Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By...

This paper presents a novel backward constraint solving technique for analyzing text processing programs. String constraints are represented using a variation of word equation called Simple Linear String Equation (SLSE). SLSE supports precise modeling of various regular string substitution semantics in Java regex, which allows it to capture user input validation operations widely used in web ap...

The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial charge of ions is injected into the ball. The steady state equation is similar to the Liouville-Gelfand-Bratú-type equation with the difference that the bounda...

We study the Dirichlet problem for the 2D Laplace equation in a domain bounded by smooth closed curves and smooth cracks. In the formulation of the problem, we do not require compatibility conditions for Dirichlet’s boundary data at the tips of the cracks. However, if boundary data satisfies the compatibility conditions at the tips of the cracks, then this is a particular case of our problem. T...

This paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. The two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low Reynolds number. The exact solutions of reduced momentum equation and magnetic force function have been computed in wave...

The peridynamic model is a framework for continuum mechanics based on the idea that pairs of particles exert forces on each other across a finite distance. The equation of motion in the peridynamic model is an integro-differential equation. In this paper, a notion of a peridynamic stress tensor derived from nonlocal interactions is defined. At any point in the body, this stress tensor is obtain...

Macroscopic description of the diffusion of interstitial impurity atoms considering the influence of elastic stress on the drift of interstitial species Abstract The diffusion equation for nonequilibrium interstitial impurity atoms taking into account their charge states and drift of all mobile interstitial species in the built-in electric field and in the field of elastic stress was obtained. ...

Bottom boundary layer effects on the linear wave propagation over mild slope bottoms are analyzed. A modifiedWKB approximation is presented including boundary layer effects. Within the boundary layer, two cases are considered: laminar (constant viscosity) and turbulent. Boundary layer effects are introduced by coupling the velocity inside the boundary layer to the irrotational velocity in the c...

The thermal problem of this note was solved with the hope of using it to try to test the theory that the earth was formed by accretion on the dust cloud hypothesis;1 but there are many uncertain and unknown physical factors involved and, on reflection, it seems that the contemplated thermal considerations are unable at present to help in drawing conclusions. However, it is hoped that the follow...

the effect on sugar beets of water and nitrogen movement in the soil under different water conditions was assessed over two years (2000-1) at the khorasan agricultural research center. three water treatments (no water stress, continuous stress and primary stress) and three n amounts (80, 160 and 240 kg n/ha) were investigated. the amount of moisture depletion in the water treatments was 50%, 80...