Conformal Invariance and Duality in Self-Dual Gravity and (2,1) Heterotic String Theory

A system of gravity coupled to a 2-form gauge field, a dilaton and Yang-Mills fields in $2n$ dimensions arises from the (2,1) sigma model or string. The field equations imply that the curvature with torsion and Yang-Mills field strength are self-dual in four dimensions, or satisfy generalised self-duality equations in $2n$ dimensions. The Born-Infeld-type action describing this system is simplified using an auxiliary metric and shown to be classically Weyl invariant only in four dimensions. A dual form of the action is found (no isometries are required). In four dimensions, the dual geometry is self-dual gravity without torsion coupled to a scalar field. In $D>4$ dimensions, the dual geometry is hermitian and determined by a $D-4$ form potential $K$, generalising the K\"{a}hler potential of the four dimensional case, with the fundamental 2-form given by $\tilde J= i*\partial \bar \partial K$. The coupling to Yang-Mills is through a term $K\wedge tr (F\wedge F)$ and leads to a Uhlenbeck-Yau field equation $\tilde J^{ij}F_{ij}=0$.Comment: LaTeX, 14 pages, no figures. One reference added and interpretation revised; version to appear in Physics Letters

Einstein Supergravity and New Twistor String Theories

A family of new twistor string theories is constructed and shown to be free from world-sheet anomalies. The spectra in space-time are calculated and shown to give Einstein supergravities with second order field equations instead of the higher derivative conformal supergravities that arose from earlier twistor strings. The theories include one with the spectrum of N=8 supergravity, another with the spectrum of N=4 supergravity coupled to N=4 super-Yang-Mills, and a family with $N\ge 0$ supersymmetries with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills. The non-supersymmetric string with N=0 gives self-dual gravity coupled to self-dual Yang-Mills and a scalar. A three-graviton amplitude is calculated for the N=8 and N=4 theories and shown to give a result consistent with the cubic interaction of Einstein supergravity.Comment: LaTeX, 69 pages, no figures; v2: minor corrections made, footnotes and references adde

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved

Sigma models with non-commuting complex structures and extended supersymmetry

We discuss additional supersymmetries for N = (2, 2) supersymmetric non-linear sigma models described by left and right semichiral superfields.Comment: 11 pages. Talk presented by U.L. at "30th Winter School on Geometry and Physics" Srni, Czech Republic January 2010

Geometric Actions for D-Branes and M-Branes

New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fields couple both to a background or induced metric and a new auxiliary metric, whose elimination reproduces the non-polynomial Born-Infeld action. This is similar to the introduction of an auxiliary metric to simplify the Nambu-Goto string action. This simplifies the quantisation and dualisation of the gauge fields.Comment: LaTeX, 9 pages, no figures. Minor corrections; version to appear in Physics Letters

The Gauged (2,1) Heterotic Sigma-Model

The geometry of (2,1) supersymmetric sigma-models with isometry symmetries is discussed. The gauging of such symmetries in superspace is then studied. We find that the coupling to the (2,1) Yang-Mills supermultiplet can be achieved provided certain geometric conditions are satisfied. We construct the general gauged action, using an auxiliary vector to generate the full non-polynomial structure.Comment: LaTeX, 25 pages, no figures; version to appear in Nuclear Physics

Magnetohydrodynamic flow with heat and mass transfer of non-Newtonian fluid past a vertical heated plate embedded in non-Darcy porous medium with variable porosity

Numerical solutions of the nonlinear partial differential equations which describe the motion of the non-Newtonian fluid with heat and mass transfer past a semi-infinite vertical heated plate embedded in a porous medium are obtained.  The considered fluid is obeying the Eyring Powell model.  The system is stressed by an external uniform magnetic field.  The porous medium is obeying the non-Darcy Forchheimer model.  The variation of permeability, porosity and thermal conductivity are considered.  Similarity transformations are made to transform the system of equations to non-linear ordinary differential equations.  A shooting algorithm with Runge-Kutta Fehlberg integration scheme is used to solve these equations.  The velocity, temperature and concentration distributions are obtained as functions of the physical parameters of the problem.  The effects of these parameters on these distributions are discussed and illustrated graphically through a set of figures. Keywords: Magnetohydrodynamics, Mixed convection, Eyring Powell model, Non-  Darcy flow, Porous medium, Magnetic field

Application of olive mill waste-based biochar for improving wheat response to salt stress

The production of olive mill solid waste (OMSW) raises concerns due to its toxicity and negative environmental impact. However, by utilizing pyrolysis, OMSW can be converted into biochar, a carbon-rich material that detoxifies the waste and preserves its nutrient content. The OMSW-based biochar possesses alkaline properties (pH 9.6), low electrical conductivity (EC), high cation exchange capacity (CEC), a porous surface morphology, various surface functional groups, and high mineral content. This study assessed the influence of two concentrations (5% and 10%) of OMSW-based biochar on wheat plants' growth biomarkers and physiological characteristics subjected to salt stress conditions (150 mM NaCl). Findings of the study revealed that salt stress had deleterious effects on various parameters, including shoot height, fresh and dry weights of shoots and roots, relative water content (RWC%), membrane stability index (MSI%), photosynthetic pigments, and photosynthetic parameters such as the coefficient of the effective quantum yield of photochemical energy conversion of PSII (ØPSII), photochemical quenching (qP), and photochemical efficiency of PSII (Fo, Fm, Fv/Fo, and Fv/Fm). Furthermore, the levels of lipid peroxidation (MDA), hydrogen peroxide (H2O2), superoxide dismutase (SOD), and peroxidase (POD) activities significantly increased in stressed plants. On the other hand, applying both concentrations of OMSW-based biochar effectively improved the overall performance of wheat plants, irrespective of the presence of salinity. OMSW-based biochar is a promising strategy for promoting wheat growth in salt-stressed soil by improving various growth parameters and mitigating plant oxidative stress