A note on teleparallel Killing vector fields in Bianchi type Ⅷ and Ⅸ space-times in teleparallel theory of gravitation

In this paper we classify Bianchi type Ⅷ and Ⅸ space-times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique.It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5.From the above study we have shown that the Killing vector fields for Bianchi type VIII and IX space-times in the context of teleparallel theory are different from that in general relativity.     

Modified Faddeev–Jackiw quantization of massive non-Abelian Yang–Mills fields and Lagrange multiplier fields

Massive Yang–Mills fields and Lagrange multiplier fields are quantized by the modified Faddeev–Jackiw quantization method, and the method's comparisons with Dirac method and the usual Faddeev–Jackiw method are also given. We show that this method not only is equivalent to Dirac method, but also remains all the virtues of the usual Faddeev–Jackiw method. Moreover, the modified Faddeev–Jackiw quantization method is simpler than the usual one when obtaining new secondary constraints. Therefore, the modified Faddeev–Jackiw method is more economical and effective than Dirac method and the usual Faddeev–Jackiw method. Meanwhile, we find the new meanings of the Lagrange multipliers, and discover that the Lagrange multipliers and the zeroth components of gauge field are just a pair of canonical field variables except a constant factor in this system.     

Kinetic analysis of n-decane–hydrogen blend combustion in premixed and non-premixed supersonic flows

Numerical analysis of ignition and combustion of an n-decane–hydrogen fuel blend in a premixed supersonic flow and in a model scramjet duct is performed using a reduced reaction mechanism built especially to describe the oxidation of blended n-C₁₀H₂₂–H₂ fuel in air at the temperature T₀ > 900–1000 K in the pressure range P₀ = 0.1–13 atm. The developed kinetic mechanism involves the principal reactions responsible for chain mechanism development both for n-decane and for hydrogen oxidation. It has been shown that using blended n-C₁₀H₂₂–H₂ fuel makes it possible to enhance the ignition and combustion both in premixed and in non-premixed supersonic fuel–air flows compared to burning pure hydrogen–air and n-decane–air mixtures. This allows high combustion completeness in the scramjet duct at the distance of ～1 m even at extremely low air temperature T₀ = 1000 K and pressure P₀ = 0.3 atm. This is due to the interaction of kinetics of the formation of highly reactive atoms and radicals, carriers of chain mechanism, in H₂–air and n-C₁₀H₂₂–air mixtures.     

Quantum vs. Classical Integrability in Ruijsenaars–Schneider and Calogero–Moser Systems

The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider (R-S) and Calogero-Moser systems is addressed. The classical Calogero and Sutherland systems (based on any root system) at equilibrium have many remarkable properties; for example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all integer valued. These are related to the energy eigenvalues of the quantum Calogero and Sutherland systems. Similar features and results hold for the R-S type of integrable systems based on the classical root systems.     

Self-dual connections and the equations of fundamental fields in a Weyl–Cartan space

Spaces with a Weyl-type connection and torsion of a special type that are determined by the structure of the differentiability conditions in the algebra of complex quaternions are considered. These conditions are consistent only if the curvature of the connection is self-dual. The Maxwell and SL(2,?) Yang–Mills fields associated with the irreducible components of the connection also turn out to be self-dual, so that the corresponding equations are fulfilled on the solutions of the generating system. Using the twistor structure of the latter, its general solution is obtained. The singular locus has a string-like (particle-like) structure generating the self-consistent algebraic dynamics of the string system.     

A positive-weight next-to-leading-order Monte Carlo simulation of deep inelastic scattering and Higgs boson production via vector–boson fusion in Herwig++

The positive weight next-to-leading-order matching formalism (POWHEG) is applied to Deep Inelastic Scattering?(DIS) and the related Higgs boson production via vector?Cboson fusion process in the Herwig++ Monte Carlo event generator. This scheme combines parton shower simulation and next-to-leading-order calculation in a consistent way which only produces positive weight events. The simulation contains a full implementation of the truncated shower required to correctly model soft emissions in an angular-ordered parton shower.     

Completeness of first and second order ODE flows and of Euler–Lagrange equations

Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to Lagrangian mechanics and gravitational waves are given.     

Cosmological model of interacting phantom and Yang–Mills fields

In this paper, we consider a model of interacting phantom and Yang?CMills (YM) fields by assuming dilaton-type coupling. Using the specific solution for YM equation previously found by the author, we obtain simple exact solutions for the accelerated expansion of the Friedmann?CRobertson?CWalker (FRW) cosmological model. Besides, we derive induced potentials of phantom field corresponding to some given regimes of expansion. The effective equations of state (EoS) have been reconstructed for all types of models considered here.     

Inclusion of Yang–Mills fields in string corrected supergravity

We consistently incorporate Yang–Mills matter fields into string corrected (deformed) D=10$D=10$, N=1$N=1$ supergravity. We solve the Bianchi identities within the framework of the modified beta function favored constraints to second order in the string slope parameter γ also including the Yang–Mills fields. In the torsion, curvature and H   sectors we find that a consistent solution is readily obtained with a Yang–Mills modified supercurrent A_abc$A_{abc}$. We find a solution in the F sector following our previously developed method.     

Scattering and bound states of fermions in a mixed vector–scalar smooth step potential

The scattering of a fermion in the background of a smooth step potential is considered with a general mixing of vector and scalar Lorentz structures with the scalar coupling stronger than or equal to the vector coupling. Charge-conjugation and chiral-conjugation transformations are discussed and it is shown that a finite set of intrinsically relativistic bound-state solutions appears as poles of the transmission amplitude. It is also shown that those bound solutions disappear asymptotically as one approaches the conditions for the realization of the so-called spin and pseudospin symmetries in a four-dimensional space–time.     

Fermions in the background of mixed vector–scalar–pseudoscalar square potentials

The general Dirac equation in 1+1$1+1$ dimensions with a potential with a completely general Lorentz structure is studied. Considering mixed vector–scalar–pseudoscalar square potentials, the states of relativistic fermions are investigated. This relativistic problem can be mapped into a effective Schrödinger equation for a square potential with repulsive and attractive delta-functions situated at the borders. An oscillatory transmission coefficient is found and resonant state energies are obtained. In a special case, the same bound energy spectrum for spinless particles is obtained, confirming the predictions of literature. We showed that existence of bound-state solutions is conditioned by the intensity of the pseudoscalar potential, which possess a critical value.     

Eulerian simulation of sedimentation flows in vertical and inclined vessels

Sedimentation of particles in inclined and vertical vessels is numerically simulated using a finite volume method where the Eulerian multiphase model is applied. The particulate phase as well as the fluid phase is regarded as a continuum while the viscosity and solid stress of the particulate phase are modelled by the kinetic theory of granular flows. The numerical results show an interesting phenomenon of the emergence of two circulation vortices of the sedimentation flow in a vertical vessel but only one in the inclined vessel. Several sensitivity tests are simulated to understand the factors that influence the dual-vortex flow structure in vertical sedimentation. Results show that a larger fluid viscosity makes the two vortex centres much closer to each other and the boundary layer effect at lateral walls is the key factor to induce this phenomenon. In the fluid boundary layer particles settle down more rapidly and drag the local carrier fluid to flow downward near the lateral walls and thus form the dual-vortex flow pattern.     

Exact solution of the Dirac–Weyl equation in graphene under electric and magnetic fields

In this paper, we have obtained exact analytical solutions for the bound states of a graphene Dirac electron in magnetic fields with various q-parameters under an electrostatic potential. In order to solve the time-independent Dirac–Weyl equation, the Nikoforov–Uvarov (NU) and Frobenius methods have been used. We have also investigated the thermodynamic properties by using the Hurwitz zeta function method for one of the states. Finally, some of the numerical results are also shown.     

Extended structures and new infinite-dimensional hidden symmetries for the Einstein–Maxwell-dilaton-axion theory with multiple vector fields

A so-called extended elliptical-complex (EEC) function method is proposed and used to further study the Einstein–Maxwell-dilaton-axion theory with p vector fields (EMDA-p theory, for brevity) for . An Ernst-like matrix EEC potential is introduced and the motion equations of the stationary axisymmetric EMDA-p theory are written as a so-called Hauser–Ernst-like self-dual relation for the EEC matrix potential. In particular, for the EMDA-2 theory, two Hauser–Ernst-type EEC linear systems are established and based on their solutions some new parametrized symmetry transformations are explicitly constructed. These hidden symmetries are verified to constitute an infinite-dimensional Lie algebra, which is the semidirect product of the Kac–Moody algebra and Virasoro algebra (without centre charges). These results show that the studied EMDA-p theories possess very rich symmetry structures and the EEC function method is necessary and effective.     

Calogero–Moser systems for simple Lie groups and characteristic classes of bundles

This paper is a continuation of our paper Levin et al. [1]. We consider Modified Calogero–Moser (CM) systems corresponding to the Higgs bundles with an arbitrary characteristic class over elliptic curves. These systems are generalization of the classical Calogero–Moser systems with spin related to simple Lie groups and contain CM subsystems related to some (unbroken) subalgebras. For all algebras we construct a special basis, corresponding to non-trivial characteristic classes, the explicit forms of Lax operators and quadratic Hamiltonians. As by product, we describe the moduli space of stable holomorphic bundles over elliptic curves with arbitrary characteristic classes.     

A Generalization of the Goldberg–Sachs theorem and its consequences

The Goldberg–Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl tensor is algebraically special severe geometric restrictions are imposed. In particular it is demonstrated that the simple self-dual eigenbivectors of the Weyl tensor generate integrable isotropic planes. Another result obtained here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat manifold of (2,2) signature the manifold must be Calabi–Yau or symplectic and admits a solution for the source-free Einstein–Maxwell equations.     

On the eigenfunctions of hyperbolic quantum Calogero–Moser–Sutherland systems in a Morse potential

Letters in Mathematical Physics - We zoom in on special instances of recently found eigenfunctions for the hyperbolic quantum Calogero–Moser–Sutherland n-particle system in a Morse...