CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR.

Microwave-Assisted Au and Ag Nanoparticle Synthesis: An Energy Phase-Space Projection Analysis

Microwave-assisted synthesis of gold and silver nanoparticles, as a function of Green Chemistry, non Green Chemistry, and four applicator types are reported. The applicator types are Domestic microwave ovens, commercial temperature controlled microwave chemistry ovens (TCMC), digesters, and axial field helical antennae. For each of these microwave applicators the process energy budget where estimated (Watts multiplied by process time = kJ) and energy density (applied energy divided by suspension volume = kJ·ml-1) range between 180 ± 176.8 kJ, and 79.5 ± 79 kJ·ml-1, respectively. The axial field helical field an-tenna applicator is found to be the most energy efficient (0.253 kJ·m-1 per kJ, at 36 W). Followed by microwave ovens (4.47 ± 3.9 kJ·ml-1 per 76.83 ± 39 kJ), and TCMC ovens (2.86 ± 2.3 kJ·m-1 per 343 ± 321.5 kJ). The digester applicators have the least energy efficiency (36.2 ± 50.7 kJ·m-1 per 1010 ± 620 kJ). A comparison with reconstructed ‘non-thermal’ microwave oven inactivation microorganism experiments yields a power-law signature of n = 0.846 (R2 = 0.7923) four orders of magnitude. The paper provides a discussion on the Au and Ag nanoparticle chemistry and bio-chemistry synthesis aspects of the microwave applicator energy datasets and variation within each dataset. The visual and analytical approach within the energy phase-space projection enables a nanoparticle synthesis route to be systematically characterized, and where changes to the synthesis are to be mapped and compared directly with historical datasets. In order to help identify lower cost nanoparticle synthesis, in addition to potentially reduce synthesis energy to routes informed changes to potentially reduce synthesis energy budget, along with nanoparticle morphology and yield.

Symmetry phases of asymmetric simple exclusion processes on two lanes with an intersection

This paper studies two-lane asymmetric simple exclusion processes(ASEPs)with an intersection.In the upstream segments of the intersection,one particle can move to the next site with rate 1 if the site is empty,and the other particle can move forward with rate p in the sites of downstream segments.The parameter p can represent the rate of slowing of motion,and the parameter is introduced to investigate spontaneous symmetry breaking(SSB)phenomenon.Extensive Monte Carlo simulations are carried out.It is shown that three symmetric phases exist and the SSB does not exist in the system.Simple mean field approach in which correlation of sites is ignored is firstly adopted to analyze the system,and the system is divided into four independent segments.It is found that the analytical results deviate from the simulation ones,especially when p is small.In addition,the inexsitence of SSB can only be explained qualitatively.Motivated by this,we carry out the cluster mean field analysis in which correlation of five sites is considered.It is shown that densities of the two upstream segments are equal,which demonstrates that the SSB does not exist.It is also shown that,as expected,the cluster mean field analysis performs much better than the simple mean field analysis.

Anomalous time-reversal symmetric non-Hermitian systems

The conditions for the emergence of the non-Hermitian skin effect, as a unique physical response of non-Hermitian systems, have now become one of the hot research topics. In this paper, we study the novel physical responses of nonHermitian systems with anomalous time-reversal symmetry, in both one dimension and two dimensions. Specifically, we focus on whether the systems will exhibit a non-Hermitian skin effect. We employ the theory of generalized Brillouin zone and also numerical methods to show that the anomalous time-reversal symmetry can prevent the skin effect in onedimensional non-Hermitian systems, but is unable to exert the same effectiveness in two-dimensional cases.

Simultaneous guidance of electromagnetic and elastic waves via glide symmetry phoxonic crystal waveguides

A phoxonic crystal waveguide with the glide symmetry is designed,in which both electromagnetic and elastic waves can propagate along the glide plane at the same time.Due to the glide symmetry,the bands of the phoxonic crystal super-cell degenerate in pairs at the boundary of the Brillouin zone.This is the so-called band-sticking effect and it causes the appearance of gapless guided-modes.By adjusting the magnitude of the glide dislocation the edge bandgaps,the bandgap of the guided-modes at the boundary of the Brillouin zone,can be further adjusted.The photonic and phononic guided-modes can then possess only one mode for a certain frequency with relatively low group velocities,achieving single-mode guided-bands with relatively flat dispersion relationship.In addition,there exists acousto-optic interaction in the cavity constructed by the glide plane.The proposed waveguide has potential applications in the design of novel optomechanical devices.

The breaking of spin symmetry in the single-particle resonances in deformed nuclei

The exploration of spin symmetry (SS) in nuclear physics has been instrumental in identifying atomic nucleus structures.In this study,we solve the Dirac equation from the relativistic mean field (RMF) in complex momentum representation.We investigated SS and its breaking in single-particle resonant states within deformed nuclei,with a focus on the illustrative nucleus168Er.This was the initial discovery of a resonant spin doublet in a deformed nucleus,with the expectation of the SS approaching the continuum threshold.With increasing single-particle energy,the splitting of the resonant spin doublets widened significantly.This escalating splitting implies diminishing adherence to the SS,indicating a departure from the expected behavior as the energy levels increase.We also analyzed the width of the resonant states,showing that lower orbital angular momentum resonances possess shorter decay times and that SS is preserved within broad resonant doublets,as opposed to narrow resonant doublets.Comparing the radial density of the upper components for the bound-state and resonant-state doublets,it becomes evident that while SS is well-preserved in the bound states,it deteriorates in the resonant states.The impact of nuclear deformation (β_(2)) on SS was examined,demonstrating that an increase in β_(2) resulted in higher energy and width splitting in the resonant spin doublets,which is attributed to increased component mixing.Furthermore,the sensitivity of spin doublets to various potential parameters such as surface diffuseness (a),radius (R),and depth (Σ0) is discussed,emphasizing the role of these parameters in SS.This study provides valuable insights into the behavior of spin doublets in deformed nuclei and their interplay with the nuclear structure,thereby advancing our understanding of SS in the resonance state.

Unification of Gravitational and Strong Interaction Fields Using Partial Gauge Symmetry

We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms like the well-type potential where a particle behaves almost freely but is very hard to escape without external energy, which can be interpreted as local confinement and asymptotic freedom. By assuming a 2-dimensional metric tensor in 4-dimensional space-time, we suggest the existence of 3 kinds of particles that resemble QCD with 3 color charges. We also show that the mass term exists but comes to zero and derive the charge and spin values. We can regard the particle with this new potential as a gluon, and the interaction in this well-type potential as a strong interaction for the properties of mass, charge, spin, and its behavior. We suggest the eight-fold way with this new particle, which is similar to the existing method based on SU (3) symmetry. Even though the strong interaction has been analyzed in the standard model and string theory, we build a new consistent model based on the theory of relativity including Riemann geometry, and show the unification of gravitational and strong interactional field.

Two-fold symmetry of the in-plane resistance in kagome superconductor Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with enhanced superconductivity

The kagome superconductor CsV_(3)Sb_(5) has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave(CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V_(1-x)Ta_(x))_(3)Sb_(5) by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T_(c) ~ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V_(1-x)Ta_(x))_(3)Sb_(5)(x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance(AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V_(1-x)Ta_(x))_(3)Sb_(5). Our findings demonstrate that Cs(V_(1-x)Ta_(x))_(3)Sb_(5) with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.

Symmetry quantification and segmentation in STEM imaging through Zernike moments

We present a method using Zernike moments for quantifying rotational and reflectional symmetries in scanning transmission electron microscopy(STEM)images,aimed at improving structural analysis of materials at the atomic scale.This technique is effective against common imaging noises and is potentially suited for low-dose imaging and identifying quantum defects.We showcase its utility in the unsupervised segmentation of polytypes in a twisted bilayer TaS_(2),enabling accurate differentiation of structural phases and monitoring transitions caused by electron beam effects.This approach enhances the analysis of structural variations in crystalline materials,marking a notable advancement in the characterization of structures in materials science.

THE RADIAL SYMMETRY OF POSITIVE SOLUTIONS FOR SEMILINEAR PROBLEMS INVOLVING WEIGHTED FRACTIONAL LAPLACIANS

This paper deals with the radial symmetry of positive solutions to the nonlocal problem(-Δ)_(γ)~su=b(x)f(u)in B_(1){0},u=h in R~N B_(1),where b:B_1→R is locally Holder continuous,radially symmetric and decreasing in the|x|direction,F:R→R is a Lipschitz function,h:B_1→R is radially symmetric,decreasing with respect to|x|in R^(N)/B_(1),B_(1) is the unit ball centered at the origin,and(-Δ)_γ~s is the weighted fractional Laplacian with s∈(0,1),γ∈[0,2s)defined by(-△)^(s)_(γ)u(x)=CN,slimδ→0+∫R^(N)/B_(δ)(x)u(x)-u(y)/|x-y|N+2s|y|^(r)dy.We consider the radial symmetry of isolated singular positive solutions to the nonlocal problem in whole space(-Δ)_(γ)^(s)u(x)=b(x)f(u)in R^(N)\{0},under suitable additional assumptions on b and f.Our symmetry results are derived by the method of moving planes,where the main difficulty comes from the weighted fractional Laplacian.Our results could be applied to get a sharp asymptotic for semilinear problems with the fractional Hardy operators(-Δ)^(s)u+μ/(|x|^(2s))u=b(x)f(u)in B_(1)\{0},u=h in R^(N)\B_(1),under suitable additional assumptions on b,f and h.

Characteristic analysis of 5D symmetric Hamiltonian conservative hyperchaotic system with hidden multiple stability

Conservative chaotic systems have unique advantages over dissipative chaotic systems in the fields of secure communication and pseudo-random number generator because they do not have attractors but possess good traversal and pseudorandomness. In this work, a novel five-dimensional(5D) Hamiltonian conservative hyperchaotic system is proposed based on the 5D Euler equation. The proposed system can have different types of coordinate transformations and time reversal symmetries. In this work, Hamilton energy and Casimir energy are analyzed firstly, and it is proved that the new system satisfies Hamilton energy conservation and can generate chaos. Then, the complex dynamic characteristics of the system are demonstrated and the conservatism and chaos characteristics of the system are verified through the correlation analysis methods such as phase diagram, equilibrium point, Lyapunov exponent, bifurcation diagram, and SE complexity. In addition, a detailed analysis of the multistable characteristics of the system reveals that many energy-related coexisting orbits exist. Based on the infinite number of center-type and saddle-type equilibrium points, the dynamic characteristics of the hidden multistability of the system are revealed. Then, the National Institute of Standards and Technology(NIST)test of the new system shows that the chaotic sequence generated by the system has strong pseudo-random. Finally, the circuit simulation and hardware circuit experiment of the system are carried out with Multisim simulation software and digital signal processor(DSP) respectively. The experimental results confirm that the new system has good ergodicity and realizability.

New quantification of symmetry energy from neutron skin thicknesses of^(48)Ca and^(208)Pb

Precise knowledge of the nuclear symmetry energy can be tentatively calibrated using multimessenger constraints.The neutron skin thickness of a heavy nucleus is one of the most sensitive indicators for probing the isovector components of effective interactions in asymmetric nuclear matter.Recent studies have suggested that the experimental data from the CREX and PREX2 collaborations are not mutually compatible with existing nuclear models.In this study,we review the quantification of the slope parameter of the symmetry energy L from the neutron skin thicknesses of^(48)Ca and^(208)Pb.Skyrme energy density functionals classified by various isoscalar incompressibility coefficients K were employed to evaluate the bulk properties of finite nuclei.The calculated results suggest that the slope parameter L deduced from^(208)Pb is sensitive to the compression modulus of symmetric nuclear matter,but not that from^(48)Ca.The effective parameter sets classified by K=220 MeV can provide an almost overlapping range of L from^(48)Ca and^(208)Pb.

Symmetry of upper eyelid after unilateral blepharoptosis repair with minimally invasive conjoint fascial sheath suspension technique

AIM:To investigate the symmetry of upper eyelid in patients with unilateral mild and moderate blepharoptosis who underwent unilateral minimally invasive combined fascia sheath(CFS)suspension.METHODS:A retrospective study of patients who underwent unilateral minimally invasive CFS suspension surgery between January 2018 and December 2021.Inclusion criteria included unilateral mild and moderate ptosis,good levator muscle function(>9 mm)and follow-up of at least 6mo.Pre-and post-operative symmetry was graded subjectively for marginal reflex distance 1(MRD1),tarsal platform show(TPS)and eyebrow fat span(BFS).A t-test was used to evaluate MRD1,TPS and BFS asymmetry by calculating delta values.The Bézier curve tool of the Image J software was used to extract the upper eyelid contours,where the symmetry was measured by the percentage of overlapping curvatures(POC).RESULTS:Totally 105 patients(105 eyelids)were included(mild group,n=84;moderate group,n=21).Postoperatively,all patients increased MRD1 and decreased TPS in the ptotic eye while maintaining unchanged BFS.The asymmetric delta value for MRD1 was measured to be 1.48±0.86 preoperatively,and it decreased to 0.58±0.67 postoperatively in all cases(P=0.0004).In patients with mild ptosis,the asymmetry value of TPS fell significantly from 1.15±0.62 to 0.68±0.38(P=0.0187).The symmetry of the upper eyelid contour increased in all subgroups of patients,with a POC of 59.39%±13.45%preoperatively and POC of 78.29%±13.80%postoperatively.CONCLUSION:Minimally invasive CFS suspension is proved to be an effective means of improving the symmetry of unilateral ptosis in terms of MRD1(all subgroups),POC(all subgroups)and TPS(only mild group),whereas BFS is unaffected.

Angle-resolved photoemission study of NbGeSb with non-symmorphic symmetry

We investigate the electronic structure of NbGeSb with non-symmorphic symmetry.We employ angle-resolved photoemission spectroscopy(ARPES)to observe and identify the bulk and surface states over the Brillouin zone.By utilizing high-energy photons,we identify the bulk Fermi surface and bulk nodal line along the direction X–R,while the Fermi surface of the surface state is observed by using low-energy photons.We observe the splitting of surface bands away from the high-symmetry point X.The density functional theory calculations on bulk and 1 to 5-layer slab models,as well as spin textures of NbGeSb,verify that the band splitting could be attributed to the Rashba-like spin–orbit coupling caused by space-inversion-symmetry breaking at the surface.These splitted surface bands cross with each other,forming two-dimensional Weyl-like crossings that are protected by mirror symmetry.Our findings provide insights into the two-dimensional topological and symmetry-protected band inversion of surface states.

Decompositions of the Kadomtsev-Petviashvili equation and their symmetry reductions

Starting with a decomposition conjecture,we carefully explain the basic decompositions for the Kadomtsev-Petviashvili(KP)equation as well as the necessary calculation procedures,and it is shown that the KP equation allows the Burgers-STO(BSTO)decomposition,two types of reducible coupled BSTO decompositions and the BSTO-KdV decomposition.Furthermore,we concentrate ourselves on pointing out the main idea and result of Bäcklund transformation of the KP equation based on a special superposition principle in the particular context of the BSTO decompositions.Using the framework of standard Lie point symmetry theory,these decompositions are studied and the problem of computing the corresponding symmetry constraints is treated.

Kármán vortex street in a spin–orbit-coupled Bose–Einstein condensate with PT symmetry

The dynamics of spin–orbit-coupled Bose–Einstein condensate with parity-time symmetry through a moving obstacle potential is simulated numerically. In the miscible two-component condensate, the formation of the Kármán vortex street is observed in one component, while ‘the half-quantum vortex street' is observed in the other component. Other patterns of vortex shedding, such as oblique vortex dipoles, V-shaped vortex pairs, irregular turbulence, and combined modes of various wakes, can also be found. The ratio of inter-vortex spacing in one row to the distance between vortex rows is approximately0.18, which is less than the stability condition 0.28 of classical fluid. The drag force acting on the obstacle potential is simulated. The parametric regions of Kármán vortex street and other vortex patterns are calculated. The range of Kármán vortex street is surrounded by the region of combined modes. In addition, spin–orbit coupling disrupts the symmetry of the system and the gain-loss affects the local particle distribution of the system, which leads to the local symmetry breaking of the system, and finally influences the stability of the Kármán vortex street. Finally, we propose an experimental protocol to realize the Kármán vortex street in a system.

Rigidity Symmetry Line for Thermodynamic Fluid Equations-of-State

We report progress towards a modern scientific description of thermodynamic properties of fluids following the discovery (in 2012) of a coexisting critical density hiatus and a supercritical mesophase defined by percolation transitions. The state functions density ρ(p,T), and Gibbs energy G(p,T), of fluids, e.g. CO2, H2O and argon exhibit a symmetry characterised by the rigidity, ω = (dp/dρ)T, between gaseous and liquid states along any isotherm from critical (Tc) to Boyle (TB) temperatures, on either side of the supercritical mesophase. Here, using experimental data for fluid argon, we investigate the low-density cluster physics description of an ideal dilute gas that obeys Dalton’s partial pressure law. Cluster expansions in powers of density relate to a supercritical liquid-phase rigidity symmetry (RS) line (ω = ρrs(T) = RT) to gas phase virial coefficients. We show that it is continuous in all derivatives, linear within stable fluid phase, and relates analytically to the Boyle-work line (BW) (w = (p/ρ)T = RT), and to percolation lines of gas (PB) and liquid (PA) phases by: ρBW(T) = 2ρPA(T) = 3ρPB(T) = 3ρRS(T)/2 for T TB. These simple relationships arise, because the higher virial coefficients (bn, n ≥ 4) cancel due to clustering equilibria, or become negligible at all temperatures (0 T TB) within the gas phase. The Boyle-work line (p/ρBW)T is related exactly at lower densities as T → TB, and accurately for liquid densities, by ρBW(T) = −(b2/b3)T. The RS line, ω(T) = RT, defines a new liquid-density ground-state physical constant (ρRS(0) = (2/3)ρBW(0) for argon). Given the gas-liquid rigidity symmetry, the entire thermodynamic state functions below TB are obtainable from b2(T). A BW-line ground-state crystal density ρBW(0) can be defined by the pair potential minimum. The Ar2 pair potential, ∅ij(rij) determines b2(T) analytically for all T. This report, therefore, advances the salient objective of liquid-state theory: an argon p(ρ,T) Equation-of-state is obtained from ∅ij(rij) for all fluid states, without any adjustable parameters.

A new(2+1)-dimensional supersymmetric Boussinesq equation and its Lie symmetry study

According to the conjecture based on some known facts of integrable models, a new （2＋1）-dimensional supersymmetric integrable bilinear system is proposed. The model is not only the extension of the known （2＋1）-dimensional negative Kadomtsev-Petviashvili equation but also the extension of the known （1＋1）-dimensional supersymmetric Boussinesq equation. The infinite dimensional Kac-Moody-Virasoro symmetries and the related symmetry reductions of the model are obtained. Furthermore, the traveling wave solutions including soliton solutions are explicitly presented.

Effect of normalized plasma frequency on electron phase-space orbits in a free-electron laser

Irregular phase-space orbits of the electrons are harmful to the electron-beam transport quality and hence deteriorate the performance of a free-electron laser （FEL）. In previous literature, it was demonstrated that the irregularity of the electron phase-space orbits could be caused in several ways, such as varying the wiggler amplitude and inducing sidebands. Based on a Hamiltonian model with a set of self-consistent differential equations, it is shown in this paper that the electron- beam normalized plasma frequency functions not only couple the electron motion with the FEL wave, which results in the evolution of the FEL wave field and a possible power saturation at a large beam current, but also cause the irregularity of the electron phase-space orbits when the normalized plasma frequency has a sufficiently large value, even if the initial energy of the electron is equal to the synchronous energy or the FEL wave does not reach power saturation.

Symmetry Reductions, Exact Solutions and Conservation Laws of Asymmetric Nizhnik-Novikov-Veselov Equation

By applying a direct symmetry method, we get the symmetry of the asymmetric Nizhnik-Novikov-Veselov equation （ANNV）. Taking the special case, we have a finite-dimensional symmetry. By using the equivalent vector of the symmetry, we construct an eight-dimensional symmetry algebra and get the optimal system of group-invariant solutions. To every case of the optimal system, we reduce the ANNV equation and obtain some solutions to the reduced equations. Furthermore, we find some new explicit solutions of the ANNV equation. At last, we give the conservation laws of the ANNV equation.