Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Searching for cavities of various densities in the Earth's crust with a low-energy electron-antineutrino beta-beam

We propose searching for deep underground cavities of different densities in the Earth's crust using a long-baseline electron-antineutrino disappearance experiment, realized through a low-energy beta-beam with highly-enhanced luminosity. We focus on four cases: cavities with densities close to that of water, iron-banded formations, heavier mineral deposits, and regions of abnormal charge accumulation that have been posited to appear prior to the occurrence of an intense earthquake. The sensitivity to identify cavities attains confidence levels higher than $3\sigma$ and $5\sigma$ for exposures times of 3 months and 1.5 years, respectively, and cavity densities below 1 g cm$^{-3}$ or above 5 g cm$^{-3}$, with widths greater than 200 km. We reconstruct the cavity density, width, and position, assuming one of them known while keeping the other two free. We obtain large allowed regions that improve as the cavity density differs more from the Earth's mean density. Furthermore, we demonstrate that knowledge of the cavity density is important to obtain O(10%) error on the width. Finally, we introduce an observable to quantify the presence of a cavity by changing the orientation of the electron-antineutrino beam, with which we are able to identify the presence of a cavity at the $2\sigma$ to $5\sigma$ C.L.Comment: 7 pages, 5 figures; matches published versio

Ecological host fitting of Trypanosoma cruzi TcI in Bolivia: mosaic population structure, hybridization and a role for humans in Andean parasite dispersal.

An improved understanding of how a parasite species exploits its genetic repertoire to colonize novel hosts and environmental niches is crucial to establish the epidemiological risk associated with emergent pathogenic genotypes. Trypanosoma cruzi, a genetically heterogeneous, multi-host zoonosis, provides an ideal system to examine the sylvatic diversification of parasitic protozoa. In Bolivia, T. cruzi I, the oldest and most widespread genetic lineage, is pervasive across a range of ecological clines. High-resolution nuclear (26 loci) and mitochondrial (10 loci) genotyping of 199 contemporaneous sylvatic TcI clones was undertaken to provide insights into the biogeographical basis of T. cruzi evolution. Three distinct sylvatic parasite transmission cycles were identified: one highland population among terrestrial rodent and triatomine species, composed of genetically homogenous strains (Ar = 2.95; PA/L = 0.61; DAS = 0.151), and two highly diverse, parasite assemblages circulating among predominantly arboreal mammals and vectors in the lowlands (Ar = 3.40 and 3.93; PA/L = 1.12 and 0.60; DAS = 0.425 and 0.311, respectively). Very limited gene flow between neighbouring terrestrial highland and arboreal lowland areas (distance ~220 km; FST = 0.42 and 0.35) but strong connectivity between ecologically similar but geographically disparate terrestrial highland ecotopes (distance >465 km; FST = 0.016-0.084) strongly supports ecological host fitting as the predominant mechanism of parasite diversification. Dissimilar heterozygosity estimates (excess in highlands, deficit in lowlands) and mitochondrial introgression among lowland strains may indicate fundamental differences in mating strategies between populations. Finally, accelerated parasite dissemination between densely populated, highland areas, compared to uninhabited lowland foci, likely reflects passive, long-range anthroponotic dispersal. The impact of humans on the risk of epizootic Chagas disease transmission in Bolivia is discussed

Shifted loops and coercivity from field imprinted high energy barriers in ferritin and ferrihydrite nanoparticles

We show that the coercive field in ferritin and ferrihydrite depends on the maximum magnetic field in a hysteresis loop and that coercivity and loop shifts depend both on the maximum and cooling fields. In the case of ferritin we show that the time dependence of the magnetization also depends on the maximum and previous cooling fields. This behavior is associated to changes in the intra-particle energy barriers imprinted by these fields. Accordingly, the dependence of the coercive and loop shift fields with the maximum field in ferritin and ferrihydrite can be described within the frame of a uniform-rotation model considering a dependence of the energy barrier with the maximum and the cooling fields.Comment: 8 pages, 5 figures. Accepted for publication in Phys. Rev. B. Final version with improved writing and figure

Dynamic force spectroscopy of DNA hairpins. II. Irreversibility and dissipation

We investigate irreversibility and dissipation in single molecules that cooperatively fold/unfold in a two state manner under the action of mechanical force. We apply path thermodynamics to derive analytical expressions for the average dissipated work and the average hopping number in two state systems. It is shown how these quantities only depend on two parameters that characterize the folding/unfolding kinetics of the molecule: the fragility and the coexistence hopping rate. The latter has to be rescaled to take into account the appropriate experimental setup. Finally we carry out pulling experiments with optical tweezers in a specifically designed DNA hairpin that shows two-state cooperative folding. We then use these experimental results to validate our theoretical predictions.Comment: 28 pages, 12 figure

Partitioning Edge-Colored Hypergraphs into Few Monochromatic Tight Cycles

Confirming a conjecture of Gy´arf´as, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of the hypergraph) of monochromatic tight cycles. We further prove that, for all natural numbers p and r, the vertices of every r-edge-colored complete graph can be partitioned into a bounded number of pth powers of cycles, settling a problem of Elekes, Soukup, Soukup, and Szentmikl´ossy [Discrete Math., 340 (2017), pp. 2053–2069]. In fact we prove a common generalization of both theorems which further extends these results to all host hypergraphs of bounded independence number

Elasticity of semi-flexible polymers

We present a numerical solution of the Worm-Like Chain (WLC) model for semi-flexible polymers. We display graphs for the end-to-end distance distribution and the force-extension relation expected from the model. We predict the expected level of fluctuations around the mean value in force-extension curves. Our treatment analyses the entire range of polymer lengths and reproduces interesting qualitative features seen in recent computer simulations for polymers of intermediate length. These results can be tested against experiments on single molecules. This study is relevant to mechanical properties of biological molecules.Comment: five pages revtex five figures, slightly improved version with recent references adde