H\"older Regularity For Integro-Differential Equations With Nonlinear Directional Dependence

We prove H\"older regularity results for a class of nonlinear elliptic integro-differential operators with integration kernels whose ellipticity bounds are strongly directionally dependent. These results extend those in [9] and are also uniform as the order of operators approaches 2

Coupling generalised-α methods: analysis, adaptivity, and numerics

Abstract. In this article we consider the generalised-α methods, make an analysis of the methods and apply them to a coupled model problem. A new adaptive timestep control is presented

Uncertainty quantification of coupled odes with stochastic galerkin methods using adaptive higher order Runge–Kutta methods

Many real world problems are so complex that simplifications of these problems are needed. Otherwise the computing costs would be so high that specific problems, for example uncertainty quantification, could not be solved. In this paper we consider a system of coupled ODEs and discretise the subsystems in time with adaptive high order Runge–Kutta methods. This approach is called ”partitioned method”, and we use a Block Gauss-Seidel method for solving the final linear or non-linear systems. The motivation for using high order methods is the computation of very accurate numerical results. Moreover, these time integration methods are more effective than lower order methods, and in the case of the partitioned approach they need less iterations than lower order methods. For the stochastic discretisation we use a stochastic Galerkin method which only needs a few solutions of the deterministic ODE system. We show that using higher order methods in time leads to a better and more accurate quantification of uncertainties because we can expect a higher accuracy and a faster convergence for the deterministic problem. Numerical results show the advantages of the novel approach

Bharati Mukherjee and the American Immigrant: Reimaging the Nation in a Global Context

With its focus on immigration to the United States and development of American identity, Bharati Mukherjee’s fiction eludes literary categorization. It engages with the various contexts of multiculturalism, postcolonialism, and globalization, yet Mukherjee adamantly positions herself as an American author writing American literature. In this essay, I investigate the intersections between Mukherjee’s focus on the American character, culture, and people and developing theories and critical debates on globalization. Through Mukherjee’s works, we can see American identity in a state of flux, made possible by the immigrant and the relationships established between the transnational individual and America. Mukherjee’s immigrant characters challenge and expose American mythology from the American Dream of individual achievement to the canonical literature of Nathaniel Hawthorne’s The Scarlet Letter, rewriting them to show how foundational the immigrant is to American culture. I trace Mukherjee’s redefinition of the American character in and through three successive novels – Wife, Jasmine, and The Holder of the World. In Wife, Mukherjee challenges America’s adoption of multiculturalism because she considers it a means of essentializing ethnicity and both maintaining and enhancing difference. This multiculturalism, as part of America’s assumed principles of acceptance, alienates the protagonist Dimple from her immigrant community and the larger American culture, resulting in her violent attempts to force her Americanization. Jasmine continues to work against multiculturalism by explicitly inserting the immigrant into the American mythos, reshaping the Western literary canon to include the transnational individual and to assert the immigrant foundations of American ideology. Mukherjee expands her focus in Holder of the World as her protagonist Hannah travels to England, India, and the bourgeoning United States, rewriting The Scarlet Letter to suggest that globalizing forces have been present throughout American cultural history, not just at the end of the 20th century when critical debates began to flourish. Through analysis of these novels, I argue that Mukherjee’s reformulation of American character reasserts American ideals by including and developing with the rise of globalization theory

An iteration-free, partitioned method for solving coupled problems

Coupled problems consist of two or more problems which in most cases describe different physical phenomena. An example of such a problem is the interaction of fluid and structure. Usually, the most accurate way to solve coupled problems is the monolithical approach. But often, due to different reasons, a partitioned method is used, where the subproblems are solved with different software packages and there may be different discretisation methods. One reason for partitioning a coupled problem is that existing codes and the best discretisation schemes can be used. In this note we introduce an iteration-free, partitioned method which is based on a linear-implicit time integration method