Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

An Empirical Potential of Interatomic Interaction

A potential of interatomic interaction for simulating complex structural states of solids (grain boundaries and heterogeneous equilibrium states) is put forward. In simulating heterogeneous states of systems, the potential must simultaneously provide for stability conditions for several phases in equilibrium and correct values of a number of macroscopic parameters such as lattice constants, elastic moduli, internal energy, heat capacity, and stability parameters. The existing empirical potentials of interatomic interaction fail to provide agreement of the calculated and experimentally obtained parameters determining the structure of the system and structural transformations due to changes in the external parameters. The potential under discussion is a polynomial representing a solution to the problem of interpolation of functions and their derivatives to the nth order prescribed on a finite system of points (Hermit interpolation problem). The relation for a general solution to the foregoing problem is so complicated that it is virtually inapplicable. A new polynomial is constructed on the basis of the Lagrangian interpolation polynomial. The interpolation of the known interatomic potentials with allowance for the fourth-order derivatives by the polynomial is achieved with high accuracy where three to four interpolation nodes are specified. Local changes can easily be introduced to the polynomial. In doing so, the values of the potential and its derivatives in other regions of space are retained. This allows mechanical stability for stable and metastable phases to be ensured.     

Thin-layer chromatography of radioactively labelled cholesterol and precursors from biological material

Summary The investigation methods of the action of xenobiotics on sterol biosynthesis from ¹⁴C-acetate in rat hepatocyte cultures can be developed, with regard to extraction using Extrelut and the separation of the sterol pattern by thin-layer chromatography, in such a way that they are suitable for wider application, e.g., screening. Good visualisation and recognition of changes in the sterol pattern are possible using autoradiography of the thin-layer chromatogram.

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Dünnschicht-Chromatographie von radioaktiv markiertem Cholesterin und Vorstufen aus biologischem Material. Eine einfache und empfindliche Methode zur Untersuchung einer Beeinflussung des Sterolbiosynthesewegs

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Dedicated to Dr. E. Roesch on occasion of his 65th birthday     

A hybrid finite-element–volume-of-fluid method for simulating free surface flows and interfaces

A numerical technique is developed for the simulation of free surface flows and interfaces. This technique combines the strength on the finite element method (FEM) in calculating the field variables for a deforming boundary and the versatility of the volume-of-fluid (VOF) technique in advection of the fluid interfaces. The advantage of the VOF technique is that it allows the simulation of interfaces with large deformations, including surface merging and breaking. However, its disadantage is that is solving the flow equations, it cannot resolve interfaces smaller than the cell size, since information on the subgrid scale is lost. Therefore the accuracy of the interface reconstruction and the treatment of the boundary conditions (i.e. viscous stresses and surface tension forces) become grid-size-dependent. On the other hand, the FEM with deforming interface mesh allows accurate implementation of the boundary conditions, but it cannot handle large surface deformations occurring in breaking and merging of liquid regions. Combining the two methods into a hybrid FEM-VOF method eliminates the major shortcomings of both. The outcome is a technique which can handle large surface deformations with accurate treatment of the boundary conditions. For illustration, two computational examples are presented, namely the instability and break-up of a capillary jet and the coalescence collision of two liquid drops.     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis and comparative solution properties of single‐, twin‐, and triple‐tailed associating ionic polymers based on diallylammonium salts

The cycloterpolymerizations of single‐, twin‐, and triple‐tailed hydrophobes with hydrophilic monomer N,N‐diallyl‐N‐carboethoxymethylammonium chloride and sulfur dioxide afforded a series of cationic polyelectrolytes (CPEs) in excellent yields. These CPEs, upon the acidic hydrolysis of the pendent ester groups, gave the corresponding pH‐responsive cationic acid salts, which, upon a treatment with sodium hydroxide, were converted to polybetaines (PBs), anionic polyelectrolytes (APEs), and PB/APE polymers containing various proportions of zwitterionic (PB) and anionic fractions (APE) in the polymer chain. At a shear rate of 0.36 s⁻¹ at 30 °C, salt‐free water solutions of the CPEs (2 g/dL) containing 8, 4, and 2.67 mol % of the single‐, twin‐, and triple‐tailed hydrophobes (all having 8 mol % octyloxy tails) had apparent viscosity values of 70, 2800, and 396,000 cps, respectively. The PB/APE polymer with a ratio of 33:67 for the zwitterionic and anionic fractions in the polymer chain gave the highest viscosity value. The superior viscosity behavior of the polymers containing the triple‐tailed hydrophobe was attributed to the blocky nature of the comonomer. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5480–5494, 2006     

The phase diagram of a single polymer chain: New insights from a new simulation method

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist only of gas and crystal phase in the limit of infinite chain length. This behavior is in agreement with findings on the phase behavior of hard-sphere systems with a relatively short-ranged attractive square well. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2542–2555, 2006