Anisotropic scaling for 3D topological models

A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent $$\nu$$ ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent $$\theta =\nu _{x}/\nu _{z}$$ θ = ν x / ν z . We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for $$\nu$$ ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation $$\nu _{\bar{\alpha }}z_{\bar{\alpha }}=2q$$ ν α ¯ z α ¯ = 2 q and $$\theta =\nu _{x}/\nu _{z}=z_{z}/z_{x}$$ θ = ν x / ν z = z z / z x for $$\nu$$ ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction $$\bar{\alpha }$$ α ¯ . An anisotropic quantum hyperscaling relation is also obtained.

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

A proposal to study topological models beyond the standard topological classification and that exhibit breakdown of Lorentz invariance is presented. The focus of the investigation relies on their anisotropic quantum critical behavior. We study anisotropic effects on three-dimensional (3D) topological models, computing their anisotropic correlation length critical exponent ν obtained from numerical calculations of the penetration length of the zero-energy surface states as a function of the distance to the topological quantum critical point. A generalized Weyl semimetal model with broken time-reversal symmetry is introduced and studied using a modified Dirac equation. An approach to characterize topological surface states in topological insulators when applied to Fermi arcs allows to capture the anisotropic critical exponent θ = νx/νz. We also consider the Hopf insulator model, for which the study of the topological surface states yields unusual values for ν and for the dynamic critical exponent z. From an analysis of the energy dispersions, we propose a scaling relation να¯ zα¯ = 2q and θ = νx/νz = zz/zx for ν and z that only depends on the Hopf insulator Hamiltonian parameters p and q and the axis direction α¯ . An anisotropic quantum hyperscaling relation is also obtained.

In situ observation of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

<p>The energy distribution at wave number space is known to be anisotropic in space plasmas. At kinetic scales, the standard Kinetic Alfven Wave model predicts anisotropy scaling of k<sub>par</sub> ∝ k<sub>perp</sub><sup>(1/3)</sup>, whereas the latest models considering the intermittency, or tearing instabilities, predict scalings such as k<sub>par</sub> ∝ k<sub>perp</sub><sup>(2/3)</sup> and k<sub>par</sub> ∝ k<sub>perp</sub><sup>(3/3)</sup>. Recent numerical simulations also payed considerable attention to this issue. Based on a unified analysis of five-point structure functions of the turbulence in three kinetic simulations, Cerri et al. 2019 obtained a converging result of l<sub>par</sub> ∝ l<sub>perp</sub><sup>(3/3)</sup>. To enrich our knowledge of the anisotropic scaling relation from an observational point of view, we conducted a statistical survey for the turbulence measured by MMS in the magnetosheath. For the 349 intervals with burst mode data, abundant evidence of 3D anisotropy at the sub-proton scale (1-100 km) is revealed by five-point second order structure functions. In particular, the eddies are mostly elongated along background magnetic field <strong>B<sub>0</sub></strong> and shortened in the two perpendicular directions. The ratio between eddies’ parallel and perpendicular lengths features a trend of rise then fall toward small scales, whereas the anisotropy in the perpendicular plane appears scale invariant. Moreover, over 30% of the events exhibit scaling relations close to l<sub>par</sub> ∝ l<sub>perp</sub><sup>(2/3)</sup>. In order to explain such signature, additional factors such as intermittency caused by different coherent structures may be required in addition to the critical balance premise.</p>

Holographic approach to thermalization in general anisotropic theories

We employ the holographic approach to study the thermalization in the quenched strongly-coupled field theories with very general anisotropic scalings including Lifshitz and hyperscaling violating fixed points. The holographic dual is a Vaidya-like time-dependent geometry where the asymptotic metric has general anisotropic scaling isometries. We find the Ryu-Takanayagi extremal surface and use it to calculate the time-dependent entanglement entropy between a strip region with width 2R and its outside region. In the special case with an isotropic metric, we also explore the entanglement entropy for a spherical region of radius R. The growth of the entanglement entropy characterizes the thermalization rate after a quench. We study the thermalization process in the early times and late times in both large R and small R limits. The allowed scaling parameter regions are constrained by the null energy conditions as well as the condition for the existence of the Ryu-Takanayagi extremal surfaces. This generalizes the previous works on this subject. All obtained results can be compared with experiments and other methods of probing thermalization.

Direct Seamless Parametrization

We present a method for seamless surface parametrization. Recent popular methods first generate a cross-field, where curvature is concentrated at singular vertices. Next, in a separate step, the surface is laid out in the domain subject to derived seamlessness constraints. This decoupling of the process into two independent problems, each with its own objective, leads to suboptimal results. In contrast, our method solves both problems together using domain variables. The key ingredient to the robustness of our method is a rounding strategy based on local estimation. The insight is that testing a small patch to decide between two likely possibilities is a good estimator. Most distortion measures can be used with our method, which get minimized consistently throughout the pipeline. Our method also enables feature alignment, as well as alignment to principle curvatures, and isotropic and anisotropic scaling.

Research on Sugarcane Seed-Bud Location Based on Anisotropic Scaling Transformation

Highlights A method of locating sugarcane seed bud based on anisotropy transformation is proposed.Using computer binocular vision technology, the location of the sugarcane seed bud was determined by edge feature matching of the sugarcane seed bud.There are few methods to study the automatic location of sugarcane seed buds, and our research provides a new research idea.Abstract. Sugarcane is a major economic crop in China, but the degree of mechanization in sugarcane cultivation is low. To improve the economic benefit of sugarcane planting, promoting the use of mechanization in sugarcane planting is necessary. Currently, the sugarcane planted using mechanization has a low survival rate and the mechanization efficiency is low because the existing sugarcane precutting machine fails to address the problem of damaging seed buds. This study proposed a sugarcane bud localization method based on computer binocular vision technology. The sugarcane stem segment positions can be determined by the grayscale horizontal projection after preprocessing the sugarcane image based on color and grayscale features. Then, the bud area can be intercepted according to the positional relationship between the seed bud and the stem node, and the planar position of the seed bud will be determined by using the color space conversion and the gray vertical projection. Finally, the anisotropic scaling transformation is used to match the seed-bud area and restore the spatial coordinates of the seed bud, and the spatial position of the seed bud can be determined. The image pyramid acceleration matching process is adopted, which can make the method more suitable for real-time applications. The experimental results show that the accuracy of seed-bud matching based on the anisotropic scaling transformation is 98%, which provides a basis for research on the anti-injury germ system in the automatic planting process of sugarcane. Keywords: Anisotropic scaling, Binocular vision, Image pyramid, Mechanization planting of sugarcane, Seed bud location.

Quantum critical scaling and holographic bound for transport coefficients near Lifshitz points

The transport behavior of strongly anisotropic systems is significantly richer compared to isotropic ones. The most dramatic spatial anisotropy at a critical point occurs at a Lifshitz transition, found in systems with merging Dirac or Weyl point or near the superconductor-insulator quantum phase transition. Previous work found that in these systems a famous conjecture on the existence of a lower bound for the ratio of a shear viscosity to entropy is violated, and proposed a generalization of this bound for anisotropic systems near charge neutrality involving the electric conductivities. The present study uses scaling arguments and the gauge-gravity duality to confirm the previous analysis of universal bounds in anisotropic Dirac systems. We investigate the strongly-coupled phase of quantum Lifshitz systems in a gravitational Einstein-Maxwell-dilaton model with a linear massless scalar which breaks translations in the boundary dual field theory and sources the anisotropy. The holographic computation demonstrates that some elements of the viscosity tensor can be related to the ratio of the electric conductivities through a simple geometric ratio of elements of the bulk metric evaluated at the horizon, and thus obey a generalized bound, while others violate it. From the IR critical geometry, we express the charge diffusion constants in terms of the square butterfly velocities. The proportionality factor turns out to be direction-independent, linear in the inverse temperature, and related to the critical exponents which parametrize the anisotropic scaling of the dual field theory.

On the regularization of Lifshitz-type field theories

We consider Lifshitz-type scalar theories with explicit breaking of the Lorentz symmetry that, in addition, exhibit anisotropic scaling laws near the ultraviolet fixed point. Using the proper time regularization method on the spatial coordinates only, we derive the regularized form of the one-loop effective potential in such theories. We study the main features of the one-loop effective potential and, also, the RG flow of the scale-dependent potential both in the IR and UV regimes. The beta functions for the couplings are derived.