Equivalence between duality and gradient flow solutions for one-dimensional aggregation equations

Existence and uniqueness of global in time measure solution for a one dimensional nonlinear aggregation equation is considered. Such a system can be written as a conservation law with a velocity field computed through a selfconsistant interaction potential. Blow up of regular solutions is now well established for such system. In Carrillo et al. (Duke Math J (2011)), a theory of existence and uniqueness based on the geometric approach of gradient flows on Wasserstein space has been developped. We propose in this work to establish the link between this approach and duality solutions. This latter concept of solutions allows in particular to define a flow associated to the velocity field. Then an existence and uniqueness theory for duality solutions is developped in the spirit of James and Vauchelet (NoDEA (2013)). However, since duality solutions are only known in one dimension, we restrict our study to the one dimensional case

Numerical methods for one-dimensional aggregation equations

We focus in this work on the numerical discretization of the one dimensional aggregation equation \pa_t\rho + \pa_x (v\rho)=0, $v=a(W'*\rho)$, in the attractive case. Finite time blow up of smooth initial data occurs for potential $W$ having a Lipschitz singularity at the origin. A numerical discretization is proposed for which the convergence towards duality solutions of the aggregation equation is proved. It relies on a careful choice of the discretized macroscopic velocity $v$ in order to give a sense to the product $v \rho$. Moreover, using the same idea, we propose an asymptotic preserving scheme for a kinetic system in hyperbolic scaling converging towards the aggregation equation in hydrodynamical limit. Finally numerical simulations are provided to illustrate the results

Agricultural Distortions, Poverty and Inequality in South Africa

South Africa has rapidly reduced trade barriers since the end of Apartheid, yet agricultural production and exports have remained sluggish. Also, poverty and unemployment have risen and become increasingly concentrated in rural areas. This paper examines the extent to which remaining price distortions, both domestic and foreign, are contributing to the underperformance of the agricultural sector vis-à-vis the rest of the economy. We draw on a computable general equilibrium (CGE) and micro-simulation model of South Africa that are linked to the results of a global trade model. This framework is used to examine the effects of eliminating global and domestic price distortions. Model results indicate that South Africa’s agricultural sector currently benefits from global price distortions, and that removing these would create more jobs for lower-skilled workers, thereby reducing income inequality and poverty. We also find that South Africa’s own policies are biased against agriculture and that removing domestic distortions would raise agricultural production. Job losses in nonagricultural sectors would be outweighed by job creation in agriculture, such that overall employment rises and poverty falls. Overall, our findings suggest that South Africa’s own policies are more damaging to its welfare, poverty and inequality than distortionary policies in the rest of the world. Existing national price distortions may thus explain some of the poor performance of South Africa’s agricultural sector and rural development.Distorted incentives, agricultural and trade policy reforms, national agricultural development, Agricultural and Food Policy, International Relations/Trade, F13, F14, Q17, Q18,

Statistical vs. Identified Lives in Benefit-Cost Analysis

Economic evaluation of projects involving changes in mortality risk conventionally assumes that lives are statistical, i.e., that risks and policy-induced changes in risk are small and similar among a population. In reality, baseline mortality risks and policy-induced changes in risk often differ among individuals although these differences are imperfectly known. We examine the effects of information about heterogeneity of risk on economic evaluation. Although social welfare (defined as aggregate expected utility) is unaffected by information about risk heterogeneity, the economic valuation of changes in risk (the sum of individual compensating or equivalent variations) is sensitive to this information. The effect of information on economic valuation and hence the outcome of a benefit-cost analysis (BCA) depends on: i) whether information is about heterogeneity of the baseline and/or change in risk, ii) whether risk is valued using willingness to pay (WTP) or willingness to accept (WTA) measures, iii) the status quo policy, and iv) whether individuals are risk-averse or risk-neutral in wealth. We show that BCA does not systematically favor identified over statistical lives and suggest some political factors that may explain the apparent public-decision bias toward protecting identified lives.

Two-Pulse Ionization Injection into Quasi-Linear Laser Wakefields

We describe a scheme for controlling electron injection into the quasi-linear wakefield driven by a guided drive pulse via ionization of a dopant species by a collinear injection laser pulse with a short Rayleigh range. The scheme is analyzed by particle in cell simulations which show controlled injection and acceleration of electrons to an energy of 370 MeV, a relative energy spread of 2%, and a normalized transverse emittance of 3.0 {\mu}m. This is an arXiv version of the original APS paper. It should be cited as N. Bourgeois, J. Cowley, and S. M. Hooker, Phys. Rev. Lett. 111, 155004 (2013). APS link here: http://link.aps.org/doi/10.1103/PhysRevLett.111.155004Comment: 5 pages, 4 figure