Premixed-flame shapes and polynomials
Copyright policy )Premixed-flame shapes and polynomials
The nonlinear nonlocal Michelson-Sivashinsky equation for isolated crests of unstable flames is studied, using pole-decompositions as starting point. Polynomials encoding the numerically computed 2N flame-slope poles, and auxiliary ones, are found to closely follow a Meixner Pollaczek recurrence; accurate steady crest shapes ensue for N>=3. Squeezed crests ruled by a discretized Burgers equation involve the same polynomials. Such explicit approximate shape still lack for finite-N pole-decomposed periodic flames, despite another empirical recurrence.
Accepted for publication in Physica D :Nonlinear Phenomena
recurrence, polynomials, flame shapes, FOS: Physical sciences, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], [SPI.FLUID] Engineering Sciences [physics]/Reactive fluid environment, Pattern Formation and Solitons (nlin.PS), PDEs in connection with fluid mechanics, Polynomials, Nonlinear Sciences - Pattern Formation and Solitons, Integro-partial differential equations, Flame shapes, Recurrence, nonlinear nonlocal equation, [NLIN.NLIN-PS] Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], Nonlinear Nonlocal Equation, Poles, poles
recurrence, polynomials, flame shapes, FOS: Physical sciences, [SPI.MECA.MEFL] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], [SPI.FLUID] Engineering Sciences [physics]/Reactive fluid environment, Pattern Formation and Solitons (nlin.PS), PDEs in connection with fluid mechanics, Polynomials, Nonlinear Sciences - Pattern Formation and Solitons, Integro-partial differential equations, Flame shapes, Recurrence, nonlinear nonlocal equation, [NLIN.NLIN-PS] Nonlinear Sciences [physics]/Pattern Formation and Solitons [nlin.PS], Nonlinear Nonlocal Equation, Poles, poles
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