Strategy for solving semi-analytically three-dimensional transient flow in a coupled <Emphasis Type="Italic">N</Emphasis>-layer aquifer system

Efficient strategies for solving semi-analytically the transient groundwater head in a coupled N-layer aquifer system , i = 1, ... , N, with radial symmetry, with full z-dependency, and partially penetrating wells are presented. Aquitards are treated as aquifers with their own horizontal and vertical permeabilities. Since the vertical direction is fully taken into account, there is no need to pose the Dupuit assumption, i.e., that the flow is mainly horizontal. To solve this problem, integral transforms will be employed: the Laplace transform for the t-variable (with transform parameter p), the Hankel transform for the r-variable (with transform parameter α) and a particular form of a generalized Fourier transform for the vertical direction z with an infinite set of eigenvalues (with the discrete index m). It is possible to solve this problem in the form of a semi-analytical solution in the sense that an analytical expression in terms of the variables r and z, transform parameter p, and eigenvalues of the generalized Fourier transform can be given or in terms of the variables z and t, transform parameter α, and eigenvalues . The calculation of the eigenvalues and the inversion of these transformed solutions can only be done numerically. In this context the application of the generalized Fourier transform is novel. By means of this generalized Fourier transform, transient problems with horizontal symmetries other than radial can be treated as well. The notion of analytical solution versus numerical solution is discussed and a classification of analytical solutions is proposed in seven classes. The expressions found in this paper belong to Class 6, meaning that the transformed solutions are written in terms of eigenvalues which depend on one transform parameter (here p or α). Earlier solutions to the transient problem belong to Class 7, where the eigenvalues depend on two transform parameters. The theory is applied to three examples.     

DFT-based Word Normalization in Finite Supersolvable Groups

In this paper we discuss the word normalization problem in pc presented finite supersolvable groups: given two group elements a and b in normal form the normal form of the product a·b is to be computed. As an alternative to classical collection strategies we present a new DFT-based strategy, which uses fragments of certain irreducible representations of the underlying group. This strategy allows an explicit running time analysis. For example, in the special case of a pc presented p-group G of order pⁿ one needs at most 5·p·n² additions in _e:=/e for the computation of the normal form, where e denotes the exponent of G. Interpreting pc presentations as polynomials in multivariate non-commutative polynomial rings we derive an algorithm for fast polynomial division.     

Isochoric p–ρ–T Measurements for 2,2-Dichloro-1,1,1-Trifluoroethane (R123) at Temperatures from 176 to 380 K and 1-Chloro-1,2,2,2-Tetrafluoroethane (R124) from 104 to 400 K at Pressures to 35 MPa

The p––T relationships were measured for 2,2-dichloro-1,1,1-trifluoroethane (R123) and 1-chloro-1,2,2,2-tetrafluoroethane (R124) by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 176 to 380 K for R123 and from 104 to 400 K for R124, while pressures extended up to 35 MPa. Measurements were conducted on compressed liquid samples. Most published p––T data are in good agreement with this study. The uncertainty is 0.03 K for temperature and 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a 2-SD estimate) of the density measurements is estimated to be 0.05%.     

Isochoric p–ρ–T and Heat Capacity Cv Measurements for Ternary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), and 1,1,1,2-Tetrafluoroethane (R134a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships and constant volume heat capacity C _v were measured for ternary refrigerant mixtures by isochoric methods with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K for p––T and from 203 to 345 K for C _v, while for both data types pressures extended to 35 MPa. Measurements of p––T were carried out on compressed gas and liquid samples with the following mole fraction compositions: 0.3337 R32+0.3333 R125+0.3330 R134a and 0.3808 R32+0.1798 R125+0.4394 R134a. Measurements of C _v were carried out on liquid samples for the same two compositions. Published p––T data are in good agreement with this study. For the p––T apparatus, the uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%. For the C _v calorimeter, the uncertainty of the temperature rise is 0.002 K and for the change-of-volume work it is 0.2%; the latter is the principal source of uncertainty. When all components of experimental uncertainty are considered, the expanded relative uncertainty of the heat capacity measurements is estimated to be 0.7%.     

On irreducible polynomials of small height over finite fields

It is shown that, for an arbitrary function(x) , for almost all prime numbersp of any interval of the form [N–,N] there exists an irreducible modulop polynomial with coefficients of orderO((p)).     

The Effect of Zn-Substitution on the Anomalous Resistance Behavior of La1−x Ca x Mn1−y Zn y O3 Compounds

We have studied the effect of Zn substitution on the temperature dependence of the resistivity and the Curie temperature T _p of La_1–x Ca _x Mn_1–y Zn _y O₃ system (with x=0, y=0, and x=0.33, 0.00y0.15) during their pass to the paramagnetic conducting phase. All the specimens show a clear metal-insulator transition passing through the Curie temperature T _p . With increasing Zn concentration, T _p decreases for La/Ca substitution and also for Zn/Mn substitution with fixed 33 at.% of Ca. T _p is found to be slightly decreases for low concentrations of Zn (up to y=0.075) followed by a sharp decrease up to y=0.15. A possible explanation is given. Moreover, the activation energy E _a is calculated in the three different temperature regions characterized in the (-T) curve. Decreasing the temperature below T _p can increase the parallel alignment of the Mn spins and, thus decreases the resistivity of the samples. E _a increases with Zn content (up to y=0.075) followed by a sharp decrease. A strong correlation in the behavior of the normal state and residual resistivity as well as T _p and E _a with Zn content is reported.     

Isochoric p-ρ-T Measurements on 1,1-Difluoroethane (R152a) from 158 to 400 K and 1,1,1-Trifluoroethane (R143a) from 166 to 400 K at Pressures to 35 MPa

The p--T relationships have been measured for 1,1-difluoroethane (R152a) and 1,1,1-trifluoroethane (R143a) by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 158 to 400 K for R152a and from 166 to 400 K for R143a, while pressures were up to 35 MPa. Measurements were conducted on compressed liquid samples. Determinations of saturated liquid densities were made by extrapolating each isochore to the vapor pressure, and determining the temperature and density at the intersection. Published p--T data are in good agreement with this study. For the p--T apparatus, the uncertainty of the temperature is ±0.03 K, and for pressure it is ±0.01% at p>3 MPa and ±0.05% at p&#60;3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), which has a standard uncertainty of ±0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and thus a two-standard deviation estimate) of the density measurements is estimated to be ±0.05%.     

Effect of intermittent polishing on low-cycle fatigue of pure aluminium

Low-cycle fatigue tests of aluminium were interrupted in order to remove surface roughening and superficial cracks produced by prior loading. Depending on the frequency of intermittent polishing and the strain level considerable increases in endurance life were observed.Nomenclature _t total strain range - _p plastic strain range - _e elastic strain range - N _p the number of cycles at which the intermittent polishing is carried out (single-step tests) - N _mp the number of cycles at which the last intermittent polishing action is performed in addition to preceding ones in every 50 cycles (multi-step tests) - N _pf the endurance life in the case of intermittent polishing (single- or multi-step tests) - N _f the endurance life without intermittent polishing     

Improved upper complexity bounds for the discrete fourier transform

The linear complexityL ₂ (G) of a finite groupG is the minimal number of additions, subtractions and multiplications by complex constants of absolute value 2 sufficient to evaluate a suitable Fourier transform of G. Combining and modifying several classical FFT-algorithms, we show thatL ₂(G)8|G|log₂|G| for any finite metabelian groupG.     

Monodisperse micron-sized polymethylmethacrylate particles having a crosslinked network structure. V

Highly monodisperse micron-sized polymethylmethacrylate (PMMA) particles crosslinked with carboxylic group-containing urethane acrylates (CUA) were produced by simple dispersion polymerization in methanol. In proper condition, CUA employed as a crosslinker had an excellent ability to achieve the monodisperse PMMA particles to the concentration of about 10 wt%. This arose from the fact that CUA formed monomer-swellable primary particles due to its structurally long tetramethylene oxide groups in the molecule. The influence of the concentrations of the initiator and CUA on the particle diameter (D _n), particle number density (N _p), and polymerization rate (R _p) was found to obey the following approximate relationship, D _n [initiator]^0.41[CUA]^–0.06, N _p [initiator]^–1.22 [CUA]^0.21, and R _p [initiator]^0.34±0.03, respectively. The power law dependence of D _n and N _p on the initiator concentration coincided well with that of linear polymers in the literature. Especially, in this study, it was found that CUA did not have a serious influence on the nucleation. However, the dependence of R _p on the initiator concentration was observed to be higher than that of linear polymers, suggesting that uniquely, the solution polymerization process competed with the heterogeneous polymerization during polymerization, because of the crosslinked network structure of the primary particles.     

Influence of long-range and strong correlation effects on the electron-phonon coupling in high-Tc oxides

Calculations of the Eliashberg function ²F and the corresponding transport function _tr ² F for high-T _c oxides are presented using a screened ionic model (rigidly shifted ionic potentials screened by charge carriers in the CuO₂ planes within the RPA) for the electron-phonon coupling. It is shown that this model yields a large difference between the transport and the superconducting electron-phonon interaction due to imperfect screening and contributions beyond nearest-neighbor interactions. Using these results, the electron and the lattice heat conductivities are calculated both in the normal and the superconducting state and compared with experiment. Finally, effects due to a strong on-site electron-electron repulsion are included in leading order in an 1/N expansion, whereN is the number of spin degrees of freedom. In particular, it is shown for the infiniteU, one-band Hubbard model that correlations tend to suppress _tr ² F strongly and ² F somewhat.The author thanks M. Kulic for discussions and cooperation on the topic discussed in Section 4.     

Isochoric p–ρ–T Measurements for Binary Refrigerant Mixtures Containing Difluoromethane (R32), Pentafluoroethane (R125), 1,1,1,2-Tetrafluoroethane (R134a), and 1,1,1-Trifluoroethane (R143a) from 200 to 400 K at Pressures to 35 MPa

The p––T relationships were measured for binary refrigerant mixtures by an isochoric method with gravimetric determinations of the amount of substance. Temperatures ranged from 200 to 400 K, while pressures extended up to 35 MPa. Measurements were conducted on compressed gas and liquid samples with the following mole fraction compositions: 0.4997 R32+0.5003 R134a, 0.3288 R32+0.6712 R134a, 0.4996 R32+0.5004 R125, 0.5001 R125+0.4999 R134a, and 0.5000 R125+0.5000 R143a. Most published p––T data are in good agreement with this study. The uncertainty is 0.03 K for temperature and is 0.01% for pressure at p>3 MPa and 0.05% at p<3 MPa. The principal source of uncertainty is the cell volume (28.5 cm³), with a standard uncertainty of 0.003 cm³. When all components of experimental uncertainty are considered, the expanded relative uncertainty (with a coverage factor k=2 and, thus, a two-standard deviation estimate) of the density measurements is estimated to be 0.05%.     

Periodic Sequences with Maximal Linear Complexity and Large <Emphasis Type="Italic">k</Emphasis>-Error Linear Complexity

The linear complexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. Keystreams that are suitable for stream ciphers must have large values of these complexity measures. We study periodic sequences over an arbitrary finite field _q and establish conditions under which there are many periodic sequences over _q with period N, maximal linear complexity N, and k-error linear complexity close to N. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.     

Effective dimensionality of cuprate superconductors

A novel optical method for accurate monitoring of the carrier densityN in layered conductors is introduced. It is applied to several cuprate superconductors, and it is found thatT _c doesnot scale withN. However, if the closely spaced pairs or triplets of CuO₂ planes were coupled together to act as distinct metallic slabs, the relevant variable could ben, theslab carrier density. Indeed, we found thatT _c does scale nicely withn. This suggests that high-T _c superconductivity is effectively a two-dimensional phenomenon; it can occur in a cuprate slab which is only one unit cell thick. Finally, estimates are obtained for the length scales of localization of charge carriers:d 8 Å andd 2 Å in all the cuprates under study.     

Viscosities of nonelectrolyte liquid mixtures. I. binary mixtures containing p-dioxane

Viscosity measurements are reported for p-dioxans with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, tetrachloroethane, chloroform, pentachloroethane, and ethyl acetate at 303.15 K. Excess Gibbs energies of activation G ^*E of viscous flow have been calculated with Eyring's theory of absolute reaction rates. The deviations of the viscosities from a linear dependence on the mole fraction and values of G ^*E for binary mixtures have been explained in terms of molecular interactions between unlike pairs. The Prigogine-Flory-Patterson theory has been used to estimate the excess viscosity, ln , and corresponding enthalpy ln _H, entropy ln _S, and free volume ln _v terms for binary mixtures of p-dioxane with cyclohexane, n-hexane, benzene, toluene, carbon tetrachloride, and chloroform. Estimates of excess viscosities from this theory for p-dioxane with benzene, toluene, and carbon tetrachloride are good, while for the other three mixtures they are poor. The local-composition thermodynamic model of Wei and Rowley estimates the excess viscosity quite well even for p-dioxane mixtures with cyclohexane and n-hexane.     

Measurements of Vapor Pressures from 280 to 369 K and (p, ρ, T) Properties from 340 to 400 K at Pressures to 200 MPa for Propane

Measurements of (p, ρ, T) properties for compressed liquid propane have been obtained by means of a metal-bellows variable volumometer at temperatures from 340 to 400 K at pressures up to 200 MPa. The volume- fraction purity of the propane sample was 0.9999. The expanded uncertainties (k = 2) of temperature, pressure, and density measurements have been estimated to be less than 3 mK; 1.5 kPa ( MPa), 0.06% (7 MPa MPa), 0.1% (50 MPa MPa) , and 0.2% (p>150 MPa); and 0.11%, respectively. Four (p, ρ, T) measurements at the same temperatures and pressures as literature values have been conducted for comparisons. In addition, vapor pressures were measured at temperatures from 280 to 369 K. Furthermore, comparisons of available equations of state with the present measurements are reported.Paper presented at the 17th European Conference on Thermophysical Properties, September 5–8, 2005, Bratislava, Slovak Republic.     

Thermal diffusivity measurement by the transient hot-wire technique: A reappraisal

The theory of the transient hot-wire technique for thermal conductivity measurements is reassessed in the special context of thermal diffusivity measurements. A careful examination of the working equation and an error analysis are employed to identify the principal sources of error. Notwithstanding earlier claims to the contrary, the best precision that can be attained in thermal diffusivity measurements is of the order of ±3%, while the accuracy is inevitably poorer. Experimental evidence is adduced from two different instruments that supports the analysis given here. Although the technique cannot yield values of the thermal diffusivity, k, as accurate as can be achieved by the use of the best possible individual values of ,, and C _p in the relation k=/C _p, the simplicity of the technique makes it attractive for many purposes. It is even possible to derive values of the isobaric heat capacity C _p for many fluids not available from other methods.     

“Power law” version of Bradford's law: Statistical tests and methods of estimation

Is is shown, using rigorous statistical tests, that the number of journals (J) carryingp papers in a given subject can be expressed as a simple power law functionJ(p)=K p ^– , K and being constants. The standard maximum likelihood method of estimating has been suitably modified to take acoount of the fact thatp is a discrete integer variable. The parameter entirely characterises the scatter of articles in journals in a given bibliography. According to a dynamic model proposed earlier by the author, is a measure of the relative growth rates of papers and journals pertaining to the subject.     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.