Travelling waves for an epidemic model with non-smooth treatment rates

This is the post-print version of the final published paper that is available from the link below. Copyright @ 2010 IOP Publishing Ltd and SISSA.We consider a susceptible–infected–removed (SIR) epidemic model with two types of nonlinear treatment rates: (i) piecewise linear treatment rate with saturation effect, (ii) piecewise constant treatment rate with a jump (Heaviside function). For case (i), we compute travelling front solutions whose profiles are heteroclinic orbits which connect either the disease-free state to an infective state or two endemic states with each other. For case (ii), it is shown that the profile has the following properties: the number of susceptibles is monotonically increasing and the number of infectives approaches zero at infinity, while their product converges to a constant. Numerical simulations are performed for all these cases. Abnormal behaviour like travelling waves with non-monotonic profile or oscillations is observed

Stability, transition and turbulence

A glimpse is provided of the research program in stability, transition and turbulence based on numerical simulations. This program includes both the so-called abrupt and the restrained transition processes. Attention is confined to the prototype problems of channel flow and the parallel boundary layer in the former category and the Taylor-Couette flow in the latter category. It covers both incompressible flows and supersonic flows. Some representative results are presented

Some recent developments in spectral methods

This paper is solely devoted to spectral iterative methods including spectral multigrid methods. These techniques are explained with reference to simple model problems. Some Navier-Stokes algorithms based on these techniques are mentioned. Results on transition simulation using these algorithms are presented

Non-linear evolution of a second mode wave in supersonic boundary layers

The nonlinear time evolution of a second mode instability in a Mach 4.5 wall-bounded flow is computed by solving the full compressible, time-dependent Navier-Stokes equations. High accuracy is achieved by using a Fourier-Chebyshev collocation algorithm. Primarily inviscid in nature, second modes are characterized by high frequency and high growth rates compared to first modes. Time evolution of growth rate as a function of distance from the plate suggests this problem is amenable to the Stuart-Watson perturbation theory as generalized by Herbert

The Secular and the Sacred: Complementary And/or Conflictual?

The issue of the relation of the sacred to the secular has become paramount in virtually every country in the world. From church-state relations in the US, with the debates around abortion and same-sex marriage, to the vitriolic discussions in France over the veil (hijab) sacred-secular, faith-reason, transcendence-imminence -- impacts every aspect of personal, social, and political life. Indeed, the questions often asked are whether Huntington s, Clash of Civilizations is today s reality? Is clash and conflict inevitable? This volume collects papers from scholars from all around the globe and digs into that question. Do the sacred and the secular necessarily end in conflict? Building on scholars such as Charles Taylor, Hans-Georg Gadamer, Jurgen Habermaus, and John Rawls, as well as the world s great religious traditions, the authors assembled here respond with a nuanced, but resounding, NO. A deeper read demands the possibility, indeed, necessity, of complementarity. It has become ever more urgent to discover the proper and complementary relation between the two so that both can be promoted through mutual collaboration. The deeper implications of the discussion can be perceived in many current global problems: cultural identity, multiculturalism, pluralism, nationalism, economic inequality, race, terrorism, migration, public education, and climate change. The volume unfolds in seven sections: Foundations; Sacred and Secular; Complement or Conflict; Hermeneutics; African traditions; South Asian Traditions; Chinese Traditions; and Islamic Traditions. It is fascinating to observe how the various authors grapple with unfolding the relation of sacred/secular, faith/reason, church-mosque/state, transcendence/imminence. The section on Islam illustrates this. These chapters deal with the thorny, usually misunderstood debate between the scholars and those, westerners refer to as fundamentalists or radicals. In the latter, there is no space left to reason, interpretation, or historical criticism. This ugly divide usually emerges in the hot-button issues like the treatment of women and religion-related terrorism. However, these oversimplifications betray the intellectual roots of Islamic tradition. Here the argument is advanced that there are common and multiple meanings of rationality in the Islamic primary sources and that doctrine, the Qur an, and the Sunnah, open considerable space for the rational and the secular in Islamic teachings. Unknown to most in the West, the grappling within Islam goes on. Moreover, the grappling seems to be heating up in all traditions. We are all called to the discussion. Our globe needs it

The Shared Concerns of Nietzsche and Rumi on Humanity

Nietzsche and Rumi belong to two different time and spaces: one a Germen Post-modern Philosopher, the other an Afghani Middle Ages Sufi. After an introduction about both figures and methodology used here, this paper presents a detailed discussion on commonalities between Nietzsche and Rumi. The first section illustrates on the shared methodology of writings which are the rousing language, hidden ideas amid simple points, and the paradoxical teachings. The second part studies the shared fundamental concepts among these philosophers. These concepts are Anti-idolism, the intuitional knowledge, and the authenticity of person. The last section of this paper called “inspirations” explains how those shared methodology and ideas serve two aims: mutual understanding between two different philosophies as well as enhancing our comprehension of humanity

Spectral methods in fluid dynamics

Fundamental aspects of spectral methods are introduced. Recent developments in spectral methods are reviewed with an emphasis on collocation techniques. Their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed. The key role that these methods play in the simulation of stability, transition, and turbulence is brought out. A perspective is provided on some of the obstacles that prohibit a wider use of these methods, and how these obstacles are being overcome

A three-dimensional spectral algorithm for simulations of transition and turbulence

A spectral algorithm for simulating three dimensional, incompressible, parallel shear flows is described. It applies to the channel, to the parallel boundary layer, and to other shear flows with one wall bounded and two periodic directions. Representative applications to the channel and to the heated boundary layer are presented

Finite length effects in Taylor-Couette flow

Axisymmetric numerical solutions of the unsteady Navier-Stokes equations for flow between concentric rotating cyclinders of finite length are obtained by a spectral collocation method. These representative results pertain to two-cell/one-cell exchange process, and are compared with recent experiments

Multiple paths to subharmonic laminar breakdown in a boundary layer

Numerical simulations demonstrate that laminar breakdown in a boundary layer induced by the secondary instability of two-dimensional Tollmien-Schlichting waves to three-dimensional subharmonic disturbances need not take the conventional lambda vortex/high-shear layer path