Wave propagation in saturated ground using the volume fractions

The purpose of this paper is to study the dynamic behavior of soft ground including a porous layer by considering the porosity change. In order to take the porosity change into account, the concept of the volume fraction, which has been proposed in continuum mechanics, is introduced. The constitutive equations presented by Bowen are applied to the analysis of the porous media. According to Bowen's theory, the porosity is considered as a variable called the volume fraction and has its own constitutive equation. The constitutive equation of the volume fraction has thermoelastic equation coefficients and is determined by the strains of the solid and the fluid. This means that the compressibilities of the solid and the fluid are considered. When the special condition is assumed, Bowen's theory can contain Biots's theory, which has been applied in earthquake engineering. The wave propagation in the ground including a porous layer, modeled by Bowen's theory, is studied and compared with that of Biot's theory. One-dimensional attenuation and surface amplitude are calculated. The effect of the volume fraction is discussed with respect to the compressibilities of the solid and the fluid.     

Phase and velocity distributions in vertically upward high-viscosity two-phase flow

The two-phase pressure drop in vertical industrial pipes is mainly determined by gravitation and acceleration of the fluid, which means that the void fraction is key an important parameter in any model to predict pressure drops. Typically, these models are applied in industry to size pumps and, e.g., emergency relief systems. There is a shortage of void fraction data in the literature for liquids with a dynamic viscosity above 1000 mPa s. Adiabatic experiments have been performed of mixtures of nitrogen and solutions of polyvinylpyrrolidone (Luviskol^®) in water with dynamic viscosities in the range 900–7000 mPa s. Inner tube diameter was 54.5 mm. Mass flux and quality were varied in a wide range: 8–3500 kg/m²/s and 0–82%, respectively. The corresponding superficial velocities were 0.005–3.4 m/s for the liquid and 0–30 m/s for the nitrogen. For comparison, reference measurements were taken of mixtures of nitrogen with water (1 mPa s). Care has been taken to measure only well-developed flows.     

Spin-lattice relaxation times of bound water—Its determination and implications for tissue discrimination

Measurements were made of T1 of bound water (T1b) and bound water fraction () for gelatin solutions and human tissues (sera, brain tumor, cerebral white matter). Bound water fraction in each sample was measured by means of thermal analysis (differential scanning calorimetry: DSC). T1 values were measured by FONAR QED 80-. T1b values were calculated by an equation derived from the fast-exchange two-state model. In the study of gelatin solutions, the relationship between T1 and water content differed depending on the sort of solutions. This was considered to be due to differences in T1b values. In each biological tissue the values of T1b and had different distributions. These results indicate that values of T1b and for biological tissues may be altered in correspondence to the changes in pathophysiological states in those tissues.     

Isotactic poly(p-fluorostyrene): Conformation and molecular packing analysis

The chain conformation and molecular packing of isotactic poly(p-fluorostyrene) have been examined using calculations made with semiempirical potential energy functions. Isolated chain conformational energies indicate no difference in conformation for the fluoropolymer from the conformation for isotactic polystyrene. The energy for packing poly(p-fluorostyrene) chains into a crystalline array as 3₁ or 4₁ helices was also compared with the energies for packing polystyrene in both of these helical forms. While not being the lowest energy mode of packing for poly(p-fluorostyrene), the packing of 4₁-helices does yield a local energy minimum. Such packing of 4₁ helical polystrene chains is considerably less energetically feasible. The results indicate the causes for the experimentally observed difference in the crystalline conformations of the two isotactic polymers as being due to intermolecular influences.     

A distributional limit law for the continued fraction digit sum

We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalised fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalised linearly we determine a large deviation asymptotic. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the ionic conductivity of polymer electrolytes in terms of hole fraction

A theoretical model to interpret the conductivity of ions through polymer electrolytes is established in terms of the temperature and pressure‐dependent hole fraction computed from Simha‐Somcynsky hole theory. The model successfully linearizes the logarithm of PPG and PEG conductivity data with NaCF₃SO₃ in a 20:1 ratio for a broad range of temperature and pressure. The conductivity parameter and transmission coefficient with an additive hole fraction constant are discussed and compared for both species. The derivative of the logarithm of conductivity with respect to the hole fraction decreases inversely with the hole fraction and saturates at about 0.08 and 0.12 hole fractions for PPG and PEG, respectively. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2249–2254, 2008     

On the relaxation time of Gauss's continued-fraction map I. The Hilbert space approach (Koopmanism)

It is shown thatU ^*, the adjoint of Koopman's isometric operatorUf(x) =f(Tx) corresponding to the mapTx=x ^–1 (mod 1) of the unit interval, is isomorphic to a symmetric integral operator when restricted to a Hilbert space of holomorphic functionsf This result, also obtained by Babenko in a different setting, allows us to derive new trace formulas. Using generalized Temple's inequalities, we determine the relaxation time of the above system with great accuracy. In contrast to a widespread belief, it appears to be unrelated to the entropy of the mapT.     

On the solutions of the Wick-Cutkosky model in the instantaneous approximation

By reexamining the analysis of Basu and Biswas, based on the stereographic projection method of Fock and Levy, it is shown that the general solution of the Wick-Cutkosky model in the instantaneous approximation, hitherto unreported, involves only one quantum number; this is contrasted with the well-known solution which involves two quantum numbers, but for which the spectrum is degenerate with respect to one of them. The latter situation is shown to hold under a rather special circumstance.     

An experimental study on effects of solid concentration and ζ-potential on pseudoplastic flow of suspensions

The pseudoplastic flow of suspensions, alumina or styrene-acrylamide copolymer particles in water or an aqueous solution of glycerin has been studied by the step-shear-rate method. The relation between the shear rate,D, and the shear stress,, in the step-shear-rate measurements, where the state of dispersion was considered to be constant, was expressed as = AD ^1/2 +CD. The effective solid volume fraction,ø _F, andA were dependent on the shear rate and expressed byø _F =aD ^b andA = D . Combining the above relations, the steady flow curve was expressed by = D ^{1/2 +} + ₀ (1 – a D ^b/0.74)^–1.85 D, where ₀ is the viscosity of the medium.With an increase in solid volume fraction and a decreases in the absolute value of the-potential, the flow behavior of the suspensions changed from Newtonian ( = = b = 0), slightly pseudoplastic ( = b = 0), pseudoplastic ( = 0) to a Bingham-like behavior.The change in viscosity of the medium had an effect on the change in the effective volume fraction.