Sediment management and the renewability of floodplain clay for structural ceramics

The Netherlands has vast resources of clay that are exploited for the fabrication of structural ceramic products such as bricks and roof tiles. Most clay is extracted from the so-called embanked floodplains along the rivers Rhine and Meuse, areas that are flooded during high-discharge conditions. Riverside clay extraction is-at least in theory-compensated by deposition. Based on a sediment balance (deposition versus extraction), we explore the extent to which clay can be regarded as a renewable resource, with potential for sustainable use. Beyond that, we discuss the implications for river and sediment management, especially for the large engineering works that are to be undertaken to increase the discharge capacities of the Rhine and Meuse. Extraction rates are based on production statistics for clay, as well as those for fired end-products. Deposition rates are estimated from published and unpublished geological data (clay volumes and thicknesses, datings, etc.) and from morphological modeling studies. Comparisons between extraction and deposition are made at three different time-space scales: (1) long term (post-1850)/large scale (all Dutch floodplains), (2) present/large scale, and (3) present/site scale. The year 1850 is relevant because it approximately marks the beginning of the current, fully engineered river systems, in which depositional processes are constrained by dikes and groynes. As the Industrial Revolution began in the same period, post-1850 sediments can be identified by their pollution with heavy metals. (1) We estimate the post-1850 clay volume in situ at about 0.20 km(3), and the total extracted volume in the same period at about 0.17 km(3). This puts the net long-term average deposition rate of clay at similar to 1.3 million m(3)/year and the corresponding extraction rate at similar to 1.1 million m(3)/year. (2) Current accumulation is approximately 0.4 million m(3)/year and expected to increase, and current extraction is about 0.7 million m(3)/year and expected to decrease. (3) Clay extraction creates a depression that has an increased sediment-trapping efficiency. This local effect is not considered explicitly in large-scale morphological modeling. Based on maximum observed sedimentation rates, we estimate that replenishment of a clay site takes in the order of 150 years. As clay extraction lowers some 0.5 km(2) of floodplain yearly, a surface area of approximately 75 km(2) would be required for sustainable clay extraction. This is about 1/6 of the total surface area of the embanked floodplains. On the long term, clay extraction from the embanked floodplain depositional environment has been sustainable. At strongly decreasing deposition rates, the ratio between extraction and replenishment seems to have shifted towards unsustainable. However, current sedimentation is estimated conservatively. The site-scale approach suggests that, even if extraction would currently exceed deposition, this could be resolved with sediment management, that is, with site restoration measures aimed at higher sediment-trapping efficiency. Our results have implications for river engineering, especially where substantial digging is involved (floodplain lowering, high-discharge bypass channels, obstacle removal). First, this inevitably affects the clay resources that we studied, while resource sterilization should be avoided. Secondly, the effect that any form of digging has on subsequent sedimentation-increased rates-relates to long-term river maintenance. We conclude that floodplain clay is a renewable resource, especially if managed accordingly. Beyond that, we established that clay extraction is a significant, lasting factor in floodplain evolution along the Rhine and Meuse Rivers. The interests of the extractive industry and river managers could be served jointly with sediment management plans that are based on sediment-budget analyse

Overlapping Unit Cells in 3d Quasicrystal Structure

A 3-dimensional quasiperiodic lattice, with overlapping unit cells and periodic in one direction, is constructed using grid and projection methods pioneered by de Bruijn. Each unit cell consists of 26 points, of which 22 are the vertices of a convex polytope P, and 4 are interior points also shared with other neighboring unit cells. Using Kronecker's theorem the frequencies of all possible types of overlapping are found.Comment: LaTeX2e, 11 pages, 5 figures (8 eps files), uses iopart.class. Final versio

Q-Dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-Invariant Ising Models

We study the q-dependent susceptibility chi(q) of a series of quasiperiodic Ising models on the square lattice. Several different kinds of aperiodic sequences of couplings are studied, including the Fibonacci and silver-mean sequences. Some identities and theorems are generalized and simpler derivations are presented. We find that the q-dependent susceptibilities are periodic, with the commensurate peaks of chi(q) located at the same positions as for the regular Ising models. Hence, incommensurate everywhere-dense peaks can only occur in cases with mixed ferromagnetic-antiferromagnetic interactions or if the underlying lattice is aperiodic. For mixed-interaction models the positions of the peaks depend strongly on the aperiodic sequence chosen.Comment: LaTeX2e, 26 pages, 9 figures (27 eps files). v2: Misprints correcte

Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable chiral Potts spin chain for chains of length 3,4,5. From these results we present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices

It has been shown in earlier works that for Q=0 and L a multiple of N, the ground state sector eigenspace of the superintegrable tau_2(t_q) model is highly degenerate and is generated by a quantum loop algebra L(sl_2). Furthermore, this loop algebra can be decomposed into r=(N-1)L/N simple sl_2 algebras. For Q not equal 0, we shall show here that the corresponding eigenspace of tau_2(t_q) is still highly degenerate, but splits into two spaces, each containing 2^{r-1} independent eigenvectors. The generators for the sl_2 subalgebras, and also for the quantum loop subalgebra, are given generalizing those in the Q=0 case. However, the Serre relations for the generators of the loop subalgebra are only proven for some states, tested on small systems and conjectured otherwise. Assuming their validity we construct the eigenvectors of the Q not equal 0 ground state sectors for the transfer matrix of the superintegrable chiral Potts model.Comment: LaTeX 2E document, using iopart.cls with iopams packages. 28 pages, uses eufb10 and eurm10 fonts. Typeset twice! Version 2: Details added, improvements and minor corrections made, erratum to paper 2 included. Version 3: Small paragraph added in introductio

Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.Comment: 12 pages, 10 figures; submitte

p-species integrable reaction-diffusion processes

We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j with rate $r_{ij}.$ We study the range of parameters (interactions) for which the model is integrable. The wavefunctions of this multi--parameter family of integrable models are found. We also extend the 2--species model to the case in which the particles are able to diffuse to their right or left neighboring sites.Comment: 16 pages, LaTe

New symmetries of the chiral Potts model

In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.Comment: 19 pages, improved notation, made the text easier to read, corrected some typo