Cutoff Surface Research Articles

Stretched horizon from conformal field theory

Recently, it has been observed that the Hartle-Hawking correlators, a signature of smooth horizon, can emerge from certain heavy excited state correlators in the (manifestly non-smooth) BTZ stretched horizon background, in the limit when the stretched horizon approaches the real horizon. In this note, we develop a framework of quantizing the CFT modular Hamiltonian, that explains the necessity of introducing a stretched horizon and the emergence of thermal features in the AdS-Rindler and (planar) BTZ backgrounds. In more detail, we quantize vacuum modular Hamiltonian on a spatial segment of S1, which can be written as a particular linear combination of sl(2,ℝ) generators. Unlike radial quantization, (Euclidean) time circles emerge naturally here which can be contracted smoothly to the ‘fixed points’(end points of the interval) of this quantization thus providing a direct link to thermal physics. To define a Hilbert space with discrete normalizable states and to construct a Virasoro algebra with finite central extension, a natural regulator (ϵ) is needed around the fixed points. Eventually, in the dual description the fixed points correspond to the horizons of AdS-Rindler patch or (planar) BTZ and the cut-off being the stretched horizon. We construct a (Lorentzian) highest weight representation of that Virasoro algebra where vacuum can be identified with certain boundary states on the cut-off surface. We further demonstrate that two point function in a (vacuum) descendant state of the regulated Hilbert space will reproduce thermal answer in ϵ → 0 limit which is analogous to the recent observation of emergent thermality in (planar) BTZ stretched horizon background. We also argue the thermal entropy of this quantization coincides with entanglement entropy of the subregion. Conversely, the microcanonical entropy corresponding to high energy density of states exactly reproduce the BTZ entropy. Quite remarkably, all these dominant high lying microstates are defined only at finite ϵ in the regulated Hilbert space. We expect that all our observations can be generalized to BTZ in stretched horizon background where the boundary spatial coordinate is compactified.

Entanglement island and Page curve for one-sided charged black hole

In this paper, we extend the method of calculating the entanglement entropy of Hawking radiation of black holes using the “in” vacuum state, which describes one-sided asymptotically flat neutral black hole formed by gravitational collapse, to dynamic charged black holes. We explore the influence of charge on the position of the boundary of island ∂I and the Page time. Due to their distinct geometric structures, we discuss non-extremal and extremal charged black holes separately. In non-extremal cases, the emergence of island saves the bound of entropy at late times, and the entanglement entropy of Hawking radiation satisfies the Page curve. Moreover, we also find that the position of the boundary of island ∂I depends on the position of the cutoff surface (observers), differing from the behavior in eternal charged black holes. In extremal black holes, when the island exists, the entanglement entropy is approximately equal to the Bekenstein-Hawking entropy, while the entanglement entropy becomes ill-defined when island is absent. Our analysis underscores how different geometric configurations significantly influence the behavior of entropy.

End of the world brane meets TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}

End of the world branes in AdS have been recently used to study problems deeply connected to quantum gravity, such as black hole evaporation and holographic cosmology. With non-critical tension and Neumann boundary condition, the end of the world brane often represents part of the degrees of freedom in AdS gravity and geometrically it is only part of the entire boundary. On the other hand, holographic TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document} deformation can also give a boundary as a cutoff surface for AdS gravity. In this paper we consider AdS gravity with both the end of the world boundary and the cutoff boundary. Using partial reduction we obtain a brane world gravity glued to a TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document} deformed bath. We compute both entanglement entropy and Page curve, and find agreement between the holographic results and island formula results.

Extremal surfaces in glue-on AdS/TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document} holography

TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document} deformed CFTs with positive deformation parameter have been proposed to be holographically dual to Einstein gravity in a glue-on AdS3 spacetime [1]. The latter is constructed from AdS3 by gluing a patch of an auxiliary AdS3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}_3^{\\ast } $$\\end{document} spacetime to its asymptotic boundary. In this work, we propose a glue-on version of the Ryu-Takayanagi formula, which is given by the signed area of an extremal surface. The extremal surface is anchored at the endpoints of an interval on a cutoff surface in the glue-on geometry. It consists of an RT surface lying in the AdS3 part of the spacetime and its extension to the AdS3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}_3^{\\ast } $$\\end{document} region. The signed area is the length of the RT surface minus the length of the segments in AdS3∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ extrm{AdS}}_3^{\\ast } $$\\end{document}. We find that the Ryu-Takayanagi formula with the signed area reproduces the entanglement entropy of a half interval for TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFTs on the sphere. We then study the properties of extremal surfaces on various glue-on geometries, including Poincaré AdS3, global AdS3, and the BTZ black hole. When anchored on multiple intervals at the boundary, the signed area of the minimal surfaces undergoes phase transitions with novel properties. In all of these examples, we find that the glue-on extremal surfaces exhibit a minimum length related to the deformation parameter of TT¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ T\\overline{T} $$\\end{document}-deformed CFTs.

Effect of Cut-Off Irrigation levels on Production of Teosinte Forage Crop in Clay Soil

The present study was carried out at Sakha Agricultural Research Station (clay soils) middle north of Nile Delta area during summer seasons 2021 and 2022 in randomized complete block design with three replications. The objective of this research was to find out the response of yield, water saving and some water functions for teosinte forage crop to cut-off surface irrigation owing to produce " more per less”. Three irrigation levels were executed; 100% i.e., full irrigation, 90% cut-off irrigation and 80% cut-off irrigation. The mean performances of plant height, fresh and dry forage yields in the two seasons and combined are significantly affected by irrigation levels applied, whereas normal or control treatment with100% irrigation i.e., no cut-off (Trt. A) has the tallest of plant height. On the other hand, the low irrigation level with 80% cut-off (Trt. C) has the shortest plants at the three cuts. Also, traits reduced with the decrease of irrigation water level at the three cuts. Both fresh and dry forage yields are severely decreased when plants irrigated by 80% cut-off. Decreasing the irrigation water level than the commonly controlled of 100% without cut-off (Trt.A) markedly reduced all studied growth characters at the three cuts. The inhibiting effect of the water deficit stress on the studied parameters notably appeared more pronounced under the 80% cut-off than that of 90% .The obtained results may refer to that decreasing the irrigation water lowered the soil moisture content which restricted the mobility of nutrients to plant that would reduce the efficiency of physiological and metabolic processes needed for plant growth. Regarding water relations, irrigation with 90% cut-off resulted in several advantages; almost same yield as obtained under full irrigation, 10% water saving as well as the highest values of crop-water functions of water productivity (WP) and productivity of irrigation water (PIW). The mean values of fresh forage yield of 100% irrigation levels recorded 610 and 685 Kg/strip with compared to 585 and 655kg/strip for 90 %irrigation treatment at first and second cuts, respectively in the first season.

Theoretical investigations on cutoff wave number of quad-polar waveguide

The hollow waveguides with angular deformation are widely used in high power millimeter wave system. In this manuscript, the cutoff wave number of the quad-polar waveguide with a boundary of is theoretically analyzed based on the perturbation analysis. Using the boundary condition and the orthogonal properties of the trigonometric functions, a determinant is obtained and then the exact closed-form expression of cutoff wave number is deduced from the determinant. Based on the cutoff wave number, the eigen field is calculated by nonlinear programming method. The values of the cutoff wavenumbers, eigen fields and surface currents for the first few modes are calculated and compared with the results obtained from simulation software. The high correspondence of the calculated values with the simulated results proves that the proposed method is an appropriate option for fast and precise analyzing quad-polar waveguides.

Dirac-Born-Infeld counter-term and black hole thermodynamics

Abstract We revisit the Dirac-Born-Infeld–like boundary counter-term for the four-dimensional theory of gravity. We show that it correctly executes complete background subtraction for both asymptotically Anti-de Sitter and asymptotically flat geometries. With an appropriate choice of ensemble, we reproduce dyonic black hole thermodynamics with both types of asymptotics by studying local thermodynamics on the cut-off surface.

Numerical modelling of thermal weakening of granite under dynamic loading

A numerical method to predict thermal weakening of granite rock under low- and moderate rate dynamic loading conditions is developed. Thermal weakening of granite under uniform heating, leading to degradation of the material stiffness and strength, is modelled with the continuum approach, using a damage-viscoplasticity model. The viscoplastic part is based on a special power law criterion for granite under compression and the rounded tensile cut-off surface, while the damage part is equipped with separate damage variables in tension and compression. The strain rate sensitivity of rock is accounted for by viscoplasticity. The global thermo-mechanical initial/boundary value problem is solved with an explicit (in time) staggered method with mass scaling applied to increase the critical time step. Rock heterogeneity is described as random clusters of linear tetrahedral finite elements assigned with the constituent mineral, here quartz, feldspar, and biotite, material properties. The temperature dependence of the thermal and elasticity properties of the minerals is included in the model up to 850 °C, i.e. well beyond the α-β transition of quartz. However, as the model aims to predict the thermal weakening, the temperature dependence of the rock strength is not used as an input. In the numerical examples, low-rate uniaxial tension and compression tests are first simulated on heated and intact rock samples to demonstrate the performance of the model. Finally, crushing of heat-treated and intact granite balls by diametral dynamic compression is numerically replicated with a fair accuracy.

Glue-on AdS holography for Toverline{T} -deformed CFTs

The Toverline{T} deformation is a solvable irrelevant deformation whose properties depend on the sign of the deformation parameter μ. In particular, Toverline{T} -deformed CFTs with μ < 0 have been proposed to be holographically dual to Einstein gravity where the metric satisfies Dirichlet boundary conditions at a finite cutoff surface. In this paper, we put forward a holographic proposal for Toverline{T} -deformed CFTs with μ > 0, in which case the bulk geometry is constructed by gluing a patch of AdS3 to the original spacetime. As evidence, we show that the Toverline{T} trace flow equation, the spectrum on the cylinder, and the partition function on the torus and the sphere, among other results, can all be reproduced from bulk calculations in glue-on AdS3.

High-resolution 3D strain and orientation mapping within a grain of a directed energy deposition laser additively manufactured superalloy

The industrialization of Laser Additive Manufacturing (LAM) is challenged by the undesirable microstructures and high residual stresses originating from the fast and complex solidification process. Non-destructive assessment of the mechanical performance controlling deformation patterning is therefore critical. Here, we use Dark Field X-ray Microscopy (DFXM) to map the 3D subsurface intragranular orientation and strain variations throughout a surface-breaking grain within a directed energy deposition nickel superalloy. DFXM results reveal a highly heterogenous 3D microstructure in terms of the local orientation and lattice strain. The grain comprises ≈ 5 μm-sized cells with alternating strain states, as high as 5 ×10−3, and orientation differences <0.5°. The DFXM results are compared to Electron Backscatter Diffraction measurements of the same grain from its cut-off surface. We discuss the microstructure developments during LAM, rationalising the development of the deformation patterning from the extreme thermal gradients during processing and the susceptibility for solute segregation.

What distinguishes 100-year precipitation extremes over central European river catchments from more moderate extreme events?

Abstract. Historical extreme flooding events in central European river catchments caused high socioeconomic impacts. Previous studies have analysed single events in detail but have not focused on a robust analysis of the underlying extreme precipitation events in general, as historical events are too rare for a robust assessment of their generic dynamical causes. This study tries to fill this gap by analysing a set of realistic daily 100-year large-scale precipitation events over five major European river catchments with the help of operational ensemble prediction data from the ECMWF. The dynamical conditions during such extreme events are investigated and compared to those of more moderate extreme events (20 to 50 year); 100-year precipitation events are generally associated with an upper-level cutoff low over central Europe in combination with a surface cyclone southeast of the specific river catchment. The 24 h before the event is decisive for the exact location of this surface cyclone, depending on the location and velocity of the upper-level low over western Europe. The difference between 100-year and more moderate extreme events varies from catchment to catchment. Dynamical mechanisms such as an intensified upper-level cutoff low and surface cyclone are the main drivers distinguishing 100-year events in the Oder and Danube catchments, whereas thermodynamic mechanisms such as a higher moisture supply in the lower troposphere east of the specific river catchment are more relevant in the Elbe and Rhine catchments. For the Weser and Ems catchment, differences appear in both dynamical and thermodynamic mechanisms.

Page curves and entanglement islands for the step-function Vaidya model of evaporating black holes

It was proposed recently that the fine-grained entropy of the Hawking radiation can be expressed by the semiclassical island formula, which reproduces the unitary Page curve. In this paper, we choose the “in” vacuum state and apply the quantum extremal surface construction to study the Page curve for the step-function Vaidya model of evaporating black holes in four dimensions, which is produced by the spherical null shells. Metrics of the three regions of this spacetimes are obtained. In addition, the entanglement islands for the step-function Vaidya model of evaporating black holes at very late times are studied. When cutoff surface A is located in Minkowski region III with uA< uH at very late times, we find that the location of the boundary of island ∂I depends on the value of 8M − vA + vI. Specifically, ∂I is inside, at or outside the horizon when 8M − vA + vI is less than, equal to or larger than zero respectively. Moreover, when cutoff surface A is located in Minkowski region III with uA> uH after the black hole evaporates completely, we find that entanglement island still exists and ∂I is located on an equal-time Cauchy surface of the observer A when {r}_{(A)}^2 ≥ 64GNκc.

FINITE ELEMENT ANALYSIS ON THE NONLINEAR BEHAVIOR OF THE RC SHEAR WALL WITH REGULAR OPENINGS INFLUENCED BY HIGH-STRENGTH STEEL

This paper presented a nonlinear finite element analysis of lateral loading RC shear walls with regular openings using the 3D-NLFEA program. The RC shear walls model was generated from the available test results in the literature. To model the concrete under a complex stress state, a multi-surface plasticity model which combines compression failure surface with tension cut-off failure surface was used. The model was intended to look at the load-displacement relationship and the crack pattern between the model and the numerical model. In addition to the numerical model verification, parametric studies were carried out to investigate the use of high-strength steel (HSS) of the two different grades (grades 100 and 120) to replace all the normal-strength steel (NSS) or only some of it. The parametric studies found that the shear wall with the NSS bar demonstrated higher stiffness and achieved higher lateral load with the lowest extent of damage (compared to the RC shear wall with the HSS bar). On the other hand, using the HSS bar resulted in lower stiffness, lower lateral load, and higher damage region, which was expected as more strain is required to yield the HSS bar.

Beam model of Doppler backscattering

We use beam tracing—implemented with a newly-written code, Scotty—and the reciprocity theorem to derive a model for the linear backscattered power of the Doppler backscattering (DBS) diagnostic. Our model works for both the O-mode and X-mode in tokamak geometry (and certain regimes of stellarators). We present the analytical derivation of our model and its implications for the DBS signal localisation and the wavenumber resolution. In determining these two quantities, we find that it is the curvature of the field lines and the magnetic shear that are important, rather than the curvature of the cut-off surface. We also provide an explicit formula for the hitherto poorly-understood quantitative effect of the mismatch angle. Consequently, one can use this model to correct for attenuation due to mismatch, avoiding the need for empirical optimisation. This is especially important in spherical tokamaks, since the magnetic pitch angle is large and varies both spatially and temporally.

Island and Page curve for one-sided asymptotically flat black hole

Great breakthrough in solving black hole information paradox took place when semiclassical island rule for entanglement entropy of Hawking radiation was proposed in recent years. Up to now, most papers which discussed island rule of asymptotic flat black hole with D ≥ 4 focus on eternal black hole. In this paper, we take one more step further by discussing island of “in” vacuum state which describes one-sided asymptotically flat black hole formed by gravitational collapse in D ≥ 4. We find that island I emerges at late time and saves entropy bound. And boundary of island ∂I depends on the position of cutoff surface. When cutoff surface is far from horizon, ∂I is inside and near horizon. When cutoff surface is set to be near horizon, ∂I is outside and near horizon. This is different from the case of eternal black hole in which ∂I is always outside horizon no matter cutoff surface is far from or near horizon. We will see that different states will manifestly affect Sent in island formula when cutoff surface is far from horizon and thus have different result for Page time.

A 2D generic multi-surface cohesive zone model for simulating FRP-to-concrete mixed-mode debonding failure

This paper proposes a 2D generic multi-surface cohesive zone model to simulate the debonding failure process of FRP-to-concrete joints within the framework of plasticity theory. The model combines a tension cut-off yield surface with a Coulomb friction yield surface, which can accurately predict the coupled mixed-mode debonding behaviour. Non-associated flow rule is adopted by the Coulomb friction yield formulation to reproduce the dilation effect, while the tension cut-off criterion is responsible for simulating the separation in the normal direction between two bonded substrates. Given the potential non-convergence problems caused by the presence of vertex region at the intersections between two yield surfaces, a remedy measure using the implicit backward Euler integration method incorporating Koiter’s rule and coupled independent state variables is applied. The proposed 2D interface model is versatile, and its accuracy has been validated by comparing the predicted results with their test counterparts from literature in different aspects, including the capacities of capturing mixed-mode failure, dilation behaviour, lateral compression effect, FRP deformation, and local bond stress-slip relationship. The model’s good compatibility with the constitutive relationship of CDP (concrete damaged plasticity) is also demonstrated.

Holographic complexity in dSd+1

We study the CV, CA, and CV2.0 approaches to holographic complexity in (d + 1)-dimensional de Sitter spacetime. We find that holographic complexity and corresponding growth rate presents universal behaviour for all three approaches. In particular, the holographic complexity exhibits ‘hyperfast’ growth [1] and appears to diverge with a universal power law at a (finite) critical time. We introduce a cutoff surface to regulate this divergence, and the subsequent growth of the holographic complexity is linear in time.

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.

Bending the Bruhat-Tits tree. Part II. The p-adic BTZ black hole and local diffeomorphism on the Bruhat-Tits tree

In this sequel to [1], we take up a second approach in bending the Bruhat-Tits tree. Inspired by the BTZ black hole connection, we demonstrate that one can transplant it to the Bruhat-Tits tree, at the cost of defining a novel “exponential function” on the p-adic numbers that is hinted by the BT tree. We demonstrate that the PGL(2, Qp) Wilson lines [2] evaluated on this analogue BTZ connection is indeed consistent with correlation functions of a CFT at finite temperatures. We demonstrate that these results match up with the tensor network reconstruction of the p-adic AdS/CFT with a different cutoff surface at the asymptotic boundary, and give explicit coordinate transformations that relate the analogue p-adic BTZ background and the “pure” Bruhat-Tits tree background. This is an interesting demonstration that despite the purported lack of descendents in p-adic CFTs, there exists non-trivial local Weyl transformations in the CFT corresponding to diffeomorphism in the Bruhat-Tits tree.

From Rindler fluid to dark fluid on the holographic cutoff surface

As an approximation to the near horizon regime of black holes, the Rindler fluid was proposed on an accelerating cutoff surface in the flat spacetime. The concept of the Rindler fluid was then generalized into a flat bulk with the cutoff surface of the induced de Sitter and FRW universe, such that an effective description of dark fluid in the accelerating universe can be investigated.