The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure

D-branes as a Bubbling Calabi-Yau

We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in X_b. The physical interpretation of the ''bubbling'' Calabi-Yau X_b is as the space obtained by letting the D-branes in X undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere.Comment: 32 pages; v.2 reference adde

Novel compatibilizers and plasticizers developed from epoxidized and maleinized chia oil in composites based on PLA and chia seed flour

[EN] Novel compatibilizers and plasticizers derived from epoxidized chia seed oil (ECO) and maleinized chia seed oil (MCO) have been applied in composites based on poly(lactic acid) (PLA) and 15 wt% chia seed flour (CSF). Results obtained have been compared to conventional silane coupling agent, (3-glycidyloxypropyl) trimethoxysilane (GPS), and a petroleum-based compatibilizer, poly(styrene-co-glycidyl methacrylate) copolymer (Xibond, (R)). The compatibilization effect of green composites were assessed by FTIR. The addition of all four compatibilizers improved the ductile mechanical and thermal properties of the composites. The morphology analysis revealed an improvement of interfacial adhesion of the CSF particles into the PLA matrix. In particular, ECO and MCO composites showed a roughness with long filaments in their morphology which plays a crucial role in improving the ductile properties highly. The elongation at break was 10 and 8 times higher using ECO and MCO, respectively, compared to uncompatibilized composite. Moreover, the composites manufactured showed low values (<9%) in the water uptake assay and a negligible compostability delay. The use of novel compatibilizers based on modified vegetable oils could mean an interesting proposal to obtain an entirely environmentally friendly composite with a remarkable ductile property.This research work was funded by the Ministry of Science and Innovation-¿Retos de la Sociedad¿. Project references: PID2020-119142RA-I00. I. Dominguez-Candela wants to thank Universitat Politècnica de València for his FPI grant (PAID-2019-SP20190013) and Generalitat Valenciana-GVA (ACIF/2020/233). J. Gomez-Caturla wants to thank Generalitat Valenciana-GVA, for his FPI grant (ACIF/2021/185) and grant FPU20/01732 funded by MCIN/AEI/10.13039/ 501100011033.Domínguez-Candela, I.; Gómez-Caturla, J.; Cardona, SC.; Lora-García, J.; Fombuena, V. (2022). Novel compatibilizers and plasticizers developed from epoxidized and maleinized chia oil in composites based on PLA and chia seed flour. European Polymer Journal. 173(111289):1-14. https://doi.org/10.1016/j.eurpolymj.2022.11128911417311128

Extreme times for volatility processes

We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that is far from being that of a simple Wiener process. It seems necessary to include a framework like the one provided by stochastic volatility models with a reverting force driving volatility toward its normal level to take into account memory and clustering effects in volatility dynamics. We also detect in data a very different behavior in the mean first-passage time depending whether the level is higher or lower than the normal level of volatility. For this reason, we discuss asymptotic approximations and confront them to empirical results with a good agreement, specially with the ExpOU model.Comment: 10, 6 colored figure

Taxonomic and nomenclatural rearrangements in Artemisia subgen. Tridentatae, including a redefinition of Sphaeromeria (Asteraceae, Anthemideae)

[EN]A recent molecular phylogenetic study of all members of Artemisia subgenus Tridentatae, as well as most of the other New World endemic Artemisia and the allied genera Sphaeromeria and Picrothamnus, raised the necessity of revising the taxonomic framework of the North American endemic Artemisia. Composition of the subgenus Tridentatae is enlarged to accommodate other North American endemics and is organized into 3 sections: Tridentatae, Nebulosae, and Filifoliae. This paper deals with the combination of one section, the amendment of 2 more sections, and the combination in or the reversion to Artemisia of some Sphaeromeria and Picrothamnus species. The new names given for previous Sphaeromeria species are Artemisia macarthurii (for S. argentea), A. albicans (for S. cana), A. constricta (for S. compacta), and A. inaequifolia (for S. diversifolia). The other Sphaeromeria we studied (S. capitata, S. potentilloides, S. ruthiae, and S. simplex) had been formerly considered Artemisia (respectively, A. capitata, A. potentilloides, A. ruthiae, and A. simplex), and their previous nomenclature is therefore recommended[ES]Un estudio reciente sobre la filogenia molecular de todos los miembros del subgénero Tridentatae de Artemisia, así como de la mayoría de las otras especies de Artemisia endémicas del Nuevo Mundo y los géneros afines Sphaeromeria y Picrothamnus, hizo ver la necesidad de revisar el marco taxonómico de las especies de Artemisia endémicas a Norteamérica. La composición del subgénero Tridentatae se ha ampliado para dar cabida a las otras especies endémicas de Norteamérica, y está organizado en 3 secciones: Tridentatae, Nebulosae y Filifoliae. El presente artículo trata sobre la combinación de una sección y la enmienda de 2 más, y propone la incorporación o reversión a Artemisia de algunas especies de Sphaeromeria y Picrothamnus. Los nuevos nombres de las especies previamente asignadas a Sphaeromeria son Artemisia macarthurii (para S. argentea), A. albicans (para S. cana), A. constricta (para S. compacta) y A. inaequifolia (para S. diversifolia). Las otras especies de Sphaeromeria estudiadas (S. capitata, S. potentilloides, S.ruthiae y S. simplex) habían sido previamente consideradas como miembros de Artemisia (A. capitata, A. potentilloides, A. ruthiae y A. simplex, respectivamente), por lo quese recomienda utilizar su nomenclatura anteriorThis work was subsidized by projects CGL2007-64839-C02-01/BOS and CGL2007-64839-C02-02/BOS of the Spanish government. SG was granted a JAE-DOC contract from the CSIC and a short stay in the Shrub Sciences Laboratory (USDA) in Utah, also from the CSIC.Peer reviewe

Qualitative study in Loop Quantum Cosmology

This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e., to show whether the other orbits converge or diverge to these analytic solutions at early and late times.Comment: 12 pages, 7 figures. Version accepted for publication in CQ

Constraints on Cosmic Strings due to Black Holes Formed from Collapsed Cosmic String Loops

The cosmological features of primordial black holes formed from collapsed cosmic string loops are studied. Observational restrictions on a population of primordial black holes are used to restrict $f$, the fraction of cosmic string loops which collapse to form black holes, and $\mu$, the cosmic string mass-per-unit-length. Using a realistic model of cosmic strings, we find the strongest restriction on the parameters $f$ and $\mu$ is due to the energy density in $100 MeV$ photons radiated by the black holes. We also find that inert black hole remnants cannot serve as the dark matter. If earlier, crude estimates of $f$ are reliable, our results severely restrict $\mu$, and therefore limit the viability of the cosmic string large-scale structure scenario.Comment: (Plain Tex, uses tables.tex -- wrapped lines corrected), 11 pages, FERMILAB-Pub-93/137-

Wilson Loops, Geometric Transitions and Bubbling Calabi-Yau's

Motivated by recent developments in the AdS/CFT correspondence, we provide several alternative bulk descriptions of an arbitrary Wilson loop operator in Chern-Simons theory. Wilson loop operators in Chern-Simons theory can be given a description in terms of a configuration of branes or alternatively anti-branes in the resolved conifold geometry. The representation of the Wilson loop is encoded in the holonomy of the gauge field living on the dual brane configuration. By letting the branes undergo a new type of geometric transition, we argue that each Wilson loop operator can also be described by a bubbling Calabi-Yau geometry, whose topology encodes the representation of the Wilson loop. These Calabi-Yau manifolds provide a novel representation of knot invariants. For the unknot we confirm these identifications to all orders in the genus expansion.Comment: 26 pages; v.2 typos corrected, explanations clarified; v.3 typos corrected, reference adde

Integrated random processes exhibiting long tails, finite moments and 1/f spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Levy distribution -which can be obtained from our model in certain limits- which has no finite moments. The evaluation of the power spectrum and the form of the probability density function in the tails of the distribution shows that the model exhibits a 1/f spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Levy processes together with another part representing the deviation of our model from the Levy process. This allows our process to be viewed as a generalization of the Levy process which has finite moments.Comment: Revtex (aps), 15 pages, no figures. Submitted to Phys. Rev.

Integrability and chaos: the classical uncertainty

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now named by the more fashionable term of deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical mechanics. Based on the Hamiltonian formalism, the main objective of this article is to provide, from the physicist's point of view, an overall and intuitive review of this broad subject (with some emphasis on the KAM theorem and the stability of planetary motions) which may be useful to both students and instructors.Comment: 24 pages, 10 figure