Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and super-diffusive spreading. A perturbation analysis yields a crossover time between diffusive and super-diffusive behavior. The time’s dependence on the convection vel...

The effect of randomness on the stability of deep water surface gravity waves in the presence of a thin thermocline is studied. A previously derived fourth order nonlinear evolution equation is used to find a spectral transport equation for a narrow band of surface gravity wave trains. This equation is used to study the stability of an initially homogeneous Lorentz shape of spectrum to small lo...

We present a smoothed analysis of Gaussian elimination, both with partial pivoting and without pivoting. Let A be any matrix and let A be a slight random perturbation of A. We prove that it is unlikely that A has large condition number. Using this result, we prove it is unlikely that A has large growth factor under Gaussian elimination without pivoting. By combining these results, we bound the ...

Experimental study of a shock-decelerated ablation front is reported. A planar solid plastic target is accelerated by a laser across a vacuum gap and collides with a lower-density plastic foam layer. While the target is accelerated, a fast Rayleigh-Taylor (RT) growth of the seeded single-mode perturbation at the ablation front is observed. After the collision, the velocity of the ablation front...

perturbation of the fluid interface has an exponential growth The Rayleigh–Taylor instability is a gravity driven instability of a contact surface between fluids of different densities. The growth of this instability is sensitive to numerical or physical mass diffusion. h(t) 5 h0e, (1.1) For this reason, high resolution of the contact discontinuity is particularly important. In this paper, we a...

When groups compete for members, the resulting dynamics of human social activity may be understandable with simple mathematical models. Here, we apply techniques from dynamical systems and perturbation theory to analyze a theoretical framework for the growth and decline of competing social groups. We present a new treatment of the competition for adherents between religious and irreligious segm...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

In a Rayleigh-Taylor instability a dense fluid sits metastably atop a less dense fluid, a configuration that can be stabilized using a magnetic field gradient when one fluid is highly paramagnetic. On switching off the magnetic field, the instability occurs as the dense fluid falls under gravity. By affixing appropriately shaped magnetically permeable wires to the outside of the cell, one may i...