Triad Field Research Articles

Forest Gardening on Abandoned Agricultural Land Contribute to Ground Cover Change and Food Security

Various forest products such as nuts, mangoes, bananas, lime, silk from mulberry leaves,essential oil, timber, animal food, perfume from tree blossoms, mulch and biochar, possess high potential to increase rural income. However, farming families in Nepal can hardly afford the investment to create such productive ecosystems. Connecting to the global market through Carbon dioxide (CO2)– certificates could serve to finance the creation of forest gardens. To test and demonstrate such approach, a project on ‘building village economies through climate farming and forest gardening (BeChange)’ has been implemented by 276 farming families in fourdistricts (Tanhun, Lamjung, Gorkha and Kaski) of Nepal. Using Global Positioning System (GPS) point survey, household surveys, focus group discussions (FGDs), a triad group system, field observation and reports, the success of establishing privately owned forest gardens was assessed. A total of 42,205 mixed tree species such as Michelia, Elaeocarpus, and Cinnamomum tamala were planted on abandoned agriculture land of 276 families. The set-up and maintenance of the forest gardens was financed with advanced payments for the carbon sink services of the planted trees. Farmers who succeeded with tree survival rates above 70 per cent received anadditional yearly carbon sink fee. This activity was linked to other income generating activities such as cultural eco-tourism, cinnamon leaf essential oil distillation, and intercropping of high value shade loving crops such as ginger, turmeric, and lentils. The outcomes of the project show significant improvements of the livelihood and food security in the project villages.

Quantum Gravity at the Corner

We investigate the quantum geometry of a 2d surface S bounding the Cauchy slices of a 4d gravitational system. We investigate in detail for the first time the boundary symplectic current that naturally arises in the first-order formulation of general relativity in terms of the Ashtekar–Barbero connection. This current is proportional to the simplest quadratic form constructed out of the pull back to S of the triad field. We show that the would-be-gauge degrees of freedo arising from S U ( 2 ) gauge transformations plus diffeomorphisms tangent to the boundary are entirely described by the boundary 2-dimensional symplectic form, and give rise to a representation at each point of S of S L ( 2 , R ) × S U ( 2 ) . Independently of the connection with gravity, this system is very simple and rich at the quantum level, with possible connections with conformal field theory in 2d. A direct application of the quantum theory is modelling of the black horizons in quantum gravity.

Charged anti-de Sitter BTZ black holes in Maxwell-f(T) gravity

Inspired by the Bañados, Teitelboim and Zanelli (BTZ) formalism, we discuss the Maxwell-[Formula: see text] gravity in [Formula: see text] dimensions. The main task is to derive exact solutions for a special form of [Formula: see text], with [Formula: see text] being the torsion scalar of Weitzenböck geometry. To this end, a triad field is applied to the equations of motion of charged [Formula: see text] and sets of circularly symmetric noncharged and charged solutions have been derived. We show that, in the charged case, the monopole-like and the [Formula: see text] terms are linked by a correlative constant despite the known results in teleparallel geometry and its extensions.[Formula: see text] Furthermore, it is possible to show that the event horizon is not identical with the Cauchy horizon due to such a constant. The singularities and the horizons of these black holes are examined: they are new and have no analogue in the literature due to the fact that their curvature singularities are soft. We calculate the energy content of these solutions by using the general vector form of the energy–momentum within the framework of [Formula: see text] gravity. Finally, some thermodynamical quantities, like entropy and Hawking temperature, are derived.

The geometro-hydrodynamical representation of the torsion field

We construct the geometro-hydrodynamical formalism for a spinning particle based on the six-dimensional manifold of autoparallelism geometry which is represented as a vector bundle with a base formed by the manifold of the translational coordinates and a fiber specified at each point by the field of an orthogonal coordinate frame underlying the classical spin. We show that the geometry of oriented points leads to the existence of torsion field with the source – the classical spin. We expand the geometro-hydrodynamical representation of Pauli field developed by Takabayasi and Vigier. We show that the external torsion field has a force effect on the velocity and spin fields via the spin-vorticity, which is characteristic of the space structure with the inhomogene triad field. The possible experimental effects of torsion field are discussed.

An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods

The objective of this work is the development of a new finite element formulation for beams according to the Kirchhoff theory of thin rods, which includes the deformation states of axial tension, torsion and bending. The proposed formulation accounts for large deformations in three-dimensional problem settings consisting of slender, prismatic beams with arbitrarily curved initial geometries and arbitrary cross-section shapes. Like in geometrically exact Reissner theories the derived deformation measures are geometrically exact in the sense that they are consistent with the strong and weak form of the balance equations and the beam geometry for any configuration and for arbitrarily large translations, rotations and strains. A novel orthogonal interpolation strategy is applied to the triad field representing the cross-section orientation in order to fulfill the Kirchhoff constraint of vanishing shear strains in a strong sense and to preserve the objectivity of the spatially discretized problem. The continuity requirements resulting from the corresponding weak form are fulfilled by a cubic Hermite interpolation, thus leading to a C1-continuous representation of the beam centerline. Fundamental properties such as objectivity, path-independence, consistency and accuracy of the developed beam element are verified by means of suitable numerical examples.

Erratum: Area is the length of Ashtekar’s triad field [Phys. Rev. D47, 1703 (1993)

Erratum: Area is the length of Ashtekar’s triad field [Phys. Rev. D<b>47</b>, 1703 (1993)

Non-commutative holonomies in 2 + 1 LQG and Kauffman's brackets

We investigate the canonical quantization of 2+1 gravity with Λ > 0 in the canonical framework of LQG. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of where the SU(2) connection A and the triad field e are the conjugated variables of the theory. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection Aλ = A + λe Ae acting on spin network links of the kinematical Hilbert space of LQG. We provide an explicit construction of the quantum holonomy operator, exhibiting a close relationship between the action of the quantum holonomy at a crossing and Kauffman's q-deformed crossing identity. The crucial difference is that the result is completely described in terms of standard SU(2) spin network states.

Canonical quantization of non-commutative holonomies in 2 + 1 loop quantum gravity

In this work we investigate the canonical quantization of 2 + 1 gravity with cosmological constant Λ > 0 in the canonical framework of loop quantum gravity. The unconstrained phase space of gravity in 2 + 1 dimensions is coordinatized by an SU(2) connection A and the canonically conjugate triad field e. A natural regularization of the constraints of 2 + 1 gravity can be defined in terms of the holonomies of $ {A_\pm } = A\pm \sqrt {{\Lambda e}} $ . As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection A λ = A + λe (for λ ∈ $ \mathbb{R} $ ) on the kinematical Hilbert space of loop quantum gravity. The holonomy operator associated to a given path acts non trivially on spin network links that are transversal to the path (a crossing). We provide an explicit construction of the quantum holonomy operator. In particular, we exhibit a close relationship between the action of the quantum holonomy at a crossing and Kauffman’s q-deformed crossing identity (with $ q = \exp \left( {i\hbar \lambda /2} \right) $ ). The crucial difference is that (being an operator acting on the kinematical Hilbert space of LQG) the result is completely described in terms of standard SU(2) spin network states (in contrast to q-deformed spin networks in Kauffman’s identity). We discuss the possible implications of our result.

Connection with torsion from Ashtekar–Barbero connection

A natural three-dimensional covariant derivative with torsion emerges from the Ashtekar–Barbero connection in the canonical approach to general relativity. The torsion is related to the extrinsic curvature when the Barbero–Immirzi parameter β does not vanish. Alternatively, torsion can be avoided, but at the price of a nonvanishing covariant derivative of the triad field. The properties of both cases are discussed.

Area is the length of Ashtekar's triad field.

The variables introduced by Ashtekar in general relativity have several useful and nice properties. We point out a further feature of these variables: the so(3)-invariant norm of the variable conjugate to Ashtekar’s connection, namely, the inverse densitized triad or the analogue of the electric field, is the area two-form; that is, it is the two-form that gives physical area to any surface. The new variables naturally determine areas in the same way in which the metric tensor naturally determines lengths.

A new view of the ECSK theory with a Dirac spinor

A formulation of the ECSK (Einstein-Cartan-Sciama-Kibble) theory with a Dirac spinor is given in terms of differential forms with values in exterior vector bundles associated with a fixed principalSL(2, ℂ)-bundle over a 4-manifold. In particular, tetrad fields are represented as soldering forms. In this setting, both the scalar curvature (Einstein-Hilbert) action density and the Dirac action density are well-defined polynomial functions of the soldering form and an independentSL(2,ℂ)-connection form. Thus, these densities are defined even where the tetrad field is degenerate (e.g. when fluctuations in the gravitational field are large). A careful analysis of the initial-value problem (in terms of an evolving triad field, SU(2)-connection, second-fundamental form and spinor field) reveals a first-order hyperbolic system of 27 evolution equations (not including the 8 evolution equations for the Dirac spinor) and 16 constraints. There are 10 conservation equations (due to local Poincare invariance) which team up with some of the evolution equations to guarantee that the 16 constraints are preserved under the evolution.

Correlated Birkeland current signatures from the Triad and MAGSAT magnetic field data

On November 1, 1979, the MAGSAT satellite was successfully launched into a 400 km polar orbit from which it could measure the earth’s magnetic field. During the first part of MAGSAT’s eight‐month lifetime, the orbit was nearly coplanar with that of the TRIAD satellite at 800 km altitude. This study has concentrated on transverse magnetic disturbances, associated with Birkeland currents, measured by the two spacecraft. The satellites were nearly coplanar from November through the middle of December 1979. Data were compared when the satellites were over the TRIAD/Chatanika receiving station. Of the approximately 150 comparisons of magnetic disturbances, 75% are very similar in shape and magnitude. For these cases, the TRIAD peak disturbances were, on the average, larger than the peak MAGSAT disturbances by 7%, which is less than many uncertainties in these measurements (due to baselines, calibration). Better agreement in the large‐scale well‐defined field‐aligned currrent signatures occurs during periods of higher Kp even with time separations as large as 45 minutes. The discrepancies in the remaining cases may be due to temporal, longitudinal and height effects of the Birkeland current system.