A one-dimensional nonlinear dynamical system is examined as a simplified model of the dynamics ensued by the Navier-Stokes equations. The model has a richer dynamical behaviour than the Burgers equation and shows several features similar to the ones that are associated with the threedimensional Navier-Stokes. Although the spatial dimension is only one, there are still three velocity components ...

A comparative study of non-coplanar binary dislocation junctions in magnesium (Mg) and beryllium (Be) is presented to examine the effects of elastic properties and active Burgers vectors on junction formation and destruction in hexagonal close-packed (hcp) crystals via discrete dislocation dynamics simulations. Two junction configurations formed at intersecting prismatic ð01 10Þ=basal ð0001Þ pl...

We investigate the non-perturbative results of multi-dimensional forced Burgers equation coupled to the continuity equation. In the inviscid limit, we derive the exact exponents of two-point density correlation functions in the universal region in arbitrary dimensions. We then find the universal generating function and the tails of the probability density function (PDF) for the longitudinal vel...

We define a new model of interface roughening which has the property that the minimum of interface height is conserved locally during the growth. This model corresponds to the limit q → ∞ of the q-color dimer deposition-evaporation model introduced by us earlier [Hari Menon M K and Dhar D 1995 J. Phys. A: Math. Gen. 28 6517]. We present numerical evidence from Monte Carlo simulations and the ex...

Analysis has been conducted to present the generalized magnetic field effects on the flow of a Burgers' nanofluid over an inclined wall. Mathematical modelling for hydro-magnetics reveals that the term "[Formula: see text]" is for the Newtonian model whereas the generalized magnetic field term (as mentioned in Eq 4) is for the Burgers' model which is incorporated in the current analysis to get ...

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report...

We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the gaussian unitary ensemble, on which we focus in this paper, we show that the characteristics polynomials and their inverse evolve according to a...