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The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to examine the anisotropy induced by regular inhomogeneity arrangements. The proposed framework is based on the idea of Molinari & El Mouden (1996) to improve classical mean-field models of thermoelastic media by taking into account the interactions between each pair of inhomogeneities within the material volume, known as a cluster model. Both elastic and elasto-plastic regimes are examined. A new extension of the original formulation, aimed to account for the non-linear plastic regime, is performed with the use of the modified tangent linearization of the metal matrix constitutive law. The model uses the second stress moment to track the accumulated plastic strain in the matrix. In the examples, arrangements of spherical inhomogeneities in three Bravais lattices of cubic symmetry (Regular Cubic, Body-Centered Cubic and Face-Centered Cubic) are considered for two basic material scenarios: "hard-in-soft" (MMC) and "soft-in-hard" (PM). As a means of verification, the results of micromechanical mean-field modeling are compared with those of numerical homogenization performed using the Finite Element Method (FEM). In the elastic regime, a comparison is also made with several other micromechanical models dedicated to periodic composites. Within both regimes, the results obtained by the cluster model are qualitatively and quantitatively consistent with FEM calculations, especially for volume fractions of inclusions up to 40%., Comment: 36 pages Accepted for publication in Int. J. Engineering Science on 11 July 2024

A new approach to problem of glueball search is presented. It refers to early J. Rosner's attempts to detect the tensor glueball. In the present description the glueball state is treated on equal footing with singlet $q\bar{q}$ one. Mixing glueball with $q\bar{q}$ nonet creates decuplet. Glueball can be detected as its component. Our approach is based on hypothesis of vanishing exotic commutators described as VEC model. The model describes all multiplets of light mesons. This makes possible to compare the mass patterns of different multiplets. According to VEC description some abnormal nonets can be interpreted as incomplete decuplets. This makes possible to relate the anomaly of the nonet to a glueball component of decuplet. The model reflects rich diversity of strong interaction properties. The treatment presented is quite elementary: only masses of physical states are required to be known., Comment: 13 pages, added afterward, several minor changes in the main body of text

We continue the study of flavor aspects of strong interaction. The answer to the question of glueball existence is probably a necessary step in this investigation. The existence of the glueball implies the existence of the decuplet. The model we consider requires that the mass of meson decuplet dominated by the glueball is enclosed between the masses of the ideal nonet N and S states. This description is applied to the two sets of the tensor mesons. One of them comprise the well known particles which are attributed to the widely known nonet $2^{++}$. We argue that they belong to a decuplet if there exists the isoscalar tensor meson having the mass obeying the condition on glueball dominated meson; the meson $f_2(1430)$ could be a candidate. Another set includes large number of mesons lying in the 2GeV region. This set is used to test ability of the model to select particles belonging to the decuplet., Comment: 21 pages. Published version

The properties of the $0^{++}$ and $0^{-+}$ meson multiplets are discussed. Quoted are the $0^{++}$ and $0^{-+}$ glueball masses determined from data fit., Comment: 4 pp

Complex-mass (finite-width) $0^{++}$ nonet and decuplet are investigated by means of exotic commutator method. The hypothesis of vanishing of the exotic commutators leads to the system of master equations (ME). Solvability conditions of these equations define relations between the complex masses of the nonet and decuplet mesons which, in turn, determine relations between the real masses (mass formulae), as well as between the masses and widths of the mesons. Mass formulae are independent of the particle widths. The masses of the nonet and decuplet particles obey simple ordering rules. The nonet mixing angle and the mixing matrix of the isoscalar states of the decuplet are completely determined by solution of ME; they are real and do not depend on the widths. All known scalar mesons with the mass smaller than $2000MeV$ (excluding $\sigma(600)$) and one with the mass $2200\div2400MeV$ belong to two multiplets: the nonet $(a_0(980), K_0(1430), f_0(980), f_0(1710))$ and the decuplet $(a_0(1450), K_0(1950), f_0(1370), f_0(1500), f_0(2200)/f_0(2330))$. It is shown that the famed anomalies of the $f_0(980)$ and $a_0(980)$ widths arise from an extra "kinematical" mechanism, suppressing decay, which is not conditioned by the flavor coupling constant. Therefore, they do not justify rejecting the $q\bar{q}$ structure of them. A unitary singlet state (glueball) is included into the higher lying multiplet (decuplet) and is divided among the $f_0(1370)$ and $f_0(1500)$ mesons. The glueball contents of these particles are totally determined by the masses of decuplet particles. Mass ordering rules indicate that the meson $\sigma(600)$ does not mix with the nonet particles., Comment: 22 pp, 1 fig, a few changes in argumentation, conclusions unchanged. Final version to appear in EPJC

Mass formulae for light meson multiplets derived by means of exotic commutator technique are written for complex masses and considered as complex mass sum rules (CMSR). The real parts of the (CMSR) give the well known mass formulae for real masses (Gell-Mann--Okubo, Schwinger and Ideal Mixing ones) and the imaginary parts of CMSR give appropriate sum rules for the total hadronic widths - width sum rules (WSR). Most of the observed meson nonets satisfy the Schwinger mass formula (S nonets). The CMSR predict for S nonet that the points $(m,\Gamma{})$ form the rectilinear stitch (RS) on the complex mass plane. For low-mass nonets WSR are strongly violated due to ``kinematical'' suppression of the particle decays, but the violation decreases as the mass icreases and disappears above $\sim 1.5 GeV$. The slope $k_s$ of the RS is not predicted, but the data show that it is negative for all S nonets and its numerical values are concentrated in the vicinity of the value -0.5. If $k_s$ is known for a nonet, we can evaluate ``kinematical'' suppressions of its individual particles. The masses and the widths of the S nonet mesons submit to some rules of ordering which matter in understanding the properties of the nonet. We give the table of the S nonets indicating masses, widths, mass and width orderings. We show also mass-width diagrams for them. We suggest to recognize a few multiplets as degenerate octets. In Appendix we analyze the nonets of $1^+$ mesons., Comment: 20 pages, 3 figures; title and discussion expanded; additional text; final version accepted for publication in EPJC

Mass sum rules for meson multiplets derived from exotic commutators may be written for complex masses. Then the real parts give the well known mass formulae (GM-O, Schwinger, Ideal) and the imaginary ones give the corresponding sum rules for total hadronic widths. The masses and widths of the meson nonets submit to a definite orders. It thus follows that tables of the meson nonets should include information about masses, widths and the orders as well as the mixing angle. The width sum rule for the nonet complying with Schwinger mass formula may be depicted as a straight line in the $(m,\Gamma)$ plane. It is easily verifiable and satisfied better for high mass nonets., Comment: LaTeX, 4pp, 1 figure. To appear in Proceedings of "Hadron 2001"

The bicovariant differential calculus on the three-dimensional Kappa-Poincar'e group and the corresponding Lie-algebra structure are described. The equivalence of this Lie-algebra structure and the three-dimensional $\kappa$-Poincar\'e algebra is proved., Comment: AMSTeX, Pages 15

A nonlinear transformation in the momentum space is constructed which converts the deformed action of Lorentz and Weyl generators on momenta into the standard one., Comment: AMSTeX, Pages 5