Pepperdine Magazine - Vol. 3, Iss. 1 (Spring 2011)

Megan Huard, editor.https://digitalcommons.pepperdine.edu/peppmagazine/1006/thumbnail.jp

Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems

A new approach to the solution of quasilinear nonelliptic first-order systems of inhomogeneous PDEs in many dimensions is presented. It is based on a version of the conditional symmetry and Riemann invariant methods. We discuss in detail the necessary and sufficient conditions for the existence of rank-2 and rank-3 solutions expressible in terms of Riemann invariants. We perform the analysis using the Cayley-Hamilton theorem for a certain algebraic system associated with the initial system. The problem of finding such solutions has been reduced to expanding a set of trace conditions on wave vectors and their profiles which are expressible in terms of Riemann invariants. A couple of theorems useful for the construction of such solutions are given. These theoretical considerations are illustrated by the example of inhomogeneous equations of fluid dynamics which describe motion of an ideal fluid subjected to gravitational and Coriolis forces. Several new rank-2 solutions are obtained. Some physical interpretation of these results is given.Comment: 19 page

Transport properties of graphene with one-dimensional charge defects

We study the effect of extended charge defects in electronic transport properties of graphene. Extended defects are ubiquitous in chemically and epitaxially grown graphene samples due to internal strains associated with the lattice mismatch. We show that at low energies these defects interact quite strongly with the 2D Dirac fermions and have an important effect in the DC-conductivity of these materials.Comment: 6 pages, 5 figures. published version: one figure, appendix and references adde

Mobilizing Greater Crop and Land Potentials with Conservation Agriculture

Based on worldwide empirical and scientific evidence, it appears generally evident that CA can play a major role in accelerating production output growth to meet future global food needs. The evidence also suggests that it can do so while arresting soil degradation and improving factor productivity (efficiency of input use) and profit margins, as well as add the much needed resilience to cropping systems and ecosystem services. There is growing evidence to show that CA through improved soil quality enables better phenotypic performance from any adapted genotype, traditional or improved. This is because CA enables agricultural soil and landscape to be treated as living biological entities in which soil biota and their symbiotic relationships with root systems are encouraged while maintaining improved and efficient soil-plant-moisture-nutrient relationships (Jat et al., 2014)

Towards the classification of integrable differential-difference equations in 2 + 1 dimensions

We address the problem of classification of integrable differential-difference equations in 2+1 dimensions with one/two discrete variables. Our approach is based on the method of hydrodynamic reductions and its generalisation to dispersive equations. We obtain a number of classification results of scalar integrable equations including that of the intermediate long wave and Toda type.Comment: 16 page