosis occurs by gradual loss of intracellular contents and nuclei, 45–110 min after exposure to UpC-NPs. Mummification is apparent as an increase in the rigidity of the neutrophils' membrane and acquisition of a characteristic bumpy shape with numerous protrusions; this structure does not change during atomic force microscopy scanning. Coating UpC-NPs with protein by incubation with serum leads to (1) formation of nanoparticle aggregates in the nm and μm size range, (2) a reduction in toxicity, (3) reduced mummification of neutrophils, and (4) no significant reduction of the elasticity of the membrane-cytoskeletal complex of neutrophils 30 min after exposure to coated UpC-NPs. The study shows that serum proteins greatly curb the toxicity of nanoparticles and reveals mummification as a novel mechanism of UpC-NP-induced cell death.     

Effect of nematic ordering on the elasticity and yielding in disordered polymeric solids

The relation between elasticity and yielding is investigated in a model polymer solid by Molecular‐Dynamics simulations. By changing the bending stiffness of the chain and the bond length, semicrystalline and disordered glassy polymers — both with bond disorder — as well as nematic glassy polymers with bond ordering are obtained. It is found that in systems with bond disorder the ratio τ_Y/G between the shear yield strength τ_Y and the shear modulus G is close to the universal value of the atomic metallic glasses. The increase of the local nematic order in glasses leads to the increase of the shear modulus and the decrease of the shear yield strength, as observed in experiments on nematic thermosets. A tentative explanation of the subsequent reduction of the ratio τ_Y/G in terms of the distributions of the per‐monomer stress is offered. © 2017 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2017 , 55, 1760–1769     

An approach to find redundant objective function(s) and redundant constraint(s) in multi-objective nonlinear stochastic fractional programming problems

Structural redundancies in mathematical programming models are nothing uncommon and nonlinear programming problems are no exception. Over the past few decades numerous papers have been written on redundancy. Redundancy in constraints and variables are usually studied in a class of mathematical programming problems. However, main emphasis has so far been given only to linear programming problems. In this paper, an algorithm that identifies redundant objective function(s) and redundant constraint(s) simultaneously in multi-objective nonlinear stochastic fractional programming problems is provided. A solution procedure is also illustrated with numerical examples. The proposed algorithm reduces the number of nonlinear fractional objective functions and constraints in cases where redundancy exists.     

Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg     

Stress–Strain Dependence of Segmented Polyurethanes and Polyurethane Ureas

The stress–strain dependences of segmented elastomers based on polyetherurethanes, polyesterurethane ureas, and polybutadieneurethane ureas were investigated. These dependences were adequately described using the generalized approach proposed earlier by the authors for amorphous elastomers. The experimental data obtained for four series of samples with chemical cross-linking confirmed an applicability of this approach for segmented elastomers. Unlike amorphous elastomers, the effective network density value was affected not only by the density of the chemical network, but the contribution of the network formed by the hard domains also needs be taken into account.     

Elastomeric Properties of Polysiloxane Networks. Bimodal Elastomers that are Spatially Inhomogeneous and Others that are Very Broadly Multimodal

End‐linking poly(dimethylsiloxane) was used to prepare bimodal elastomers networks so as to have inhomogeneous nanostructures, and also to prepare others having very broadly multimodal chain‐length distributions. Macroscopic phase separation, probably high crosslink density clusters, was observed to occur in some of the bimodal networks. The mechanical properties in simple extension and in equilibrium swelling were measured. The bimodal elastomers that were not obviously inhomogeneous showed very good mechanical properties, but the macroscopically phase‐separated networks, and the broadly multimodal network were weak. Analysis of the Mooney‐Rivlin profiles suggests that the reinforcing mechanism could have a structural component in addition to that from the limited extensibilities of the short chains. The mechanical properties and the extents of swelling support the cluster conjecture, in accord with previous morphological studies on spatially‐inhomogeneous polysiloxane elastomers.