Low-frequency vibrations of soft colloidal glasses

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational spectrum and the nature of the modes are very similar to those predicted for zero-temperature idealized sphere models and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.Comment: 4 figure

Local agency, adaptation and the shadow system: The institutional architecture of social learning in rural areas of the UK and India

Rural communities across the world face at times a range of environmental, social and economic pressures that threaten their viability in their current form. The ability of local actors to exercise agency in response to potential and emerging threats is of key interest in understanding their capacity to adapt. This paper argues that top-down narratives which focus on canonical organisations and formal institutions are at best a partial account of rural adaptation. More attention needs to be paid to the shadow system, the web of informal and often hidden relationships that permeate public and private life. In the organisational and institutional literature, shadow systems have been discounted as either too complex to be tractable or an inevitable source of corruption and nepotism. Two case studies are presented to establish that neither claim is inexorably true: (i) the adaptation of dairy farmers to market and climate change in Carmarthenshire, South Wales and (ii) NGO mediation of community/state interaction in Tamilnadu, South India. In conclusion, some theoretical and methodological themes are highlighted for further research. These hold the potential to enable a better understanding of the shadow system, and its potential and pitfalls as a site of local agency in rural adaptation. Acnowledgements: This paper draws on learning from two research projects: (i) 'Rapid climate change in the UK: towards an institutional theory of adaptation', funded by the UK Economic and Social Science Research Council's Environment and Human Behaviour Programme, and (ii) 'Thaan Vuzha Nilam Tharisu: The land without a farmer becomes barren', carried out by SPEECH, a Tamil NGO, as part of a larger International Institute for Environment and Development research programme – 'Policies that Work for Sustainable Agriculture and Regenerating Rural Economies.� The authors gratefully acknowledge the financial and institutional assistance that made this research possible

Stability of monotone solutions for the shadow Gierer-Meinhardt system with finite diffusivity

We consider the following shadow system of the Gierer-Meinhardt model: \left\{\begin{array}{l} A_t= \epsilon^2 A_{xx} -A +\frac{A^p}{\xi^q},\, 00,\\ \tau \xi_t= -\xi + \xi^{-s} \int_0^1 A^2 \,dx,\\ A>0,\, A_x (0,t)= A_x(1, t)=0, \end{array} \right. where 1<p<+\infty,\, \frac{2q}{p-1} >s+1,\, s\geq 0, and \tau >0. It is known that a nontrivial monotone steady-state solution exists if and only if \ep < \frac{\sqrt{p-1}}{\pi}. In this paper, we show that for any \ep < \frac{\sqrt{p-1}}{\pi}, and p=2 or p=3, there exists a unique \tau_c>0 such that for \tau\tau_c it is linearly unstable. (This result is optimal.) The transversality of this Hopf bifurcation is proven. Other cases for the exponents as well as extensions to higher dimensions are also considered. Our proof makes use of functional analysis and the properties of Weierstrass functions and elliptic integrals

Canard-like phenomena in piecewise-smooth Van der Pol systems

We show that a nonlinear, piecewise-smooth, planar dynamical system can exhibit canard phenomena. Canard solutions and explosion in nonlinear, piecewise-smooth systems can be qualitatively more similar to the phenomena in smooth systems than piecewise-linear systems, since the nonlinearity allows for canards to transition from small cycles to canards ``with heads." The canards are born of a bifurcation that occurs as the slow-nullcline coincides with the splitting manifold. However, there are conditions under which this bifurcation leads to a phenomenon called super-explosion, the instantaneous transition from a globally attracting periodic orbit to relaxations oscillations. Also, we demonstrate that the bifurcation---whether leading to canards or super-explosion---can be subcritical.Comment: 17 pages, 11 figure