Heun and Mathieu functions as solutions of the Dirac equation

We give examples of where the Heun function exists as solutions of wave equations encountered in general relativity. While the Dirac equation written in the background of Nutku helicoid metric yields Mathieu functions as its solutions in four spacetime dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. We must apply Atiyah-Patodi-Singer spectral boundary conditions to this system since the metric has a singularity at the origin.Comment: 5 pages, Prepared for the Spanish Relativity Meeting (ERE 2007), Tenerife, Spain, 10-14 Sep 200

Ignition and burning of fibreboard exposed to transient irradiation

Natural materials like wood are increasingly used in the construction industry, making the understanding of their ignition and burning behaviour in fires crucial. The state of the art of wood flammability is based mostly on studies at constant heating. However, accidental fires are better represented by transient heating. Here, we study the piloted ignition and burning of medium density fibreboard (MDF) under transient irradiation. Experiments are conducted in a Fire Propagation Apparatus under parabolic heat flux pulses with peak irradiation ranging from 30 to 40 kW/m2 and time-to-peak irradiation from 160 to 480 s. The experimental results reveal that the critical conditions for ignition of fibreboard vary over wide ranges: mass flux between 4.9 to 7.4 g/m2-s, surface temperature between 276 to 298°C, and heat flux between 29 to 40 kW/m2. Flameout conditions are studied as well, with observations of when it leads either to extinction or to smouldering combustion. We explored the experiments further with a one-dimensional pyrolysis model in Gpyro and show that predictions are accurate. Assuming a non-uniform density profile (a realistic assumption) improves the predictions in comparison to a uniform density profile by increasing the mass loss rate by 12%, decreasing the temperatures by 45%, and increasing the ignition time by 20 s. These results further support previous findings that a single critical condition for igntion or flameout established under constant irradiation does not hold under transient irradiation which indicates that ignition and extinction theories need improvements

Higher Derivative Gravity and Torsion from the Geometry of C-spaces

We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are Clifford algebra valued objects, called polyvectors. This provides a natural framework for description of supersymmetry, since spinors are just left or right minimal ideals of Clifford algebra. The geometry of curved $C$-space is investigated. It is shown that the curvature in $C$-space contains higher orders of the curvature in the underlying ordinary space. A $C$-space is parametrized not only by 1-vector coordinates $x^\mu$ but also by the 2-vector coordinates $\sigma^{\mu \nu}$, 3-vector coordinates $\sigma^{\mu \nu \rho}$, etc., called also {\it holographic coordinates}, since they describe the holographic projections of 1-lines, 2-loops, 3-loops, etc., onto the coordinate planes. A remarkable relation between the "area" derivative \p/ \p \sigma^{\mu \nu} and the curvature and torsion is found: if a scalar valued quantity depends on the coordinates $\sigma^{\mu \nu}$ this indicates the presence of torsion, and if a vector valued quantity depends so, this implies non vanishing curvature. We argue that such a deeper understanding of the $C$-space geometry is a prerequisite for a further development of this new theory which in our opinion will lead us towards a natural and elegant formulation of $M$-theory.Comment: 19 pages; A section describing the main physical implications of C-space is added, and the rest of the text is modified accordingl

What potential do mosses have as biomonitors of POPs? A comparative study of hexachlorocyclohexane sorption

Persistent organic pollutants (POPs) pose a significant global threat to human health and the environment, and require continuous monitoring due to their ability to migrate long distances. Active biomonitoring using cloned mosses is an inexpensive but underexplored method to assess POPs, mainly due to the poor understanding of the loading mechanisms of these pollutants in mosses. In this work, Fontinalis antipyretica (aquatic moss) and Sphagnum palustre (terrestrial moss) were evaluated as potential biomonitors of hexachlorocyclohexanes (HCHs: α-, β-, γ-, δ-HCH), crucial POPs. Moss clones, grown in photobioreactors and subsequently oven-dried, were used. Their lipid composition and distribution were characterized through molecular and histochemical studies. Adsorption experiments were carried out in the aqueous phase using the repeated additions method and in the gas phase using an active air sampling technique based on solid-phase extraction, a pioneering approach in moss research. F. antipyretica exhibited greater lipid content in the walls of most cells and higher adsorption capacity for all HCH isomers in both gaseous and liquid environments. These findings highlight the need for further investigation of POP loading mechanisms in mosses and open the door to explore other species based on their lipid contentThis work was supported by the Governments of Spain (PID2019- 107879RB-100; PID2022-140985NB-C22) and Galicia (ED431C 2022/ 40; ED431B 2023/04, ED431C 2020/19) and was co-funded by ERDF (EU

Exploration of Possible Quantum Gravity Effects with Neutrinos II: Lorentz Violation in Neutrino Propagation

It has been suggested that the interactions of energetic particles with the foamy structure of space-time thought to be generated by quantum-gravitational (QG) effects might violate Lorentz invariance, so that they do not propagate at a universal speed of light. We consider the limits that may be set on a linear or quadratic violation of Lorentz invariance in the propagation of energetic neutrinos, v/c=[1 +- (E/M_\nuQG1)] or [1 +- (E/M_\nu QG2}^2], using data from supernova explosions and the OPERA long-baseline neutrino experiment.Comment: 8 pages, 6 figures, proceedings for invited talk by A.Sakharov at DISCRETE'08, Valencia, Spain; December 200

Identifying emergent dynamical structures in network models

The identification of emergent structures in dynamical systems is a major challenge in complex systems science. In particular, the formation of intermediate-level dynamical structures is of particular interest for what concerns biological as well as artificial network models. In this work, we present a new technique aimed at identifying clusters of nodes in a network that behave in a coherent and coordinated way and that loosely interact with the remainder of the system. This method is based on an extension of a measure introduced for detecting clusters in biological neural networks. Even if our results are still preliminary, we have evidence for showing that our approach is able to identify these \u201cemerging things\u201d in some artificial network models and that it is way more powerful than usual measures based on statistical correlation. This method will make it possible to identify mesolevel dynamical structures in network models in general, from biological to social network

Singularity Structure and Stability Analysis of the Dirac Equation on the Boundary of the Nutku Helicoid Solution

Dirac equation written on the boundary of the Nutku helicoid space consists of a system of ordinary differential equations. We tried to analyze this system and we found that it has a higher singularity than those of the Heun's equations which give the solutions of the Dirac equation in the bulk. We also lose an independent integral of motion on the boundary. This facts explain why we could not find the solution of the system on the boundary in terms of known functions. We make the stability analysis of the helicoid and catenoid cases and end up with an appendix which gives a new example where one encounters a form of the Heun equation.Comment: Version to appear in JM

Tunable Excitons in Biased Bilayer Graphene

Recent measurements have shown that a continuously tunable bandgap of up to 250 meV can be generated in biased bilayer graphene [Y. Zhang et al., Nature 459, 820 (2009)], opening up pathway for possible graphene-based nanoelectronic and nanophotonic devices operating at room temperature. Here, we show that the optical response of this system is dominated by bound excitons. The main feature of the optical absorbance spectrum is determined by a single symmetric peak arising from excitons, a profile that is markedly different from that of an interband transition picture. Under laboratory conditions, the binding energy of the excitons may be tuned with the external bias going from zero to several tens of meV's. These novel strong excitonic behaviors result from a peculiar, effective ``one-dimensional'' joint density of states and a continuously-tunable bandgap in biased bilayer graphene. Moreover, we show that the electronic structure (level degeneracy, optical selection rules, etc.) of the bound excitons in a biased bilayer graphene is markedly different from that of a two-dimensional hydrogen atom because of the pseudospin physics

Decoherence induced CPT violation and entangled neutral mesons

We discuss two classes of semi-microscopic theoretical models of stochastic space-time foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of non-critical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuations, connecting distinct mass eigenstates (or the appropriate generalisation thereof in the case of K-mesons), and it is proportional to the relevant momentum transfer (along the direction of motion of the meson pair). There are two kinds of CPT-violating effects in this case, which can be experimentally disentangled: one (termed ``omega-effect'') is associated with the failure of the indistinguishability between the neutral meson and its antiparticle, and affects certain symmetry properties of the initial state of the two-meson system; the second effect is generated by the time evolution of the system in the medium of the space-time foam, and can result in time-dependent contributions of the $omega-effect type in the time profile of the two meson state. Estimates of both effects are given, which show that, at least in certain models, such effects are not far from the sensitivity of experimental facilities available currently or in the near future. The other class of quantum gravity models involves a medium of gravitational fluctuations which behaves like a ``thermal bath''. In this model both of the above-mentioned intrinsic CPT violation effects are not valid