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- EQUATION (2)
- Combustion; Composting; Heat conduction; Non-linear dynamics; Safety; Self-heating (1)
- EQUATIONS (1)
- Higher order Hirota equation; Embedded solitons; Soliton perturbation theory; Solitary wave tails (1)
- Higher-order Hirota equation; Asymptotic transformation; Solitary wave interaction; Higher-order coordinate and phase shifts; Embedded solitons; Soliton perturbation theory; Solitary wave tails (1)
- Initial-boundary value problem; magma flow; modulation theory; undular bore; solitary waves (1)
- KdV equation; modulation theory; initial boundary-value problems (1)
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- Liquids and polymers Mathematical physics Computational physics Optics (1)
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- Microwave heating; Limit-cycles; Stability analysis; Hopf bifurcations; Control process; Thermal runaway (1)
- Microwave heating; Thawing; Stefan problem; Maxwell's equations; Semi-analytical solutions (1)
- Microwave heating; thermal runaway; Arrhenius law; TM waveguide mode; three-dimensional bodies (1)
- Modified Korteweg-de Vries equation; Soliton; Undular bore; Modulation theory; Initial-boundary value problem (1)
- NEMATIC LIQUID-CRYSTALS; INTERNAL OSCILLATIONS; VARIATIONAL APPROACH; VECTOR SOLITONS; OPTICAL FIBERS; PROPAGATION (1)
- NLS equation; solitary waves; asymptotic transformation; elastic and inelastic collisions; higher-order phase and coordinate shifts (1)
- NONLINEAR SCHRODINGER-EQUATION; SOLITARY WAVE INTERACTION; DEEP-WATER (1)
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- Reaction-diffusion equations catalytic pellet singularity theory Hopf bifurcations semi-analytical solutions Arrhenius law (1)
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Articles 31 - 34 of 34
Full-Text Articles in Physics
Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant
Semi-Analytical Solutions For Continuous-Flow Microwave Reactors, Prof. Tim Marchant
Tim Marchant
A prototype chemical reaction is examined in both one and two-dimensional continuous-flow microwave reactors, which are unstirred so the effects of diffusion are important. The reaction rate obeys the Arrhenius law and the thermal absorptivity of the reactor contents is assumed to be both temperature- and concentration-dependent. The governing equations consist of coupled reaction-diffusion equations for the temperature and reactant concentration, plus a Helmholtz equation describing the electric-field amplitude in the reactor. The Galerkin method is used to develop a semi-analytical microwave reactor model, which consists of ordinary differential equations. A stability analysis is performed on the semi-analytical model. This …
The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant
The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant
Tim Marchant
The initial boundary-value problem for the Korteweg-de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one boundary condition needed at x = 0 for the positive quarter-plane problem. Solutions of the KdV equation on the infinite line, such as the soliton, cnoidal wave, mean height variation and undular bore solution, are used to find approximate …
The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant
The Microwave Heating Of Three-Dimensional Blocks: Semi-Analytical Solutions, Prof. Tim Marchant
Tim Marchant
The microwave heating of three-dimensional blocks, by the transverse magnetic waveguide mode TM11, is considered in a long rectangular waveguide. The governing equations are the forced heat equation and a steady-state version of Maxwell's equations, while the boundary conditions take into account both convective and radiative heat loss. Semi-analytical solutions, valid for small thermal absorptivity, are found using the Galerkin method. The electrical conductivity and the thermal absorptivity are assumed to be temperature dependent, while both the electrical permittivity and magnetic permeability are taken to be constant. Both a quadratic relation and an Arrhenius-type law are used for the temperature …
Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant
Numerical Solitary Wave Interaction: The Order Of The Inelastic Effect, Prof. Tim Marchant
Tim Marchant
Solitary wave interaction is examined using an extended Benjamin-Bona-Mahony (eBBM) equation. This equation includes higher-order nonlinear and dispersive effects and is is asymptotically equivalent to the extended Korteweg-de Vries (eKdV) equation. The eBBM formulation is preferable to the eKdV equation for the numerical modelling of solitary wave collisions, due to the stability of its finite-difference scheme. In particular, it allows the interaction of steep waves to be modelled, which due to numerical instability, is not possible using the eKdV equation. Numerical simulations of a number of solitary wave collisions of varying nonlinearity are performed for two special cases corresponding to …