Brownian Molecules Formed by Delayed Harmonic Interactions

A time-delayed response of individual living organisms to information exchanged within flocks or swarms leads to the emergence of complex collective behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9 3864), employing synthetic microswimmers, allows to emulate and study such behavior in a controlled way, in the lab. Motivated by these experiments, we study a system of N Brownian particles interacting via a retarded harmonic interaction. For $N \leq 3$ , we characterize its collective behavior analytically, by solving the pertinent stochastic delay-differential equations, and for $N>3$ by Brownian dynamics simulations. The particles form molecule-like non-equilibrium structures which become unstable with increasing number of particles, delay time, and interaction strength. We evaluate the entropy and information fluxes maintaining these structures and, to quantitatively characterize their stability, develop an approximate time-dependent transition-state theory to characterize transitions between different isomers of the molecules. For completeness, we include a comprehensive discussion of the analytical solution procedure for systems of linear stochastic delay differential equations in finite dimension, and new results for covariance and time-correlation matrices.Comment: 36 pages, 26 figures, current version: further improvements and one correctio

Do overlapping property rights reduce agricultural investment ? evidence from Uganda

The need for land-related investment to ensure sustainable land management and increase productivity of land use is widely recognized. However, there is little rigorous evidence on the effects of property rights for increasing agricultural productivity and contributing toward poverty reduction in Africa. Whether and by how much overlapping property rights reduce investment incentives, and the scope for policies to counter such disincentives, are thus important policy issues. Using information on parcels under ownership and usufruct by the same household from a nationally representative survey in Uganda, the authors find significant disincentives associated with overlapping property rights on short and long-term investments. The paper combines this result with information on crop productivity to obtain a rough estimate of the magnitudes involved. The authors make suggestions on ways to eliminate such inefficiencies.Wetlands,Labor Policies,Common Property Resource Development,,Municipal Housing and Land

Structure and evolution of protoplanetary disks

We present here a few thoughts on how high-angular resolution observations can give clues to some properties of protoplanetary disks that are fundamental to theories of planet formation. High-angular resolution infrared spectroscopy, either with a large single mirror telescope, or by using infrared interferometry, allows us to probe the abundance of thermally processed dust in the disk as a function of distance to the star. We show that this radial abundance profile can give information about the early evolution of the protoplanetary disk as well as about the nature of the turbulence. Since turbulence is one of the main ingredients in theories of planet formation, this latter result is particularly important. We also show that Nature itself provides an interesting way to perform high-angular resolution observations with intermediate-angular resolution telescopes: if a disk has a (nearly) edge-on orientation and is located in a low-density ambient dusty medium, the disk casts a shadow into this medium, as it blocks the starlight in equatorial direction. We argue how these shadows can be used to characterize the dust in the disk

A sub-determinant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs

We study implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into sub-determinants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple sub-determinant identity which has a non-trivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo orbits of different length than known previously. We reformulate Newton identities and the spectral density in terms of sub-determinant expansions and point out the implications of the sub-determinant identity for these expressions. We analyse furthermore the effect of the identity on spectral correlation functions such as the auto-correlation and parametric cross correlation functions of the spectral determinant and the spectral form factor.Comment: 25 pages, one figur