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.

Programa de ajuste multiparamétrico de curvas de titulação potenciométricas de ácidos húmicos

Tendo em vista a dificuldade de determinação dos pontos de inflexão na curva de titulação potenciométrica de ácidos húmicos, por metodologias tradicionais, foi desenvolvido foi desenvolvido um programa na linguagem Delphi para ajuste multiparamétrico de dados de titulação potenciométrica. Para isso um processo iterativo para estimar as raízes de um polinômio, com base no método de Newton-Raphson, foi utilizado. Os dados das titulações potenciométricas de ácidos húmicos usados nas regressões foram obtidos em um sistema automatizado de titulação potenciométrica. O programa desenvolvido na linguagem Delphi permite maior versatilidade e facilidade de operação, com uma interação mais amigável com o usuário. As curvas de titulação potenciométricas ajustadas sobrepuseram-se quase que totalmente às curvas experimentais. Os valores de pKa e as percentagens de grupos tituláveis dos ácidos húmicos, parâmetros ajustáveis na regressão multiparamétrica, apresentaram valores comparáveis com dados da literatura.

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.

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.

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.

Concilium Parisiense, 825.

Lettres des empereurs MICHEL et THEOPHILE à Louis le Pieux (5) ; — Libellus synodalis parisiensis (11v) ; — Lettres des empereurs LOUIS et LOTHAIRE à Eugène II (103), à Jérémie, archev. de Sens, et Jonas, év. d'Orléans (104). — (Ms. P de Werminghoff, M. G., Conc., II, 475-535). F. 1v Formules de lettres. F. 2-4, 16v, 51, 78v-83v et 105v-107v Manuel tironien (Legendre, Un manuel tironien du Xe s.).

Revisión del catastro romano de Illici (Elche)

En el presente trabajo se ha realizado un estudio del catastro romano del Ager de Illici (Elche), analizando su incidencia en el paisaje, su importancia histórica así como en que medida se ha conservado hasta nuestros días. Además este estudio ha permitido experimentar una metodología de trabajo dirigida al análisis rápido y sistemático de la morfología histórica del territorio en relación a otros elementos del paisaje, que ha permitido evaluar el potencial arqueológico de la zona. El análisis arqueomorfológico del Llano de Elche, junto al estudio metrológico y a la red viaria, han demostrado la existencia en esta zona de una ordenación de carácter ortogonal que presenta una orientación de 7,50 respecto al N geográfico y que responde a un módulo de 710 metros de lado, que es compatible a una centuriatio romana.

Support for a colleague

As collaborators of Anders Pape Møller, we were shocked and surprised to read that he was accused of data fabrication ("Ecologists roiled by misconduct case," G. Vogel, F. Proffitt, R. Stone, News of the Week, 30 Jan., p. 606). We have never had cause to be concerned about any aspect of our collaborations with Møller. He is an amazing scientist, and his great organizational skills are a model for how to be productive in the face of competing time demands. Most of us are capable of much more than we actually accomplish, but we lack the dedication and self-discipline to follow through like Anders Møller. This is the secret of his phenomenal effectiveness that has been so puzzling to the scientific community. His achievements may have caused negative responses from some of his competitors. We would like to see a full, objective, and independent inquiry into the allegations. Our experience tells us that Anders Møller has an exceptionally complete focus on any task at hand, be it fieldwork, data analysis, or paper writing; this, combined with more than a little natural talent, is sufficient to explain his exceptional productivity. We have worked with him on a variety of projects, including collecting data, sometimes under arduous conditions, and in all our dealings with him, his behavior has been beyond reproach. We would ask colleagues to restrain from further public condemnation until such time as any allegations have been proven beyond doubt.

Lagrangian-Hamiltonian unified formalism for field theory

The RuskSkinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations. 2004 American Institute of Physics.

Distribuição de raízes de laranja "Pêra" sob sequeiro e irrigação por microaspersão em solo arenoso

O trabalho teve por objetivo avaliar a distribuição de raízes de laranja "Pêra" sob condições não-irrigadas e irrigadas por microaspersão em solo arenoso de tabuleiro costeiro. As raízes foram extraídas em trincheiras, a partir do tronco, nas direções longitudinal e ortogonal à fileira de plantas, pelo método do monolito. Uma vez separadas, foram digitalizadas com uso de computador e scanner, para obter, com o uso do software Rootedge, os comprimentos e diâmetros dos segmentos de raízes de todas as amostras, que foram mapeados nos perfis amostrados. O sistema radicular sob irrigação por microaspersão apresentou maior expansão, tanto em profundidade como em distância radial do tronco, do que o sistema radicular sob condições não-irrigadas. Houve maior porcentagem de raízes finas nos perfis de solo sob microaspersão, em relação à condição não-irrigada, indicando a possibilidade de maior atividade do sistema radicular nesse sistema de irrigação. As posições mais adequadas para instalação de sensores de água do solo para a cultura da laranja sob microaspersão estão entre 0 e 2,5 m de distância radial a partir do tronco, em profundidades entre 0 e 1,0 m.

Hamiltonian formalism for nonlocal Lagrangians

A Hamiltonian formalism is set up for nonlocal Lagrangian systems. The method is based on obtaining an equivalent singular first order Lagrangian, which is processed according to the standard Legendre transformation and then, the resulting Hamiltonian formalism is pulled back onto the phase space defined by the corresponding constraints. Finally, the standard results for local Lagrangians of any order are obtained as a particular case.

Variáveis ruminais avaliadas por meio de funções matemáticas contínuas

O objetivo deste trabalho foi avaliar as variáveis pH e concentração de nitrogênio amoniacal ruminal em bovinos por meio de funções matemáticas contínuas, utilizando-se o polinômio trigonométrico em série de Fourier. Foram utilizados quatro conjuntos de dados simulados referentes à alimentação de vacas em lactação em confinamento e bovinos suplementados em pastejo. Os ajustamentos dos modelos foram realizados por procedimentos iterativos. Os efeitos nutricionais nas diferentes situações de alimentação simuladas foram estimados por operações de cálculo integral. As séries de Fourier apresentam elevada capacidade de ajustamento para descrição do comportamento diário do pH e concentração de nitrogênio amoniacal ruminal. As variáveis geradas por integração das funções ajustadas apresentam elevada capacidade discriminatória, o que permite refinamentos sobre a interpretação dos efeitos nutricionais de diferentes dietas das características físico-químicas do ambiente ruminal.