Phase diagram of a Heisenberg spin-Peierls model with quantum phonons

Using a new version of the density-matrix renormalization group we determine the phase diagram of a model of an antiferromagnetic Heisenberg spin chain where the spins interact with quantum phonons. A quantum phase transition from a gapless spin-fluid state to a gapped dimerized phase occurs at a nonzero value of the spin-phonon coupling. The transition is in the same universality class as that of a frustrated spin chain, to which the model maps in the diabatic limit. We argue that realistic modeling of known spin-Peierls materials should include the effects of quantum phonons.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Theoretical and numerical analyses of convective instability in porous media with upward throughflow

Exact analytical solutions have been obtained for a hydrothermal system consisting of a horizontal porous layer with upward throughflow. The boundary conditions considered are constant temperature, constant pressure at the top, and constant vertical temperature gradient, constant Darcy velocity at the bottom of the layer. After deriving the exact analytical solutions, we examine the stability of the solutions using linear stability theory and the Galerkin method. It has been found that the exact solutions for such a hydrothermal system become unstable when the Rayleigh number of the system is equal to or greater than the corresponding critical Rayleigh number. For small and moderate Peclet numbers (Pe less than or equal to 6), an increase in upward throughflow destabilizes the convective flow in the horizontal layer. To confirm these findings, the finite element method with the progressive asymptotic approach procedure is used to compute the convective cells in such a hydrothermal system. Copyright (C) 1999 John Wiley & Sons, Ltd.

Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field

We present some exact results for the effect of disorder on the critical properties of an anisotropic XY spin chain in a transverse held. The continuum limit of the corresponding fermion model is taken and in various cases results in a Dirac equation with a random mass. Exact analytic techniques can then be used to evaluate the density of states and the localization length. In the presence of disorder the ferromagnetic-paramagnetic or Ising transition of the model is in the same universality class as the random transverse field Ising model solved by Fisher using a real-space renormalization-group decimation technique (RSRGDT). If there is only randomness in the anisotropy of the magnetic exchange then the anisotropy transition (from a ferromagnet in the x direction to a ferromagnet in the y direction) is also in this universality class. However, if there is randomness in the isotropic part of the exchange or in the transverse held then in a nonzero transverse field the anisotropy transition is destroyed by the disorder. We show that in the Griffiths' phase near the Ising transition that the ground-state energy has an essential singularity. The results obtained for the dynamical critical exponent, typical correlation length, and for the temperature dependence of the specific heat near the Ising transition agree with the results of the RSRODT and numerical work. [S0163-1829(99)07125-8].

Finite element modelling of reactive mass transport problems in fluid-saturated porous media

We use the finite element method to solve reactive mass transport problems in fluid-saturated porous media. In particular, we discuss the mathematical expression of the chemical reaction terms involved in the mass transport equations for an isothermal, non-equilibrium chemical reaction. It has turned out that the Arrhenius law in chemistry is a good mathematical expression for such non-equilibrium chemical reactions especially from the computational point of view. Using the finite element method and the Arrhenius law, we investigate the distributions of PH (i.e. the concentration of H+) and the relevant reactive species in a groundwater system. Although the main focus of this study is on the contaminant transport problems in groundwater systems, the related numerical techniques and principles are equally applicable to the orebody formation problems in the geosciences. Copyright (C) 1999 John Wiley & Sons, Ltd.

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Incorporating phase retardation effects into radiofrequency resonator models: application to magnetic resonance microscopy

A method is presented for including path propagation effects into models of radiofrequency resonators for use in magnetic resonance imaging. The method is based on the use of Helmholtz retarded potentials and extends our previous work on current density models of resonators based on novel inverse finite Hilbert transform solutions to the requisite integral equations. Radiofrequency phase retardation effects are most pronounced at high field strengths (frequencies) as are static field perturbations due to the magnetic materials in the resonators themselves. Both of these effects are investigated and a novel resonator structure presented for use in magnetic resonance microscopy.

Role of the crystallite phase of TiO2 in heterogeneous photocatalysis for phenol oxidation in water

A series of TiO2 samples with different anatase-to-rutile ratios was prepared by calcination, and the roles of the two crystallite phases of titanium(IV) oxide (TiO2) on the photocatalytic activity in oxidation of phenol in aqueous solution were studied. High dispersion of nanometer-sized anatase in the silica matrix and the possible bonding of Si-O-Ti in SiO2/TiO2 interface were found to stabilize the crystallite transformation from anatase to rutile. The temperature for this transformation was 1200 degrees C for the silica-titania (ST) sample, much higher than 700 degrees C for Degussa P25, a benchmarking photocatalyst. It is shown that samples with higher anatase-to-rutile ratios have higher activities for phenol degradation. However, the activity did not totally disappear after a complete crystallite transformation for P25 samples, indicating some activity of the rutile phase. Furthermore, the activity for the ST samples after calcination decreased significantly, even though the amount of anatase did not change much. The activity of the same samples with different anatase-to-rutile ratios is more related to the amount of the surface-adsorbed water and hydroxyl groups and surface area. The formation of rutile by calcination would reduce the surface-adsorbed water and hydroxyl groups and surface area, leading to the decrease in activity.

Finite element analysis of heat transfer and mineralization in layered hydrothermal systems with upward throughflow

We use the finite element method to solve the coupled problem between convective pore-fluid flow, heat transfer and mineralization in layered hydrothermal systems with upward throughflow. In particular, we present the improved rock alteration index (IRAI) concept for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in the systems. To validate the numerical method used in the computation, analytical solutions to a benchmark problem have been derived. After the numerical method is validated, it is used to investigate the pattern of pore-fluid Aom, the distribution of temperature and the mineralization pattern of gold minerals in a layered hydrothermal system with upward throughflow. The related numerical results have demonstrated that the present concept of IRAI is useful and applicable for predicting the most probable precipitation and dissolution regions of gold (Au) minerals in hydrothermal systems. (C) 2000 Elsevier Science S.A. All rights reserved.

X-ray absorption and phase contrast imaging to study the interplay between plant roots and soil structure

Plant performance is, at least partly, linked to the location of roots with respect to soil structure features and the micro-environment surrounding roots. Measurements of root distributions from intact samples, using optical microscopy and field tracings have been partially successful but are imprecise and labour-intensive. Theoretically, X-ray computed micro-tomography represents an ideal solution for non-invasive imaging of plant roots and soil structure. However, before it becomes fast enough and affordable or easily accessible, there is still a need for a diagnostic tool to investigate root/soil interplay. Here, a method for detection of undisturbed plant roots and their immediate physical environment is presented. X-ray absorption and phase contrast imaging are combined to produce projection images of soil sections from which root distributions and soil structure can be analyzed. The clarity of roots on the X-ray film is sufficient to allow manual tracing on an acetate sheet fixed over the film. In its current version, the method suffers limitations mainly related to (i) the degree of subjectivity associated with manual tracing and (ii) the difficulty of separating live and dead roots. The method represents a simple and relatively inexpensive way to detect and quantify roots from intact samples and has scope for further improvements. In this paper, the main steps of the method, sampling, image acquisition and image processing are documented. The potential use of the method in an agronomic perspective is illustrated using surface and sub-surface soil samples from a controlled wheat trial. Quantitative characterization of root attributes, e.g. radius, length density, branching intensity and the complex interplay between roots and soil structure, is presented and discussed.

Prediction of rock alteration patterns: a potential tool in mineral exploration

Hydrothermal alteration of a quartz-K-feldspar rock is simulated numerically by coupling fluid flow and chemical reactions. Introduction of CO2 gas generates an acidic fluid and produces secondary quartz, muscovite and/or pyrophyllite at constant temperature and pressure of 300 degrees C and 200 MPa. The precipitation and/or dissolution of the secondary minerals is controlled by either mass-action relations or rate laws. In our simulations the mass of the primary elements are conserved and the mass-balance equations are solved sequentially using an implicit scheme in a finite-element code. The pore-fluid velocity is assumed to be constant. The change of rock volume due to the dissolution or precipitation of the minerals, which is directly related to their molar volume, is taken into account. Feedback into the rock porosity and the reaction rates is included in the model. The model produces zones of pyrophyllite quartz and muscovite due to the dissolution of K-feldspar. Our model simulates, in a simplified way, the acid-induced alteration assemblages observed in various guises in many significant mineral deposits. The particular aluminosilicate minerals produced in these experiments are associated with the gold deposits of the Witwatersrand Basin.

Experimental study of phase equilibria in the systems Fe-Zn-O and Fe-Zn-Si-O at metallic iron saturation

The reported experimental work on the systems Fe-Zn-O and Fe-Zn-Si-O in equilibrium with metallic iron is part of a wider research program that combines experimental and thermodynamic computer modeling techniques to characterize zinc/lead industrial slags and sinters in the system PbO-ZnO-SiO2-CaO-FeO-Fe2O3. Extensive experimental,investigations using high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA) were carried out. Special experimental; procedures were developed to enable accurate measurements in these ZnO-containing systems to be performed in equilibrium with metallic iron; The systems Fe-Zn-O and FeZn-Si-O were experimentally investigated in equilibrium with metallic iron in the temperature ranges 900 degreesC to 1200 degreesC (1173 to 1473 K) and from 1000 degreesC to 1350 degreesC (1273 to 1623 K), respectively. The liquidus surface in the system Fe-Zn-Si-O in equilibrium with metallic iron was characterized in the composition ranges 0 to 33 wt pet ZnO and 0 to 40 wt pet SiO2. The wustite (Fe,Zn)O, zincite (Zn,Fe)O, willemite (Zn,Fe)(2)SiO4, arid fayalite: (Fe,Zn)(2)SiO4 solid solutions in equilibrium with metallic iron were measured.

Experimental study of phase equilibria in the PbO-MgO-SiO2 system

Equilibrium phase relations in the PbO-Al2O3-SiO2 system have been investigated experimentally by means of high-temperature equilibration, quenching, and electron probe X-ray microanalysis (EPMA). The system has 21 primary phase fields including three monoxides (PbO, Al2O3, and SiO2), seven binary compounds (Al6Si2O13, PbAl2O4, PbAl12O19, Pb2Al2O5, PbSiO3, Pb2SiO4, and Pb4SiO6), and eleven ternary compounds (PbAl2Si2O8, Pb3Al10SiO20, Pb4Al2Si2O11, Pb4Al4SiO12, Pb4Al4Si3O16, Pb4Al4Si5O20, Pb5Al2Si10O28, Pb6Al2Si6O21, Pb8Al2Si4O19, Pb12Al2Si17O49, and Pb12Al2Si20O55). Three new ternary compounds, Pb4Al4SiO12, Pb4Al4Si5O20, and Pb12Al2Si17O49, were observed and characterized by EPMA. No extensive solid solution in any of the compounds was found in the present study. The liquidus isotherms were experimentally determined in most of the primary phase fields in the temperature range from 923 to 1873 K, and the ternary phase diagram of the PbO-Al2O3-SiO2 System has been constructed.