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.Comment: Accepted for publication in Physica D :Nonlinear Phenomen

Interaction Grammars

Interaction Grammar (IG) is a grammatical formalism based on the notion of polarity. Polarities express the resource sensitivity of natural languages by modelling the distinction between saturated and unsaturated syntactic structures. Syntactic composition is represented as a chemical reaction guided by the saturation of polarities. It is expressed in a model-theoretic framework where grammars are constraint systems using the notion of tree description and parsing appears as a process of building tree description models satisfying criteria of saturation and minimality

Que signifie l'expression « les corps politiques et les corporations » utilisée à l'article 33 du Code de procédure civile du Québec?

À l'aide des règles d'interprétation reconnues relatives aux lois codifiées, aux lois refondues et aux lois bilingues et, suivant la jurisprudence et la doctrine britanniques, l'auteur démontre que l'expression « les corps politiques et les corporations », utilisée à l'article 33 du Code de procédure civile (C.P.C.) du Québec, signifie seulement « les corporations ».Applying the main principles of construction relating to consolidated, codified and bilingual statutes and, following British authorities and doctrine, the author shows that the phrase « les corps politiques et les corporations » (bodies politic and corporate), used in article 33 of the Code of Civil procedure of Quebec, means only « corporations »

Regional Integration and Dynamic Adjustments: Evidence from a Gross National Product Function for Canada and the United States

We propose an empirical trade model to test for structural change and dynamic effects induced by free trade agreements for the Canadian and US economies. We estimated a translog Gross National Product (GNP) function along with output and factor shares and tested for structural change (abrupt or gradual) which is endogenously determined by the data. After this, we estimated Stolper-Samuelson (SS) and Rybcynski (R) elasticities, and assessed the stability of their sign and magnitude link to the structural change. The null hypothesis of no structural change is soundly rejected for both countries. For Canada, we found gradual structural change that started prior to the implementation of CUSTA and lasted for several years. In the US case, we found evidence of an abrupt structural change occurring in 1995, a year after NAFTA came into force. More interestingly, several SS and R elasticities experienced sign reversals and a magnification effect over the different sub-periods, implying that the categorization of goods in terms of friends or enemies of labour and capital changed during the transition.GNP function; regional integration; structural change; smooth transition regression; dynamic adjustments.

Flame Wrinkles From The Zhdanov-Trubnikov Equation

International audienceThe Zhdanov-Trubnikov equation describing wrinkled premixed flames is studied, using pole decomposi tions as starting points. Its one-parameter (−1 0 (over-stabilisation) such analytical solutions can yield accurate flame shapes for 0 < c < 0.6. Open problems are invoked

Wrinkled flames and geometrical stretch

Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity (S) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/S > 0. A large constantS > 0 weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereasS < 0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked

Shapes and speeds of forced premixed flames

Steady premixed flames subjected to space-periodic steady forcing are studied via inhomogeneous Michelson-Sivashinsky (MS) and then Burgers equations. For both, the flame slope is posited to comprise contributions from complex poles to locate, and from a base-slope profile chosen in three classes (pairs of cotangents, single-sine functions or sums thereof). Base-slope-dependent equations for the pole locations, along with formal expressions for the wrinkling-induced flame-speed increment and the forcing function, are obtained on excluding movable singularities from the latter. Besides exact few-pole cases, integral equations that rule the pole-density for large wrinkles are solved analytically. Closed-form flame-slope and forcing-function profiles ensue, along with flame-speed increment vs forcing-intensity curves; numerical checks are provided. The Darrieus-Landau instability mechanism allows MS flame speeds to initially grow with forcing intensity much faster than those of identically forced Burgers fronts; only the fractional difference in speed increments slowly decays at intense forcing, which numerical (spectral) timewise integrations also confirm. Generalizations and open problems are evoked.Comment: Revised version submitted to Phys. Rev.