Symmetric Field Research Articles

Global shift symmetry on an ADM hypersurface: Toward emergent gravity

Generalized symmetries and their spontaneous breakdown serve as the fundamental concept to constrain the many-body entanglement structure, which allows us to characterize quantum phases of matter and emergent collective excitations. For example, emergent photons may be understood by spontaneous 1-form symmetry breaking, which results from a long-ranged entanglement structure between UV microscopic degrees of freedom. In this study, we show that emergent “gravity” may also arise in a similar fashion, where quotes have been used to emphasize that the symmetry-constrained gravitons show unconventional properties compared to usual gravitons. As the electric 1-form symmetry in Maxwell theory is realized as a global shift symmetry of the spatial component of the U(1) gauge field, generated by the electric field, we demonstrate that a constant shift of the Arnowitt-Deser-Misner (ADM) metric on the spatial hypersurface can be viewed as a global symmetry, generated by the ADM canonical momentum. Deriving a vector-type conserved charge from the variation of action, we construct a shift symmetry operator. Considering a Wick rotation, we demonstrate that a gravitational Wilson loop is charged under the action of this shift symmetry operator, which thus confirms the existence of a generalized global symmetry on the ADM hypersurface. Based on the Ward identity, we show that the spontaneous breaking of this global shift symmetry may give rise to a nonpropagating massless symmetric gauge field at the boundary of the hypersurface. Published by the American Physical Society 2024

Intensification of flocculation efficiency in multi-stage reactors by optimizing the multi-cone segment configuration

Flocculation is widely used in water treatment, and creating an optimal environment for floc growth is essential to enhancing flocculation efficiency. In this paper, we developed a multi-stage flocculation reactor (MFR) with strong, moderate, and weak mixing zones. Specifically, multi-cone structures with varying diameter ratios (DR) were incorporated in the moderate zone to promote floc growth. Computational simulations revealed that an MFR with a DR of 0.5 generated a uniform and symmetric flow field, reducing zero-velocity zones and forming distinct vortices within cones. This environment facilitated gradual floc growth while minimizing breakage. When applied to treating fracturing flowback fluid, a complex and challenging wastewater, the MFR produced larger and denser flocs, with an average chord length of 180 μm and a fractal dimension of 1.7170. These flocs exhibited high viscoelasticity, with a strength factor of 68.22 and a recovery factor of 47.77, indicating superior shear resistance and recovery ability after breakage. Consequently, the MFR achieved COD and turbidity removal rates of 92.05% and 93.61%, respectively, outperforming a stirred flocculation reactor, which achieved rates of 72.29% and 83.53% for the same parameters. Additionally, the MFR demonstrated excellent pollutant removal efficiency for both mineral processing wastewater and dyeing wastewater. With gradually decreasing energy along the flow direction, the MFR provided appropriate mixing intensities for different stages of floc growth, promoting efficient formation. These findings underscore the MFR’s potential as a highly effective solution for wastewater treatment applications.

Hall-like behaviour of higher rank Chern-Simons theory of fractons

Fracton phases of matter constitute an interesting point of contact between condensed matter and high-energy physics. The limited mobility property of fracton quasi-particles finds applications in many different contexts, including quantum information, spin liquids, elasticity, hydrodynamics, gravity and holography. In this paper we adopt a field theoretical approach to investigate the three dimensional action of a rank-2 symmetric tensor field invariant under the covariant fracton symmetry. The theory appears as a non-topological higher rank generalization of the ordinary Chern-Simons model, depending only on the traceless part of the tensor gauge field. After defining a field strength, a rank-2 traceless “electric” field and a “magnetic” vector field are identified, in analogy with the standard Chern-Simons ones. Once matter is introduced, a Hall-like behaviour with fractonic features emerges. In particular, our model shows a Hall-like dipole current, together with a vectorial “flux-attachment” relation for dipoles. This gives a possible starting point for a fracton-vortex duality. A gauge-fixing term is then introduced, from which propagators are computed and the counting of the degrees of freedom is performed. Finally, the energy-momentum tensor is shown to be conserved and the integrated energy density is proved to be zero, which reminds the topological nature of the standard Chern-Simons model.

Simulations of X-ray focusing by zone plates in rotationally symmetric optical field utilizing the matrix-free Finite Difference Beam Propagation Method

We present the use of a finite difference method based on Crank-Nicholson scheme and recurrence scheme for computationally efficient simulation of the X-ray propagation through a zone plate. By introducing boundary and central conditions and by avoiding large matrix operations, the method achieves considerable speed, little memory occupation and low background noise. Accommodating refractive index profiles of arbitrary shape, it can be applied to assist optimizing X-ray zone plates and understanding focusing mechanism.

A Fourier approach to tomographic reconstruction of tensor fields in the plane

We consider the problem of inversion of the X-ray transform for sums of 1-forms and symmetric 2-tensor fields. Such a problem arises after linearization of a related travel time tomography problem, described via Mañé's action potential of the energy level 1/2 for a magnetic flow. In a strictly convex bounded domain in the Euclidean plane, we show when and how to recover simultaneously both unknown 1-tensor and symmetric 2-tensor field uniquely from measurement of radiating flux at the boundary. The approach to reconstruction is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps.

Self-resonance during preheating: The case of [formula omitted]-attractor models

In this paper, for the first time, we obtain a new class of solutions for the Hill-type differential equations, which emerge in the preheating self-resonance phase of the expanding Universe. We study, in particular, the class of symmetric and asymmetric scalar field potentials coming from the so-called α-attractor models of the early Universe cosmology. By making a series expansion of the potential and employing perturbative techniques we reformulate the Mukhanov–Sasaki equation, which captures the dynamics of the curvature perturbation in these models, into a Hill equation. This last includes higher-order terms that were never solved in the literature. Namely, those coming from the cubic and quartic contributions of the scalar field potential. Then, we derive the expressions for the Floquet exponents of the Mukhanov–Sasaki variable. Our analytical results are then compared with numerical computations, showing a good agreement and thus making this method valuable for obtaining theoretical predictions with new observational applications in the contexts of Primordial Black Holes and Scalar-Induced Gravitational Waves.

Fully metallic geodesic lenses as analog electromagnetic models of static and spherically symmetric gravitational fields

Fully metallic geodesic lenses as analog electromagnetic models of static and spherically symmetric gravitational fields

Electric Field Features and Charge Behavior in Oil-Pressboard Composite Insulation under Impulse Voltage

Oil-pressboard/paper insulation materials are essential in transformers for ensuring their safe and stable operation, primarily due to their roles in spatial electric field distribution and charge migration mechanisms. Current spatial distribution analyses rely on computational methods that lack empirical validation, particularly for oil-pressboard/paper composites. This study leverages the principles of the Kerr electro-optic effect to develop a rapid measurement platform for electric fields within oil-pressboard/paper insulation under impulse voltage conditions, which measures the spatial electric field characteristics using Cu-Cu and Al-Al electrodes under various scenarios: with asymmetric and symmetric pressboard coverage and different numbers of insulating paper layers. Findings indicated: (1) In asymmetric pressboard models, Cu-Cu electrodes exhibit a consistent peak electric field of approximately 16 kV/mm, while Al-Al electrodes show peak values of 18.13 kV/mm and −14.98 kV/mm. Charge density patterns are similar, with Cu-Cu at about 68 μC/m2 and Al-Al at 11.2 μC/m2 and −124.8 μC/m2. (2) Symmetric models present consistent peak electric fields and charge densities for both polarities. (3) Increasing insulating paper layers elevates electric field strengths. Both electrodes show the similar peak field of about 17 kV/mm with differing paper layers due to higher charge injection from the Al electrode. (4) Utilizing the Schottky effect and field emission principles, the study clarifies charge generation and migration mechanisms. These insights could provide a theoretical foundation for designing and verifying oil-pressboard/paper insulation structures in transformers.

A Construction of Approximately Self-Similar Naked Singularities for the Spherically Symmetric Einstein-Scalar Field System

A Construction of Approximately Self-Similar Naked Singularities for the Spherically Symmetric Einstein-Scalar Field System

Stokes-type conjugate heat transfer and thermoelasticity analysis of a hollow spherical particle in a slip flow

Conjugate heat transfer around a spherical particle submerged in a viscous heat-conducting fluid at very low Reynolds numbers is analytically investigated. The cases of spherically symmetric and axisymmetric temperature fields are solved. The temperature jump condition of dilute gas dynamics is assumed. The induced thermal stresses in the sphere in the case of spherical symmetry are analytically solved as well. The effect of temperature jump, heat conductivity ratio between the solid and fluid media, the heat generation and the inner radius of the sphere on the temperature, displacement, radial stress and circumferential stresses are studied. Furthermore, an exact correlation is proposed between the Reynolds, Knudsen and Nusselt numbers as well as the drag coefficient of the sphere, which is valid for slip flow at the Stokes limit. Whether it is accurate at higher Reynolds numbers would need further research.

Asymmetric electric field structure boosts photocharge spatial separation and transfer to enhance antibiotics removal: In-situ construction and directed induction

The symmetric electric field structure within layered Bi-based photocatalysts hinders the long-distance transport and spatial separation of bulk photocharges. Herein, the BiOI/BiOIO3 heterostructures featuring a strong interfacial electric field were prepared through in-situ hydrothermal reduction, disrupting the symmetry of the internal electric field in pristine BiOIO3. The intrinsic polarization electric field ({0 1 0}) and the interfacial electric field ({0 0 1}) within the BiOI/BiOIO3 heterostructure directionally induced the separation and transport of photocharges along distinct pathways, significantly enhancing the dynamics of photogenerated charges and improving photocatalytic activity. Specifically, with the addition of 15 mL of glycol, the CBI-15 sample with a BiOI/BiOIO3 structure achieved a 75.5 % removal rate of tetracycline and a 99.1 % removal rate of sulfisoxazole, which were 1.50 and 1.23 times higher than those of BiOIO3, respectively. Furthermore, continuous flow degradation experiments using photocatalytic membranes (CBI-PVDF) in real water media demonstrated the promising potential of CBI-15 for antibiotic removal. This work presents a novel approach to the directional induction of photocharges separation and transfer, providing valuable insights for developing highly efficient photocatalysts aimed at antibiotic removal.

Symmetric twin paradox for free-falling frames: Argument against the relativistic time dilation?

The twin paradox, a classical puzzle in Special Relativity (SR), is typically resolved by acknowledging the asymmetry introduced by the acceleration of one twin's frame, associated with a rocket's motion through space. A similar paradox arises without any accelerated system, involving three or more inertial systems. This is commonly resolved by employing the relativistic concepts of clock synchronization and simultaneity. Here, we reformulate the paradox for two free-falling systems, where the twins traverse identical circular orbits in opposite directions around a central mass with a spherically symmetric gravitational field. This redefined version of the paradox eliminates asymmetry inherent in the original problem. Since both frames are free-falling, they can be viewed as locally inertial according to Einstein's Equivalence Principle. Additionally, no synchronization with clocks in other frames is needed. We explore a potential resolution to the paradox and highlight that there may be a misinterpretation of the Lorentz transformation in SR.

Irrational Moments and Signatures of Higher-Rank Gauge Theories in Diluted Classical Spin Liquids

Classical spin liquids (CSLs) have proved to be a fruitful setting for the emergence of exotic gauge theories. Vacancy clusters in CSLs can introduce gauge charges into the system, and the resulting behavior in turn reveals the nature of the underlying theory. We study these effects for a series of CSLs on the honeycomb lattice. We find that dilution leads to the emergence of effective free spins with tuneable, and generally irrational, size. For a specific higher-rank CSL, described by a symmetric tensor gauge fields, dilution produces spin textures with a characteristic quadrupolar angular structure and infinite-ranged interactions between dilution clusters. Published by the American Physical Society 2024

Investigation on flame behaviors in the mesoscale channel of one sudden-expansion step during the preliminary stage of ignition

The dynamic flame behaviors at the preliminary stage of ignition in the mesoscale sudden-expansion channel are numerically investigated in this study under the isothermal condition (300 K) at walls by using a two-dimensional model without symmetric assumption at the centerline. It is found that the flashback velocity is dominated by the upstream channel height; nevertheless, the blowoff velocity is determined by not only the downstream channel height but also the flow recirculation behind the sudden-expansion steps. As the expansion ratio is sufficiently large, the flame could exist within a substantially wider range of inlet flow velocity. In addition, four types of flame behaviors are found at the expansion ratio of 2: (I) steady convex flame, (II) steady concave flame, (III) simple oscillating flame, and (IV) complex oscillating flame. Above the flashback velocity, the convex flame exists steadily. With the increase in flow velocity, the flame becomes concave to the upstream and is stabilized by the wall-quenching effect of sudden-expansion steps. If the flow velocity is further increased, the flame becomes unstable and oscillates periodically (simple oscillating flame) due to the interaction of flame and the symmetric flow field in the sudden-expansion channel, while the occurrence of complex oscillating flame at high flow velocities is attributed to the asymmetric flow pattern. The frequency of oscillating flames decreases with the increase in flow velocity.

Type II string theory on AdS3×S3×T4 and symmetric orbifolds

We discuss in detail the 1+1-dimensional superconformal field theory dual to type II string theory on AdS3×S3×T4, emphasizing the string theoretic aspects of this duality. For one unit of Neveu-Schwarz (NS-NS) 5-brane flux (Q5=1), this string theory has been suggested to be dual to a grand-canonical ensemble of T4N/SN free symmetric orbifold conformal field theories (CFTs). We show how the string genus expansion emerges to all orders for the free orbifold grand-canonical correlation functions. We also discuss how the strong coupling limit of the NS-NS string theory arises (even at large N) in the free orbifold description, and argue why this limit does not have a weakly coupled RR description. The dual conformal field theory (CFT) includes (for all values of Q5) an extra T4 factor that is decoupled from perturbative string theory. We discuss the exactly marginal deformations that relate the different values of Q5, including the precise JJ¯ deformations mixing this extra T4 with the symmetric orbifold. Published by the American Physical Society 2024

Correction: Bychkov et al. The σ− Cohomology Analysis for Symmetric Higher-Spin Fields. Symmetry 2021, 13, 1498

There was an error in the original publication [...]

Lagrangian formulation of the Tsallis entropy

We investigate the gravitational origin of the Tsallis entropy, characterized by the nonadditive index δ. Utilizing Wald's formalism within the framework of f(R) modified theories of gravity, we evaluate the entropy on the black hole horizon for constant curvature solutions to the spherically symmetric vacuum field equations. In so doing, we demonstrate that the Tsallis entropy can be effectively derived from a generalization of the Lagrangian L∝R1+ϵ, where ϵ=δ−1 quantifies small deviations from general relativity. In conclusion, we examine the physical implications of our findings in light of cosmological observations and elaborate on the possibility of solving the thermodynamic instability of Schwarzschild black holes.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime* *Supported by the National Natural Science Foundation of China (11925503) and the Guangdong Major project of Basic and Applied Basic Research (2019B030302001). The computation is completed on the HPC Platform of Huazhong University of Science and Technology

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime. Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field. Through our numerical results, we obtain a formula that determines critical amplitude in terms of cosmological constant Λ: , where σ denotes the initial width of the scalar field and is the initial position of the scalar field. Notably, we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

Water structures in tip-charged carbon nanotubes.

Carbon nanotubes (CNTs) have potential applications in separation membranes and nanofluidic devices. It is well known that the behavior of water molecules confined in CNTs is affected by surface functional groups and external electric fields, leading to structural changes. The understanding of these structural changes of water within various CNTs is crucial, particularly in the context of material separation. While there have been many investigations into the effects of individual specific functional groups, a comprehensive understanding of the effect of these functional groups and the electric fields they generate on water molecules remains elusive. In this study, we investigate the properties of water molecules in tip-charged CNTs of (8,8), (10,10), and (12,12) chiral vectors with positive charges at one tip and negative charges at the other tip. Abstraction of ionized functional groups as tip charges enables a comprehensive understanding that is independent of individual functional groups. The symmetrically arranged tip-charges spontaneously generate a strong and symmetric electric field in the CNTs. However, the strength and directionality of the electric field are non-uniform and complex. In the interiors of (8,8) and (10,10) tip-charged CNTs, helical and square structures, which have disturbances caused by the non-uniformity of the electric field, are observed. The properties of the water molecules differed significantly in the center of the CNTs and near positive and negative charges, despite the electric field symmetry. In (12,12) tip-charged CNTs with 12 charges, a local ring structure is observed in the vicinity of negative charges but not in the vicinity of positive charges. It is concluded that the water structures in tip-charged CNTs have different characteristics from those in plain CNTs under a uniform electric field.

Extended legality of curved boundary integral method

The angular spectrum method is an efficient approach for synthesizing electromagnetic beams from planar electric field distributions. The electric field definition is restricted to a plane, which can introduce inaccuracy when applying the synthesized beam to curved surface features. The angular spectrum method can also be interpreted as a pure source method defining the field symmetrically with respect to the creation plane. Recently, we generalized that symmetric field method to arbitrary source distributions, which are valid at any point on compact, regular surface Ω in R3. We call this approach the Curved Boundary Integral method. The electromagnetic fields synthesized with this method satisfy the Helmholtz equation and are adjusted via amplitude and phase at the desired surface. The fields are obtained as a relatively simple integral. However, restrictions on where in space the synthesized field is valid were included in the mathematical proof length to avoid obscuring the main points. These restrictions can be significant depending on the shape and degree of curvature of surface Ω. In this article, we remove these restrictions so that the integral representation of the electromagnetic beam becomes valid at all points r∈R3∖Ω, with a minor restriction. Its modification can work even on Ω. We demonstrate the importance of this extended legality with a source field parametrized into the torus surface. The electromagnetic radiation of this structure would not be valid at any point in space without this extension. Finally, we show that by changing the order of integration, the field singularity at each source point is eliminated.