Mass conservative three-dimensional water tracer distribution from Markov chain Monte Carlo inversion of time-lapse ground-penetrating radar data

Time-lapse geophysical measurements are widely used to monitor the movement of water and solutes through the subsurface. Yet commonly used deterministic least squares inversions typically suffer from relatively poor mass recovery, spread overestimation, and limited ability to appropriately estimate nonlinear model uncertainty. We describe herein a novel inversion methodology designed to reconstruct the three-dimensional distribution of a tracer anomaly from geophysical data and provide consistent uncertainty estimates using Markov chain Monte Carlo simulation. Posterior sampling is made tractable by using a lower-dimensional model space related both to the Legendre moments of the plume and to predefined morphological constraints. Benchmark results using cross-hole ground-penetrating radar travel times measurements during two synthetic water tracer application experiments involving increasingly complex plume geometries show that the proposed method not only conserves mass but also provides better estimates of plume morphology and posterior model uncertainty than deterministic inversion results.

Dielectric constant obtained from TDR and volumetric moisture of soils in southern Brazil

Soil moisture is the property which most greatly influences the soil dielectric constant, which is also influenced by soil mineralogy. The aim of this study was to determine mathematical models for soil moisture and the dielectric constant (Ka) for a Hapludalf, two clayey Hapludox and a very clayey Hapludox and test the reliability of universal models, such as those proposed by Topp and Ledieu and their co-workers in the 80's, and specific models to estimate soil moisture with a TDR. Soil samples were collected from the 0 to 0.30 m layer, sieved through a mesh of 0.002 m diameter and packed in PVC cylinders with a 0.1 m diameter and 0.3 m height. Seven samples of each soil class were saturated by capillarity and a probe composed of two rods was inserted in each one of them. Moisture readings began with the saturated soil and concluded when the soil was near permanent wilting point. In each step, the samples were weighed on a precision scale to calculate volumetric moisture. Linear and polynomial models were adjusted for each soil class and for all soils together between soil moisture and the dielectric constant. Accuracy of the models was evaluated by the coefficient of determination, the standard error of estimate and the 1:1 line. The models proposed by Topp and Ledieu and their co-workers were not adequate for estimating the moisture in the soil classes studied. The adjusted linear and polynomial models for the entire set of data of the four soil classes did not have sufficient accuracy for estimating soil moisture. The greater the soil clay and Fe oxide content, the greater the dielectric constant of the medium for a given volumetric moisture. The specific models, θ = 0.40283 - 0.04231 Ka + 0.00194 Ka² - 0.000022 Ka³ (Hapludox) θ = 0.01971 + 0.02902 Ka - 0.00086 Ka² + 0.000012 Ka³ (Hapludox -PF), θ = 0.01692 - 0.00507 Ka (Hapludalf) and θ = 0.08471 + 0.01145 Ka (Hapludox-CA), show greater accuracy and reliability for estimating soil moisture in the soil classes studied.

Chronofunctions of Heilu soil developed from Loess in Luochuan, on the chinese Loess plateau

Soil chronofunctions are an alternative for the quantification of soil-forming processes and underlie the modeling of soil genesis. To establish soil chronofunctions of a Heilu soil profile on Loess in Luochuan, selected soil properties and the 14C ages in the Holocene were studied. Linear, logarithmic, and third-order polynomial functions were selected to fit the relationships between soil properties and ages. The results indicated that third-order polynomial function fit best for the relationships between clay (< 0.002 mm), silt (0.002-0.02 mm), sand (0.02-2 mm) and soil ages, and a trend of an Ah horizon ocurrence in the profile. The logarithmic function indicated mainly variations of soil organic carbon and pH with time (soil age). The variation in CaCO3 content, Mn/Zr, Fe/Zr, K/Zr, Mg/Zr, Ca/Zr, P/Zr, and Na/Zr ratios with soil age were best described by three-order polynomial functions, in which the trend line showed migration of CaCO3 and some elements.

Gauge transformations in the Lagrangian and Hamilton formalisms of generally covariant theories

We study spacetime diffeomorphisms in the Hamiltonian and Lagrangian formalisms of generally covariant systems. We show that the gauge group for such a system is characterized by having generators which are projectable under the Legendre map. The gauge group is found to be much larger than the original group of spacetime diffeomorphisms, since its generators must depend on the lapse function and shift vector of the spacetime metric in a given coordinate patch. Our results are generalizations of earlier results by Salisbury and Sundermeyer. They arise in a natural way from using the requirement of equivalence between Lagrangian and Hamiltonian formulations of the system, and they are new in that the symmetries are realized on the full set of phase space variables. The generators are displayed explicitly and are applied to the relativistic string and to general relativity.

Influence of organic-mineral fertilization of an oxisol on soil chemical properties and Bracharia brizantha production

The use of organic-mineral fertilizer produced by the manufacturing industry of lysine and threonine amino acids can improve the fertility of tropical soils. The objective of this study was to evaluate the influence of different doses of the organic-mineral fertilizer named Ajifer L-14 on chemical properties and on the response with increased production of a forage on a Red Latosol in the northwestern region of São Paulo State, Brazil. A randomized block design was used with seven treatments and four replications. The treatments consisted of: T1- control (without application of Ajifer L-14); T2- control (natural vegetation); T3- mineral fertilization according to crop requirements and soil analysis (application of 1.35 kg plot-1 of urea, 2.20 single superphosphate, and 0.51 KCl, corresponding to 60 of N, 40 P2O5 and 30 kg ha-1 of K2O); T4- fertilization with Ajifer L-14 according to the recommendation resulting from the soil chemical analysis (40 L plot-1, corresponding to 60 kg ha-1 N); T5- fertilization with Ajifer L-14, at a rate of 150 % of the recommended values (60 L plot-1, corresponding to 90 kg ha-1 N); T6- fertilization with Ajifer L-14 at a rate of 50 % of the recommended values (20 L plot-1, corresponding to 30 kg ha-1 N); T7- fertilization with Ajifer L-14 at a rate of 125 % of the recommended values (50 L plot-1, corresponding to 75 kg ha-1 N); T8- fertilization with Ajifer L-14 at a rate of 75 % of the recommended values (30 L plot-1, corresponding to 45 kg ha-1 N). The following soil chemical properties were evaluated (layers 0.0-0.1 and 0.1-0.2 m): P, organic matter, pH, K+, Ca2+, Mg2+, cation exchange capacity, potential acidity, and base saturation. The application of this organic-mineral fertilizer does not influence the soil chemical properties. Regression analysis indicated a polynomial relationship between the application rates of organic-mineral fertilizer and the production of dry matter and crude protein of Bracharia Brizantha.

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

Gauge transformations in Einstein-Yang-Mills theories

We discuss the relation between spacetime diffeomorphisms and gauge transformations in theories of the YangMills type coupled with Einsteins general relativity. We show that local symmetries of the Hamiltonian and Lagrangian formalisms of these generally covariant gauge systems are equivalent when gauge transformations are required to induce transformations which are projectable under the Legendre map. Although pure YangMills gauge transformations are projectable by themselves, diffeomorphisms are not. Instead, the projectable symmetry group arises from infinitesimal diffeomorphism-inducing transformations which must depend on the lapse function and shift vector of the spacetime metric plus associated gauge transformations. Our results are generalizations of earlier results by ourselves and by Salisbury and Sundermeyer. 2000 American Institute of Physics.

Computational problems in perfect phylogeny haplotyping: typing without calling the allele.

A haplotype is an m-long binary vector. The XOR-genotype of two haplotypes is the m-vector of their coordinate-wise XOR. We study the following problem: Given a set of XOR-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny (PP) tree. The question is motivated by studying population evolution in human genetics, and is a variant of the perfect phylogeny haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is "full" genotypes, here we assume less informative input, and so may be more economical to obtain experimentally. Building on ideas of Gusfield, we show how to solve the problem in polynomial time, by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by that tree they map onto, and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes, and present a linear algorithm for identifying those genotypes.

Plant-available soil water capacity: estimation methods and implications

The plant-available water capacity of the soil is defined as the water content between field capacity and wilting point, and has wide practical application in planning the land use. In a representative profile of the Cerrado Oxisol, methods for estimating the wilting point were studied and compared, using a WP4-T psychrometer and Richards chamber for undisturbed and disturbed samples. In addition, the field capacity was estimated by the water content at 6, 10, 33 kPa and by the inflection point of the water retention curve, calculated by the van Genuchten and cubic polynomial models. We found that the field capacity moisture determined at the inflection point was higher than by the other methods, and that even at the inflection point the estimates differed, according to the model used. By the WP4-T psychrometer, the water content was significantly lower found the estimate of the permanent wilting point. We concluded that the estimation of the available water holding capacity is markedly influenced by the estimation methods, which has to be taken into consideration because of the practical importance of this parameter.

Pedotransfer functions to predict water retention for soils of the humid tropics: a review

Over the past three decades, pedotransfer functions (PTFs) have been widely used by soil scientists to estimate soils properties in temperate regions in response to the lack of soil data for these regions. Several authors indicated that little effort has been dedicated to the prediction of soil properties in the humid tropics, where the need for soil property information is of even greater priority. The aim of this paper is to provide an up-to-date repository of past and recently published articles as well as papers from proceedings of events dealing with water-retention PTFs for soils of the humid tropics. Of the 35 publications found in the literature on PTFs for prediction of water retention of soils of the humid tropics, 91 % of the PTFs are based on an empirical approach, and only 9 % are based on a semi-physical approach. Of the empirical PTFs, 97 % are continuous, and 3 % (one) is a class PTF; of the empirical PTFs, 97 % are based on multiple linear and polynomial regression of n th order techniques, and 3 % (one) is based on the k-Nearest Neighbor approach; 84 % of the continuous PTFs are point-based, and 16 % are parameter-based; 97 % of the continuous PTFs are equation-based PTFs, and 3 % (one) is based on pattern recognition. Additionally, it was found that 26 % of the tropical water-retention PTFs were developed for soils in Brazil, 26 % for soils in India, 11 % for soils in other countries in America, and 11 % for soils in other countries in Africa.

Hamiltonian formalism for path-dependent Lagrangians

A presymplectic structure for path-dependent Lagrangian systems is set up such that, when applied to ordinary Lagrangians, it yields the familiar Legendre transformation. It is then applied to derive a Hamiltonian formalism and the conserved quantities for those predictive invariant systems whose solutions also satisfy a Fokker-type action principle.

Quantitative Assessment of Soil Physical Quality in Northern China Based on S-theory

ABSTRACT Quantitative assessment of soil physical quality is of great importance for eco-environmental pollution and soil quality studies. In this paper, based on the S-theory, data from 16 collection sites in the Haihe River Basin in northern China were used, and the effects of soil particle size distribution and bulk density on three important indices of theS-theory were investigated on a regional scale. The relationships between unsaturated hydraulic conductivityKi at the inflection point and S values (S/hi) were also studied using two different types of fitting equations. The results showed that the polynomial equation was better than the linear equation for describing the relationships between -log Ki and -logS, and -log Kiand -log (S/hi)2; and clay content was the most important factor affecting the soil physical quality index (S). The variation in the S index according to soil clay content was able to be fitted using a double-linear-line approach, with decrease in the S index being much faster for clay content less than 20 %. In contrast, the bulk density index was found to be less important than clay content. The average S index was 0.077, indicating that soil physical quality in the Haihe River Basin was good.

Equidistribution of Fekete Points on the Sphere

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.