Transport phenomena in a plane shock wave

With the use of the nonpolynomial closure 1/ _z in the Mott-Smith approximation of the solution of the Boltzmann equation, we obtain a value of the density gradient in the limit of a very weak shock wave that is close to the correct value. For the determination of the transverse temperature gradient we calculated the _x ² / _z moment of the Mott-Smith collision integral. The effective values of viscosity and thermal conductivity in the limit of a very weak shock wave were calculated for inverse-power potentials and found to agree almost exactly with the Chapman-Enskog values. Such a comparison can serve as a criterion for the evaluation of different bimodal theories. Various bimodal theories give different values of viscosity and thermal conductivity, but all of them give 33 % too high a value of the Eucken ratio.     

Headspace-gas chromatography: The influence of sample volume on analytical results

Summary The role of the volume of the sample and the sample vial in equilibrium headspace-gas chromatography is discussed. A new term, thesample phase fraction (_S) is introduced. It is shown that if the value of _S is kept constant, the vial's volume has no influence on the sensitivity of the headspace analysis (which is proportional to the concentration of the analyte in the headspace). In a given headspace sampling system, concentration of the compound of interest in the headspace (c _G ^* ) at equilibrium is related to the value of _S: a higher _S will increase c _G ^* . However, the influence is important only in the case of low distribution coefficients: in the case of higher distribution coefficients this influence is negligible. This conclusion is also true for small changes in the sample volume in duplicate analyses: exact reproducibility of the sample volume is important only in the case of low distribution coefficient values.     

Enhancement of the solubilities of polycyclic aromatic hydrocarbons by weak hydrogen bonds with water

Summary The thermodynamics of mobile order is applied to predict the aqueous solubility of liquid and solid aliphatic and polycyclic aromatic hydrocarbons. The solubility values are mainly determined by the magnitude of the hydrophobic effect. However, contrary to the solubilities of the alkanes, the solubilities of polycyclic aromatic hydrocarbons in water predicted in absence of solute-solvent hydrogen (H) bonds are systematically too low. This shows the contribution of weak specific interactions between the OH groups and the electrons of the aromatic substances. According to the theory, these interactions are characterized by a stability bility constant K_o which can be derived from solubility data. At 25°C, this constant amounts to 80 cm³/mol, the order of magnitude of which can be explained by the competition of these intermolecular bonds with the rather weak self-association bonds in the secondary chains of water.     

Phenomenology of nonlocal cellular automata

Dynamical systems with nonlocal connections have potential applications to economic and biological systems. This paper studies the dynamics of nonlocal cellular automata. In particular, all two-state, three-input nonlocal cellular automata are classified according to the dynamical behavior starting from random initial configurations and random wirings, although it is observed that sometimes a rule can have different dynamical behaviors with different wirings. The nonlocal cellular automata rule space is studied using a mean-field parametrization which is ideal for the situation of random wiring. Nonlocal cellular automata can be considered as computers carrying out computation at the level of each component. Their computational abilities are studied from the point of view of whether they contain many basic logical gates. In particular, I ask the question of whether a three-input cellular automaton rule contains the three fundamental logical gates: two-input rules AND and OR, and one-input rule NOT. A particularly interesting edge-of-chaos nonlocal cellular automaton, the rule 184, is studied in detail. It is a system of coupled selectors or multiplexers. It is also part of the Fredkin's gate—a proposed fundamental gate for conservative computations. This rule exhibits irregular fluctuations of density, large coherent structures, and long transient times.     

Quantum qualitative dynamics

We describe our work on qualitative methods for visualizing the quantum eigenstates of systems with nonlinear classical dynamics. For two-degree-of-freedom systems, our approach is based on the use of generalized coherent states, and allows systems with nonoscillator kinematics to be investigated. The general approach is illustrated with two examples involving vibration-rotation interaction in polyatomic molecules. We apply the coherent states of the Lie groupH ₄SU(2) to define quantum surfaces of section for a model involving centrifugal coupling of a harmonic bend with molecular rotation, andSU(2)SU(2) coherent states to study two harmonic normal modes coupled to overall molecular rotation through coriolis interaction. In both systems, quantum states are visualized on the rotational surface of section and compared with the corresponding classical phase space structure. Striking classical-quantum correspondence is observed. We then describe recent results on the quantum states of (N 3)-dimensional systems of coupled nonlinear oscillators, which reveal a quantum delocalization that is reminiscent of classical Arnold diffusion.     

Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

Kinetic limits of the HPP cellular automaton

We study the Boltzmann-Grad limit in various versions of the two-dimensional HPP cellular automaton. In the completely deterministic case we prove convergence to an evolution that is not of kinetic type, a well-known phenomenon after Uchyiama's paper on the Broadwell gas, whereas the limiting equation becomes of kinetic type in the model with random collisions. The main part of the paper concerns the case where the collisions are deterministic and the randomness comes from inserting, between any two successive HPP updatings, ^- stirring updatings, <1 being any fixed positive number and a parameter which tends to 0. The initial measure is a product measure with average occupation numbers of the order of (low-density limit) and varying on distances of the order of ^–1. The limit as 0 of the system evolved for times of the order of ^-1- corresponds to the Boltzmann-Grad limit. We prove propagation of chaos and that the renormalized average occupation numbers (i.e., divided by) converge to the solution of the Broadwell equation. Convergence is proven at all times for which the solution of the Broadwell equation is bounded.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

Novel multiply hydrogen-bonded heterodimers based on heterocyclic ureas. Folding and stability

A new series of multiply hydrogen-bonded heterodimers have been self-assembled in chloroform-d, with ureidopyrimidone derivatives 2 and 3 and 2,7-diamino-1,6-naphthyridine diamide 4 and ureas 5 and 6 as monomers. The self-associating behavior of the compounds and the binding modules of the new heterodimers have been investigated. New tri-center hydrogen bonds have been proposed to explain the stability of the new heterodimers. 2D-NOESY, COSY and temperature variable ¹H NMR studies revealed that all the new heterodimers are substantially more stable than the ureidopyrimidone-based quadruply hydrogen-bonded homodimers in chloroform-d. As a result, heterodimers 2·4 and 3·4 were assembled quantitatively, while heterodimers 2·5, 3·5, 2·6, and 3·6 were formed in 80-85% yields. It is also revealed that intramolecular hydrogen bonds formed in monomers 5 and 6 reduce the stability of the corresponding heterodimers.