Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also presents multistability shown in the planes of the basin of attractions.     

Degradation of Polystyrene in Solution by Ultrasonation - A Molecular Weight Distribution Study

Ultrasonically induced degradation of polystyrene in tetrahydrofuran solutions has been studied. Four narrow molecular weight distribution (MWD) samples, a material with a wide MWD, and a bimodal MWD sample were degraded at various concentrations, temperatures, and ultrasonic intensities. The MWDs after a number of ultrasonation time periods were obtained from gel permeation chromatograms corrected for instrumental spreading. Degradation index DI, defined as the number of bonds broken per original number of molecules, has been used to describe the extent of degradation. The results of the experiments were used to determine the values of two parameters occurring in the degradation model developed previously. It was found that the course of the changes in MWDs predicted by the model are in good agreement with those observed experimentally when the following values of the model parameters are used. The probability of scission of a molecule with molecular weight M is proportional to the product of its number fraction and the 1.25 power of M. The probability density function of the location of scission along the chain is described by a Caussian curve centered at the midpoint of the chain with a standard deviation of 35% of the chain lengths and truncated 3I the chain ends.

The agreement between observed and calculated MWDs was good for degrees of degradation as high as DI = 15. The course of the changes in MWDs was independent of the initial MWD and of the experimental conditions of concentration, temperature, and sonation intensity and, therefore, independent of the rate of degradation which varied greatly.     

Cylindrical Approximation of Constrained Chain Model for Rubber Elasticity. I. Constant Volume Deformations

This paper reports a new model for rubber elasticity based on the geometric constraints imposed on a network chain and the chain segments by the crosslinks at each end. Through consideration of these constraints, the number of conformations available to a network chain can be calculated directly assuming the chain is on a lattice. By simplifying the model and by assuming affine deformation, the rigorous equations for the conformational entropy are reduced to an analytic expression for the strain-energy function. From this function, equations describing extension, compression and pure shear are derived. The model is tested against literature data for natural rubber and polybutadiene and is found to reproduce quantitatively all the salient features of the experimental stress-strain curves In the three modes of deformation. It is shown that the decrease in the Gaussian modulus with extension, often characterized by the C₂ term in the Mooney-Rivlin theory, arises naturally from the conformational entropy of a network chain, and special effects such as structure, topology, etc., need not be invoked to explain this phenomenon. The theory also predicts the near-constant modulus of extended highly swollen gels, an effect often considered as verification of Gaussian theory.     

Synthesis, structure, and thermochemistry of adduct formation between N-heterocyclic carbenes and isocyanates or mesitylnitrile oxide

Reaction of N-heterocyclic carbenes (NHCs) with isocyanates yields stable zwitterionic imidates/amidates in toluene solution. These compounds were fully characterized and the crystal structures of several species were determined by X-ray crystallography. The thermochemistry of binding of these and related species was studied by solution calorimetry. Comparison is made of the enthalpies of binding of NHC to isocyanates (RNCO) and isomeric nitrile oxides (RCNO) as well as CO₂. DFT calculations were performed to additionally assess the nature of bonding in these compounds.     

Particle Size Determination by Laser Reflection: Methodology and problems

The particle size distribution of crystalline solids has progressively become a key parameter in manufacturing processes, as important as chemical purity. Among the particle size determination and counting systems available on the market, very few offer the possibility of continuous in situ monitoring of the particle size evolution during crystallization. For this reason, much interest has been aroused by the appearance of the Par Tec 100, patented by Laser Sensor Technology [1, 2]. A study has been carried out in a stirred vessel to verify the precision and reproducibility of particle size measurement and elucidate the influence of experimental parameters on data accessible with this instrument. Optimum reproducibility has logically been achieved by fixing the highest possible cycle time and taking the mean of several cycles. Determinations with the Par Tec 100 are influenced variously, according to whether they relate to the total number of particles counted or to the mean size. Thus, the number of counts measured by a particle size probe largely depends on the operating conditions and more particularly on the hydrodynamic conditions, solvent, temperature and focal point position. Its dependence relative to the concentration of the solid in suspension is normal and linear for a solid and for a given monodisperse sample. To establish the relationship between the number of counts and the population density would therefore necessitate delicate calibration on a case-by-case basis. The mean size determined does not depend on suspension homogeneity, provided that the stirring speed is sufficient for a statistically significant total count. On the other hand, for a given sample, a displacement of the focal point can lead to considerable variations in the size determined. The optimal focal point position for small sizes is in fact highly sensitive. Lastly, the optimal position of the focal point is considerably dependent on the true size of the particles, which means that this counter is unsuitable for the precise analysis of a dispersed sample since each particle size class would require a different setting of the focal point. In addition, the sizes determined, irrespective of the products studied, appear to be underestimated for large particles and over estimated for small particles.     

Gamma-ray and delayed neutron branching data for the new or little known isotopes84,85Ge and84,85As

The branchings (absolute intensities) of γ-rays following the decay of^84,85Ge and^84,85As have been determined using mass-separated samples. Our results include the first identification of⁸⁵Ge and the first γ-ray data for⁸⁴Ge. Values of the delayed neutron emission probabilities, P_n, of⁸⁴Ge and⁸⁵As were also deduced from the data, together with a lower limit of this quantity for⁸⁵Ge. The deduced P_n of about 39 % for the important neutron emitter⁸⁵As is substantially larger than the values of about 22–23 % obtained in previous indirect determinations.     

Investigation into the enantioselection mechanism of ruthenium-arene-diamine transfer hydrogenation catalysts using fluorinated substrates

The effects of both steric and electronic properties of ketones on the selectivity in asymmetric transfer hydrogenation have been studied with aryl alkyl/fluoroalkyl ketones using four ruthenium based catalysts and two different media. The 1-arylethanones, 1-aryl-2-fluoroethanones and 2,2-difluoroacetophenones could be reduced with medium to high ee (86-99%), while the 1-aryl-2,2,2-trifluoroethanones were reduced with low selectivity in most systems. The change in enantioselectivity upon structural variation has been rationalised aided by regression analysis with substituent constants and the partial charge of the carbonyl carbon as predictors. The steric bulk of the alkyl/fluoroalkyl chain was found to be the major factor in determining selectivity in formic acid/triethylamine, while for reduction of a series of substituted 1-arylethanones and 1-aryl-2-fluoroethanones, the selectivity was found to depend on the electronic properties of the aromatic ring, supporting previous evidence that π-π interaction between the substrate and catalyst is important in determining the selectivity. For reductions in water using sodium formate as the hydrogen donor, altered and more complex selectivity mechanisms were observed. Experiments and regression focused on the variation of the alkyl/fluoroalkyl group of phenyl and 1-naphthyl ketones, showed that the selectivity correlated with the size of the substituent, but also the partial charge of the carbonyl carbon.     

Benzoylated uronic acid building blocks and synthesis of N-uronate conjugates of lamotrigine

A chemoenzymatic approach towards benzoylated uronic acid building blocks has been investigated starting with benzoylated hexapyranosides using regioselective C-6 enzymatic hydrolysis as the key step. Two of the building blocks were reacted with the antiepileptic drug lamotrigine. Glucuronidation of lamotrigine using methyl (2,3,4-tri-O-benzoyl-α-D-glycopyranosyl bromide)uronate proceeded to give the N2-conjugate. However, lamotrigine-N2-glucuronide was most efficiently synthesised from methyl (2,3,4-tri-O-acetyl-α-D-glucopyranosyl bromide)uronate. Employing nitromethane as solvent with CdCO(3) as a base lamotrigine-N2 glucuronide was prepared in a high yield (41%). Also methyl (2,3-di-O-benzoyl-4-deoxy-4-fluoro-α-D-glucosyl bromide)uronate underwent N-glucuronidation, but the product was unstable, eliminating hydrogen fluoride to give the corresponding enoate conjugate.