12,703 research outputs found
Exponential asymptotics with multiple stokes lines
No full textWhen asymptotic series methods are applied in order to solve problems that arise in applied mathematics in the limit that some parameter becomes small, they are unable to demonstrate behaviour that occurs on a scale that is exponentially small compared to the algebraic terms of the asymptotic series. There are many examples of physical systems where behaviour on this scale has important effects and, as such, a range of techniques known as exponential asymptotic techniques were developed that may be used to examinine behaviour on this exponentially small scale. Many problems in applied mathematics may be represented by behaviour within the complex plane, which may subsequently be examined using asymptotic methods. These problems frequently demonstrate behaviour known as Stokes phenomenon, which involves the rapid switches of behaviour on an exponentially small scale in the neighbourhood of some curve known as a Stokes line. Exponential asymptotic techniques have been applied in order to obtain an expression for this exponentially small switching behaviour in the solutions to orginary and partial differential equations. The problem of potential flow over a submerged obstacle has been previously considered in this manner by Chapman & Vanden-Broeck (2006). By representing the problem in the complex plane and applying an exponential asymptotic technique, they were able to detect the switching, and subsequent behaviour, of exponentially small waves on the free surface of the flow in the limit of small Froude number, specifically considering the case of flow over a step with one Stokes line present in the complex plane. We consider an extension of this work to flow configurations with multiple Stokes lines, such as flow over an inclined step, or flow over a bump or trench. The resultant expressions are analysed, and demonstrate interesting implications, such as the presence of exponentially sub-subdominant intermediate waves and the possibility of trapped surface waves for flow over a bump or trench. We then consider the effect of multiple Stokes lines in higher order equations, particu- larly investigating the behaviour of higher-order Stokes lines in the solutions to partial differential equations. These higher-order Stokes lines switch off the ordinary Stokes lines themselves, adding a layer of complexity to the overall Stokes structure of the solution. Specifically, we consider the different approaches taken by Howls et al. (2004) and Chap- man & Mortimer (2005) in applying exponential asymptotic techniques to determine the higher-order Stokes phenomenon behaviour in the solution to a particular partial differ- ential equation
Street dancers. Film américain de Christopher B. Stokes
No full textVideau André. Street dancers. Film américain de Christopher B. Stokes . In: Hommes et Migrations, n°1250, Juillet-août 2004. Réseaux sociaux en migration. pp. 116-117
Street dancers. Film américain de Christopher B. Stokes
No full textVideau André. Street dancers. Film américain de Christopher B. Stokes . In: Hommes et Migrations, n°1250, Juillet-août 2004. Réseaux sociaux en migration. pp. 116-117
Interview with Nicholas Christopher, author of Somewhere in the Night: Film Noir and the American City
No full textInterview with Nicholas Christopher, author of Somewhere in the Night: Film Noir and the American Cit
Exponentially accurate solution tracking for nonlinear ODEs, the higher order Stokes phenomenon and double transseries resummation
No full textWe demonstrate the conjunction of new exponential-asymptotic effects in the context of a second order nonlinear ordinary differential equation with a small parameter. First, we show how to use a hyperasymptotic, beyond-all-orders approach to seed a numerical solver of a nonlinear ordinary differential equation with sufficiently accurate initial data so as to track a specific solution in the presence of an attractor. Second, we demonstrate the necessary role of a higher order Stokes phenomenon in analytically tracking the transition between asymptotic behaviours in a heteroclinic solution. Third, we carry out a double resummation involving both subdominant and sub-subdominant transseries to achieve the two-dimensional (in terms of the arbitrary constants) uniform approximation that allows the exploration of the behaviour of a two parameter set of solutions across wide regions of the independent variable. This is the first time all three effects have been studied jointly in the context of an asymptotic treatment of a nonlinear ordinary differential equation with a parameter. This paper provides an exponential asymptotic algorithm for attacking such problems when they occur. The availability of explicit results would depend on the individual equation under study
Appearance of the higher-order Stokes phenomenon in a discrete Airy equation
No full textWe study a discrete variant of the Airy equation and show that discretization produces amore intricate Stokes structure than in the continuous case, inducing the higher-orderStokes phenomenon and infinite accumulations of Stokes and anti-Stokes curves. Thesefeatures are absent in the continuous Airy equation and are typically seen only in solutionsof at least third-order linear homogeneous, second-order or higher linear inhomogeneous, ornonlinear differential equations. Remarkably, this behavior is seen here to arise in asecond-order homogeneous linear difference equation. Using exponential asymptoticmethods, we derive the asymptotic solutions and the corresponding Stokes structure, withnumerical simulations confirming our predictions. We conjecture that the higher orderStokes phenomenon is able to be present in other second order linear difference equations
The structure of shock waves as a test of Brenner's modifications to the Navier-Stokes equations
No full textBrenner (Physica A, vol. 349, 2005a, b, pp. 11, 60) has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume that would be significant for flows with high density gradients. So the viscous structure of shock waves in gases should provide an excellent test case for this new model. In this paper we detail the shock structure problem and propose exponents for the gas viscosity-temperature relation based on empirical viscosity data that is independent of shock experiments. We then simulate monatomic gas shocks in the range Mach 1.0-12.0 using the Navier-Stokes equations, both with and without Brenner's modifications. Initial simulations showed that Brenner's modifications display unphysical behaviour when the coefficient of volume diffusion exceeds the kinematic viscosity. Our subsequent analyses attribute this behaviour to both an instability to temporal disturbances and a spurious phase velocity-frequency relationship. On equating the volume diffusivity to the kinematic viscosity, however, we find the results with Brenner's modifications are significantly better than those of the standard Navier-Stokes equations, and broadly similar to those from the family of extended hydrodynamic models that includes the Burnett equations. Brenner's modifications add only two terms to the Navier-Stokes equations, and the numerical implementation is much simpler than conventional extended hydrodynamic models, particularly in respect of boundary conditions. We recommend further investigation and testing on a number of different benchmark non-equilibrium flow cases
Matt Christopher Papers - Accession 1309
No full textThe collection includes letters written by the children’s book author, Matt Christopher, to his son, Marty Christopher. Many of the letters also contain newspaper articles of interest to Matt Christopher, which deal with local sports teams, his writing career, his participation in an exhibition baseball game against the New York Giants in 1938, and other of general interest. Most of the letters are personal in nature, however, a majority of the letters delve into Matt Christopher’s writing career, personal interests, the author’s health, as well as his family life.https://digitalcommons.winthrop.edu/manuscriptcollection_findingaids/2649/thumbnail.jp
Matt Christopher Papers - Accession 1221
No full textMatt Christopher (1917-1997) was a prolific author of children’s books having written over 100 books as well as over 300 short stories, articles, poems, and screenplays. Most of his writings dealt with sports themes, but he also wrote fantasy and mystery themed stories as well. The Matt Christopher Papers consist of both published and unpublished manuscripts, articles, and short stories. Also included are personal and business correspondence, biographical information, scrapbooks, photographs, and memorabilia.https://digitalcommons.winthrop.edu/manuscriptcollection_findingaids/1976/thumbnail.jp
Dr. Christopher von Rueden – Faculty Author Interview
No full textDr. Christopher von Rueden, an anthropologist and Assistant Professor in the Jepson School of Leadership Studies, discusses a recent article entitled, “Men’s status and reproductive success in 33 non-industrial societies: Effects of subsistence, marriage system, and reproductive strategy,” which he co-authored with Dr. Adrian Jaeggi, an anthropologist at Emory University. Their findings were recently published in the journal, Proceedings of the National Academy of Sciences
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