Peculiarities of temperature dependence for generalized Hall-Petch law and two-phase model for deformable polycrystalline materials

In the framework of the suggested in [arxiv:1803.08247 [cond-mat.mtrl-sci]] statistical theory of the equilibrium flow stress, including yield strength, ${\sigma}_y$, of polycrystalline materials under quasi-static (in case of tensile strain) plastic deformation in dependence on average size, d, of the crystallites (grains) in the range, $10^{-8}$ m - $10^{-2}$ m. it is found the coincidences of the theoretical and experimental data of ${\sigma}_y$ for the materials with BCC (${\alpha}$- Fe), FCC (Cu, Al, Ni) and HCP (${\alpha}$-Ti, Zr) crystal lattice at T=300K. The temperature dependence of the strength characteristics is studied. It is shown on the example of Al, that the yield strength grows with decreasing of the temperature for all grains with d greater than $3*d_0$ (with $d_0$ being extremal size of the grain for maximal ${\sigma}_y$) and then ${\sigma}_y$ decreases in the nano-crystalline region, thus determining a temperature-dimension effect. Stress-strain curves, ${\sigma}={\sigma}({\epsilon})$, are constructed for the pure crystalline phase of ${\alpha}$-Fe with Backofen-Consid\'ere fracture criterion validity. The single-phase model of polycrystalline material is augmented by means of inclusion of a softening grain boundary phase.Comment: 11 pages, 3 figures, 4 tables, pdf-version only, bad term "vacancy" is changed on "nanopore", definition of temperature-dimension effect introduced, footnotes 2,4,6 added, description of twinning in terms of partial dislocations, equilibrium flow stress and comments added, typo in Eq. 2 corrected, Eq.3 extended, 3 references adde

Gauge-invariant Lagrangians for mixed-antisymmetric higher spin fields

Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[\hat{s}_1,\hat{s}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $\Phi_{[\mu]_{\hat{s}_1}, [\mu]_{\hat{s}_2}}$ subject to $Y[\hat{s}_1,\hat{s}_2]$ with an additional tower of gauge parameters realizing the $(\hat{s}_1-1)$-th stage of reducibility with a specific dependence on the value $(\hat{s}_1-\hat{s}_2)=0,1,...,\hat{s}_1$. Minimal BRST--BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.Comment: 8 pages, extended Contribution to the Proceedings of the International Workshop "Supersymmetry and Quantum Symmetries" (SQS'2015, August 3 - August 8, 2015, Dubna, Russia); corrections in (4),(19) were made; ref.25, footnote 1 added; acknowledgements, footnote 2 with comments on gauge transformations in [28, 29] updated; resulting actions (18), (19) correcte

General Lagrangian Formulation for Higher Spin Fields with Arbitrary Index Symmetry. 2. Fermionic fields

We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having $k$ rows, on a basis of the BRST--BFV approach suggested for bosonic fields in our first article (Nucl. Phys. B862 (2012) 270, [arXiv:1110.5044[hep-th]). Starting from a description of fermionic mixed-symmetry higher-spin fields in a flat space of any dimension in terms of an auxiliary Fock space associated with a special Poincare module, we realize a conversion of the initial operator constraint system (constructed with respect to the relations extracting irreducible Poincare-group representations) into a system of first-class constraints. To do this, we find, in first time, by means of generalized Verma module the auxiliary representations of the constraint subsuperalgebra, to be isomorphic due to Howe duality to $osp(k|2k)$ superalgebra, and containing the subsystem of second-class constraints in terms of new oscillator variables. We suggest a universal procedure of finding unconstrained gauge-invariant Lagrangians with reducible gauge symmetries, describing the dynamics of both massless and massive fermionic fields of any spin. It is shown that the space of BRST cohomologies with a vanishing ghost number is determined only by constraints corresponding to an irreducible Poincare-group representation. As examples of the general approach, we propose a method of Lagrangian construction for fermionic fields subject to an arbitrary Young tableaux having 3 rows, and obtain a gauge-invariant Lagrangian for a new model of a massless rank-3 spin-tensor field of spin (5/2,3/2) with first-stage reducible gauge symmetries and a non-gauge Lagrangian for a massive rank-3 spin-tensor field of spin (5/2,3/2).Comment: 69 pages, no figures, published version, misprints with HS subsuperalgebra osp(1|2k) correcte

On Composite fields approach to Gribov copies elimination in Yang-Mills theories

We suggest a method of introducing the Gribov--Zwanziger horizon functional, $H$, for Yang--Mills theories by using the composite fields technique: $\sigma (\phi )=H$. A different form of the same horizon functional in gauges $\chi$ and $\chi ^{\prime }$ is taken into account via (gauged) field-dependent BRST transformations connecting quantum Yang--Mills actions in these gauges. We introduce generating functionals of Green's functions with composite fields and derive the corresponding Ward identities. A study of gauge dependence shows that the effective action in Yang--Mills theories with the composite field $H$ does not depend on the gauge on the extremals determined by the Yang--Mills fields $\phi$ alone.Comment: 7 pages, no figures, extended Contribution to the Proceedings of the International Workshop "Supersymmetry and Quantum Symmetries" (SQS'2013, July 29 - August 3, 2013, Dubna, Russia); acknowledgments and references adde

On Lagrangian Formulation for Half-integer HS Fields within Hamiltonian BRST Approach

A recent progress in a gauge-invariant Lagrangian description of massive and massless half-integer higher-spin fields in AdS and Minkowski spaces is presented. The procedure is based on a BFV-BRST operator, encoding the initial conditions realized by constraints in a Fock space and extracting the higher-spin fields from unitary irreducible representations of the AdS (Poincare) group. The construction is applicable to higher-spin tensor fields with a multi-row Young tableaux.Comment: 5 pages, Contribution to Proceedings of the International Workshop "Supersymmetries and Quantum Symmetries", Dubna, July, 30 - August, 4, 2007, added referenc

Statistical approach to flow stress and generalized Hall-Petch law for polycrystalline materials under plastic deformations

A theory of flow stress is proposed, including the yield strength, $\sigma_y$, of polycrystalline materials in the case of quasi-static plastic deformations depending on the average size, d, of a crystallite (grain) in the range of $10^{-8}$-$10^{-2}$ m. The dependence is based on a statistical model of energy spectrum distribution in each crystallite of a single-modal polycrystalline material over quasi-stationary levels under plastic loading with the highest level equal to the maximum dislocation energy in the framework of a disclination-dislocation deformation mechanism. The distribution of an equilibrium scalar dislocation density in each crystallite leads to a flow stress from the Taylor's strain hardening mechanism containing the usual (normal) and anomalous Hall-Petch relations for coarse and nanocrystalline grains, respectively, and gains the maximum at flow stress values for an extreme grain size, $d_0$, of the order $10^{-8}$-$10^{-7}$ m. The maximum undergoes a shift to the region of larger grains for decreasing temperatures and increasing strains \varepsilon.Comment: 14 pages, 11 figures, pdf-version only, bad term "vacancy" is changed on "nanopore", 4 footnotes added with dislocation substructures, sequence of equilibrium processes, zone of localized plasticity, partial dislocations, comments to Fig. 2 on fluctuation thermal origin of dislocation added, twinning type defects; misprint in Eq. (23) corrected, Eq. (11) improved, minor change

Elements of Fedosov Geometry in Lagrangian BRST Quantization

A Lagrangian BRST quantization for generic gauge theories in general irreducible non-Abelian hypergauges is proposed on a basis of the multilevel Batalin--Tyutin formalism and a special BV--BFV dual description for a reducible gauge model in a symplectic supermanifold $\mathcal{M}_0$ locally parameterized by antifields for Lagrangian multipliers and by the fields of the BV method. The quantization rules are based on a set of nilpotent anticommuting operators $\Delta^\mathcal{M}, {V}^\mathcal{M}, {U}^\mathcal{M}$ defined using some odd and even symplectic structures in a supersymplectic manifold $\mathcal{M}$ whose local representation is an odd (co)tangent bundle over $\mathcal{M}_0$ provided by the choice of a flat Fedosov connection and a compatible non-symplectic metric in $\mathcal{M}_0$. The generating functional of Green's functions is constructed in terms of general coordinates in $\mathcal{M}$ with the help of contracting homotopy operators with respect to ${V}^\mathcal{M}$ and ${U}^\mathcal{M}$. We prove the gauge independence of the S-matrix and derive the Ward identity.Comment: 8 pages, LaTeX, no figures, v5: typos corrected in Eqs. (7), (9)-(12), (18), (20), (22), (24), (35), presentation improved. Published in the Proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'05, Dubna, July 27-31, 2005) eds. E.A.Ivanov, B.M. Zupnik, 2006, p.262-26

On general Lagrangian formulations for arbitrary mixed-symmetric higher-spin fermionic fields on Minkowski backgrounds

The details of unconstrained Lagrangian formulations (being continuation of earlier developed research for Bose particles in NPB 862 (2012) 270, [arXiv:1110.5044[hep-th]], Phys. of Part. and Nucl. 43 (2012) 689, [arXiv:1202.4710 [hep-th]]) are reviewed for Fermi particles propagated on an arbitrary dimensional Minkowski space-time and described by the unitary irreducible half-integer higher-spin representations of the Poincare group subject to Young tableaux $Y(s_1,...,s_k)$ with $k$ rows. The procedure is based on the construction of the Verma modules and finding auxiliary oscillator realizations for the orthosymplectic $osp(k|2k)$ superalgebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Applying of an universal BRST-BFV approach permit to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive fermionic fields of any spin with appropriate number of gauge and Stukelberg fields. The general construction possesses by the obvious possibility to derive Lagrangians with only holonomic constraints.Comment: 6 pages, Contribution to the Proceedings of the Conference "Quantum Field Theory and Gravity 2012", Tomsk, Russia, July, 31 - August, 5, 2 reference adde

Towards Lagrangian formulations of mixed-symmetry Higher Spin Fields on AdS-space within BFV-BRST formalism

The spectrum of superstring theory on the $AdS_5 \times S_5$ Ramond-Ramond background in tensionless limit contains integer and half-integer higher-spin fields subject at most to two-rows Young tableaux $Y(s_1,s_2)$. We review the details of a gauge-invariant Lagrangian description of such massive and massless higher-spin fields in anti-de-Sitter spaces with arbitrary dimensions. The procedure is based on the construction of Verma modules, its oscillator realizations and of a BFV-BRST operator for non-linear algebras encoding unitary irreducible representations of AdS group.Comment: Slightly enlarged contribution to the Proceedings of the International Bogolyubov Conference-2009 "Problems of Theoretical and Mathematical Physics", Moscow - Dubna, August 21 - 27, 2009, 9 pages, no figure

Notes on soft breaking of BRST symmetry in the Batalin-Vilkovisky formalism

We have proved the nilpotency of the operators which describe the gauge dependence of the generating functionals of Green's functions for the gauge theories with the soft breaking of BRST symmetry in the Batalin-Vilkovisky formalism.Comment: 1+6 page