On the first Townsend coefficient at high electric field

Based on the simplified approach it is shown and experimentally confirmed that gas gain in wire chambers at very low pressure becomes higher on thicker wires at the same applied high voltage. This is a consequence of the fact that the first Townsend coefficient at high reduced electric field depends almost entirely on the mean free path of electrons.Comment: 10 pages, 3 figures; version 2: revised, a few references adde

N=2 minimal conformal field theories and matrix bifactorisations of x^d

We establish an action of the representations of N=2-superconformal symmetry on the category of matrix factorisations of the potentials x^d and x^d-y^d for d odd. More precisely we prove a tensor equivalence between (a) the category of Neveu–Schwarz-type representa-tions of the N = 2 minimal super vertex operator algebra at central charge 3–6/d, and (b) a full subcategory of graded matrix factorisations of the potential x^d − y^d . The subcategory in (b) is given by permutation-type matrix factorisations with consecutive index sets. The physical motivation for this result is the Landau–Ginzburg/conformal field theory correspondence, where it amounts to the equivalence of a subset of defects on both sides of the correspondence. Our work builds on results by Brunner and Roggenkamp [BR], where an isomorphism of fusion rules was established

Taxonomy, Nomenclature, and Evolution of the Early Schubertellid Fusulinids

The types of the species belonging to the fusulinid genera Schubertella and Eoschubertella were examined from publications and type collections. Eoschubertella in general possesses all the features of Schubertella and therefore is a junior synonym of the latter. However, the concept of Eoschubertella best describes the genus Schubertina with its type species Schubertina curculi. Schubertina is closely related to the newly established genus Grovesella the concept of which is emended in this paper. Besides Schubertella, Schubertina, and Grovesella, the genera Mesoschubertella, Biwaella are reviewed and three new species, Grovesella nevadensis, Biwaella zhikalyaki, and Biwaella poletaevi, are described. The phylogenetic relationships of all Pennsylvanian—Cisuralian schubertellids are also proposed. Barrel-shaped Grovesella suggested being the very first schubertellid that appears sometimes in the middle—late Bashkirian time. In late Bashkirian it is then developed into ovoid to fusiform Schubertina. The latter genus gave rise into Schubertella in early Moscovian. First Fusiella derived from Schubertella in late Moscovian, Biwaella—in early Gzhelian and Boultonia—in late Gzhelian time. Genus Mesoschubertella also developed from Schubertella at least in Artinskian, but may be in late Sakmarian

Atomic States Entanglement in Carbon Nanotubes

The entanglement of two atoms (ions) doped into a carbon nanotube has been investigated theoretically. Based on the photon Green function formalism for quantizing electromagnetic field in the presence of carbon nanotubes, small-diameter metallic nanotubes are shown to result in a high degree of the two-qubit atomic entanglement for long times due to the strong atom-field coupling.Comment: 4 pages, 2 figure

Optimization of the Spatial Distribution of Pollution Emission in Water Bodies

The environmental protection of water bodies in Europe is based on the Water Framework Directive, which combines the so called Emission Limits Value and the Water Quality Objective (QO) approaches. The first one sets limits to particular type of emissions, for example the Nitrate Directive, while the second establishes Quality Standards for Biological, Chemical and Hydromorphological Quality Elements, in order to ensure the functioning of freshwater and marine ecosystem and the sustainable use of water bodies. To this regard, mathematical models are valuable tools for reconciliating these approaches, since they allow one to establish a causal link between emission levels and the Quality Standards ("direct problem") and vice-versa ("inverse problem"). In general, Quality Elements are variables or proper combination of variables which define the "status" of a water body. For example, the "chemical status" can be defined by a set of concentrations of chemicals which are potentially harmful for the ecosystem and humans, or the biological status may be based on Quality Elements which include the density of phytoplankton, the presence/absence of Submerged Aquatic Vegetation, the presence/absence of sensitive species etc. In many instances, the Quality Standards can then be expressed as threshold values, below or above which the functioning of the ecosystem is compromised and/or the risk for human health is not acceptable. If this is the case, management policies should be aimed at improving the state of the system and meet those Standards in the near future. In order to be carried in a cost-effective manner, such interventions should be based on a quantitative understanding of the relationships between the Pressures on the system and its State. This task could be very complex in large water bodies, where transport processes play a major role in creating marked gradients and pollution sources may be spatially distributed and/or not well identified. From the scientific point of view, the problem can be stated as follows: a mathematical model should enable one to "map" the spatial distribution of inputs (emissions) into the spatial distribution of the requested output, namely the "indicator" or "metric", which is subjected to a given constraint, the Quality Standard (QS), within the computational dominion. Such analysis may reveal that the QS are not respected only in a given fraction of the water body and, in the most favorable circumstances, identify the pollution sources which cause the problem. In such a case, a selective intervention, aimed at lowering the emission levels of those sources, would probably be more cost effective than the general reduction of the emission levels in the whole area. The spatial distribution of emission sources may also affect the pollution level and, in some instances, a proper redistribution of those sources in a given area, which leaves unchanged the total load, could have positive effect on the pollution level. In this paper, we are going to investigate the above problems in the simplest possible setting, in order to provide a clear interpretation of the results in relation to the most relevant parameters. The paper is organized as follows: in the "methods" section, we present the basic equations and provide insights for solving the problem in the general case as well as in the specific one here presented. The analytical solutions are presented and discussed in the next two sessions and some concluding remarks are then summarized in the conclusive section

A Variational Approach to Nonlocal Exciton-Phonon Coupling

In this paper we apply variational energy band theory to a form of the Holstein Hamiltonian in which the influence of lattice vibrations (optical phonons) on both local site energies (local coupling) and transfers of electronic excitations between neighboring sites (nonlocal coupling) is taken into account. A flexible spanning set of orthonormal eigenfunctions of the joint exciton-phonon crystal momentum is used to arrive at a variational estimate (bound) of the ground state energy for every value of the joint crystal momentum, yielding a variational estimate of the lowest polaron energy band across the entire Brillouin zone, as well as the complete set of polaron Bloch functions associated with this band. The variation is implemented numerically, avoiding restrictive assumptions that have limited the scope of previous assaults on the same and similar problems. Polaron energy bands and the structure of the associated Bloch states are studied at general points in the three-dimensional parameter space of the model Hamiltonian (electronic tunneling, local coupling, nonlocal coupling), though our principal emphasis lay in under-studied area of nonlocal coupling and its interplay with electronic tunneling; a phase diagram summarizing the latter is presented. The common notion of a "self-trapping transition" is addressed and generalized.Comment: 33 pages, 11 figure

Stability of C20 fullerene chains

The stability of (C20)N chains with N = 3 - 7 is analyzed by numerical simulation using a tight-binding potential and molecular dynamics. Various channels of losing the cluster-chain structure of the (C20)N complexes are observed, including the decay of C20 clusters, their coalescence, and the separation of one C20 fullerene from the chain.Comment: To appear in JETP Letter