Dispersion chain of Vlasov equations

On the basis of the Vlasov chain of equations, a new infinite dispersion chain of equations is obtained for the distribution functions of mixed higher order kinematical values. In contrast to the Vlasov chain, the dispersion chain contains distribution functions with an arbitrary set of kinematical values and has a tensor form of writing. For the dispersion chain, new equations for mixed Boltzmann functions and the corresponding chain of conservation laws for fluid dynamics are obtained. The probability is proved to be a constant value for a particle to belong the region where the quasi-probability density is negative (Wigner function).

On Maxwell Electrodynamics in Multi-Dimensional Spaces

The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action, which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the electromagnetic field in multi-dimensional pseudo-Euclidean (flat) spaces has also been developed and investigated. Based on the two arising first-class constraints, we have generalized to multi-dimensional spaces a number of different gauges known for the three-dimensional electromagnetic field. For multi-dimensional spaces of non-zero curvature the governing equations for the multi-dimensional electromagnetic field are written in a manifestly covariant form. Multi-dimensional Einstein’s equations of metric gravity in the presence of an electromagnetic field have been re-written in the true tensor form. Methods of scalar electrodynamics are applied to analyze Maxwell equations in the two and one-dimensional spaces.

Current-Component Independent Transition Form Factors for Semileptonic and Rare D ⟶ π K Decays in the Light-Front Quark Model

We investigate the exclusive semileptonic and rare D ⟶ π K decays within the standard model together with the light-front quark model (LFQM) constrained by the variational principle for the QCD-motivated effective Hamiltonian. The form factors are obtained in the q + = 0 frame and then analytically continue to the physical timelike region. Together with our recent analysis of the current-component independent form factors f ± q 2 for the semileptonic decays, we present the current-component independent tensor form factor f T q 2 for the rare decays to make the complete set of hadronic matrix elements regulating the semileptonic and rare D ⟶ π K decays in our LFQM. The tensor form factor f T q 2 are obtained from two independent sets J T + ⊥ , J T + − of the tensor current J T u v . As in our recent analysis of f − q 2 , we show that f T q 2 obtained from the two different sets of the current components gives the identical result in the valence region of the q + = 0 frame without involving the explicit zero modes and the instantaneous contributions. The implications of the zero modes and the instantaneous contributions are also discussed in comparison between the manifestly covariant model and the standard LFQM. In our numerical calculations, we obtain the q 2 -dependent form factors ( f ± , f T ) for D ⟶ π K and branching ratios for the semileptonic D ⟶ π K ℓ v ℓ ℓ = e , μ decays. Our results show in good agreement with the available experimental data as well as other theoretical model predictions.

Bc → J/ψ tensor form factors at large momentum recoil

We present a next-to-leading order (NLO) relativistic correction to [Formula: see text] tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears [Formula: see text] with [Formula: see text] matrices [Formula: see text] in the [Formula: see text] transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for [Formula: see text] meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil.

Heavy Quark Expansion of Λb→Λ*(1520) Form Factors beyond Leading Order

I review the parametrisation of the full set of Λb→Λ*(1520) form factors in the framework of Heavy Quark Expansion, including next-to-leading-order O(αs) and, for the first time, next-to-leading-power O(1/mb) corrections. The unknown hadronic parameters are obtained by performing a fit to recent lattice QCD calculations. I investigate the compatibility of the Heavy Quark Expansion and the current lattice data, finding tension between these two approaches in the case of tensor and pseudo-tensor form factors, whose origin could come from an underestimation of the current lattice QCD uncertainties and higher order terms in the Heavy Quark Expansion.

Modeling of the Resonant X-ray Response of a Chiral Cubic Phase

The structure of a continuous-grid chiral cubic phase made of achiral constituent molecules is a hot topic in the field of thermotropic liquid crystals. Several structural models have been proposed so far. Resonant X-ray scattering (RXS), which gives information on the molecular orientation in the unit cell, could be applied to select the most appropriate model. We modeled the RXS response for the recently proposed chiral cubic phase structure with an all-hexagon chiral continuous grid. A tensor form factor of a unit cell is constructed, which enables calculation of intensities of peaks for all Miller indices. We find that all the symmetry allowed peaks are resonantly enhanced, and their intensity is much stronger than the intensity of the symmetry forbidden (resonant) peaks. In particular, we predict that a strong resonant enhancement of the symmetry allowed peaks (011) and (002), not observed in a nonresonant scattering, could be observed by RXS at the carbon absorption edge. By RXS at the sulfur absorption edge, one might observe a resonant peak (113) and resonantly enhanced peak (233), and resonant enhancement of all the peaks that are observed in a nonresonant scattering, which probably hide the rest of the predicted resonant peaks.

A new tensor approach of computing pure and mixed Unilateral Support Equilibria

In this paper, we locate pure unilateral support equilibrium (USE) among pure Nash and pure Berge equilibrium using tensors. The differences between these equilibria are shown using tensor form of a game and are illustrated with numerical examples. Tensors will help to specify the location of each equilibrium using a system of coordinates based on tensors which will bring a solid mathematical foundations of all equilibria and will provide the possibility to solve high dimensional problems as we will see in a numerical example with a $15-$player game. Additionally, we extend the notion of pure USE to mixed USE when the sets of strategies of all players are discrete and finite. We prove a lemma dedicated to inaugurate a method of computing mixed USE profiles. We write corresponding formulas using tensors and their operations, then we illustrate this method by a numerical example of a $7-$player game.

Multilinear POD-DEIM model reduction for 2D and 3D semilinear systems of differential equations

<p style='text-indent:20px;'>We are interested in the numerical solution of coupled semilinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard space discretizations of the differential operators and illustrate how the resulting system of ordinary differential equations (ODEs) can be treated directly in matrix or tensor form. Moreover, in the framework of the proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM) we derive a two- and three-sided model order reduction strategy that is applied directly to the ODE system in matrix and tensor form respectively. We discuss how to integrate the reduced order model and, in particular, how to solve the tensor-valued linear system arising at each timestep of a semi-implicit time discretization scheme. We illustrate the efficiency of the proposed method through a comparison to existing techniques on classical benchmark problems such as the two- and three-dimensional Burgers equation.</p>