A method for dense packing discovery

The problem of packing a system of particles as densely as possible is foundational in the field of discrete geometry and is a powerful model in the material and biological sciences. As packing problems retreat from the reach of solution by analytic constructions, the importance of an efficient numerical method for conducting \textit{de novo} (from-scratch) searches for dense packings becomes crucial. In this paper, we use the \textit{divide and concur} framework to develop a general search method for the solution of periodic constraint problems, and we apply it to the discovery of dense periodic packings. An important feature of the method is the integration of the unit cell parameters with the other packing variables in the definition of the configuration space. The method we present led to improvements in the densest-known tetrahedron packing which are reported in [arXiv:0910.5226]. Here, we use the method to reproduce the densest known lattice sphere packings and the best known lattice kissing arrangements in up to 14 and 11 dimensions respectively (the first such numerical evidence for their optimality in some of these dimensions). For non-spherical particles, we report a new dense packing of regular four-dimensional simplices with density $\phi=128/219\approx0.5845$ and with a similar structure to the densest known tetrahedron packing.Comment: 15 pages, 5 figure

Hamiltonians separable in cartesian coordinates and third-order integrals of motion

We present in this article all Hamiltonian systems in E(2) that are separable in cartesian coordinates and that admit a third-order integral, both in quantum and in classical mechanics. Many of these superintegrable systems are new, and it is seen that there exists a relation between quantum superintegrable potentials, invariant solutions of the Korteweg-De Vries equation and the Painlev\'e transcendents.Comment: 19 pages, Will be published in J. Math. Phy

Global convergence of a non-convex Douglas-Rachford iteration

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration [2] was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given

Top predators affect the composition of naive protist communities, but only in their early-successional stage

Introduced top predators have the potential to disrupt community dynamics when prey species are naive to predation. The impact of introduced predators may also vary depending on the stage of community development. Early-succession communities are likely to have small-bodied and fast-growing species, but are not necessarily good at defending against predators. In contrast, late-succession communities are typically composed of larger-bodied species that are more predator resistant relative to small-bodied species. Yet, these aspects are greatly neglected in invasion studies. We therefore tested the effect of top predator presence on early- and late-succession communities that were either naive or non-naive to top predators. We used the aquatic community held within the leaves of Sarracenia purpurea. In North America, communities have experienced the S. purpurea top predator and are therefore non-naive. In Europe, this predator is not present and its niche has not been filled, making these communities top-predator naive. We collected early- and late-succession communities from two non-naive and two naive sites, which are climatically similar. We then conducted a common-garden experiment, with and without the presence of the top predator, in which we recorded changes in community composition, body size spectra, bacterial density, and respiration. We found that the top predator had no statistical effect on global measures of community structure and functioning. However, it significantly altered protist composition, but only in naive, early-succession communities, highlighting that the state of community development is important for understanding the impact of invasion

La Société de protection des plantes du Québec, 1908-2008

À l’aide de documents écrits et d’archives, l’histoire de la Société de protection des plantes du Québec (SPPQ) est retracée tout au cours de son existence. Son but et ses objectifs sont décrits ainsi que les moyens employés pour protéger les plantes et lutter contre leurs ennemis. Au cours de son existence, la SPPQ a contribué, par ses congrès annuels et directement par ses membres, à faire avancer la lutte aux ennemis des cultures. Ses publications ont aussi mené au développement d’outils qui ont aidé à mieux connaître et à identifier les insectes, les maladies et les mauvaises herbes qui affectent les cultures et les forêts.With the help of written documents and archives, the history of the Québec Society for the Protection of Plants (QSPP) is revealed along with its objectives and the methods used to protect plants from their enemies. Over the last century, the QSPP has contributed, through its annual congresses and more directly through its members, to the development of methods to control plant enemies. Its publications have also helped to develop tools that have led to a better understanding and identification of insects, diseases and weeds affecting plant crops and forests

Fundamental limitations on "warp drive" spacetimes

"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to confront the foundations of general relativity, and among other things, to precisely formulate the notion of "superluminal" communication. We verify the non-perturbative violation of the classical energy conditions of the Alcubierre and Natario warp drive spacetimes and apply linearized gravity to the weak-field warp drive, testing the energy conditions to first and second order of the non-relativistic warp-bubble velocity. We are primarily interested in a secondary feature of the warp drive that has not previously been remarked upon, if it could be built, the warp drive would be an example of a "reaction-less drive". For both the Alcubierre and Natario warp drives we find that the occurrence of significant energy condition violations is not just a high-speed effect, but that the violations persist even at arbitrarily low speeds. An interesting feature of this construction is that it is now meaningful to place a finite mass spaceship at the center of the warp bubble, and compare the warp field energy with the mass-energy of the spaceship. There is no hope of doing this in Alcubierre's original version of the warp-field, since by definition the point in the center of the warp bubble moves on a geodesic and is "massless". That is, in Alcubierre's original formalism and in the Natario formalism the spaceship is always treated as a test particle, while in the linearized theory we can treat the spaceship as a finite mass object. For both the Alcubierre and Natario warp drives we find that even at low speeds the net (negative) energy stored in the warp fields must be a significant fraction of the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments and discussion, no physics changes, accepted for publication in Classical and Quantum Gravit

Sapling age structure and growth series reveal a shift in recruitment dynamics of sugar maple and American beech over the last 40 years

Northern hardwoods have undergone a marked change in their dynamics, with American beech (Fagus grandifolia Ehrh.) increasing in abundance relative to sugar maple (Acer saccharum Marsh.). This study aims to better understand this sudden shift in recruitment dynamics. We performed an extensive analysis of the age structure, radial growth pattern, and release history on >700 saplings from 34 mature maple–beech stands of southern Quebec. We found (i) that the sapling age structures showed a progressive decrease in the establishment of maple relative to beech starting about 40 years ago, (ii) a change in the species growth hierarchy that started in the 1980s due to increasing radial growth of beech, (iii) that this growth trend is negligible for both maple and beech when we account for size and suppression status, and finally (iv) that the growth trend appears to be independent of present soil conditions. These results contrast with previous studies conducted at the adult stage that reported a growth decline for maple. We conclude that this change in recruitment dynamics is not related to growth, and consequently, further studies investigating this phenomenon should concentrate on establishment and survival

Singularity confinement and algebraic integrability

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved quantities whereas singularity confinement is associated with the local analysis of singularities. In this paper, the relationship between these two notions is explored for birational autonomous mappings. Two types of results are obtained: first, algebraically integrable mappings are shown to have the singularity confinement property. Second, a proof of the non-existence of algebraic conserved quantities of discrete systems based on the lack of confinement property is given.Comment: 18 pages, no figur

Assessment of Trans-Environmental Transitions of Heavy Metals and Arsenic in Herbal Drugs and Herbal Medicinal Products of Valerian Rhizomes with Roots and Motherwort Herb

Scientific relevance. In the context of pharmacopoeial harmonisation, the available methods for quantifying the total heavy metal content in tinctures are not sufficient to demonstrate the safety of liquid dosage forms based on herbal drugs. However, the establishment of individual limits for the heavy metal content requires analysing the patterns of environmental toxicant transitions from plant raw materials to herbal medicinal products in finished dosage forms.Aim. This study aimed to analyse the trans-environmental transitions of heavy metals and arsenic from the soil through plants to herbal medicinal products using a case study of aqueous and alcoholic extracts of valerian and motherwort herbal drugs.Materials and methods. The study focused on motherwort herb and valerian rhizomes with roots, the corresponding herbal medicinal products, and the rhizospheric soil. The elemental composition of the studied samples was determined by inductively coupled plasma mass spectrometry.Results. The authors determined the content of 15 elements (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Sr, Cd, Sb, Hg, and Pb) in plant raw materials, the rhizosphere, and herbal drug infusions and tinctures. The concentrations of elements were 0.002–109.884 mg/kg in motherwort herb samples and 0.017–866.618 mg/kg in the samples of valerian rhizomes with roots. Pb, Cd, and As were detected in all plant raw materials, while Hg was found only in 25% of the study samples. The content of these elements was within acceptable limits. Valerian and motherwort infusions contained all elements, except for Hg; valerian tinctures were free from Fe and Hg; and motherwort tinctures included no Fe, Hg, Sr, Cd, and Pb. The concentrations of elements in the infusions did not exceed 3.169 mg/kg, while the concentrations of elements in the tinctures were below 1.27 mg/kg. In the tinctures, Zn, Cu, Mg, and Ti were the most abundant elements, and Sb and Cd were present in minimum amounts.Conclusions. Valerian and motherwort plants can concentrate Cu, Cr, Fe, and V from the soil. The transition of heavy metals and arsenic into infusions did not exceed 65% of the content of these elements in herbal drugs, while tinctures contained less than 30% of the content of heavy metals and arsenic in herbal drugs. Some elements passed into infusions 1.5–5 times more efficiently than into tinctures