Global attractors for the one dimensional wave equation with displacement dependent damping

We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly positive near the origin then this equation possesses a global attractor

Supra-organismal interactions in the human intestine

The term “supraorganism ” (which we pre-fer to the more common but slightly less informative “superorganism”) refers to a collection of individuals which behave as

Global Attractors For Wave Equations With Nonlinear Interior Damping And Critical Exponents

In this paper we study the global attractors for wave equations with nonlinear interior damping. We prove the existence, regularity and finite dimensionality of the global attractors without assuming a large value for the damping parameter, when the growth of the nonlinear terms is critical. (c) 2006 Elsevier Inc. All rights reserved.WoSScopu

Creating an earthquake scenario in China: A case study in Weinan City, Shaanxi province

In efforts to address government-identified gaps between top-down policies and local-level preparedness approaches, a team from China, the UK and the US undertook a transdisciplinary, participatory project to develop an earthquake scenario for two administrative districts of Weinan, Shaanxi province, located east of Xi'an. We designed the scenario study and communication materials, a first of their kind in China, to help local agencies describe and communicate earthquake risk to local decision-makers and the public. Weinan was destroyed by the 1556 M8¼ Huaxian earthquake, China's deadliest so far, and damaged by the 1568 M~7 Shaanxi Gaoling earthquake (also known as the M6¾ Northeast Xi'an earthquake). We chose a repeat of this 1568 event, because earthquakes of the size of the 1556 Huaxian event are extremely rare in the Weihe basin (and similar tectonic environments worldwide). We modelled the ground motion of the 1568 event, prepared a loss estimate, conducted field charrettes comprising field work and local consultations, and carried out disaster issue-focused social surveys to understand Weinan's main earthquake risk problems. We used a storytelling approach to create two science-based narratives, in Chinese and English, of the scenario earthquake's aftermath. One is a short graphic novel with earthquake mitigation and preparedness tips for the general public; the other is a narrative story with technical content and recommendations for relevant local agencies. The narratives can help people visualize the estimated losses and impacts, and provide mitigation and preparedness recommendations that, if implemented, will help reduce earthquake damage and consequences

Global attractors for von Karman evolutions with a nonlinear boundary dissipation

Dynamic von Karman equations with a nonlinear boundary dissipation are considered. Questions related to long time behaviour, existence and structure of global attractors are studied. It is shown that a nonlinear boundary dissipation with a large damping parameter leads to an existence of global (compact) attractor for all weak (finite energy) solutions. This result has been known in the case of full interior dissipation, but it is new in the case when the boundary damping is the main dissipative mechanism in the system. In addition, we prove that fractal dimension of the attractor is finite. The proofs depend critically on the infinite speed of propagation associated with the von Karman model considered. © 2003 Elsevier Inc. All rights reserved

Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation

We consider a semilinear wave equation, defined on a two-dimensional bounded domain Ω, with a nonlinear dissipation. Our main result is that the flow generated by the model is attracted by a finite dimensional global attractor. In addition, this attractor has additional regularity properties that depend on regularity properties of nonlinear functions in the equation. To our knowledge this is a first result of this type in the context of higher dimensional wave equations. © 2002 Elsevier Science (USA). All rights reserved