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.

The effect of cover crop and crop rotation on soil water storage and on sorghum yield

Crop rotation and cover crop can be important means for enhancing crop yield in rainfed areas such as the lower Coastal Bend Region of Texas, USA. A trial was conducted in 1995 as part of a long-term cropping experiment (7 years) to investigate the effect of oat (Avena sativa L.) cover and rotation on soil water storage and yield of sorghum (Sorghum bicolor L.). The trial design was a RCB in a split-plot arrangement with four replicates. Rotation sequences were the main plots and oat cover crop the subplots. Cover crop reduced sorghum grain yield. This effect was attributed to a reduced concentration of available soil N and less soil water storage under this treatment. By delaying cover termination, the residue with a high C/N acted as an N sink through competition and/or immobilization instead of an N source to sorghum plants. Crop rotation had a significantly positive effect on sorghum yield and this effect was attributed to a significantly larger amount of N concentration under these rotation sequences.

Cardiac rotation and relaxation in patients with aortic valve stenosis.

BACKGROUND: Diastolic dysfunction with delayed relaxation and abnormal passive elastic properties has been described in patients with severe pressure overload hypertrophy. The purpose of this study was to evaluate the time course of rotational motion of the left ventricle in patients with aortic valve stenosis using myocardial tagging. METHODS: Myocardial tagging is a non-invasive method based on magnetic resonance which makes it possible to label ('tag') specific myocardial regions. From the motion of the tag's cardiac rotation, radial displacement and translational motion can be determined. In 12 controls and 13 patients with severe aortic valve stenosis systolic and diastolic wall motion was assessed in an apical and basal short axis plane. RESULTS: The normal left ventricle performs a systolic wringing motion around the ventricular long axis with clockwise rotation at the base (-4.4+/-1.6 degrees) and counter-clockwise rotation at the apex (+6.8+/-2.5 degrees) when viewed from the apex. During early diastole an untwisting motion can be observed which precedes diastolic filling. In patients with aortic valve stenosis systolic rotation is reduced at the base (-2.4+/-2.0 degrees; P<0.01) but increased at the apex (+12.0+/-6.0 degrees; P<0.05). Diastolic untwisting is delayed and prolonged with a decrease in normalized rotation velocity (-6.9+/-1.1 s(-1)) when compared to controls (-10.7+/-2.2 s(-1); P<0.001). Maximal systolic torsion is 8.0+/-2.1 degrees in controls and 14.1+/-6.4 degrees (P<0.01) in patients with aortic valve stenosis. CONCLUSIONS: Left ventricular pressure overload hypertrophy is associated with a reduction in basal and an increase in apical rotation resulting in increased torsion of the ventricle. Diastolic untwisting is delayed and prolonged. This may explain the occurrence of diastolic dysfunction in patients with severe pressure overload hypertrophy.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.