Richard Pincak

Localized electron states near pentagons in variously shaped carbon nanoparticles

The electronic structure of variously shaped carbon nanoparticles (nanocone, fullerene, and hyperboloid) is investigated within a gauge field-theory model. Both the eigenfunctions and the local density of states (DOS) near the pentagonal defects are numerically calculated. The numerical study shows that the low-energy DOS has a cusp which drops to zero at the Fermi energy for any number of pentagons at the tip except three. For three pentagons, the nonzero DOS across the Fermi level is formed. The peculiarities in the case of graphitic hyperboloid are discussed.

With string model to time series forecasting

Overwhelming majority of econometric models applied on a long term basis in the financial forex market do not work sufficiently well. The reason is that transaction costs and arbitrage opportunity are not included, as this does not simulate the real financial markets. Analyses are not conducted on the non equidistant date but rather on the aggregate date, which is also not a real financial case. In this paper, we would like to show a new way how to analyze and, moreover, forecast financial market. We utilize the projections of the real exchange rate dynamics onto the string-like topology in the OANDA market. The latter approach allows us to build the stable prediction models in trading in the financial forex market. The real application of the multi-string structures is provided to demonstrate our ideas for the solution of the problem of the robust portfolio selection. The comparison with the trend following strategies was performed, the stability of the algorithm on the transaction costs for long trade periods was confirmed.

Analogies in electronic properties of graphene wormhole and perturbed nanocylinder

Abstract The electronic properties of the wormhole and the perturbed nanocylinder were investigated using two different methods: the continuum gauge field-theory model that deals with the continuum approximation of the surface and the Haydock recursion method that transforms the surface into a simplier structure and deals with the nearest-neighbor interactions. Furthermore, the changes of the electronic properties were investigated for the case of enclosing the appropriate structure, and possible substitutes for the encloser were derived. Finally, the character of the electron flux through the perturbed wormhole was predicted from the model based on the multiwalled nanotubes. The effect of the “graphene blackhole” is introduced.

The string prediction models as invariants of time series in the forex market

In this paper we apply a new approach of string theory to the real financial market. The models are constructed with an idea of prediction models based on the string invariants (PMBSI). The performance of PMBSI is compared to support vector machines (SVM) and artificial neural networks (ANN) on an artificial and a financial time series. A brief overview of the results and analysis is given. The first model is based on the correlation function as invariant and the second one is an application based on the deviations from the closed string/pattern form (PMBCS). We found the difference between these two approaches. The first model cannot predict the behavior of the forex market with good efficiency in comparison with the second one which is, in addition, able to make relevant profit per year. The presented string models could be useful for portfolio creation and financial risk management in the banking sector as well as for a nonlinear statistical approach to data optimization.

Low-energy electronic states in spheroidal fullerenes

(February 6, 2008)The field-theory model is proposed to study the electronic states near the Fermi energy inspheroidal fullerenes. The low energy electronic wavefunctions obey a two-dimensional Dirac equa-tion on a spheroid with two kinds of gauge fluxes taken into account. The first one is so-called Kspin flux which describes the exchange of two different Dirac spinors in the presence of a conicalsingularity. The second flux (included in a form of the Dirac monopole field) is a variant of the ef-fective field approximation for elastic flow due to twelve disclination defects through the surface of aspheroid. We consider the case of a slightly elliptically deformed sphere which allows us to apply theperturbation scheme. It is shown exactly how a small deformation of spherical fullerenes provokesan appearance of fine structure in the electronic energy spectrum as compared to the spherical case.In particular, two quasi-zero modes in addition to the true zero mode are predicted to emerge inspheroidal fullerenes. An additional ’hyperfine’ splitting of the levels (except the quasi-zero-modestates) is found.I. INTRODUCTION

Electronic structure of disclinated graphene in a uniform magnetic field

The electronic structure in the vicinity of the 1-heptagonal and 1-pentagonal defects in the carbon graphene plane is investigated for the case of hyperboloidal geometry. Using a continuum gauge field-theory model, the local density of states around the Fermi energy is calculated for both cases. In this model, the disclination is represented by a SO(2) gauge vortex and the corresponding metrics follows from the elasticity properties of the graphene membrane. To enhance the interval of energies, a self-consistent perturbation scheme is used. The Landau states are investigated and compared with the predicted values. A discussion on the influence of the Zeeman effect is included.

Electronic properties of disclinated flexible membrane beyond the inextensional limit: application to graphene

A gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of a 2D surface into R(3). The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.

Electronic pathway in reaction centers from Rhodobacter sphaeroides and Chloroflexus aurantiacus.

The reaction centers (RC) of Chloroflexus aurantiacus and Rhodobacter sphaeroidesH(M182)L mutant were investigated. Prediction for electron transfer (ET) at very low temperatures was also performed. To describe the kinetics of the C. aurantiacus RCs, the incoherent model of electron transfer was used. It was shown that the asymmetry in electronic coupling parameters must be included to explain the experiments. For the description of R. sphaeroidesH(M182)L mutant RCs, the coherent and incoherent models of electron transfer were used. These two models are discussed with regard to the observed electron transfer kinetics. It seems likely that the electron transfer asymmetry in R. sphaeroides RCs is caused mainly by the asymmetry in the free energy levels of L- and M-side cofactors. In the case of C. aurantiacus RCs, the unidirectionality of the charge separation can be caused mainly by the difference in the electronic coupling parameters in two branches.

Kolmogorov Space in Time Series Data

We provide the proof that the space of time series data is a Kolmogorov space with

Spheroidal geometry approach to fullerene molecules

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