Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof

In this paper, we present and apply a computer-assisted method to study steady states of a triangular cross-diffusion system. Our approach consist in an a posteriori validation procedure, that is based on using a fxed point argument around a numerically computed solution, in the spirit of the Newton-Kantorovich theorem. It allows us to prove the existence of various non homogeneous steady states for different parameter values. In some situations, we get as many as 13 coexisting steady states. We also apply the a posteriori validation procedure to study the linear stability of the obtained steady states, proving that many of them are in fact unstable

Butler 2020: Integrate. Exemplify excellence in the liberal arts, professional education, and their effective integration.

2015 Topic: Vision for the Future In describing Butler 2020 (http://www.butler.edu/butler-2020/) the university makes use of six different verbs to articulate the university\u27s vision for its future, a vision deeply informed by and invested in the liberal arts. Select one of the verbs that are part of the vision for Butler 2020 and write an essay describing how your liberal arts education has made that verb part of your own vision for the future. In other words, think about and illustrate how you will be better able to enact that verb as a result of your liberal arts educatio

Rigorous numerics for nonlinear operators with tridiagonal dominant linear part

We present a method designed for computing solutions of infinite dimensional non linear operators $f(x) = 0$ with a tridiagonal dominant linear part. We recast the operator equation into an equivalent Newton-like equation $x = T(x) = x - Af(x)$, where $A$ is an approximate inverse of the derivative $Df(\overline x)$ at an approximate solution $\overline x$. We present rigorous computer-assisted calculations showing that $T$ is a contraction near $\overline x$, thus yielding the existence of a solution. Since $Df(\overline x)$ does not have an asymptotically diagonal dominant structure, the computation of $A$ is not straightforward. This paper provides ideas for computing $A$, and proposes a new rigorous method for proving existence of solutions of nonlinear operators with tridiagonal dominant linear part.Comment: 27 pages, 3 figures, to be published in DCDS-A (Vol. 35, No. 10) October 2015 issu

The Influence of British Directors on the Fundación Siglo de Oro and its Productions of Early Modern Drama, 2007-2021

The Fundación Siglo de Oro –formerly Compañía Rakatá– has been staging Spanish Golden Age and Elizabethan theatre since it was founded in 2006. Over this time, the company has developed an identity associated not only with its staging of early modern drama, but also with the influence of a series of contemporary British theatre practitioners on its rehearsal process. Perhaps one of the most noteworthy constants in its work is a fruitful series of collaborations with British stage directors, beginning in 2007 with Laurence Boswell directing El perro del hortelano (revived in 2014), in 2009 Fuenteovejuna, and in 2015 co-directing Mujeres y criados with company founder and producer Rodrigo Arribas. While, at first, we can ascribe this collaboration to the impact of the Royal Shakespeare Company Golden Age season, curated by Boswell, which visited Madrid’s emblematic Teatro Español in 2004, the company have continued to seek out British directors including Tim Hoare on Don Juan en Alcalá (2016) and Trabajos de amor perdidos (2016), and most recently Dominic Dromgoole on a new production of El perro del hortelano (2021). This latter partnership is also the culmination of a collaboration with Shakespeare’s Globe Theatre which saw the company take part in the Cultural Olympiad with Enrique VIII (2012) and become the first company to perform Lope de Vega in Spanish at the London theatre, with El castigo sin venganza (2014). There has therefore been a clear exchange of ideas between Spanish classical theatre and contemporary British theatre practice. This article proposes to explore the methodological contributions of British directors to better understand how this has altered the in-rehearsal perspectives on the Spanish Golden Age to explain the benefits of this Anglo-Hispanic collaborative approach to the company’s work. This will be supported by an interview with Rodrigo Arribas, whose constant presence as founder, producer, actor and most recently as director can help us to understand the contributions made by Boswell, Hoare and Dromgoole to the company’s rehearsal methodology

Computation of maximal local (un)stable manifold patches by the parameterization method

In this work we develop some automatic procedures for computing high order polynomial expansions of local (un)stable manifolds for equilibria of differential equations. Our method incorporates validated truncation error bounds, and maximizes the size of the image of the polynomial approximation relative to some specified constraints. More precisely we use that the manifold computations depend heavily on the scalings of the eigenvectors: indeed we study the precise effects of these scalings on the estimates which determine the validated error bounds. This relationship between the eigenvector scalings and the error estimates plays a central role in our automatic procedures. In order to illustrate the utility of these methods we present several applications, including visualization of invariant manifolds in the Lorenz and FitzHugh-Nagumo systems and an automatic continuation scheme for (un)stable manifolds in a suspension bridge problem. In the present work we treat explicitly the case where the eigenvalues satisfy a certain non-resonance condition.Comment: Revised version, typos corrected, references adde