Conservation tillage (CT) systems have a number of potential benefits including lower crop production costs and the ability to reduce soil erosion that have made them common in several regions of the world. Although CT systems have been researched and successfully implemented on some farms in California's San Joaquin Valley (SJV), overall adoption is low and the reasons for the region's compara...

We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-v...

Many physical processes are described by conservative quasilinear systems of equations that admit a supplementary independent conservation law. A typical example is the equations of incompressible fluid dynamics. If for basic equations the conservation laws of the momentum and the volume are chosen then the conservation law of the energy is an additional conservation law. In the present paper a...

A group invariant solution for a steady two-dimensional jet is derived by considering a linear combination of the Lie point symmetries of Prandtl’s boundary layer equations for the jet. Only two Lie point symmetries contribute to the solution and the ratio of the constants in the linear combination is determined from conservation of total momentum flux in the downstream direction. A conservatio...

Material volumes and material particles 2 Laws for material particles 3 Mass conservation 3 Newton’s law of (non-relativistic) linear motion 3 Newton’s law applied to angular momentum 4 First law of thermodynamics 4 Second law of thermodynamics 4 Laws for finite material volumes 5 Mass conservation 5 Motion (linear momentum) 5 Motion (angular momentum) 6 First law of thermodynamics 6 Second law...

The size of the shock-layer governed by a conservation law is studied. The conservation law is a parabolic reaction-convection-diffusion equation with a small parameter multiplying the diffusion term and convex flux. Rigorous upper and lower bounding functions for the solution of the conservation law are established based on maximum-principle arguments. The bounding functions demonstrate that t...

From the requirement of continuous matching of bulk metric around the point of brane collision we derive a conservation law for collisions of p-branes in (p+2)-dimensional space-time. This conservation law relates energy densities on the branes before and after the collision. Using this conservation law we are able to calculate the amount of matter produced in the collision of orbifoldfixed bra...