Unimodal wave trains and solitons in convex FPU chains

We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximisation of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction potentials but refines the standard results as it provides the existence of travelling waves with unimodal and even profile functions. Moreover, we discuss the numerical approximation and complete localization of wave trains, and show that wave trains converge to solitons when the periodicity length tends to infinity.Comment: 27 pages, several figure

Interface dynamics in discrete forward-backward diffusion equations

We study the motion of phase interfaces in a diffusive lattice equation with bistable nonlinearity and derive a free boundary problem with hysteresis to describe the macroscopic evolution in the parabolic scaling limit. The first part of the paper deals with general bistable nonlinearities and is restricted to numerical experiments and heuristic arguments. We discuss the formation of macroscopic data and present numerical evidence for pinning, depinning, and annihilation of interfaces. Afterwards we identify a generalized Stefan condition along with a hysteretic flow rule that characterize the dynamics of both standing and moving interfaces. In the second part, we rigorously justify the limit dynamics for single-interface data and a special piecewise affine nonlinearity. We prove persistence of such data, derive upper bounds for the macroscopic interface speed, and show that the macroscopic limit can indeed be described by the free boundary problem. The fundamental ingredient to our proofs is a representation formula that links the solutions of the nonlinear lattice to the discrete heat kernel and enables us to derive macroscopic compactness results in the space of continuous functions.Comment: 34 pages, several figure

Agricultural Support Measures of Advanced Countries and Food Insecurity in Developing Countries

food insecurity, agricultural support, rural development, LDCs

Expectations about Coalitions and Strategic Voting under Proportional Representation

In this paper, I suggest that voters may act strategically in proportional representation elections with post-election coalition building. Based on a stylized setup involving three possible coalitions of four parties on a single policy dimension, voters whose preferred coalition is least likely to win are predicted to strategically cast their ballot for a centrist party. By contrast, those who perceive a chance for their preferred coalition to become the next government are predicted to strategically vote for a non-centrist party. I test these predictions against the standard model of sincere proximity voting, using a unique dataset on voter expectations in the Austrian parliamentary election 2006. Analyses show that believing one's preferred coalition is non-viable raises the probability of voting for a centrist vs. non-centrist party while believing one's preferred coalition to be viable lowers the probability of voting for a centrist vs. non-centrist party.

FOOD SECURITY AND AGRICULTURAL DEVELOPMENT IN TIMES OF HIGH COMMODITY PRICES

The paper provides a new perspective on rising food prices by out mapping the many complex ways in which higher food prices are affecting developing countries, in particular the poorest. The analysis presented herein develops important and differentiated policy implications by distinguishing not only between implications in the shot run and medium run, and challenges on the supply side and demand side, but also between countries with agricultural potential and countries without such potential. Although globally food security is a challenge on both the demand side and the supply side, the paper argues that not all countries can effectively address this challenge from both angles. Furthermore, while higher food prices can provide important stimulus for agricultural development, it should not be expected that agricultural output will automatically rise in response to price changes, as higher prices in international markets are frequently not passed through to producers, and as many producers lack the capacity to respond to positive price signals where they are passed on. Both failures bear important implications for policies to address the dual challenge of food security and agricultural development.

Splitting Polytopes

A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to the splits of $P$ (with a split prime remainder). This generalizes a result of Bandelt and Dress [Adv. Math. 92 (1992)] on the decomposition of finite metric spaces. Introducing the concept of compatibility of splits gives rise to a finite simplicial complex associated with any polytope $P$, the split complex of $P$. Complete descriptions of the split complexes of all hypersimplices are obtained. Moreover, it is shown that these complexes arise as subcomplexes of the tropical (pre-)Grassmannians of Speyer and Sturmfels [Adv. Geom. 4 (2004)].Comment: 25 pages, 7 figures; minor corrections and change

Asymptotic formulas for solitary waves in the high-energy limit of FPU-type chains

It is well established that the solitary waves of FPU-type chains converge in the high-energy limit to traveling waves of the hard-sphere model. In this paper we establish improved asymptotic expressions for the wave profiles as well as an explicit formula for the wave speed. The key step in our approach is the derivation of an asymptotic ODE for the appropriately rescaled strain profile.Comment: revised version with corrected typos; 25 pages, several figure