Solution of time-domain acoustic wave propagation problems using a RBF interpolation model with “a priori” estimation of the free parameter

In the last decade, Meshless Methods have found widespread application in different fields of engineering and science. Beyond novelty, their mathematical simplicity and numerical accuracy have been the key of their rapid dissemination. Among meshless techniques, RBF (Radial Basis Functions) based methods can be simple and general to solve the problems related to multiple areas of applied physics and engineering. In the specific field of acoustics, there are usually two possible approaches for solving a problem: time- and frequency-domain. In this paper, the authors propose a local time-domain approach to establish an efficient methodology for the solution of large-scale acoustic wave propagation problems. For this purpose, a local interpolation scheme, based on the reproduction of the local wave field using RBFs (MultiQuadric and Gaussian), is implemented and its accuracy is verified against known closed-form solutions. An explicit time-domain marching procedure is adopted, and the quality of the numerical results is also compared with that obtained using standard space-time Finite-Difference schemes. Additionally, the RBF interpolation model is used to simulate the propagation of a Ricker pulse in two simple test cases, and applied to simulate a more complex configuration, corresponding to an underwater sound propagation problem. In this frame, the results are also compared with those computed using a fourth-order in space and second-order in time Finite-Difference scheme.     

On Hypersurfaces of Spheres with Two Principal Curvatures

In this paper we obtain a classification of hypersurfaces in the Euclidean sphere having two principal curvatures; for some of the results we impose that the sectional curvature (Ricci curvature, resp.) is non-negative Ricci.     

Molecular interactions in nitrogen and oxygen

It is proposed that the potential energy function for interaction between pairs of polarizable quadrupolar molecules be represented as the sum of the spherically symmetric Smith-Thakkar (ST) potential and non-spherical terms due to quadrupole-quadrupole and quadrupole-induced dipole interactions. Nitrogen and oxygen are the systems chosen for study. Parameters for the ST term are determined by fixing two of the leading dispersion co-efficients to semi-empirical values and fitting to gaseous viscosity data. The parameters for the non-spherical terms are taken from independent measurements. Second virial coefficients are computed from the total potential functions so constructed. The vibrational structure of the ground states of (O₂)₂ and (N₂)₂ is computed from the ST potentials. Overall agreement with experiment is found to be excellent for nitrogen and reasonably good for oxygen.     

The relative signs of fluorine N.M.R. spin coupling constants in aromatic compounds

In two disubstituted 1,2,4-trifluorobenzenes, it has been shown by double irradiation that J ₀ ^FF has an opposite sign to J_m ^FF and J_p ^FF.     

Atomic interactions in neon and helium

The first two quantum corrections to the second virial coefficients of the Smith-Thakkar potential are calculated. Parameters for neon and helium, gases in which quantum effects are important, are then determined by fitting to semiempirical dispersion coefficients and experimental second virial coefficients. Viscosity coefficients for both gases and vibrational energy level spacings for the neon dimer are calculated as independent tests of the potentials. Overall agreement with experiment is excellent for neon and moderate for helium. The previously determined parameters for argon are found to be only very slightly perturbed by the inclusion of quantum corrections in the calculated second virial coefficients.     

The properties of some derivative autocorrelation functions computed with the atom-atom potential

High-resolution quasi-elastic neutron-scattering measurements have been made on two nematogens: DMBCA with a nematic range 108 to 119°C, and 5CB and a tail-deuteriated sample (D5CB), having a nematic range 22·6 to 35·1°C.

Results on 5CB in the crystal phase at ～18°C showed no significant quasielastic broadening, which means that any random motions of the alkyl chain are slower than about 5 × 10⁹ rad s^-1. Measurements were made at a single temperature in the nematic phases on specimens aligned in a magnetic field of 0·25T; for DMBCA with scattering vector Q⊥n (n is the nematic director) and for 5CB and D5CB with Q⊥n and Q∥n and also on the isotropic liquid phase of D5CB at 45°C. Analysis of the coherent scattering from nematic D5CB at Q = 1·2 Å^-1 and 25°C gave an order parameter <P ₂>=0·55, close to the simple mean field value for this temperature. The coherent scattering from DMBCA is too weak to allow this experiment to be performed.

The most remarkable qualitative feature of the results is the close similarity of the scattering law S(Q, ω) for D5CB (and 5CB) with Q⊥n and Q∥n. Analysis of the results in all cases was made using values for the translational diffusion constants measured previously. Corrections for multiple scattering are shown to be important and a single simple model has been devised which fits the line shapes of all the results for D5CB in nematic (Q⊥n and Q∥n) and isotropic liquid phases and DMBCA. The model involves uniaxial rotational diffusion about the long molecular axis m coupled to a displacement along the rotation axis giving a net rotation in a plane whose normal makes an angle ∝ relative to the direction m. Values for the rotational diffusion constant D _rd ns^-1 are as follows: D5CB, 25°C, 6 (∝ ～ 50°); 45°C, 10. DMBCA, 112°C, 16, (all ±10–15 per cent).

The results for D5CB and 5CB are so similar that no additional detailed model fitting was attempted for the fully hydrogenous sample and it is concluded that while the motion of the alkyl tails is freer, the time scale of the motions is not more than about a factor of 2 faster than that of the molecular cores.     

Theoretical studies of solvent effects on nuclear spin-spin coupling constants

A theoretical study is presented of the effects of solvent molecular motion on nuclear spin-spin coupling constants. Solvent molecules are treated as point dipoles arranged around the solute molecule in a cubic closest packed arrangement. Average dipole moment vectors are given by a rotational Boltzmann average and the resulting perturbation is included in the Fock matrices. Calculations of nuclear spin-spin coupling constants were performed by self-consistent perturbation theory in the INDO (intermediate neglect of differential overlap) approximation of self-consistent-field molecular orbital theory. Calculated results are compared with the experimental data as well as the results of previous models.     

Statistical physics of shear flow: a non-equilibrium problem

Complex fluids are easily and reproducibly driven into non-equilibrium steady states by the action of shear flow. The statistics of the microstructure of non-equilibrium fluids is important to the material properties of every complex fluid that flows, e.g. axle grease on a rotating bearing; blood circulating in capillaries; molten plastic flowing into a mould; the non-equilibrium onion phase of amphiphiles used for drug delivery; the list is endless. Such states are as diverse and interesting as equilibrium states, but are not governed by the same statistics as equilibrium materials. I review some recently discovered principles governing the probabilities of various types of molecular re-arrangements taking place within a sheared fluid. As well as providing new foundations for the study of non-equilibrium matter, the principles are applied to some simple models of particles interacting under flow, showing that the theory exhibits physically convincing behaviour.     

E.S.R. of sulphur-substituted purines and nucleosides; carbon-centred radicals in mercaptopurine crystals at 77 K

Single crystals of the sulphur-containing DNA-base analogue 6-methylmercaptopurine (6MeMP) and its riboside 6-methylmercaptopurine riboside (6MeMPR) have been prepared and irradiated by 4·0 MeV electrons at 77 K. Electron spin resonance techniques have been used to study the radiation-induced radicals at 77 K. The primary carbon-centred radical, common to both molecules, has been identified as a species formed by hydrogen atom abstraction from the methyl group. The principal values of the two α-proton hyperfine coupling tensors and the g-tensors were almost the same for both molecules and for 6MeMPR were: α1, -28·8, -17·9 and -6·4 G; α2, -28·2, -15·7 and -9·8 G; and g, 2·0063, 2·0024 and 2·0018. These data indicate a spin density of 0·77 on the methyl carbon atom. Molecular orbitals determined from CNDO/2 methods were used in calculations of the directions and magnitude of the g-tensor principal values. Comparison of these calculated values and experimental data suggests that contribution of spin density in d-orbitals on the sulphur atom is important in describing the g-tensor. Methyl H-abstraction radicals trapped in pairs were also detected in 6MeMP and the data are consistent with an effective interspin distance of 4·67 Å.     

Analysis of K+/Na+ selectivity of KcsA potassium channel with reference interaction site model theory

As a preliminary approach, we have successfully analysed K⁺/Na⁺ selectivity of the KcsA potassium channel for the most selective ion occupancy state (1010) at the atomic level by using the reference interaction site model (RISM) integral equation theory [Q. Cui, V.H. Smith, Chem. Phys. Lett. 365, 110 (2002)]. With similar methods, in this paper, we analyse seven other most relevant ion occupancy states: (0101), (0110), (1001), (1000), (0100), (0010) and (0001). By analysing all the most relevant states, we are able to characterize some dynamic properties of the systems. More detailed solvation structures of the selectivity filter are presented and more solvation energetic data are obtained and compared with the available molecular dynamics simulation data. We predict consistent results with the simulations in that ions are best dehydrated at binding site 2. For ion occupancy states of most interest, we obtain good relative solvation free energies in comparison with the simulation data. The results in this paper further support the conclusion in our previous paper that the selectivity filter favours K⁺ over Na⁺ from the point of view of solvation.