blocks_3d: software for general 3d conformal blocks

We introduce the software blocks_3d for computing four-point conformal blocks of operators with arbitrary Lorentz representations in 3d CFTs. It uses Zamolodchikov-like recursion relations to numerically compute derivatives of blocks around a crossing-symmetric configuration. It is implemented as a heavily optimized, multi-threaded, C++ application. We give performance benchmarks for correlators containing scalars, fermions, and stress tensors. As an example application, we recompute bootstrap bounds on four-point functions of fermions and study whether a previously observed sharp jump can be explained using the “fake primary” effect. We conclude that the fake primary effect cannot fully explain the jump and the possible existence of a “dead-end” CFT near the jump merits further study.

Large D black holes in an environment

We construct dynamical black hole solutions to Einstein Equations in presence of matter in the large D limit. The matter stress tensors that we consider are weak in the sense that they source asymptotic spacetimes with internal curvatures of the order of $$ \mathcal{O} $$ O (D0). Apart from this, we work with a generic stress tensor demanding only that the stress tensor satisfies the conservation equations. The black hole solutions are obtained in terms of the dual non-gravitational picture of membranes propagating in spacetimes equivalent to the asymptotes of the black holes. We obtain the metric solutions to the second sub-leading order in 1/D. We also obtain the equations governing the dual membranes up to the first sub-leading order in 1/D.

On the uniqueness for weak solutions of steady double-phase fluids

We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.

Thermalization in large-N CFTs

In d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors. Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators. We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case. In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

Forecasting of the Possibility of Fragile Destruction Top of Cutting Blade of a Thread Forming Tool

A model of the magnitude of the stresses of the tip of the cutting blades of a thread-forming tool based on the theory of a homogeneous body is proposed. A model of second-order materials is considered. A description of the stress state is given using two stress tensors independent of each other.

Multiple reactivation of the Rennick Geodynamic Belt (northern Victoria Land, Antarctica): insights from inversion of fault slip data

&lt;p&gt;The Rennick Geodynamic Belt (RGB, East Antarctica) is a regionally sized, ca N-S trending, deformation zone (length &gt; 100 km) where a dense fault network separates tectonic units of northern the Victoria Land, to the W from the East Antarctic Craton, to the E.&lt;/p&gt;&lt;p&gt;The RGB is long known to have been active since Cambrian-Ordovician times up to recent, but its framework and geodynamic evolution is still debated and partially investigated. The long-lived tectonic activity led to a great structural complexity, due to the superposition and polyphasic reactivation of regional faults. Such complexity is reflected by the numerous (in some cases contrasting) tectonic reconstructions of the RGB area.&lt;/p&gt;&lt;p&gt;In this contribution we explore the present-day tectonic framework of the RGB, investigating the stress field that possibly characterised the last geodynamic events in the area. We base on selected datasets of fault-slip data and fractures density (collected by the Authors in various PNRA Italian Antarctic expeditions) and combine fault-slip data inversion with the azimuthal orientation of faults and the spatial distribution of fractures intensity across the RGB.&lt;/p&gt;&lt;p&gt;To obtain a more robust portrait of the RGB geodynamic evolution, two different software based on different fault-inversion methods were used in this study: DAISY (Windows, version 3.5) and FSA (MAC, version 36.5x7i). The software DAISY implements the multiple Monte Carlo convergent method and provides the best orientation of the principal paleostresses with an estimate of the error quantified by the factor MAD (Mean Angular Deviation, corresponding to the average angular deviation between the measured pitch of the kinematic vector on the fault plane and the predicted one by applying to the fault the computed paleostress). At each step, faults are uniquely associated to the stress tensor that provides the lowest MAD. Differently, the FSA software combines a random grid search of the stress tensors following a Monte Carlo approach, under the univocal condition of fulfilment of the frictional constraint (i.e. the fault plane must form with an orientation that satisfies the Mohr-Coulomb yield criterion, i.e. t/s&lt;sub&gt;n&lt;/sub&gt; = tgf with t = shear stress, s&lt;sub&gt;n&lt;/sub&gt; = normal stress and f = angle of internal friction). Additionally, this software allows a direct examination of the reduced Mohr circle of the calculated stress tensors, so that we can select the one with the largest number of faults showing a high t/s&lt;sub&gt;n&lt;/sub&gt; ratio.&lt;/p&gt;&lt;p&gt;The paleostress tensors were computed from 373 fault-slip data collected in 34 structural stations on site. Results from this multi methodological approach revealed:&lt;/p&gt;&lt;p&gt;(i) the existence of two, N-S oriented geotectonic provinces (namely the Bowers Mts province to the W and Usarp Mts to the E) characterized by the different spatial distribution of brittle deformation, more intense in the Bower Mts domain.&lt;/p&gt;&lt;p&gt;(ii) The superposition of two recent (Meso-Cenozoic) major tectonic events, with prevalent strike-slip kinematics and characterized by faults reactivation with right-lateral movement overprinting a previous left-lateral one.&lt;/p&gt;