Hydrology

When applied to wetlands, the science of hydrology is concerned with how the storage and movement of water into and out of a wetland affects the plants and animals, and the soils on which they grow. Most wetland scientists agree that the single most important factor determining both wetland type and function is hydrology. Consequently, changes in hydrology are the leading causes of wetland degradation or destruction. The two case studies in this chapter illustrate how water was returned to a previously drained lowland swamp and a peat bog and the effects on the vegetation communities. Both sites had been drained as further dry land was desired for farming and urban development, a common scenario throughout New Zealand

Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg

A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~ exp[-(t/tau(T))^beta(T)] with an exponent beta(T) tending to ~ 1/3 at Tg. The results are compared to those which were observed by Ogielski in the 3d ISG model, and are discussed in terms of a phase space percolation transition scenario.Comment: 6 pages, 7 figure

Comment on ``Spin-glass transition of the three-dimensional Heisenberg spin glass''

Campos et al. [Phys. Rev. Lett. 97 (2006) 217204] claim that in the 3d Heisenberg Spin Glass, chiral and spin sector ordering temperatures are identical. We point out that in their analysis of their numerical data key assumptions are made which are unjustified.Comment: published versio

The Ising Spin Glass in dimension four

The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein {\it et al.} (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.Comment: 10 pages, 15 figure

An expression for land surface water storage monitoring using a two-formation geological weighing lysimeter

Field studies have demonstrated that ground surface rainfall accumulation can be detected at depth by synchronous increases in static confined groundwater pore pressures. This opens the way for “geological weighing lysimeters” providing disturbance-free water storage monitoring of the surface environment, in effect by weighing a significant land area in real time. Such systems require specific hydrogeological conditions, which are not easily verified by field observations and replicated observations from multiple geological formations are a prerequisite for quality control. Given replication over two monitored formations, we introduce an expression which utilises the respective formation piezometric water levels to give an improved combined estimate of the ground surface water budget. The expression utilises raw piezometric levels and has the advantage of direct correction for Earth tide noise, which may sometimes be influenced by local effects in addition to the pure solar/lunar tidal potential. The expression is particularly simple, if the two formations have similar (but possibly unknown) undrained Poisson ratios and porosities. Surface water budgets can then be estimated using only the respective formation barometric coefficients and piezometric levels. An example application to two vertically separated confined aquifers at a New Zealand site indicate an improved accuracy over single-formation observations. The two-formation expression for surface storage could find use as an accurate water budget tool with particular application to monitoring diffuse hydrological systems such as wetlands, arid regions, and heavily forested localities

Hyperscaling breakdown and Ising Spin Glasses: the Binder cumulant

Among the Renormalization Group Theory scaling rules relating critical exponents, there are hyperscaling rules involving the dimension of the system. It is well known that in Ising models hyperscaling breaks down above the upper critical dimension. It was shown by M. Schwartz [Europhys. Lett. {\bf 15}, 777 (1991)] that the standard Josephson hyperscaling rule can also break down in Ising systems with quenched random interactions. A related Renormalization Group Theory hyperscaling rule links the critical exponents for the normalized Binder cumulant and the correlation length in the thermodynamic limit. An appropriate scaling approach for analyzing measurements from criticality to infinite temperature is first outlined. Numerical data on the scaling of the normalized correlation length and the normalized Binder cumulant are shown for the canonical Ising ferromagnet model in dimension three where hyperscaling holds, for the Ising ferromagnet in dimension five (so above the upper critical dimension) where hyperscaling breaks down, and then for Ising spin glass models in dimension three where the quenched interactions are random. For the Ising spin glasses there is a breakdown of the normalized Binder cumulant hyperscaling relation in the thermodynamic limit regime, with a return to size independent Binder cumulant values in the finite-size scaling regime around the critical region.Comment: 11 pages, 22 figure