Small-scale vorticity filaments and structure functions of the developed turbulence

We develop a theory of turbulence based on the Navier-Stokes equation, without using dimensional or phenomenological considerations. A small scale vortex filament is the main element of the theory. The theory allows to obtain the scaling law and to calculate the scaling exponents of Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations and derivation of scaling exponents are discussed in details. A weak dependence on statistical propositions is demonstrated. The relation of the theory to the multifractal model is discussed.     

An application of Kozeny–Carman flow resistivity model to predict the acoustical properties of polyester fibre

Modelling of the acoustical properties of polyester fibre materials is usually based on variations of the Bies and Hansen empirical model [1], which allows the calculation of the air flow resistivity of a porous material. The flow resistivity is the key non-acoustical parameter which determines the ability of this kind of materials to absorb sound. The main scope of this work is to illustrate that an alternative theoretical model based on the Kozeny–Carman equation can be used to predict more accurately the flow resistivity from the fibre diameter and bulk material density data. In this paper the flow resistivity is retrieved from the acoustic absorption coefficient data for polyester fibre samples of different densities and fibre diameters. These data agree closely with the flow resistivity predicted with the proposed Kozeny–Carman model.     

Solvothermal Synthesis of [Cr7S8(en)8Cl2]Cl3 ⋅ 2H2O with Magnetically Frustrated [Cr7S8]5+ Double-Cubes**

A novel transition metal chalcohalide [Cr₇S₈(en)₈Cl₂]Cl₃ ⋅ 2H₂O, with [Cr₇S₈]⁵⁺ dicubane cationic clusters, has been synthesized by a low temperature solvothermal method, using dimethyl sulfoxide (DMSO) and ethylenediamine (en) solvents. Ethylenediamine ligand exhibits bi- and monodentate coordination modes; in the latter case ethylenediamine coordinates to Cr atoms of adjacent clusters, giving rise to a 2D polymeric structure. Although magnetic susceptibility shows no magnetic ordering down to 1.8 K, a highly negative Weiss constant, θ=−224(2) K, obtained from Curie-Weiss fit of inverse susceptibility, suggests strong antiferromagnetic (AFM) interactions between S=3/2 Cr(III) centers. Due to the complexity of the system with (2S+1)⁷=16384 microstates from seven Cr³⁺ centers, a simplified model with only two exchange constants was used for simulations. Density-functional theory (DFT) calculations yielded the two exchange constants to be J₁=−21.4 cm⁻¹ and J₂=−30.2 cm⁻¹, confirming competing AFM coupling between the shared Cr³⁺ center and the peripheral Cr³⁺ ions of the dicubane cluster. The best simulation of the experimental data was obtained with J₁=−20.0 cm⁻¹ and J₂=−21.0 cm⁻¹, in agreement with the slightly stronger AFM exchange within the triangles of the peripheral Cr³⁺ ions as compared to the AFM exchange between the central and peripheral Cr³⁺ ions. This compound is proposed as a synthon towards magnetically frustrated systems assembled by linking dicubane transition metal-chalcogenide clusters into polymeric networks.     

Combinatorial study of the mushroom-to-brush crossover in surface anchored polyacrylamide

We present a method for fabricating anchored polymers with a gradual variation of grafting densities on solid substrates. The technique for generating such structures comprises (i) formation of a molecular gradient of polymerization initiator on the solid substrate and (ii) polymerization from the substrate-bound initiator centers ("grafting from"). We measure the mushroom-to-brush transition in grafted polyacrylamides and show that the mushroom and brush behavior can be described using existing scaling theories.