From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is suppressed. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass.

Poincar-Cartan integral invariant and canonical transformation for singular lagrangians

In this work we develop the canonical formalism for constrained systems with a finite number of degrees of freedom by making use of the PoincarCartan integral invariant method. A set of variables suitable for the reduction to the physical ones can be obtained by means of a canonical transformation. From the invariance of the PoincarCartan integral under canonical transformations we get the form of the equations of motion for the physical variables of the system.

Poincar-Cartan intregral invariant and canonical trasformation for singular Lagrangians: an addendum

The results of a previous work, concerning a method for performing the canonical formalism for constrained systems, are extended when the canonical transformation proposed in that paper is explicitly time dependent.

Invariant decomposition of the retarded electromagnetic field.

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor J. These field equations are an algebraic differential first-order system of oneforms, which verifies automatically the integrability conditions.

Loop bifurcation and magnetization rotation in exchange-biased Ni/FeF2

Exchange-biased Ni/FeF2 films have been investigated using vector coil vibrating-sample magnetometry as a function of the cooling field strength HFC . In films with epitaxial FeF2 , a loop bifurcation develops with increasing HFC as it divides into two sub-loops shifted oppositely from zero field by the same amount. The positively biased sub-loop grows in size with HFC until only a single positively shifted loop is found. Throughout this process, the negative and positive (sub)loop shifts maintain the same discrete value. This is in sharp contrast to films with twinned FeF2 where the exchange field gradually changes with increasing HFC . The transverse magnetization shows clear correlations with the longitudinal subloops. Interestingly, over 85% of the Ni reverses its magnetization by rotation, either in one step or through two successive rotations. These results are due to the single-crystal nature of the antiferromagnetic FeF2 , which breaks down into two opposite regions of large domains.

From Galilean-invariant to relativistic wave equations

Through an imaginary change of coordinates in the Galilei algebra in 4 space dimensions and making use of an original idea of Dirac and Lvy-Leblond, we are able to obtain the relativistic equations of Dirac and of Bargmann and Wigner starting with the (Galilean-invariant) Schrdinger equation.

Massless minimally coupled fields in de Sitter space: O(4)-symmetric states versus de Sitter invariant vacuum

The issue of de Sitter invariance for a massless minimally coupled scalar field is examined. Formally, it is possible to construct a de Sitterinvariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observers spacetime path grows linearly with the observers proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy-momentum tensor, both in the O(4)-invariant states introduced by Allen and Follaci, and in the de Sitterinvariant vacuum. We find that the vacuum energy density in the O(4)-invariant case is larger than in the de Sitterinvariant case.

Congo grass grown in rotation with soybean affects phosphorus bound to soil carbon

The phosphorus supply to crops in tropical soils is deficient due to its somewhat insoluble nature in soil, and addition of P fertilizers has been necessary to achieve high yields. The objective of this study was to examine the mechanisms through which a cover crop (Congo grass - Brachiaria ruziziensis) in rotation with soybean can enhance soil and fertilizer P availability using long-term field trials and laboratory chemical fractionation approaches. The experimental field had been cropped to soybean in rotation with several species under no-till for six years. An application rate of no P or 240 kg ha-1 of P2O5 had been applied as triple superphosphate or as Arad rock phosphate. In April 2009, once more 0.0 or 80.0 kg ha-1 of P2O5 was applied to the same plots when Congo grass was planted. In November 2009, after Congo grass desiccation, soil samples were taken from the 0-5 and 5-10 cm depth layer and soil P was fractionated. Soil-available P increased to the depth of 10 cm through growing Congo grass when P fertilizers were applied. The C:P ratio was also increased by the cover crop. Congo grass cultivation increased P content in the soil humic fraction to the depth of 10 cm. Congo grass increases soil P availability by preventing fertilizer from being adsorbed and by increasing soil organic P.

Forms of phosphorus in an oxisol under different soil tillage systems and cover plants in rotation with maize

Phosphorus fractions play a key role in sustaining the productivity of acid-savanna Oxisols and are influenced by tillage practices. The aim of this study was to quantify different P forms in an Oxisol (Latossolo Vermelho-Amarelo) from the central savanna region of Brazil under management systems with cover crops in maize rotation. Three cover crops (Canavalia brasiliensis, Cajanus cajan (L.), and Raphanus sativus L.) were investigated in maize rotation systems. These cover crops were compared to spontaneous vegetation. The inorganic forms NaHCO3-iP and NaOH-iP represented more than half of the total P in the samples collected at the depth of 5-10 cm during the rainy season when the maize was grown. The concentration of inorganic P of greater availability (NaHCO3-iP and NaOH-iP) was higher in the soil under no-tillage at the depth of 5-10 cm during the rainy season. Concentrations of organic P were higher during the dry season, when the cover crops were grown. At the dry season, organic P constituted 70 % of the labile P in the soil planted to C. cajan under no-tillage. The cover crops were able to maintain larger fractions of P available to the maize, resulting in reduced P losses to the unavailable pools, mainly in no-tillage systems.

Surface granularity as a discriminating feature of illicit tablets

In this paper we propose an innovative methodology for automated profiling of illicit tablets bytheir surface granularity; a feature previously unexamined for this purpose. We make use of the tinyinconsistencies at the tablet surface, referred to as speckles, to generate a quantitative granularity profileof tablets. Euclidian distance is used as a measurement of (dis)similarity between granularity profiles.The frequency of observed distances is then modelled by kernel density estimation in order to generalizethe observations and to calculate likelihood ratios (LRs). The resulting LRs are used to evaluate thepotential of granularity profiles to differentiate between same-batch and different-batches tablets.Furthermore, we use the LRs as a similarity metric to refine database queries. We are able to derivereliable LRs within a scope that represent the true evidential value of the granularity feature. Thesemetrics are used to refine candidate hit-lists form a database containing physical features of illicittablets. We observe improved or identical ranking of candidate tablets in 87.5% of cases when granularityis considered.