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 NLS equation; solitary waves; asymptotic transformation; elastic and inelastic collisions; higherorder phase and coordinate shifts (1)
 Solitons and modulation theory (1)
 Mathematical modelling (1)
 Wool scouring; Finite differences; Numerical simulation (1)
 Combustion; Composting; Heat conduction; Nonlinear dynamics; Safety; Selfheating (1)
Articles 1  4 of 4
FullText Articles in Physics
SelfHeating In Compost Piles Due To Biological Effects, Tim Marchant
SelfHeating In Compost Piles Due To Biological Effects, Tim Marchant
Tim Marchant
The increase in temperature in compost piles/landfill sites due to microorganisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological selfheating is present. The heat release rate due to biological activity is modelled by a function which is a monotonic increasing function of temperature over the range 0⩽T⩽a, whilst for T⩾a it is a monotone decreasing function of temperature. This functional dependence represents the fact that microorganisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1d slab and 2d rectangular slab geometries. In both cases there ...
Solitary Wave Interaction For A HigherOrder Nonlinear Schrodinger Equation, Tim Marchant
Solitary Wave Interaction For A HigherOrder Nonlinear Schrodinger Equation, Tim Marchant
Tim Marchant
Solitary wave interaction for a higherorder version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higherorder NLS equation to a higherorder member of the NLS integrable hierarchy, if an algebraic relationship between the higherorder coefficients is satisfied. The transformation is used to derive the higherorder one and twosoliton solutions; in general, the Nsoliton solution can be derived. It is shown that the higherorder collision is asymptotically elastic and analytical expressions are found for the higherorder phase and coordinate shifts. Numerical simulations of the interaction of two higherorder solitary waves are also performed ...
Asymptotic Solitons On A NonZero Mean Level., Tim Marchant
Asymptotic Solitons On A NonZero Mean Level., Tim Marchant
Tim Marchant
The collision of solitary waves for a higherorder modified Kortewegde Vries (mKdV) equation is examined. In particular, the collision between solitary waves with sechtype and algebraic (which only exist on a nonzero mean level) profiles is considered. An asymptotic transformation, valid if the higherorder coefficients satisfy a certain algebraic relationship, is used to transform the higherorder mKdV equation to an integrable member of the mKdV hierarchy. The transformation is used to show that the higherorder collision is asymptotically elastic and to derive the higherorder phase shifts. Numerical simulations of both elastic and inelastic collisions are performed. For the example covered ...
Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant
Numerical Simulation Of Contaminant Flow In A Wool Scour Bowl., Tim Marchant
Tim Marchant
Wool scouring is the process of washing dirty wool after shearing. Our model numerically simulates contaminant movement in a wool scour bowl using the advection–dispersion equation. This is the first wool scour model to give timedependent results and to model the transport of contaminants within a single scour bowl. Our aim is to gain a better understanding of the operating parameters that will produce efficient scouring. Investigating the effects of varying the parameters reveals simple, interesting relationships that give insight into the dynamics of a scour bowl.