Six-dimensional Model Research Articles

Estimating and Correcting Mie Scattering in Synchrotron-Based Microscopic Fourier Transform Infrared Spectra by Extended Multiplicative Signal Correction

We present an approach for estimating and correcting Mie scattering occurring in infrared spectra of single cells, at diffraction limited probe size, as in synchrotron based microscopy. The Mie scattering is modeled by extended multiplicative signal correction (EMSC) and subtracted from the vibrational absorption. Because the Mie scattering depends non-linearly on alpha, the product of the radius and the refractive index of the medium/sphere causing it, a new method was developed for estimating the Mie scattering by EMSC for unknown radius and refractive index of the Mie scatterer. The theoretically expected Mie contributions for a range of different alpha values were computed according to the formulae developed by Van de Hulst (1957). The many simulated spectra were then summarized by a six-dimensional subspace model by principal component analysis (PCA). This subspace model was used in EMSC to estimate and correct for Mie scattering, as well as other additive and multiplicative interference effects. The approach was applied to a set of Fourier transform infrared (FT-IR) absorbance spectra measured for individual lung cancer cells in order to remove unwanted interferences and to estimate ranges of important alpha values for each spectrum. The results indicate that several cell components may contribute to the Mie scattering.

Window for Higgs boson mass from gauge-Higgs unification

We consider six-dimensional gauge models compactified on the orbifold T2/ZN (N=2,3,4,6) such that the Standard Model (SM) Higgs doublet arises from the extra-dimensional components of the gauge field. For Λ⩽1019GeV, where Λ denotes the compactification scale, we obtain 114.4GeV⩽mH⩽164GeV for the SM Higgs boson mass. We also consider gauge-Higgs-top and gauge-Higgs-bottom Yukawa unification which respectively yield mH=131−5+4GeV and mH=150−2+2GeV for a top quark pole mass Mt=170.9−1.8+1.8GeV. As a special case we recover the result mH⩽132GeV previously obtained for five-dimensional models.

Low energy effective theory on a regularized brane in six-dimensional flux compactifications

Conical brane singularities in six-dimensional flux compactification models can be resolved by introducing cylindrical codimension-one branes with regular caps instead of 3-branes (a la Kaluza-Klein braneworlds with fluxes). In this paper, we consider such a regularized braneworld with axial symmetry in six-dimensional Einstein-Maxwell theory. We derive a low energy effective theory on the regularized brane by employing the gradient expansion approach, and show that standard four-dimensional Einstein gravity is recovered at low energies. Our effective equations extend to the nonlinear gravity regime, implying that conventional cosmology can be reproduced in the regularized braneworld.

Using observation of teaching to improve quality: finding your way through the muddle of competing conceptions, confusion of practice and mutually exclusive intentions

This paper begins by reviewing some of the different models of third-party observation of university teaching that can be found in the literature. Having analysed these, it argues that—if ‘peer’ is taken to indicate equality of status—only one is genuinely a model of peer-observation. It proposes an alternative categorisation of third-party observations of teaching dependant on who controls the information generated by the process. A preferred six-dimensional model based on control by the person being observed of the data-flow, and other procedural aspects, is presented and explored. Evaluative comments, by university teachers who have undertaken the process, are presented to illustrate the benefits of adopting this model.

Gravity on an extended brane in six-dimensional warped flux compactifications

We study linearized gravity in a six-dimensional Einstein-Maxwell model of warped braneworlds, where the extra dimensions are compactified by a magnetic flux. It is difficult to construct a strict codimension two braneworld with matter sources other than pure tension. To overcome this problem we replace the codimension two defect by an extended brane, with one spatial dimension compactified on a Kaluza-Klein circle. Our background is composed of a warped, axisymmetric bulk and one or two branes. We find that weak gravity sourced by arbitrary matter on the brane(s) is described by a four-dimensional scalar-tensor theory. We show, however, that the scalar mode is suppressed at long distances and hence four-dimensional Einstein gravity is reproduced on the brane.

Regularization of conical singularities in warped six-dimensional compactifications

We study the regularization of the codimension-2 singularities in six-dimensional Einstein-Maxwell axisymmetric models with warping. These singularities are replaced by codimension-1 branes of a ring form, situated around the axis of symmetry. We assume that there is a brane scalar field with Goldstone dynamics, which is known to generate a brane energy momentum tensor of a particular structure necessary for the above regularization to be successful. We study these compactifications in both a non-supersymmetric and a supersymmetric setting. We see that in the non-supersymmetric case, there is a restriction to the admissible warpings and furthermore to the quantum numbers of the bulk gauge field and the brane scalar field. On the contrary, in the supersymmetric case, the warping can be arbitrary.

Gauge sector statistics of intersecting D‐brane models

AbstractIn this paper, which is based on the first part of the author's PhD thesis, we review the statistics of the open string sector in T6/(ℤ2 × ℤ2) orientifold compactifications of type IIA. After an introduction to the orientifold setup we discuss the two different techniques that have been developed, using either a saddle point approximation or a direct computer based method. We explain the two approaches by means of eight‐ and six‐dimensional toy models and present the results for the four‐dimensional models in detail. Special emphasis is placed on models containing phenomenologically interesting gauge groups, in particular those containing a standard model, Pati‐Salam or SU(5) part.

An interpenetrated cluster model of p-type Zn–Mg–Ho icosahedral quasicrystal

A six-dimensional (6D) cluster model of p-type Zn–Mg–Ho icosahedral quasicrystal has been proposed. The model consists of three large occupation domains centred at (0, 0, 0, 0, 0, 0), (½, ½, ½, ½, ½, ½), and (½, 0, 0, 0, 0, 0) in the 6D primitive unit cell. The 3D structure is described by three building blocks: rhombic triacontahedron (RTH), obtuse rhombohedron (OR) and acute rhombohedron (AR). The RTH is an extended icosahedral cluster, which includes a Bergman-type cluster inside it. The RTH clusters are placed at a subset of 12-fold vertices of the three-dimensional Penrose tiling with an edge length of about 0.5 nm. A pair of neighbour RTH clusters shares a rhombus face or an OR along 2- or 3-fold connections, respectively. The interstices of the network of RTH clusters are described by combinations of ORs and ARs with atom decorations.

Unique six-dimensional structural model for Al-Pd-Mn and Al-Cu-Fe icosahedral phases

A simple unique 6D atomic structural model for both $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ and $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ is proposed that is built with an unique and simple set of atomic surfaces and chemical subcells. The model has accurate compositions with respect to the best experimental estimates of both structures and fit reasonably well the experimental diffraction data of x-rays and neutrons spectra with no fitting parameters. It presents a surprisingly small number of chemical configurations for the basic $B$ (Bergman) and $M$ (Mackay) type clusters as compared to what could be expected for quasiperiodic ternary systems. Finally, because of its relative simplicity, the present model is well adapted for being used in discussing the physical properties of either $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Pd}\mathrm{Mn}$ or $i\text{\ensuremath{-}}\mathrm{Al}\mathrm{Cu}\mathrm{Fe}$ that are essentially dependent on the local atomic arrangements of the various chemical species.

A feasible solution technique for higher-dimensional population balance models

This paper presents a numerical technique for the solution of (multi-dimensional) population balance models. The technique is based on an extension of a so-called hierarchical two-tier technique presented previously in the context of single-dimensional population balances [Immanuel, C. D., & Doyle III, F. J., (2003a). Computationally efficient solution of population balance models incorporating nucleation, growth, and coagulation: Application to emulsion polymerization. Chemical Engineering Science, 58, 3681–3698], and later extended to a three-dimensional problem [Immanuel, C. D., & Doyle III, F. J., (2005). Solution technique for a multi-dimensional population balance model describing granulation processes. Powder Technology, 156, 213–225]. The specific contributions of this article are two-fold: 1. Development of the technique to handle breakage/division phenomena in population balance. 2. Demonstration of the feasibility of the technique to handle modestly multi-dimensional population balance models. The technique is applied to one-dimensional, three-dimensional, and six-dimensional population balance models. In each case, the results are found to be qualitatively consistent with theory. The computational times are also found to be conducive for the intended applications (process analysis, optimisation, and control).

Braneworlds in six dimensions: new models with bulk scalars

Six-dimensional bulk spacetimes with 3- and 4-branes are constructed using certain non-conventional bulk scalars as sources. In particular, we investigate the consequences of having the phantom (negative kinetic energy) and the Brans–Dicke scalar in the bulk while obtaining such solutions. We find geometries with 4-branes with a compact on-brane dimension (hybrid compactification) which may be assumed to be small in order to realize a 3-brane world. On the other hand, we also construct, with similar sources, bulk spacetimes where a 3-brane is located at a conical singularity. Furthermore, we investigate the issue of localization of matter fields (scalar, fermion, graviton, vector) on these 3- and 4-branes and conclude with comments on our six-dimensional models.

Bifurcations and Chaos in a Six-dimensional Turbulence Model of Gledzer

Gledzer's cascade shell model of turbulence with six real variables is studied numerically using mathematica 5.1. The Poincare plot of the first mode v 1 is used to determine periodic, doubly periodic and chaotic solutions and the routes to chaos via both frequency locking and period doubling. The circle map on the torus is well approximated by the summation of several sinusoidal functions. The dependence of the rotation number on the viscosity parameter is in accordance with that of the sine circle map. The complicated bifurcation structure and the revival of a stable periodic solution at a smaller viscosity parameter in the present model indicates that the turbulent state may be very sensitive to the Reynolds number.

Crime Investigation: A Course in Computer Forensics

The growing amount of crime, such as corporate frauds and virus attacks, in the last two decades highlights not only the importance of computer forensics in crime investigations but also the lack of forensic specialists in this area. An urgent need exists for universities to provide courses on computer forensics to ease the shortage of forensic specialists. This paper proposes a six-dimensional knowledge model for computer forensic courses. The six dimensions include categories of crime, computer technology, security, legislation, investigation process, and forensic tools. The paper describes in detail how the model was implemented in a postgraduate introductory computer forensic course. A brief summary of the lessons learned by the author in the course development and delivery is also presented.

Need of dark energy for dynamical compactification of extra dimensions on the brane

We consider a six-dimensional braneworld model and we study the cosmological evolution of a (4+1) brane-universe. Introducing matter on the brane we show that the scale factor of the physical three-dimensional brane-universe is related to the scale factor of the fourth dimension on the brane, and the suppression of the extra dimension compared to the three dimensions requires the presence of dark energy.

Order aggressiveness and order book dynamics

In this paper, we study the determinants of order aggressiveness and traders’ order submission strategy in an open limit order book market. Applying an order classification scheme, we model the most aggressive market orders, limit orders as well as cancellations on both sides of the market employing a six-dimensional autoregressive conditional intensity model. Using order book data from the Australian Stock Exchange, we find that market depth, the queued volume, the bid-ask spread, recent volatility, as well as recent changes in both the order flow and the price play an important role in explaining the determinants of order aggressiveness. Overall, our empirical results broadly confirm theoretical predictions on limit order book trading. However, we also find evidence for behavior that can be attributed to particular liquidity and volatility effects.

Need of dark energy for dynamical compactification of extra dimensions on the brane

We consider a six-dimensional braneworld model and we study the cosmological evolution of a (4+1) brane-universe. Introducing matter on the brane we show that the scale factor of the physical three-dimensional brane-universe is related to the scale factor of the fourth dimension on the brane, and the suppression of the extra dimension compared to the three dimensions requires the presence of dark energy.

Cosmological evolution of a purely conical codimension-2 brane world

We study the cosmological evolution of isotropic matter on an infinitely thin conical codimension-two brane-world. Our analysis is based on the boundary dynamics of a six-dimensional model in the presence of an induced gravity term on the brane and a Gauss-Bonnet term in the bulk. With the assumption that the bulk contains only a cosmological constant Lambda_B, we find that the isotropic evolution of the brane-universe imposes a tuned relation between the energy density and the brane equation of state. The evolution of the system has fixed points (attractors), which correspond to a final state of radiation for Lambda_B=0 and to de Sitter state for Lambda_B>0. Furthermore, considering anisotropic matter on the brane, the tuning of the parameters is lifted, and new regions of the parametric space are available for the cosmological evolution of the brane-universe. The analysis of the dynamics of the system shows that, the isotropic fixed points remain attractors of the system, and for values of Lambda_B which give acceptable cosmological evolution of the equation of state, the line of isotropic tuning is a very weak attractor. The initial conditions, in this case, need to be fine tuned to have an evolution with acceptably small anisotropy.

Non-Born−Oppenheimer Molecular Dynamics

Electronically nonadiabatic or non-Born-Oppenheimer (non-BO) chemical processes (photodissociation, charge-transfer, etc.) involve a nonradiative change in the electronic state of the system. Molecular dynamics simulations typically treat nuclei as moving classically on a single adiabatic potential energy surface, and these techniques are not immediately generalizable to non-BO systems due to the inherently quantum mechanical nature of electronic transitions. Here we generalize the concept of a single-surface molecular dynamics trajectory to that of a coupled-surface non-BO trajectory that evolves "semiclassically" under the influence of two or more electronic states and their couplings. Five non-BO trajectory methods are discussed. Next, we summarize the results of a series of systematic studies using a database of accurate quantum mechanical reaction probabilities and internal energy distributions for several six-dimensional model bimolecular scattering collisions. The test set includes three kinds of prototypical nonadiabatic interactions: conical intersections, avoided crossings, and regions of weak coupling. We show that the coherent switching with decay of mixing (CSDM) non-BO trajectory method provides a robust and accurate way to extend molecular dynamics to treat electronically nonadiabatic chemistry for all three kinds of nonadiabatic interactions, and we recommend it for molecular dynamics simulations involving nonradiative electronic state changes.

Stability of six-dimensional hyperstring braneworlds

We study a six-dimensional braneworld model with infinite warped extra dimensions in the case where the four-dimensional brane is described by a topological vortex of a U(1) symmetry-breaking Abelian Higgs model in the presence of a negative cosmological constant. A detailed analysis of the microscopic parameters leading to a finite-volume space-time in the extra dimensions is numerically performed. As previously shown, we find that a fine-tuning is required to avoid any kind of singularity on the brane. We then discuss the stability of the vortex by investigating the scalar part of the gauge-invariant perturbations around this fine-tuned configuration. It is found that the hyperstring forming Higgs and gauge fields, as well as the background metric warp factors, cannot be perturbed at all, whereas transverse modes can be considered stable. The warped space-time structure that is imposed around the vortex thus appears severely constrained and cannot generically support nonempty universe models. The genericness of our conclusions is discussed; this will shed some light on the possibility of describing our space-time as a general six-dimensional warped braneworld.

Nonsingular 4d-flat branes in six-dimensional supergravities

We show that six-dimensional supergravity models admit nonsingular solutions in the presence of flat three-brane sources with positive tensions. The models studied in this paper are nonlinear sigma models with the target spaces of the scalar fields being noncompact manifolds. For the particular solutions of the scalar field equations which we consider, only two brane sources are possible which are positioned at those points where the scalar field densities diverge, without creating a divergence in the Ricci scalar or the total energy. These solutions are locally invariant under 1/2 of D = 6 supersymmetries, which, however, do not integrate to global Killing spinors. Other branes can be introduced by hand by allowing for local deficit angles in the transverse space without generating any kind of curvature singularities.