Symmetric Ones Research Articles

Higher-dimensional exceptional points and peakon dynamics triggered by spatially varying Kerr nonlinear media and PTδ(x) potentials.

Higher-dimensional PT-symmetric potentials constituted by delta-sign-exponential (DSE) functions are created in order to show that the exceptional points in the non-Hermitian Hamiltonian can be converted to those in the corresponding one-dimensional (1D) geometry, no matter the potentials inside are rotationally symmetric or not. These results are first numerically observed and then are proved by mathematical methods. For spatially varying Kerr nonlinearity, 2D exact peakons are explicitly obtained, giving birth to families of stable square peakons in the rotationally symmetric potentials and rhombic peakons in the nonrotationally symmetric potentials. By adiabatic excitation, different types of 2D peakons can be transformed stably and reciprocally. Under periodic and mixed perturbations, the 2D stable peakons can also travel stably along the spatially moving potential well, which implies that it is feasible to manage the propagation of the light by regulating judiciously the potential well. However, the vast majority of high-order vortex peakons are vulnerable to instability, which is demonstrated by the linear-stability analysis and by direct numerical simulations of propagation of peakon waveforms. In addition, 3D exact and numerical peakon solutions including the rotationally symmetric and the nonrotationally symmetric ones are obtained, and we find that incompletely rotationally symmetric peakons can occur stably in completely rotationally symmetric DSE potentials. The 3D fundamental peakons can propagate stably in a certain range of potential parameters, but their stability may get worse with the loss of rotational symmetry. Exceptional points and exact peakons in n dimensions are also summarized.

Substrate DNA Promoting Binding of Mycobacterium tuberculosis MtrA by Facilitating Dimerization and Interpretation of Affinity by Minor Groove Width.

In order to deepen the understanding of the role and regulation mechanisms of prokaryotic global transcription regulators in complex processes, including virulence, the associations between the affinity and binding sequences of Mycobacterium tuberculosis MtrA have been explored extensively. Analysis of MtrA 294 diversified 26 bp binding sequences revealed that the sequence similarity of fragments was not simply associated with affinity. The unique variation patterns of GC content and periodical and sequential fluctuation of affinity contribution curves were observed along the sequence in this study. Furthermore, docking analysis demonstrated that the structure of the dimer MtrA-DNA (high affinity) was generally consistent with other OmpR family members, while Arg 219 and Gly 220 of the wing domain interacted with the minor groove. The results of the binding box replacement experiment proved that box 2 was essential for binding, which implied the differential roles of the two boxes in the binding process. Furthermore, the results of the substitution of the nucleotide at the 20th and/or 21st positions indicated that the affinity was negatively associated with the value of minor groove width precisely at the 21st position. The dimerization of the unphosphorylated MtrA facilitated by a low-affinity DNA fragment was observed for the first time. However, the proportion of the dimer was associated with the affinity of substrate DNA, which further suggested that the affinity was actually one characteristic of the stability of dimers. Based on the finding of 17 inter-molecule hydrogen bonds identified in the interface of the MtrA dimer, including 8 symmetric complementary ones in the conserved α4-β5-α5 face, we propose that hydrogen bonds should be considered just as important as salt bridges and the hydrophobic patch in the dimerization. Our comprehensive study on a large number of binding fragments with quantitative affinity values provided new insight into the molecular mechanism of dimerization, binding specificity and affinity determination of MtrA and clues for solving the puzzle of how global transcription factors regulate a large quantity of target genes.

Symmetric and asymmetric separated variables. II. A second integrable case of the complex Kirchhoff model

In the present paper, we find a second new integrable case of the complex Kirchhoff model on e*(3). We show that the obtained integrable model possesses two types of separation of variables (SoV): symmetric and asymmetric ones. The asymmetric SoV—similar to that of the Clebsch model (F. Magri and T. Skrypnyk, arXiv:1512.04872) and of the first integrable case of the complex Kirchhoff model (T. Skrypnyk, J. Geom. Phys. 172, 104418 (2022)]—is characterized by two different curves of separation. In the case of symmetric SoV, both curves of separation are the same. This case—similar to the integrable case of the complex Kirchhoff model of Skrypnyk, J. Geom. Phys. 172, 104418 (2022)—yields a direct analog of the famous Weber–Neumann separated coordinates. The obtained separation curves and Abel-type equations for the constructed model can be viewed as trigonometric degenerations of the corresponding separation curves and Abel-type equations of the Clebsch model [F. Magri and T. Skrypnyk, arXiv:1512.04872 and T. Skrypnyk, J. Geom. Phys. 135, 204–218 (2019)], while separation curves and Abel-type equations of Skrypnyk, J. Geom. Phys. 172, 104418 (2022) can be viewed as their rational degenerations.

Symmetric and asymmetric Gauss and Gauss–Lobatto quadrature rules for triangles and their applications to high-order finite element analyses

Although symmetric Gauss quadrature rules have been studied extensively, the investigations of asymmetric Gauss quadrature rules and symmetric Gauss–Lobatto (GL) quadrature rules are limited. Moreover, GL quadrature rules are essential for high-order finite element methods like the quadrature element method (QEM) and the spectral element method (SEM) in strong and weak form, and asymmetric Gauss quadrature rules are even more efficient than the symmetric ones. This work first presents new optimization methods for solving symmetric and asymmetric Gauss quadrature rules and then generalizes the techniques to solve GL and hierarchical Gauss–Lobatto (HGL) quadrature rules. Most of the asymmetric Gauss quadrature rules with precision degree range from 1 to 50, and symmetric GL and HGL quadrature rules presented in this work are new. They are attached to this article as MATLAB m-files for future usage. The GL and HGL quadrature rules are (1) used for constructing weak form QEM and HQEM with diagonal-mass-matrix (DMM) that is promising in dynamic analyses, and (2) used as interpolation nodes in high-order finite element analyses like Fekete points. Applying the present asymmetric Gauss quadrature rules and symmetric GL and HGL quadrature rules to in-plane vibration shows that both cases of usage of the GL and HGL quadrature rules can provide results with high accuracy and convergence rate.

Comparison of the short-term efficacy of different Amplatzer models and similar occluders in the treatment of patent foramen ovale.

To compare the recent efficacy and safety of different Amplatzer models and similar occluder in the treatment of patent foramen ovale (PFO). Patients with PFO complicated with cryptogenic stroke or migraine who underwent transcatheter closure of PFO in the First Affiliated Hospital of Nanjing Medical University from September 2019 to March 2021 were selected. Patients were grouped according to the type of occluder device. The basic data of the patients were collected and followed up within 1 year after occlusion. Effectiveness was defined as no recurrence of stroke/remission of migraine symptoms and a negative postoperative foaming test, and safety events were counted as the combined results of serious adverse events. A total of 92 patients were selected, including 45 cases in the symmetrical group and 47 cases in the asymmetric group. There were no serious adverse events in the 2 groups during follow-up. 3 days and 1 month after occlusion, the number of shunt patients in the asymmetric group was significantly less than that in the symmetric group (χ2 = 5.484, P = 0.019; χ2 = 5.146, P = 0.023). The negative rate of blocked residual shunts in the asymmetric group was higher than that in the symmetric group at 1, 3, 6 and 12 months after occlusion (χ2 = 6.473, P = 0.011; χ2 = 4.305, P = 0.038; χ2 = 4.842, P = 0.027; χ2 = 4.034, P = 0.045). Headache in migraine patients in the asymmetric group was significantly better than headache in patients in the symmetric group (P = 0.038; P = 0.049). Asymmetric Amplatzer and similar occluders provide greater efficacy in short-term occlusion than symmetric ones.

Enhanced capillary and heat transfer performance of asymmetric micropost wicks

We developed asymmetric capillary wicks composed of slanted microposts using inclined photolithography. Then we investigated the effects of inclination angle and wicking direction on the capillary and the heat transfer performances. The working fluid accelerates when it flows in the slope direction of the structure (forward direction, FD) and decelerates when it flows in the opposite slope direction (rear direction, RD). We applied the scaling law to the capillary rise experiment data to verify that the inclination angle and the wicking direction affect the capillary performance. The capillary performance parameter was improved by up to ∼39% with FD case and decreased by 21.3% with RD. The heat transfer performance test showed that the wick-CHF (the enhanced critical heat flux due to the formation of the wick) of the asymmetric FD case was increased by 43.3% compared to symmetric ones while maintaining the heat transfer coefficient. This work shows that asymmetric evaporator wicks can enhance the critical heat flux without sacrificing the heat transfer coefficient, which can help develop high-performance thermal management solutions.

Grapho-analytic method of determining the minimum groove at the pivot root of symmetrical switches

Switches are a barrier place in the track for setting the permissible speeds for trains on the main tracks, as they have special structural devices for branching traffic from the main track to the secondary track. Symmetrical switches have a number of advantages compared to conventional ones: with the same brand with conventional switches, symmetric ones allow significantly higher speeds for the train movement with side tracks; symmetrical switches have a shorter length with the same radii of the transfer curves; it is possible to apply crosspieces with a larger angle than in the conventional switches while preserving the length of the curve and the radius. The specified qualities of single, versatile, symmetrical switches determined their use scope. On the main transport tracks, symmetrical switches are used in sorting parks of the stations, as well as in main tracks when it is necessary to achieve increased speeds of movement on both side tracks. Symmetric switches according to the purpose and design have the significant differences from the most conventional switches, and therefore the study of these designs is important and relevant. Moreover, very few scientific works were devoted to such studies of Ukrainian railways.

Rank-Metric Codes, Semifields, and the Average Critical Problem

We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptotic density of MRD codes in the rank metric, and the Critical Problem for combinatorial geometries by Crapo and Rota. In the first part of the paper, we use methods from semifield theory to derive two lower bounds for the density function of full-rank, square MRD codes. The first bound is sharp when the matrix size is a prime number and the underlying field is sufficiently large, while the second bound applies to the binary field. We then take a new look at the Critical Problem for combinatorial geometries, approaching it from a qualitative, often asymptotic, viewpoint. We illustrate the connection between this very classical problem and that of computing the asymptotic density of MRD codes. Finally, in the third part of the paper we study the asymptotic density of some special families of codes in the rank metric, including the symmetric, alternating, and Hermitian ones. In particular, we show that the optimal codes in these three contexts are sparse.

Nonlinear dynamics of asymmetric bistable energy harvesters

The paper investigates asymmetries effects over a nonlinear vibration energy harvester dynamics. The asymmetric system performance is compared with symmetric ones. Different asymmetry levels on restoring force and gravity action are investigated from a system-sloping angle variation. Bifurcation diagrams and basins of attraction are used to examine the local and global characteristics underlying dynamical systems under different excitation energy. The results show the adverse effects of asymmetries on system dynamics. They also reveal ways to overcome them by canceling asymmetric influence from optimal sloping angle values and improving asymmetric system performance over symmetrical ones. This comprehensive numerical study provides novel valuable insights into asymmetrical energy harvester dynamics, a wide and still less explored topic.

Four-dimensional SO(3)-spherically symmetric Berwald Finsler spaces

We locally classify all [Formula: see text]-invariant four-dimensional pseudo-Finsler Berwald structures. These are Finslerian geometries which are closest to (spatially, or [Formula: see text])-spherically symmetric pseudo-Riemannian ones — and serve as ansatz to find solutions of Finsler gravity equations which generalize the Einstein equations. We find that there exist five classes of non-pseudo-Riemannian (i.e. non-quadratic in the velocities) [Formula: see text]-spherically symmetric pseudo-Finsler Berwald functions, which have either a heavily constrained dependence on the velocities, or, up to a suitable choice of the tangent bundle coordinates, no dependence at all on the “time” and “radial” coordinates.

Weak c-ideals of Leibniz algebras

A subalgebra B of a Leibniz algebra L is called a weak c-ideal of L if there is a subideal C of L such that and where is the largest ideal of L contained in B. This is analogous to the concept of a weakly c-normal subgroup, which has been studied by a number of authors. We obtain some properties of weak c-ideals and use them to give some characterizations of solvable and supersolvable Leibniz algebras generalizing previous results for Lie algebras. We note that one-dimensional weak c-ideals are c-ideals, and show that a result of Turner classifying Leibniz algebras in which every one-dimensional subalgebra is a c-ideal is false for general Leibniz algebras, but holds for symmetric ones.

Generalized Asymmetric Hermite–Gaussian and Laguerre–Gaussian Beams

We derive analytical formulae for the complex amplitudes of variants of generalized Hermite–Gaussian (HG) and Laguerre–Gaussian (LG) beams. We reveal that, at particular values of parameters of the exact solution of the paraxial propagation equation, these generalized beams are converted into conventional elegant HG and LG beams. We also deduce variants of asymmetric HG and LG beams that are described by complex amplitudes in the form of Hermite and Laguerre polynomials whose argument is shifted into the complex plane. The asymmetric HG and LG beams are, respectively, shown to present the finite superposition of the generalized HG and LG beams. We also derive an explicit relationship for the complex amplitude of a generalized vortex HG beam, which is built as the finite superposition of generalized HG beams with phase shifts. Newly introduced asymmetric HG and LG beams show promise for the study of the propagation of beams carrying an orbital angular momentum through the turbulent atmosphere. One may reasonably believe that the asymmetric laser beams are more stable against turbulence when compared with the radially symmetric ones.

Comparison of the effect of suction-injection-combination on Rayleigh–Bénard convection in the case of asymmetric boundaries with those of symmetric ones

The effect of suction-injection-combination (SIC) on the linear and weakly nonlinear stability of Rayleigh–Bénard convection is considered in the paper for the cases of symmetric and asymmetric boundary conditions. Using the Maclaurin series with an appropriate number of terms, expression for eigenfunctions is obtained. The linear theory corroborates the results obtained using the chosen eigenfunctions in the limiting case of the no-SIC effect by matching accurately with the exact values concerning the critical Rayleigh number (Rac) and the wave number (αc). It is found that the effect of SIC is to stabilize the system in the case of symmetric boundaries irrespective of SIC being pro-gravity or anti-gravity. However, the effect of SIC is to stabilize/destabilize the system depending on SIC being pro-gravity or anti-gravity in the case of the asymmetric boundaries. We also noted a similar effect in the case of αc wherein a maximum error of order 10−4 was observed. The main novelty of the present work is studying the influence of SIC on the nonlinear dynamics of the considered problem. It is shown that the effect of SIC is to hasten the onset of chaos. Using various indicators (the largest Lyapunov exponent, the time series solution, the amplitude spectrum, and the phase-space plots), the dynamical behavior of the system is analyzed and the influence of SIC on the dynamics is recorded. The change due to the boundary effect and the SIC on the size of convection rolls and the trapping region where the dynamical system evolves within a bound is highlighted in the paper.

Dynamical Susceptibilities of Confined Water from Room Temperature to the Glass Transition.

We confine water to narrow silica pores, where crystallization is suppressed, and determine the dynamical susceptibilities of the liquid from room temperature down to the glass transition by combining broadband dielectric spectroscopy (BDS) with 1H and 2H nuclear magnetic resonance (NMR), in particular, by establishing NMR field-cycling relaxometry. For the correlation times, derivative analysis reveals Vogel-Fulcher-Tammann and Arrhenius regimes at T ≥ 215 K and T ≤ 160 K, respectively, which are separated by a broad crossover region. The continuous transition in the temperature dependence is accompanied by a gradual change from asymmetric high-temperature shapes of the dynamical susceptibilities to symmetric low-temperature ones and by a steady decrease of the dielectric relaxation strength. In the Arrhenius regime (Ea = 0.48 eV) at T ≤ 160 K, 2D 2H NMR spectra reveal quasi-isotropic water reorientation. We rationalize these results in terms of a crossover to an interface-affected, noncooperative relaxation involving both rotational and translational motions.

Dynamic Vehicle Pose Estimation with Heuristic L-Shape Fitting and Grid-Based Particle Filter

Vehicle pose estimation with LIDAR plays a crucial role in autonomous driving systems. It serves as the fundamental basis for functions such as tracking, path planning, and decision-making. However, the majority of current vehicle pose estimation techniques struggle to produce satisfactory results when faced with incomplete observation measurements, such as L-shaped point cloud clusters without side contours or those including side-view mirrors. In addition, the requirement for real-time results further increases the difficulty of the pose estimation task. In this paper, we present a vehicle Pose Estimation method with Heuristic L-shape fitting and grid-based Particle Filter (PE-HL-PF). We design a geometric shape classifier module to divide clusters into symmetrical and asymmetrical ones according to their shape features. Furthermore, a contour-based heuristic L-shape fitting module is introduced for asymmetrical clusters, and a structure-aware grid-based particle filter is used to estimate the pose of symmetrical clusters. PE-HL-PF first utilizes a heuristic asymmetrical module that selects dominant contours fitting orientation in a heuristic manner, thereby avoiding the need for a complex traversal search. Additionally, a symmetrical module based on particle filtering is incorporated to enhance the stability of orientation estimation. This method achieves significant improvements in both the runtime efficiency and pose estimation accuracy of incomplete point clouds. Compared with state-of-the-art pose estimation methods, our PE-HL-PF demonstrates a notable performance improvement. Our method can estimate the pose of thousands of objects in less than 1 millisecond, a significant improvement over previous methods. The results of experiments performed on the KITTI dataset validate the effectiveness of our approach.

Dynamical friction due to fuzzy dark matter on satellites described by axisymmetric logarithmic potentials

A plausible dark matter candidate is an ultralight bosonic particle referred to as fuzzy dark matter. The equivalent mass-energy of the fuzzy dark matter boson is ∼ 10-22 eV and has a corresponding de Broglie wavelength of kiloparsec scale, thus exhibiting wave behaviour in scales comparable to a galactic core, which could not appear in conventional cold dark matter models. The presence of fuzzy dark matter in galactic clusters will impact the motion of their members through dynamical friction. In this work, we present simulations of the dynamical friction on satellites traversing an initially uniform fuzzy dark matter halo. We focus on the satellites whose shapes are beyond spherical symmetry described by ellipsoidal and logarithmic potentials. We find that the wakes created on the fuzzy dark matter halo due to the passage of such satellites are qualitatively different from those generated by spherically symmetric ones. Furthermore, we quantify the dynamical friction coefficient for such systems, finding that the same satellite may experience a drag differing by a factor of 5 depending on its ellipticity and the direction of motion. Finally, we find that the dynamical friction time-scale is close to Hubble time, assuming a satellite of 1011 M ⊙ traversing at 103 km/s a FDM halo whose mean density is ∼ 106 M ⊙ kpc-3.

Revisiting the Low-Index Surfaces of LaCoO3 with a Passivation Strategy

A proper modeling is essential for calculating the surface properties of complex oxides, for example, perovskite oxides. Many studies have shown that traditional selections of slab models, either symmetric or asymmetric ones, may vary the calculated results of the polar surfaces, which will finally affect the perception of surface properties. To solve this issue, we proposed a passivation method to handle the complex polar surfaces, where the pseudo-atoms with fractional charges were used to balance non-zero net charges on one side of the surfaces. Based on this method, we revisited the low-index surfaces of LaCoO3, including (11̅02), (1̅104), and (0001) surfaces, with different terminations. The results suggested that the (11̅02)-LaO, (11̅02)-CoO2, and (0001)-LaO3 terminations were stable surfaces in different O and Co chemical environments. The oxygen vacancy formation energies (EOv) of the (11̅02)-LaO and (11̅02)-CoO2 terminations were also evaluated. Different from the unpassivated cases, the EOv of the passivated LaO and CoO2 terminations converged rapidly when slab thickness increased. The upward shift trend of the EOv after passivation was more consistent with the experimental results. The electronic structure analysis indicated that the oxygen vacancy mainly changed the valence state of the surrounding Co atoms. This work provides a more accurate calculation method, which may benefit the study on catalytic properties of complex oxides.

Two-dimensional fractional [formula omitted]-symmetric cubic–quintic NLS equation: Double-loop symmetry breaking bifurcations, ghost states and dynamics

In this paper, we address the double-loop symmetry breaking bifurcations of optical vortex solitons in the two-dimensional (2D) fractional cubic–quintic nonlinear Schrödinger (FCQNLS) equation with an imprinted partially parity-time (PPT) symmetric complex potential. The continuous branches of asymmetric solitons bifurcate from the fundamental one as the power exceeds some critical value. It is found that the symmetry breaking point is exactly the point at which the fundamental symmetric soliton is destabilized. Intriguingly, the branches of asymmetry solitons (alias ghost states) are existing with complex conjugate propagation constants, which is solely in fractional media. Moreover, the branch of asymmetric solitons crosses the branch of fundamental symmetric ones when it reaches the second critical value, and eventually merges back into it at the third critical power point. The imaginary part of the propagation constant also exhibits a circular shape. And the stability of the fundamental symmetric soliton is restored. In addition, the stability of two branches of asymmetric solitons differs from each other. The reason generating this phenomenon is analyzed in detail. Besides, the branch of dipole solitons for the first excited state is also discussed numerically, which is always stable in the process of symmetry breaking. The stability and dynamics of symmetric (fundamental and the first excited ones) and asymmetric solitons are explored via the linear stability analysis, direct simulation, modulation as well as adiabatic excitation. These results will provide some theoretical basis for the study of spontaneous symmetry breaking phenomena and related experiments in fractional media with PPT-symmetric potentials.

Multi-spike solutions to the one-dimensional subcritical fractional Schnakenberg system

Singularly perturbed reaction–diffusion systems such as the Gierer–Meinhardt, Schankenberg, and Gray–Scott models are known to exhibit localized multi-spike solutions in which one of the species concentrates on a discrete collection of well-separated points. A recent focus has been the extension of the analysis, both rigorous and formal, of such localized solutions to the case where classical diffusion is replaced by anomalous diffusion exhibiting Lévy flights. Mathematically, such systems replace the classical Laplacian with the fractional Laplacian (−Δ)s where s is the fractional order. In this paper we consider the formal analysis of multi-spike solutions to the fractional Schnakenberg system with periodic boundary conditions when the fractional order of the activator satisfies 1/4<s1<1 and that of the substrate satisfies 1/2<s2<1. Using the method of matched asymptotic expansions we derive a nonlinear algebraic system that determines the structure of equilibrium solutions, a nonlocal eigenvalue problem that determines its linear stability over a fast, O(1), timescale, as well as a system of ordinary differential equations that determine the dynamics of multi-spike solutions over a slow, O(ɛ−2), timescale. We explicitly construct symmetric multi-spike solutions and derive stability criteria for instabilities arising over both fast and slow timescales. One of the key findings in this paper is that the slow timescale instability thresholds are, barring symmetry considerations, less degenerate than in the classical s2=1 case. In addition we numerically calculate bifurcation diagrams that show how asymmetric multi-spike solutions branch out from symmetric ones at distinct points for solutions with five or more spikes.

Combined effect of fiber hybridization and matrix modification on mechanical properties of polymer composites

Glass/carbon fiber reinforced hybrid composites are great candidates for wind turbine blade manufacturers to make larger blades. Variation of stacking sequences ensures design freedom to the composite engineers to optimize the composite structure's mechanical performance. On the other hand, matrix modification of polymer composites with nanoparticles is also of interest to introduce multifunctional properties. This research aims to scrutinize the influence of simultaneous fiber hybridization and matrix modification on polymer composites’ tensile, flexural, and low-velocity impact properties. Hybrid glass/carbon epoxy composites and hybrid glass/carbon/multi-walled carbon nanotube (MWCNT) multiscale polymer composites of stacking sequences [GCGCGC]S, [CGCGCG]S, and [G6C6] were manufactured. Fiber hybridization dramatically improved tensile strength between 51% and 76% compared to glass fiber composite. Depending on the stacking sequence, the flexural strength of the hybrid composites was improved between 10% and 16% concerning carbon fiber composite. With the introduction of MWCNTs, a slight increase in the tensile strength for unsymmetrical hybrid composites by around 5% and decreases by 7% for symmetrical ones were observed. Similar behavior was seen for bending characteristics. Additionally, low-velocity impact tests showed that it is achievable to bring greater impact peak forces up to 70% for hybrid composites than carbon fiber epoxy composites. MWCNTs modification of the matrix restrained the impact damage propagation, as proved by C-scan analysis.