Symmetric Field Research Articles

Symmetric strain fields as diffusion barrier: A new avenue to achieve diffusion-resistant, thermally stable thermoelectric interfaces

Symmetric strain fields as diffusion barrier: A new avenue to achieve diffusion-resistant, thermally stable thermoelectric interfaces

Exhibiting stable model of dark energy compact star with Tolman-VI solution under complexity free system

Several recent developments have highlighted the significance of the vanishing complexity factor formalism in understanding the structure and evolution of stellar relativistic compact objects. This formalism, introduced through a novel definition proposed by Herrera (Phys. Rev. D 97:044010, 2018), offers valuable insights into the dynamics of such systems. In this manuscript, we explored a class of realistic solutions to the static and spherically symmetric field equations characterized by two fluid distributions: ordinary stellar matter and dark energy, within the framework of this formalism. Utilizing the well-known Tolman-VI solution as the seed ansatz for the metric coefficient grr, we employed the complexity-free format to derive an analytic solution for the other metric coefficient, gtt. Subsequently, we obtained the solutions of gravitational field equations for our proposed spacetime model by incorporating the linear dark energy equation of state. These results were applied to the astrophysical compact star candidate LMC X-4, with M=1.04M⊙ and R=8.4km. The potential viability and credibility of the proposed dark star solutions were thoroughly analyzed by examining key constraints, including the regularity of metric functions, physical adequacy through matter variables, state parameter behavior, energy conditions, stability tests (such as pressure anisotropy and hydrostatic equilibrium), the speed of sound, and the mass–radius relation for this compact star candidate. Notably, the estimated values of the dark energy coupling factor, presented in Table 1, highlight the exotic nature of the fluid distribution and effectively quantify the contribution of dark energy to the structure and evolution of an ultra-relativistic dark compact star. These findings strongly support our model solutions and demonstrate improvements over previously reported results in Rej et al. (Chin J Phys 87:608, 2024).

More on unconstrained descriptions of higher spin massless particles

Here we suggest a new local action describing arbitrary integer spin-s massless particles in terms of only two symmetric fields φ and α of rank-s and (s−3) respectively. It is an unconstrained version of the Fronsdal theory where the double traceless constraint on the physical field is evaded via a rank-(s−4) Weyl like symmetry. The constrained higher spin diffeomorphism is enlarged to full diffeomorphism via the Stueckelberg field α through an appropriate field redefinition. After a partial gauge fixing where the Weyl symmetry is broken while preserving diffeomorphisms, the field equations reproduce, for arbitrary integer spin-s, diffeomorphism invariant equations of motion previously obtained via a truncation of the spectrum of the open bosonic string field theory in the tensionless limit. In the s=4 case we show that the functional integration over α leads to a unique nonlocal Weyl and diffeomorphism invariant action given only in terms of the physical field φ whose spectrum is confirmed via an analysis of the analytic structure of the spin-4 propagator for which we introduce a complete basis of projection and transition nonlocal differential operators. We also show that the elimination of α after the Weyl gauge fixing leads to a nonlocal diffeomorphism invariant action previously obtained in the literature. Published by the American Physical Society 2025

Inverse problems for third-order nonlinear perturbations of biharmonic operators

We study inverse boundary problems for third–order nonlinear tensorial perturbations of biharmonic operators on a bounded domain in ℝ n , where n≥3. By imposing appropriate assumptions on the nonlinearity, we demonstrate that the Dirichlet–to–Neumann map, known on the boundary of the domain, uniquely determines the genuinely nonlinear tensorial third-order perturbations of the biharmonic operator. The proof relies on the inversion of certain generalized momentum ray transforms on symmetric tensor fields. Notably, the corresponding inverse boundary problem for linear tensorial third-order perturbations of the biharmonic operator remains an open question.

Quasi-topological fractons: a 3D dipolar gauge theory

We consider the theory of a generic rank-2 tensor field in three spacetime dimensions, which involves a symmetric tensor field transforming under infinitesimal diffeomorphisms, and a vector field, whose gauge transformation depends on a local vector parameter. The gauge fixing shows a non-trivial structure, and some non-intuitive possibilities are listed. Despite the fact that the theory is not topological, the energy-momentum tensor vanishes on-shell, which justifies the “quasi-topological” appellation we give to this theory. We show that the theory has three degrees of freedom. Moreover, we find an interesting physical interpretation, which consists in a generalized planar electromagnetism and in the emergence of two vector charges with restricted mobility. These are typical fractonic behaviours which can be related to the so-called traceless scalar and vector charge theories.

Measurement of the electric field distribution in streamer discharges

Using electric field induced second harmonic generation (E-FISH), we performed direction-resolved absolute electric field measurements on single-channel streamer discharges in 70 mbar (7 kPa) air with 0.2 mm and 2 ns resolutions. In order to obtain the absolute (local) electric field, we developed a deconvolution method taking into account the phase variations of E-FISH. The acquired field distribution shows good agreement with the simulation results under the same conditions, in direction, magnitude, and shape. This is the first time that E-FISH is applied to streamers of this size (>0.5 cm radius), crossing a large gap. Achieving these high resolution electric field measurements benefits further understanding of streamer discharges and enables future use of E-FISH on cylindrically symmetric (transient) electric field distributions. Published by the American Physical Society 2025

STNeRF: symmetric triplane neural radiance fields for novel view synthesis from single-view vehicle images

This paper presents STNeRF, a method for synthesizing novel views of vehicles from single-view 2D images without the need for 3D ground truth data, such as point clouds, depth maps, CAD models, etc., as prior knowledge. A significant challenge in this task arises from the characteristics of CNNs and the utilization of local features can lead to a flattened representation of the synthesized image when training and validation with images from a single viewpoint. Many current methodologies tend to overlook local features and rely on global features throughout the entire reconstruction process, potentially resulting in the loss of fine-grained details in the synthesized image. To tackle this issue, we introduce Symmetric Triplane Neural Radiance Fields (STNeRF). STNeRF employs a triplane feature extractor with spatially aware convolution to extend 2D image features into 3D. This decouples the appearance component, which includes local features, and the shape component, which consists of global features, and utilizes them to construct a neural radiance field. These neural priors are then employed for rendering novel views. Furthermore, STNeRF leverages the symmetric properties of vehicles to liberate the appearance component from reliance on the original viewpoint and to align it with the symmetry of the target space, thereby enhancing the neural radiance field network’s ability to represent the invisible regions. The qualitative and quantitative evaluations demonstrate that STNeRF outperforms existing solutions in terms of both geometry and appearance reconstruction. More supplementary materials and the implementation code are available for access at the following link: https://github.com/ll594282475/STNeRF.

Numerical Investigation of Proton Exchange Membrane Fuel Cells with Symmetrical Serpentine Channels Equipped with Baffles.

The design of the flow field structure for bipolar plates significantly influences the output performance of proton exchange membrane fuel cells (PEMFCs). Adding baffles in the flow channels can enhance the transportation of reactants and electrochemical performance of the PEMFCs. In this study, three types of baffles with different shapes and sizes were designed. Computational fluid dynamics (CFD) models for the PEMFCs with a symmetrical serpentine flow field (SSFF), both without baffles and with baffles, were established using the CFD method. Numerical simulations for the PEMFCs, both without baffles and with baffles, were performed by FLUENT software. The simulation results show that the PEMFCs with baffles demonstrated improved oxygen transport and increased reaction gas concentrations in the flow channels compared to the PEMFCs without baffles. The velocity magnitude exhibited abrupt changes as the fluid passed through the baffles due to their disturbance effect. Specially, the PEMFCs without baffles had a maximum power density of 0.601 W/cm2, while the PEMFCs with rectangular baffles reached a maximum power density of 0.755 W/cm2, which was enhanced by 25.6% due to the arrangement of baffles in the symmetrical serpentine flow channels.

R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment

R-C Telescope Alignment Method Based on Astigmatism Correction of Symmetrical Field of View Misalignment

Alignment of a Ritchey-Chrétien telescope with primary mirror figure error guided by the rapid measurement of binodal astigmatism.

Nodal aberration theory (NAT) is a vectorized aberration theory that was developed to describe systems without rotational symmetry. NAT predicts non-rotationally symmetric aberration field dependences for third-order astigmatism and in particular a "binodal" behavior in which there are two points in the field of view where astigmatism vanishes. This study serves to demonstrate an alignment technique based on an understanding of this binodal behavior using a custom Ritchey-Chretien telescope. A method involving a commercial Shack-Hartmann compact-format wavefront sensor was developed to rapidly measure densely sampled full-field displays of the telescope, which has its secondary mirror mounted on a precision hexapod to allow for repeatable control of the telescope alignment. Real ray-based simulations were carried out on a model of the telescope and were consistent with the observed experimental results for both aligned and misaligned states of the telescope. We then provide guidelines on how to interpret Fringe Zernike astigmatism full-field displays for use during optical system alignment. This method is particularly relevant for freeform systems, which often have asymmetric field dependencies for multiple aberration types including astigmatism.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

Abstract We investigate the critical collapse of spherically symmetric scalar fields in asymptotically anti-de Sitter spacetime, focusing on two scenarios: real and complex scalar fields with potentials. By fine-tuning the amplitude of the initial scalar field under different cosmological constants, we find a linear relationship between the critical amplitude of the first collapse and the cosmological constant in both scenarios. Furthermore, we observe that the slope of this linear relationship varies linearly with the coupling strength.

On the maximum bound principle and energy dissipation of exponential time differencing methods for the matrix-valued Allen–Cahn equation

Abstract This work delves into the exponential time differencing (ETD) schemes for the matrix-valued Allen–Cahn equation. In fact, the maximum bound principle (MBP) for the first- and second-order ETD schemes is presented in a prior publication [SIAM Review, 63(2), 2021], assuming a symmetric initial matrix field. Noteworthy is our novel contribution, demonstrating that the first- and second-order ETD schemes for the matrix-valued Allen–Cahn equation—both being linear schemes—unconditionally preserve the MBP, even in instances of nonsymmetric initial conditions. Furthermore, we prove that these two ETD schemes preserve the energy dissipation law unconditionally for the matrix-valued Allen–Cahn equation, and their convergence analysis is also provided. Some numerical examples are presented to verify our theoretical results and to simulate the evolution of corresponding matrix fields.

All vertices for unconstrained symmetric gauge fields

Recently, the generating system that describes interacting symmetric higher-spin gauge fields at the level of equations of motion was proposed. The interaction vertices it offers are “off the mass shell” unless constrained by the prescribed factorization condition that properly removes traceful components. In this paper, we detail the structure of the unconstrained, i.e., traceful vertices. We derive their manifest form to all orders along with a net of the associated dualities, thus providing the complete higher-spin vertex analysis at the unconstrained level for the bosonic theory in any dimension. These vertices are shown to be the minimal space-time local and have a form of the peculiar integrals over a space of closed polygons, which we scrutinize in the paper. The obtained results directly apply to the holomorphic sector of the four-dimensional theory, where the interaction is on shell, producing the all-order chiral higher-spin vertices. Published by the American Physical Society 2024

Inversion of the exponential X-ray transform of symmetric 2-tensors

A unique inversion of the exponential X-ray transform of some class of symmetric 2-tensor fields supported in a two-dimensional strictly convex set is presented. The approach to inversion is based on the Cauchy problem for a Beltrami-like equation associated with A-analytic maps.

Symmetric group gauge theories and simple gauge/string dualities

Abstract We study two-dimensional topological gauge theories with gauge group equal to the symmetric group Sn and their string theory duals. The simplest such theory is the topological quantum field theory of principal Sn fiber bundles. Its correlators are equal to Hurwitz numbers. The operator products in the gauge theory for each finite value of n are coded in one partial permutation algebra. We propose a generalization of the partial permutation algebra to the symmetric orbifold topological quantum field theory of any seed theory and show that the theory factorizes into marked partial permutation combinatorics and seed Frobenius algebra properties. Moreover, we exploit the established correspondence between Hurwitz theory and the stationary sector of Gromov–Witten theory on the sphere to prove an exact gauge/string duality. The relevant field theory is a grand canonical version of Hurwitz theory and its two-point functions are obtained by summing over all values of the instanton degree of the maps covering the sphere. We stress that one must look for a multiplicative basis on the boundary to match the bulk operator algebra of single string insertions. The relevant boundary observables are completed cycles.

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.

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

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.

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.