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Full-Text Articles in Physics

Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant Dec 2006

Self-Heating In Compost Piles Due To Biological Effects, Tim Marchant

Tim Marchant

The increase in temperature in compost piles/landfill sites due to micro-organisms undergoing exothermic reactions is modelled. A simplified model is considered in which only biological self-heating 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 micro-organisms die or become dormant at high temperatures. The bifurcation behaviour is investigated for 1-d slab and 2-d rectangular slab geometries. In both cases there ...


Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant Dec 2006

Solitary Wave Interaction For A Higher-Order Nonlinear Schrodinger Equation, Tim Marchant

Tim Marchant

Solitary wave interaction for a higher-order version of the nonlinear Schrödinger (NLS) equation is examined. An asymptotic transformation is used to transform a higher-order NLS equation to a higher-order member of the NLS integrable hierarchy, if an algebraic relationship between the higher-order coefficients is satisfied. The transformation is used to derive the higher-order one- and two-soliton solutions; in general, the N-soliton solution can be derived. It is shown that the higher-order collision is asymptotically elastic and analytical expressions are found for the higher-order phase and coordinate shifts. Numerical simulations of the interaction of two higher-order solitary waves are also performed ...


Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant Dec 2006

Asymptotic Solitons On A Non-Zero Mean Level., Tim Marchant

Tim Marchant

The collision of solitary waves for a higher-order modified Korteweg-de Vries (mKdV) equation is examined. In particular, the collision between solitary waves with sech-type and algebraic (which only exist on a non-zero mean level) profiles is considered. An asymptotic transformation, valid if the higher-order coefficients satisfy a certain algebraic relationship, is used to transform the higher-order mKdV equation to an integrable member of the mKdV hierarchy. The transformation is used to show that the higher-order collision is asymptotically elastic and to derive the higher-order 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 Dec 2006

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 time-dependent 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.