We have studied the effect on 2 nd harmonic wavelength modulation spectroscopy of the use of integrating spheres as multipass gas cells. The gas lineshape becomes distorted at high concentrations, as a consequence of the exponential pathlength distribution of the sphere, introducing nonlinearity beyond that expected from the Beer-Lambert law. We have modelled this numerically for methane absorp...

We investigate traveling wave solutions in a family of reaction-diffusion equations which includes the Fisher–Kolmogorov–Petrowskii–Piscounov (FKPP) equation with quadratic nonlinearity and a bistable equation with degenerate cubic nonlinearity. It is known that, for each equation in this family, there is a critical wave speed which separates waves of exponential decay from those of algebraic d...

Numerical studies show that the m = 1 tearing mode continues to grow exponentially well into the nonlinear regime, in contrast with the slow, "Rutherford," growth of m > 1 modes. A single helicity calculation is presented which generalizes that of Rutherford [Phys. Fluids 16, 1903 ( 1973) ] to the case when the constant-t/! approximation is invalid. As in that theory, the parallel current becom...

We study a nonlinear stationary system of transport equations with specific boundary conditions describing the transport of solutes dissolved in a fluid circulating in a countercurrent tubular architecture, which constitutes a simplified model of a kidney nephron. We prove that for every Lipschitz and monotonic nonlinearity (which stems from active transport across the ascending limb), the dyna...

this paper is concerned with the study of the existence of positive solutions for a navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. the existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. our resul...

A discrete nonlinear Schrödinger (NLS) model with long-range dispersive interactions describing the dynamical structure of DNA is proposed. Dispersive interactions of two types: the power dependence r and the exponential dependence e r on the distance, r, are studied. For s less than some critical value, scr, and similarly for β ≤ βcr there is an interval of bistability where two stable station...

In this paper, we study an initial boundary value problem for a $p$-Laplacian hyperbolic equation with logarithmic nonlinearity. By combining the modified potential well method Galerkin method, existence of global weak solution is studied, and polynomial exponential decay estimation under certain conditions are also given. Moreover, by using concavity other techniques, obtain blow up results at...

Abstract In this work, we study the existence of solution for a class semilinear degenerate elliptic equations in whole space involving Grushin operator and nonlinearity that involves Grushin's critical growth exponential growth. The at least one nontrivial weak is done by combining mountain‐pass theorem, Trudinger–Moser inequality, version result due to Lions corresponding weighted Sobolev spa...