On Sasaki-Einstein manifolds in dimension five

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde

Self-organization, scaling and collapse in a coupled automaton model of foragers and vegetation resources with seed dispersal

We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who feed on randomly located vegetation patches and disperse their seeds, thus modifying the spatial distribution of resources in the long term. It is assumed that the survival probability of a seed increases with the distance to the parent patch and decreases with the size of the colonized patch. In turn, the foraging agents use a deterministic strategy with memory, that makes them visit the largest possible patches accessible within minimal travelling distances. The combination of these interactions produce complex spatio-temporal patterns. If the patches have a small initial size, the vegetation total mass (biomass) increases with time and reaches a maximum corresponding to a self-organized critical state with power-law distributed patch sizes and L\'evy-like movement patterns for the foragers. However, this state collapses as the biomass sharply decreases to reach a noisy stationary regime characterized by corrections to scaling. In systems with low plant competition, the efficiency of the foraging rules leads to the formation of heterogeneous vegetation patterns with $1/f^{\alpha}$ frequency spectra, and contributes, rather counter-intuitively, to lower the biomass levels.Comment: 11 pages, 5 figure

Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation

By numerical calculation, the Planck spectrum with zero-point radiation is shown to satisfy a natural maximum-entropy principle whereas alternative choices of spectra do not. Specifically, if we consider a set of conducting-walled boxes, each with a partition placed at a different location in the box, so that across the collection of boxes the partitions are uniformly spaced across the volume, then the Planck spectrum correspond to that spectrum of random radiation (having constant energy kT per normal mode at low frequencies and zero-point energy (1/2)hw per normal mode at high frequencies) which gives maximum uniformity across the collection of boxes for the radiation energy per box. The analysis involves Casimir energies and zero-point radiation which do not usually appear in thermodynamic analyses. For simplicity, the analysis is presented for waves in one space dimension.Comment: 11 page

Strong low-frequency quantum correlations from a four-wave mixing amplifier

We show that a simple scheme based on nondegenerate four-wave mixing in a hot atomic vapor behaves like a near-perfect phase-insensitive optical amplifier, which can generate bright twin beams with a measured quantum noise reduction in the intensity difference of more than 8 dB, close to the best optical parametric amplifiers and oscillators. The absence of a cavity makes the system immune to external perturbations, and the strong quantum noise reduction is observed over a large frequency range.Comment: 4 pages, 4 figures. Major rewrite of the previous version. New experimental results and further analysi

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

The formulae for Planck length, Hawking temperature and Unruh-Davies temperature are derived by using only laws of classical physics together with the Heisenberg principle. Besides, it is shown how the Hawking relation can be deduced from the Unruh relation by means of the principle of equivalence; the deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure

Randomizing world trade. II. A weighted network analysis

Based on the misleading expectation that weighted network properties always offer a more complete description than purely topological ones, current economic models of the International Trade Network (ITN) generally aim at explaining local weighted properties, not local binary ones. Here we complement our analysis of the binary projections of the ITN by considering its weighted representations. We show that, unlike the binary case, all possible weighted representations of the ITN (directed/undirected, aggregated/disaggregated) cannot be traced back to local country-specific properties, which are therefore of limited informativeness. Our two papers show that traditional macroeconomic approaches systematically fail to capture the key properties of the ITN. In the binary case, they do not focus on the degree sequence and hence cannot characterize or replicate higher-order properties. In the weighted case, they generally focus on the strength sequence, but the knowledge of the latter is not enough in order to understand or reproduce indirect effects.Comment: See also the companion paper (Part I): arXiv:1103.1243 [physics.soc-ph], published as Phys. Rev. E 84, 046117 (2011

Weakly nonlinear theory of grain boundary motion in patterns with crystalline symmetry

We study the motion of a grain boundary separating two otherwise stationary domains of hexagonal symmetry. Starting from an order parameter equation appropriate for hexagonal patterns, a multiple scale analysis leads to an analytical equation of motion for the boundary that shares many properties with that of a crystalline solid. We find that defect motion is generically opposed by a pinning force that arises from non-adiabatic corrections to the standard amplitude equation. The magnitude of this force depends sharply on the mis-orientation angle between adjacent domains so that the most easily pinned grain boundaries are those with an angle between four and eight degrees. Although pinning effects may be small, they do not vanish asymptotically near the onset of this subcritical bifurcation, and can be orders of magnitude larger than those present in smectic phases that bifurcate supercritically

Coarsening in potential and nonpotential models of oblique stripe patterns

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1/2}$. Further from onset, the characteristic lengths along the preferred directions $\hat{x}$ and $\hat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and Model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results of electroconvection in nematics is presented.Comment: 13 pages, 13 figures. To appear in Phys. Rev.

Modeling the mobility of living organisms in heterogeneous landscapes: Does memory improve foraging success?

Thanks to recent technological advances, it is now possible to track with an unprecedented precision and for long periods of time the movement patterns of many living organisms in their habitat. The increasing amount of data available on single trajectories offers the possibility of understanding how animals move and of testing basic movement models. Random walks have long represented the main description for micro-organisms and have also been useful to understand the foraging behaviour of large animals. Nevertheless, most vertebrates, in particular humans and other primates, rely on sophisticated cognitive tools such as spatial maps, episodic memory and travel cost discounting. These properties call for other modeling approaches of mobility patterns. We propose a foraging framework where a learning mobile agent uses a combination of memory-based and random steps. We investigate how advantageous it is to use memory for exploiting resources in heterogeneous and changing environments. An adequate balance of determinism and random exploration is found to maximize the foraging efficiency and to generate trajectories with an intricate spatio-temporal order. Based on this approach, we propose some tools for analysing the non-random nature of mobility patterns in general.Comment: 14 pages, 4 figures, improved discussio

Hydrodynamic reductions of the heavenly equation

We demonstrate that Pleba\'nski's first heavenly equation decouples in infinitely many ways into a triple of commuting (1+1)-dimensional systems of hydrodynamic type which satisfy the Egorov property. Solving these systems by the generalized hodograph method, one can construct exact solutions of the heavenly equation parametrized by arbitrary functions of a single variable. We discuss explicit examples of hydrodynamic reductions associated with the equations of one-dimensional nonlinear elasticity, linearly degenerate systems and the equations of associativity.Comment: 14 page