Blow-up regimes in failure of rock specimens

For damage evaluation, the stage of superfast catastrophic failure of a medium and its mechanical behavior in a state of self-organized criticality prior to the onset of a blow-up fracture mode is of great interest for identification of its precursors. In this work, the data of experimental and numerical investigations of mechanical behavior of a medium before its catastrophic failure and the onset of a blow-up fracture mode are presented. Rock samples and ceramic specimens are subjected to three-point bending and uniaxial compression testing. Surface velocities of the loaded specimens are registered using a laser Doppler vibrometer. The blow-up regime duration is measured to be about 10–20 ms. The specimens’ mechanical behavior is numerically simulated under experimental conditions, including the regime of catastrophic fracture. The model parameters of damage accumulation are determined from a comparison with the experimental data. A number of features of the material mechanical response before the catastrophic fracture are identified, which could be treated as failure precursors

Propagators in Coulomb gauge from SU(2) lattice gauge theory

A thorough study of 4-dimensional SU(2) Yang-Mills theory in Coulomb gauge is performed using large scale lattice simulations. The (equal-time) transverse gluon propagator, the ghost form factor d(p) and the Coulomb potential V_{coul} (p) ~ d^2(p) f(p)/p^2 are calculated. For large momenta p, the gluon propagator decreases like 1/p^{1+\eta} with \eta =0.5(1). At low momentum, the propagator is weakly momentum dependent. The small momentum behavior of the Coulomb potential is consistent with linear confinement. We find that the inequality \sigma_{coul} \ge \sigma comes close to be saturated. Finally, we provide evidence that the ghost form factor d(p) and f(p) acquire IR singularities, i.e., d(p) \propto 1/\sqrt{p} and f(p) \propto 1/p, respectively. It turns out that the combination g_0^2 d_0(p) of the bare gauge coupling g_0 and the bare ghost form factor d_0(p) is finite and therefore renormalization group invariant.Comment: 10 pages, 7 figure

Numerical Study of the Ghost-Gluon Vertex in Landau gauge

We present a numerical study of the ghost-gluon vertex and of the corresponding renormalization function \widetilde{Z}_1(p^2) in minimal Landau gauge for SU(2) lattice gauge theory. Data were obtained for three different lattice volumes (V = 4^4, 8^4, 16^4) and for three lattice couplings \beta = 2.2, 2.3, 2.4. Gribov-copy effects have been analyzed using the so-called smeared gauge fixing. We also consider two different sets of momenta (orbits) in order to check for possible effects due to the breaking of rotational symmetry. The vertex has been evaluated at the asymmetric point (0;p,-p) in momentum-subtraction scheme. We find that \widetilde{Z}_1(p^2) is approximately constant and equal to 1, at least for momenta p > ~ 1 GeV. This constitutes a nonperturbative verification of the so-called nonrenormalization of the Landau ghost-gluon vertex. Finally, we use our data to evaluate the running coupling constant \alpha_s(p^2).Comment: 19 pages, 6 figures, 9 tables, using axodraw.sty; minor modifications in the abstract, introduction and conclusion

Coulomb Energy, Remnant Symmetry, and the Phases of Non-Abelian Gauge Theories

We show that the confining property of the one-gluon propagator, in Coulomb gauge, is linked to the unbroken realization of a remnant gauge symmetry which exists in this gauge. An order parameter for the remnant gauge symmetry is introduced, and its behavior is investigated in a variety of models via numerical simulations. We find that the color-Coulomb potential, associated with the gluon propagator, grows linearly with distance both in the confined and - surprisingly - in the high-temperature deconfined phase of pure Yang-Mills theory. We also find a remnant symmetry-breaking transition in SU(2) gauge-Higgs theory which completely isolates the Higgs from the (pseudo)confinement region of the phase diagram. This transition exists despite the absence, pointed out long ago by Fradkin and Shenker, of a genuine thermodynamic phase transition separating the two regions.Comment: 18 pages, 19 figures, revtex

On practical problems to compute the ghost propagator in SU(2) lattice gauge theory

In SU(2) lattice pure gauge theory we study numerically the dependence of the ghost propagator G(p) on the choice of Gribov copies in Lorentz (or Landau) gauge. We find that the effect of Gribov copies is essential in the scaling window region, however, it tends to decrease with increasing beta. On the other hand, we find that at larger beta-values very strong fluctuations appear which can make problematic the calculation of the ghost propagator.Comment: 15 pages, 5 postscript figures. 2 Figures added Revised version as to be published in Phys.Rev.

Infrared exponents and the strong-coupling limit in lattice Landau gauge

We study the gluon and ghost propagators of lattice Landau gauge in the strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find evidence of the conformal infrared behavior of these propagators as predicted by a variety of functional continuum methods for asymptotically small momenta $q^2 \ll \Lambda_\mathrm{QCD}^2$. In the strong-coupling limit, this same behavior is obtained for the larger values of a^2q^2 (in units of the lattice spacing a), where it is otherwise swamped by the gauge field dynamics. Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass $\propto 1/a$. Perhaps unexpectedly, these deviations are thus no finite-volume effect but persist in the infinite-volume limit. They furthermore depend on the definition of gauge fields on the lattice, while the asymptotic conformal behavior does not. We also comment on a misinterpretation of our results by Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II); references and comments on subsequent work on the subject added

Strong-coupling study of the Gribov ambiguity in lattice Landau gauge

We study the strong-coupling limit beta=0 of lattice SU(2) Landau gauge Yang-Mills theory. In this limit the lattice spacing is infinite, and thus all momenta in physical units are infinitesimally small. Hence, the infrared behavior can be assessed at sufficiently large lattice momenta. Our results show that at the lattice volumes used here, the Gribov ambiguity has an enormous effect on the ghost propagator in all dimensions. This underlines the severity of the Gribov problem and calls for refined studies also at finite beta. In turn, the gluon propagator only mildly depends on the Gribov ambiguity.Comment: 14 pages, 22 figures; minor changes, matches version to appear in Eur. Phys. J.

Inconsistency of Naive Dimensional Regularizations and Quantum Correction to Non-Abelian Chern-Simons-Matter Theory Revisited

We find the inconsistency of dimensional reduction and naive dimensional regularization in their applications to Chern-Simons type gauge theories. Further we adopt a consistent dimensional regularization to investigate the quantum correction to non-Abelian Chern-Simons term coupled with fermionic matter. Contrary to previous results, we find that not only the Chern-Simons coefficient receives quantum correction from spinor fields, but the spinor field also gets a finite quantum correction.Comment: 19 pages, RevTex, Feynman diagrams drawn by FEYNMAN routin

Зоны концентрированной деформации (структуры цветка): натурные наблюдения и данные моделирования

Our study was focused on narrow linear zones that penetrate to different depths the crust and have complex infrastructure. Rocks in such zones are more intensively tectonically altered in comparison with the background. ‘Flower structures’ and ‘zones of concentrated deformation’ (ZCD) are the terms to describe these zones. The field study results combined with the data of tectonophysical and computational modeling data and supplemented by the literature analysis gave grounds for the following conclusions. In the experiments, as well as in nature, ZCDs show similar and, in some cases, identical morphological and infrastructural features and have similar stages of their evolution. A ZCD is mainly a reflection of the transpression setting. Its formation is accompanied by 3D plastic shear flow of matter and dilatancy of the deformed volume. A ZCD may be associated with the development of the ‘basement – cover’ system. It may also occur due to the intra-cover tectogenesis that does not influence the basement. Locations of ZCDs are spatially regular and predetermine the tectonic divisibility of the crust and lithosphere.В настоящее время большое внимание уделяется изучению узких линейных зон, которые, пронизывая земную кору на разную глубину, характеризуются сложной инфраструктурой и интенсивной в сравнении с фоновой тектонической переработкой горных масс. Такие структуры получили название «структуры цветка» или «зоны концентрированной деформации». Изучение натурных объектов вкупе с данными тектонофизического и расчетного моделирования, дополненное анализом литературного материала, позволило сделать следующие выводы: ЗКД в эксперименте и в природных объектах обнаруживают сходство, иногда тождество, по морфологии, инфраструктуре, этапности эволюции; ЗКД отражают преимущественно обстановки транспрессии, и их формирование сопровождается 3D пластическим сдвиговым течением вещества и дилатансией деформируемого объема; возникновение ЗКД может быть связано с развитием системы «фундамент – чехол», но может определяться и внутричехольным тектогенезом, не затрагивающим фундамент; ЗКД обладают пространственно-регулярным расположением и определяют тектоническую делимость земной коры и литосферы.

The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)−1FμνTr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu} in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension two operator $F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be consistently added to the Gribov-Zwanziger action, which implements the restriction of the path integral's domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov-Taylor identity.Comment: 30 page