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Solid-state batteries use composites of solid ion conductors and active materials as electrode materials. The effective transport of charge carriers and heat thereby strongly determines the overall solid-state battery performance and safety. However, the phase space for optimization of the composition of solid electrolyte, active material, additive is too large to cover experimentally. In this work, a resistor network model is presented that successfully describes the transport phenomena in solid-state battery composites, when benchmarked against experimental data of the electronic, ionic, and thermal conductivity of LiNi0.83Co0.11Mn0.06O2-Li6PS5Cl positive electrode composites. To highlight the broadness of the approach, literature data are examined using the proposed model. As the model is easily accessible and expandable, without the need for high computing power, it offers valuable guidance for experimentalists helping to streamline the tedious process of performing a multitude of experiments to understand and optimize the effective transport of composite electrodes. Effective conductivity is a key performance indicator for solid-state battery electrodes that is influenced by both composition and microstructure. Here, authors present a simple resistor network model to guide the development of composite electrodes towards optimized effective transport. [ABSTRACT FROM AUTHOR]

The increasing global energy demand and reliance on fossil fuels have exacerbated global warming, necessitating sustainable energy solutions. This study aims to explore the possibility of designing n-type and p-type TE materials from the Zr2FeNiSb2 double half-Heusler (DhH) compound using targeted substitutions and compositional tuning. We engineered n-type and p-type compounds by substituting Nb at the Zr site (Zr1.9Nb0.1FeNiSb2) and Sn at the Sb site (Zr2FeNiSb1.9Sn0.1). Microstructural analysis indicated a predominance of the half-Heusler phase with minor Fe-rich secondary phases. To eliminate these secondary phases and establish a direct structure–property correlation, the Fe content was reduced and compensated with increased Ni content. However, increasing Ni tends to decompose the matrix in Zr2Fe0.9Ni1.1Sb2. Further Nb/Sn substitutions stabilized the microstructure without the adverse effects from Fe/Ni tuning. Seebeck coefficient measurements from near RT to 973 K showed that all alloys except Zr2Fe0.9Ni1.1Sb1.9Sn0.1 exhibited n-type behaviour, while this Sn-substituted alloy switched from p-type to n-type upon variation of Fe/Ni ratio. This study also defines the half-Heusler phase composition space, with Fe and Ni varying within ~ 15.64 to 17.39 at% and 15.90 to 18.84 at%, respectively, providing valuable insights for designing DhH-based TE materials. [ABSTRACT FROM AUTHOR]

Al3Ni nanowires were fabricated via the selective etching of directionally solidified Al–Ni eutectic alloys. The effects of different growth rates from 2 to 1000 μm/s on the microstructure and morphology of eutectic alloys under a temperature gradient of 10 K/cm were investigated. The mechanism of the cross-sectional morphology transformation of Al3Ni nanofibers was investigated using the dynamic undercooling degree Δ T k . Then, the morphologies of the Al3Ni nanowires at different growth rates and corrosion time were studied using the constant potential corrosion method. Increasing the growth rate increased the roundness of the section and decreased the fiber phase spacing and diameter. At a growth rate of 2 μm/s, both Al and Al3Ni exhibited kinetic undercooling ( Δ T k , Al 3 Ni and Δ T k , Al ), with values below the critical kinetic undercooling ( Δ T k , Al 3 Ni c and Δ T k , Al c ). The Al3Ni fibers underwent faceted growth and developed a thin ribbon structure. At 5 μm/s, the kinetic undercooling of Al3Ni and Al exceeded Δ T k , Al 3 Ni c and Δ T k , Al c , respectively, leading to nonfaceted growth and elliptically shaped Al3Ni fibers. With prolonged corrosion time, the length of the Al3Ni nanowires increased. [ABSTRACT FROM AUTHOR]

Accurate financial time series forecasting is an important challenge in the financial field due to varying levels of interaction among multiple financial time series, complicating the extraction of valid information from these variables. This study introduces an effective and efficient multivariable financial time series forecasting model based on phase space reconstruction compensation: Phase Space Reconstruction Compensation Long Short-Term Memory (PSR-LSTM). The PSR-LSTM model leverages the long short-term memory (LSTM) network to analyze short-term data behaviors, reconstructs multiple long-term variables by phase space reconstruction method, and utilizes multivariable trend attention to capture trend information in correlated variables. This trend information is finally used to correct the LSTM network's predictive result. Experimental results demonstrate that the PSR-LSTM outperforms existing multivariable forecasting models by effectively mitigating noise interference while achieving optimal forecasting performance. [ABSTRACT FROM AUTHOR]

Light particles quadratically coupled to nucleons induce macroscopic forces in matter. While a quantum effect always exists, an additional force occurs in the presence of a finite density of the light particles. We compute and classify such background-induced forces for particles of spin 0, 1 2 , 1 in the framework of effective field theory. We show that, at short distance, the background-induced forces exhibit a universal behavior that depends solely on the moments of the phase space distribution function of the light particles. We compute the forces in the case of dark particles densities that may realistically occur in cosmology, assuming either (i) cosmically homogeneous or (ii) virialized phase space distributions. For homogeneous distributions — analogous to cosmic neutrinos, all the background-induced forces remain, unlike the quantum ones, exponentially unsuppressed at large distance, implying that large scale fifth force experiments are highly sensitive to dark relics. Moreover at zero mass the forces from dark bosons are generically enhanced with respect to their quantum counterpart due to Bose-Einstein distribution. Overall, we find that the resulting fifth force bounds can compete with those from quantum forces. For virialized distributions — identifiable as cold dark matter, the reach is also enhanced beyond the dark matter Compton wavelength. We obtain significant bounds on sub-keV scalar cold dark matter, that can appear in certain cosmological scenarios. A thorough adaptation of the results from the Eöt-Wash experiment may produce powerful additional bounds. [ABSTRACT FROM AUTHOR]

Pure and transition metal doped calcium titanate (CaTi1 − xMxO3 where M = Cr) was prepared by solid state reaction technique to study effect of doping on the structural, optical and electrical properties of calcium titanate. Structural properties were investigated by XRD. Also XRD pattern revealed the orthorhombic phase with Pbnm space group which was confirmed by calculating different parameters. SEM results showed the variation of grain size distribution ranging from 470 to 371 nm. FTIR studies confirmed the presence of the functional group modes of vibrations. Optical properties were studied by UV and FL techniques. Furthermore, from optical analysis shows that energy gap of the pure sample increased from 1.8 to 2.9 eV respectively. VSM revealed the presence of magnetic property in the sample and with substitution the magnetic behaviour first decreased for x = 0.2 then enhanced for x = 0.4 and VSM analyze that our material is a ferromagnetic in nature. [ABSTRACT FROM AUTHOR]

Building on our proposal in [1], we present in detail the construction of the extended phase space for Yang-Mills at null infinity, containing the asymptotic symmetries and the charges responsible for subn-leading soft theorems at all orders. The generality of the procedure allows it to be directly applied to the computation of both tree and loop-level soft limits. We also give a detailed study of Yang-Mills equations under the radial expansion, giving a thorough construction of the radiative phase space for decays compatible with tree-level amplitudes for both light-cone and radial gauges. This gives rise to useful recursion relations at all orders between the field strength and the vector gauge coefficients. We construct the subn-leading charges recursively, and show a hierarchical truncation such that each charge subalgebra is closed, and their action in the extended phase space is canonical. We relate these results with the infinite-dimensional algebras that have been recently introduced in the context of conformal field theories at null infinity. We also apply our method to the computation of non-universal terms in the sub-leading charges arising in theories with higher derivative interaction terms. [ABSTRACT FROM AUTHOR]

In this note, an interesting region about the Sun in phase space is described where the permanent capture of an object, P, of small mass from interstellar space can occur, under the gravitational perturbation of the resultant mass of the Galaxy. P is never ejected back into interstellar space and would not collide with the Sun. It cycles about the Sun for all time, asymptotically approaching the capture set. In addition to being permanently captured, P is also weakly captured. A recent result in Belbruno (CMDA, 2024) describes this region in general. It has a fractal structure. A capture cross section and the probability of permanent weak capture are estimated. This is applied to the permanent capture of rogue planets and other objects from interstellar space [ABSTRACT FROM AUTHOR]

We discuss a general prototypical constrained Hamiltonian system with a broad application in quantum field theory and similar contexts where dynamics is defined through a functional action obeying a stationarity principle. The prototypical model amounts to a Dirac–Bergmann singular system, whose constraints restrict the actual dynamics to occur within a differential submanifold, as is the case in the major part of field theoretical models with gauge symmetry. We apply the Dirac–Bergmann algorithm in its full generality unraveling a total of 4m second-class constraints and obtain the corresponding Dirac brackets algebra in phase space. We follow with the Faddeev–Jackiw–Barcelos–Wotzasek approach in which the geometric character of the mentioned submanifold is emphasized by means of an internal metric function encoding its symplectic properties. We consider two straightforward examples, applying our general results to constrained motion along a toroidal geometry and to a Lorentz violating toy model in field theory. Since toroidal geometry has been recently used in cosmological models, we suggest how our results could lead to different proposals for the shape of the universe in cosmology. [ABSTRACT FROM AUTHOR]

Motivated by population growth in a heterogeneous environment, this manuscript builds a reaction-diffusion model with spatially dependent parameters. In particular, a term for spatially uneven maturation durations is included in the model, which puts the current investigation among the very few studies on reaction-diffusion systems with spatially dependent delays. Rigorous analysis is performed, including the well-posedness of the model, the basic reproduction ratio formulation and long-term behavior of solutions. Under mild assumptions on model parameters, extinction of the species is predicted when the basic reproduction ratio is less than one. When the birth rate is an increasing function and the basic reproduction ratio is greater than one, uniqueness and global attractivity of a positive equilibrium can be established with the help of a novel functional phase space. Permanence of the species is shown when the birth function is in a unimodal form and the basic reproduction ratio is greater than one. The synthesized approach proposed here is applicable to broader contexts of studies on the impact of spatial heterogeneity on population dynamics, in particular, when the delayed feedbacks are involved and the response time is spatially varying. [ABSTRACT FROM AUTHOR]

This research focuses on developing effective benchmarks for quadratic unconstrained binary optimization instances, crucial for evaluating the performance of Ising hardware and solvers. Currently, the field lacks accessible and reproducible models for systematically testing such systems, particularly in terms of detailed phase space characterization. Here, we introduce universal generative models based on an extension of Hebb's rule of associative memory with asymmetric pattern weights. We conduct comprehensive calculations across different scales and dynamical equations, examining outcomes like the probabilities of reaching the ground state, planted state, spurious state, or other energy levels. Additionally, the generated problems reveal properties such as the easy-hard-easy complexity transition and complex solution cluster structures. This method offers a promising platform for analyzing and understanding the behavior of physical hardware and its simulations, contributing to future advancements in optimization technologies. The authors present a method for creating generative models that produce test instances for quadratic unconstrained binary optimization (QUBO) problems, inspired by Hebb's rule. Their approach identifies key solution patterns and complexity transitions, providing a platform to evaluate the performance of Ising hardware and solvers efficiently. [ABSTRACT FROM AUTHOR]

We study billiards in domains enclosed by circular polygons. These are closed C 1 strictly convex curves formed by finitely many circular arcs. We prove the existence of a set in phase space, corresponding to generic sliding trajectories close enough to the boundary of the domain, in which the return billiard dynamics is semiconjugate to a transitive subshift on infinitely many symbols that contains the full N-shift as a topological factor for any N ∈ N , so it has infinite topological entropy. We prove the existence of uncountably many asymptotic generic sliding trajectories approaching the boundary with optimal uniform linear speed, give an explicit exponentially big (in q) lower bound on the number of q-periodic trajectories as q → ∞ , and present an unusual property of the length spectrum. Our proofs are entirely analytical. [ABSTRACT FROM AUTHOR]

We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system that governs the driving functions. Our formulas give a simple method for mapping the class of rational functions into solutions to a non-trivial system of quadratic equations, and for directly showing that the curves in the real locus satisfy geometric commutation. These results are entirely self-contained and have no reliance on probabilistic objects, but make use of an integral of motion for the Loewner chain that is motivated by ideas from conformal field theory. We also show that the dynamics of the driving functions are a special case of the Calogero–Moser integrable system, restricted to a particular submanifold of phase space carved out by the Lax matrix. Our approach complements a recent result of Peltola and Wang, who showed that the real locus is the deterministic κ → 0 limit of the multiple SLE (κ) curves. [ABSTRACT FROM AUTHOR]

We perform the canonical analysis of an action in which 2+1-dimensional gravity with a negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting phase space is finite dimensional having geometry of SO(2, 2) group manifold. Representing the Poisson brackets by commutators results in the algebra of observables which is a quantum double D(SL(2)q). Deformation parameter q is real when the total energy of the system is below the threshold of a black hole formation, and a root of unity when it is above. Inside the black hole the spectra of the shell radius and time operator are discrete and take on a finite set of values. The Hilbert space of the black hole is thus finite-dimensional. [ABSTRACT FROM AUTHOR]

Computer holography is a prominent technique for reconstructing customized three-dimensional (3D) diffraction fields. However, the quality of optical reconstruction remains a fundamental challenge in 3D computer holography, especially for the 3D diffraction fields with physically continuous and extensive depth range. Here, we propose a 3D computer-generated hologram (CGH) optimization framework with phase space tailoring. Based on phase space analysis of the space and frequency properties in both lateral and axial directions, the intensity of the 3D diffraction field is adequately sampled across a large depth range. This sampling ensures the reconstructed intensity distribution to be comprehensively constrained with physical consistency. A physics-informed loss function is constructed based on the phase space tailoring to optimize the CGH with suppression of vortex stagnation. Numerical and optical experiments demonstrate the proposed method significantly enhances the 3D optical reconstructions with suppressed speckle noise across a continuous and extensive depth range. [ABSTRACT FROM AUTHOR]

Diboson production in association with jets is studied in the fully leptonic final states, pp → (Z/γ*)(Z/γ*) + jets → 2ℓ2ℓ′ + jets, (ℓ, ℓ′ = e or μ) in proton-proton collisions at a center-of-mass energy of 13 TeV. The data sample corresponds to an integrated luminosity of 138 fb−1 collected with the CMS detector at the LHC. Differential distributions and normalized differential cross sections are measured as a function of jet multiplicity, transverse momentum pT, pseudorapidity η, invariant mass and ∆η of the highest-pT and second-highest-pT jets, and as a function of invariant mass of the four-lepton system for events with various jet multiplicities. These differential cross sections are compared with theoretical predictions that mostly agree with the experimental data. However, in a few regions we observe discrepancies between the predicted and measured values. Further improvement of the predictions is required to describe the ZZ+jets production in the whole phase space. [ABSTRACT FROM AUTHOR]

Making accurate and reliable predictions for monthly runoff in data scarce basins is still a major challenge. In this study, a new model, the CL-NDM, is developed by combining Convolutional Neural Network-Long Short-term Memory (CNN-LSTM) and a nonlinear dynamic model. The CL-NDM can overcome the deficiency of observed data by fusing spatial and temporal dependencies in runoff sequences at different stations. First, phase space reconstruction is used to enlarge the dimensions of the runoff sequences and reconstruct the attractors of the runoff sequences. Then, the CNN-LSTM is employed to construct the mapping between non-delay and delay attractors. Finally, the prediction set of the target variable is obtained by embedding multiple times. The CL-NDM is performed for monthly runoff prediction at eleven hydrological stations in the Weihe River, China. Compared with the CNN, LSTM and CNN-LSTM models, which require a large amount of training samples, the CL-NDM behaves much better, especially in situations with small training sample sizes. The maximum increase in R is 74%, and the maximum NSE is as large as 0.8. The maximum improvement in RMSE and MAPE is 53% and 88%, respectively. The CL-NDM has stronger ability to capture peak value while LSTM, CNN-LSTM and CNN models show obvious time lag in the prediction of peak point. The improved nonlinear dynamical model may provide a valuable method for runoff prediction in data-scarce regions. [ABSTRACT FROM AUTHOR]

Integral equations with infinite delay are considered as functional equations in a Banach space. Two types of Hyers–Ulam stability criteria are established. First, it is shown that a linear autonomous equation is Hyers–Ulam stable if and only if it has no characteristic value with zero real part. Second, it is proved that the Hyers–Ulam stability of a linear autonomous equation is preserved under sufficiently small nonlinear perturbations. The proofs are based on a recently developed decomposition theory of linear integral equations with infinite delay. [ABSTRACT FROM AUTHOR]

This paper presents a new and innovative methodology for the investigation of karst systems using spring discharge. The behaviour of springs in phase space is investigated by plotting the measurements of spring discharge versus the measurements of the water level at the spring’s outlet. Such a diagram reveals new features of the function of the karst system and the discharge pattern of the spring that are not captured by common research methods. The application of this method to the Azmak Spring in southwestern Türkiye revealed the existence of five distinct discharge subsystems that operate alternately and never simultaneously. They have a specific connection between them, while the transition from one to another is not random but follows a pattern. An attempt was made to interpret these features using concepts from percolation theory. [ABSTRACT FROM AUTHOR]

Purpose: The present work primarily focuses on arriving at an analytical solution for the response of a Coulomb damped harmonic oscillator when subjected to aperiodic excitation. Methods: The signum function used in modelling the Coulomb friction model is reduced to a first harmonic term. This is carried out by assuming that vibratory motion exists for at least one full cycle, by means of harmonic balance (HB) method. The equation of motion thus reduced is solved to obtain an analytical solution for half-sine, rectangular, and triangular shock inputs. The solution thus obtained is combined with another analytical solution derived by the phase space coordinate averaging method. The total solution is now expressed as a two-part analytical solution, which comprises the response during the action of the input pulse and after the pulse ends. Results: The analytical results are compared with numerical ones to establish validity and accuracy. A comparison is also made with the experimental readings, and a reasonably good agreement is observed for the response of the oscillator with Coulomb damping. The study is extended further to plot the shock response spectrum (SRS) for the three shock inputs over a wide range of damping values (α ) and frequency ratios (Ω ). The 1 / 2 Ω range over which the n th peak of the system response is dispersed in the SRS increases with a corresponding increase in α . Conclusion: The two-part analytical solution proposed here predicts the SRS for the first dominant peak in the vibratory response to a good degree of accuracy and is quantified by directly comparing it with experiment(s). [ABSTRACT FROM AUTHOR]

The Dirichlet problem of elliptic equation from two phase problems, b (u) − div (| ∇ u) | p (x) − 2 ∇ u + μ (x) | ∇ u | q (x) − 2 ∇ u) = f (x) in Ω, u = 0 on ∂Ω is considered, where Ω is a bounded domain with a smooth boundary in R N , b is a continuous and nondecreasing function. By the theory of the weighted variable Sobolev space, the existence and uniqueness of an entropy solution for L 1 -data f are proved. [ABSTRACT FROM AUTHOR]

We synthesized the pristine and MoS2 QDs coated the UiO-66 nanostructures employing an eco-friendly drop casting method and studied the physical properties of nanostructures by experimental methods. The X-ray diffraction analysis confirmed that all samples exhibit a singular cubic phase with space group Fm3m. The presence of MoS2 quantum dots coating led to an observed growth in crystalline size and an increase in structural defects. A rise in the optical energy gap (4.02–5.05 eV) and an improvement in transmittance were noted as the concentration of coated MoS2 quantum dots increased. The film thickness of UiO-66@X%MOS2 (X% = 0, 10, 15, 20, and 25) was around 140 ± 5 nm and the increase in the concentration of MoS2QDs was found to be inversely proportional to the decrease in refractive index. The absolute part values of the dielectric constant (ε1) are more significant than the imaginary part (ε2). Optical conductivity decreases with the higher content of embedded MoS2 QDs (from 2.75 × 1010 to 1.75 × 1010) at wavelengths 300–250 nm. Thus, MoS2 QDs-coated UiO-66 nanostructures show suitable potential applications in: optoelectronics, efficient conversion of energy, and numerous other works implemented in the sphere of nanotechnology. [ABSTRACT FROM AUTHOR]

Accurate tool wear state identification models are essential to ensure manufacturing reliability and efficiency. Tool wear state recognition systems establish a mapping relationship with the tool state by extracting signal features. Therefore, this paper proposes an architecture for identifying the actual wear state of data unbalanced machining tools by applying the power of minimalism in deep learning networks, namely, VanillaNet, combined with recurrence plot encoding technology (RP). In this paper, the signal is preprocessed by RP, and the nonlinear one-dimensional time-sequential digital signal embedded in variable time-lag delay coordinate space in the phase space is converted into a two-dimensional (2D) color texture image, thereby achieving the feature extraction of tool wear. Then, the data-enhanced 2D recurrence coded image is used as the input to VanillaNet, and its minimalist network architecture is applied to establish the mapping relationship between tool wear states and wear features. This process reduces the state recognition time and achieves the fast recognition of tool wear states. The model in this paper achieves more than 95 % on all four classification metrics: accuracy, recall, F1 score, and precision in three sets of crossover experiments while reducing misclassification in the sharp wear phase. The proposed model also outperforms three DL-based methods, namely, CNN-Attention, AlexNet, and ResNet. [ABSTRACT FROM AUTHOR]

This paper aims to establish the existence of traveling wave solutions connecting different equilibria for a spatial eco-epidemiological predator–prey system in advective environments. After applying the traveling wave coordinates, these solutions correspond to heteroclinic orbits in phase space. We investigate the existence of the traveling wave solution connecting from a boundary equilibrium to a co-existence equilibrium by using a shooting method. Different from the techniques introduced by Huang, we directly prove the convergence of the solution to a co-existence equilibrium by constructing a special bounded set. Furthermore, the Lyapunov-type function we constructed does not need the condition of bounded below. Our approach provides a different way to study the existence of traveling wave solutions about the co-existence equilibrium. The existence of traveling wave solutions between co-existence equilibria are proved by utilizing the qualitative theory and the geometric singular perturbation theory. Some other open questions of interest are also discussed in the paper. [ABSTRACT FROM AUTHOR]

We report an isothermal electric field-induced first-order phase transition from a Mott insulator to the metallic state in the epitaxial thin film of V 2 O 3 in the temperature regime below its Mott transition temperature of ≈ 180 K. This isothermal electric field-induced transition is accompanied by interesting electrothermal history effects, which depend on the measurement paths followed in the electric field–temperature phase space. These interesting properties result in tuneable resistive switching and distinct memristive behaviour in V 2 O 3 . A generalized framework of disorder-influenced first-order phase transition in combination with a resistor network model has been used to explain the observed experimental features. These findings promise possibilities for Mott insulators to be used as highly energy-efficient switches in novel technologies such as neuromorphic computing. [ABSTRACT FROM AUTHOR]

Single-cell omics technologies can measure millions of cells for up to thousands of biomolecular features, enabling data-driven studies of complex biological networks. However, these high-throughput experimental techniques often cannot track individual cells over time, thus complicating the understanding of dynamics such as time trajectories of cell states. These "dynamical phenotypes" are key to understanding biological phenomena such as differentiation fates. We show by mathematical analysis that, in spite of high dimensionality and lack of individual cell traces, three time-points of single-cell omics data are theoretically necessary and sufficient to uniquely determine the network interaction matrix and associated dynamics. Moreover, we show through numerical simulations that an interaction matrix can be accurately determined with three or more time-points even in the presence of sampling and measurement noise typical of single-cell omics. Our results can guide the design of single-cell omics time-course experiments, and provide a tool for data-driven phase-space analysis. [ABSTRACT FROM AUTHOR]

Due to the lack of field monitoring points, the monitoring data is incomplete, making it difficult to obtain more complete characteristics of mining subsidence. To address this issue, a novel method for interpolating missing subsidence points is proposed. Firstly, the subsidence data are decomposed into multi-frequency domains utilizing the empirical mode decomposition (EMD) method. Subsequently, the missing subsidence data are reconstructed by combining the radial basis function (RBF) with phase space reconstruction technology. The interpolation accuracy is then analyzed under various conditions, including different mining degrees, sample numbers, and observation point locations. The results indicate that the interpolation accuracy increases with the mining degree coefficient. During the active stage of surface subsidence, a larger sample number correlates positively with higher interpolation accuracy. However, in the recession stage, the impact of sample number on interpolation accuracy is less pronounced compared to the timeliness of sample acquisition. The location of observation points has minimal effect on interpolation accuracy. By applying this method to the 833 working face in the Shanjiacun coal mine, the mean absolute percentage error (MAPE) is less than 20%, and the mean squared error (MSE) is below 0.5 mm, objectively demonstrating the method's effectiveness and engineering applicability. These research findings offer valuable technical support for mine safety production and ecological environment protection. [ABSTRACT FROM AUTHOR]

Possible squeezed states generated in a three-waveguide nonlinear coupler operating with second harmonic generation is discussed. This study is carried out using two well-known techniques; the phase space method (based on positive-P representation) and the Heisenberg-based analytical perturbative (AP) method. The effects of key design parameters were investigated under various conditions, including full frequency matching, symmetrical and asymmetrical waveguide initialization, and both codirectional and contr-adirectional propagation. The system consistently produced long-lasting oscillatory squeezed states across all three waveguides, even when only one waveguide was pumped with coherent light while the others were in a vacuum state. Also, the performance and capacities of both methods are critically evaluated. For low levels of key design parameters and in the early stages of evolution, a high level of agreement between the two methods is noticed. In the new era of quantum-based technology, the proposed system opens a new avenue for utilising nonlinear couplers in nonclassical light generation. [ABSTRACT FROM AUTHOR]

The pressure-induced structural changes in the perovskite-type (ABO 3 ) ferroelectric solid solution (1-x)Na 0.5 Bi 0.5 TiO 3 -xBaTiO 3 (NBT-xBT) at the morphotropic phase boundary (MPB) ( x MPB = 0.048 ) have been analyzed up to 12.3 GPa by single-crystal x-ray diffraction with synchrotron radiation. A pressure-induced phase transition takes place between 4.4 and 5.0 GPa, where the pseudocubic low-pressure phase transforms into an orthorhombic high-pressure phase with space group Pnma. The high-pressure phase is comprised of mixed BO 6 tilts and anti-polar A-cation displacements, without exhibiting coherent off-centered shifts of the B-site Ti 4 + cations that can be detected by synchrotron x-ray diffraction. Our results reveal that at ambient pressure and room temperature the NBT- x MPB BT structure possesses anti-phase BO 6 tilts with a relatively large correlation length and the same type of polar distortions as those present in pure NBT, but with strongly violated correlation length due to Ba 2 + -induced local elastic-stress fields. For x MPB the effect of Ba on the mesoscopic-scale structure is compensated by a mild external pressure of only 0.7 GPa, resulting in structural features resembling those of pure NBT at ambient conditions. [ABSTRACT FROM AUTHOR]

Particle accelerators are complex systems that focus, guide, and accelerate intense charged particle beams to high energy. Beam diagnostics present a challenging problem due to limited non-destructive measurements, computationally demanding simulations, and inherent uncertainties in the system. We propose a two-step unsupervised deep learning framework named as Conditional Latent Autoregressive Recurrent Model (CLARM) for learning the spatiotemporal dynamics of charged particles in accelerators. CLARM consists of a Conditional Variational Autoencoder transforming six-dimensional phase space into a lower-dimensional latent distribution and a Long Short-Term Memory network capturing temporal dynamics in an autoregressive manner. The CLARM can generate projections at various accelerator modules by sampling and decoding the latent space representation. The model also forecasts future states (downstream locations) of charged particles from past states (upstream locations). The results demonstrate that the generative and forecasting ability of the proposed approach is promising when tested against a variety of evaluation metrics. [ABSTRACT FROM AUTHOR]

Including the previously ignored dispersion of phonons we revisit the metal-insulator transition problem in one-dimensional electron-phonon systems on the basis of a modified spinless fermion Holstein model. Using matrix-product-state techniques we determine the global ground-state phase diagram in the thermodynamic limit for the half-filled band case, and show that in particular the curvature of the bare phonon band has a significant effect, not only on the transport properties characterized by the conductance and the Luttinger liquid parameter, but also on the phase space structure of the model as a whole. While a downward curved (convex) dispersion of the phonons only shifts the Tomonaga-Luttinger-liquid to charge-density-wave quantum phase transition towards stronger EP coupling, an upward curved (concave) phonon band leads to a new phase-separated state which, in the case of strong dispersion, can even completely cover the charge-density wave. Such phase separation does not occur in the related Edwards fermion-boson model. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to the phase space reconstruction technique, fractional-order phase space reconstruction (FOSS), which generalizes the traditional integer-order derivative-based method. By leveraging fractional derivatives, FOSS offers a novel perspective for understanding complex time series, revealing unique properties not captured by conventional methods. We further develop the multi-span transition entropy component method (MTECM-FOSS), an advanced complexity measurement technique that builds upon FOSS. MTECM-FOSS decomposes complexity into intra-sample and inter-sample components, providing a more comprehensive understanding of the dynamics in multivariate data. In simulated data, we observe that lower fractional orders can effectively filter out random noise. Time series with diverse long- and short-term memory patterns exhibit distinct extremities at different fractional orders. In practical applications, MTECM-FOSS exhibits competitive or superior classification performance compared to state-of-the-art algorithms when using fewer features, indicating its potential for engineering tasks. [ABSTRACT FROM AUTHOR]

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N ≫ 1 , as it undergoes a free expansion doubling its volume. The microstate of the system changes in time via Hamiltonian dynamics. Its entropy, at any time t, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time t. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells Δ α . The initial and final macrostates of the system are thermal equilibrium states in volumes V and 2V, with the same energy E and particle number N. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the Δ α . The intermediate (non-equilibrium) entropy does however depend on the size of the cells Δ α . Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining Δ v : it produces entropy at a rate proportional to Δ v . This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of Δ v and is given by the Boltzmann equation for the limit Δ v → 0 . We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes. [ABSTRACT FROM AUTHOR]

The fractional step method is used to solve the ionization equations for electron-ion plasma containing neutrals in relation to processes in stationary plasma thrusters (SPT). The method uses splitting with respect to physical processes: the evolution of plasma is represented as a superposition of pure transport in an external field in phase space with subsequent ionization. The transport is calculated using the macroparticle method. The ionization process in the case of plane symmetry is calculated using explicit analytical formulas. The resulting formulas of the fractional step method are compared with the numerical solution of the plasma evolution equation using the known physical model of ionization. [ABSTRACT FROM AUTHOR]

Tin selenide has record values of the thermoelectric performance, which is largely due to its low lattice thermal conductivity caused by strong lattice anharmonicity. In this work, the effect of temperature and volume on the phonon density of states of the low-temperature SnSe phase with the space group is analyzed using molecular dynamics simulations. Stabilization of the phase with a crystal structure at high temperatures is demonstrated. An anomalously low lattice thermal conductivity of SnSe is obtained from the numerical solution of the linearized Boltzmann transport equation, which is in agreement with experimental data over a wide temperature range. [ABSTRACT FROM AUTHOR]

The extraction of effective classification features from electroencephalogram (EEG) signals in motor imagery is a popular research topic. The Common Spatial Pattern (CSP) algorithm is widely employed in this field. However, the performance of the traditional CSP method depends significantly on the choice of a specific frequency band and channel number of EEG data. Furthermore, inter-class variance among these frequency bands and the limited number of available EEG channels can adversely affect the CSP algorithm's ability to extract meaningful features from the relevant signal frequency bands. We hypothesize that multiple Intrinsic Mode Functions (IMFS), into which the raw EEG signal is decomposed, can better capture the non-Gaussian characteristics of the signal, thus compensating for the limitations of the CSP algorithm when dealing with nonlinear and non-Gaussian distributed data with few channels. Therefore, this paper proposes a novel method that integrates Variational Mode Decomposition (VMD), Phase Space Reconstruction (PSR), and the CSP algorithm to address these issues. VMD is used to filter and enhance the quality of the collected data, PSR is employed to increase the effective data channels (data augmentation), and the subsequent CSP filtering can obtain signals with spatial features, which are decoded by Convolutional Neural Networks (CNN) for action decoding. This study utilizes self-collected EEG data to demonstrate that the new method can achieve a good classification accuracy of 82.30% on average, confirming the improved algorithm's effectiveness and feasibility. Furthermore, this study conducted validation on the publicly available BCI Competition IV dataset 2b, demonstrating an average classification accuracy of 87.49%. [ABSTRACT FROM AUTHOR]

We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension d. These discretization spaces are spanned by Gaussian coherent states, that have the key property to be localised in phase space. We carefully select the Gaussian coherent states spanning the approximation space by exploiting the (known) micro-localisation properties of the solution. For a large class of source terms (including plane-wave scattering problems), this choice leads to discrete spaces that provide a uniform approximation error for all wavenumber k with a number of degrees of freedom scaling as k d - 1 / 2 , which we rigorously establish. In comparison, for discretization spaces based on (piecewise) polynomials, the number of degrees of freedom has to scale at least as k d to achieve the same property. These theoretical results are illustrated by one-dimensional numerical examples, where the proposed discretization spaces are coupled with a least-squares variational formulation. [ABSTRACT FROM AUTHOR]

Concatenated backward ray mapping is an alternative for ray tracing in 2D. It is based on the phase-space description of an optical system. Phase space is the set of position and direction coordinates of light rays intersecting a surface. The original algorithm (Filosa, ten Thije Boonkkamp and IJzerman in J Math Ind 11(1):4, 2021) is limited to optical systems consisting of only straight surfaces; we generalize it to accommodate curved surfaces. The algorithm is applied to a standard optical system, the compound parabolic concentrator. We compare the accuracy and speed of the generalized algorithm, the original algorithm and Monte Carlo ray tracing. The results show that the generalized algorithm outperforms both other methods. [ABSTRACT FROM AUTHOR]

A dynamical system given by a diffeomorphism with a three-dimensional phase space may have a blender, which is a hyperbolic set Λ with, say, a one-dimensional stable invariant manifold that behaves like a surface. This means that the stable manifold of any fixed or periodic point in Λ weaves back and forth as a curve in phase space such that it is dense in some projection; we refer to this as the carpet property. We present a method for computing very long pieces of such a one-dimensional manifold so efficiently and accurately that a very large number of intersection points with a specified section can reliably be identified. We demonstrate this with the example of a family of Hénon-like maps H on R 3 , which is the only known, explicit example of a diffeomorphism with proven existence of a blender. The code for this example is available as a Matlab script as supplemental material. In contrast to earlier work, our method allows us to determine a very large number of intersection points of the respective one-dimensional stable manifold with a chosen planar section and render each as individual curves when a parameter is changed. With suitable accuracy settings, we not only compute these parametrised curves for the fixed points of H over the relevant parameter interval, but we also compute the corresponding parametrised curves of the stable manifolds of a period-two orbit (with negative eigenvalues) and of a period-three orbit (with positive eigenvalues). In this way, we demonstrate that our algorithm can handle large expansion rates generated by (up to) the fourth iterate of H . [ABSTRACT FROM AUTHOR]

Heatwaves are often driven by subtropical persistent highs and quasi-stationary Rossby waves along with regional factors such as soil moisture. Both temperature and humidity variability play an important role in the regional heatwave patterns. Studies have differentiated the dry and moist heatwave-related extremes both in terms of their driving mechanism and in their impact on human health. With the observed increase in the intensity, frequency and duration of heatwaves in recent decades, the impact-based forecasting and monitoring (IBF) of heatwaves has assumed significance. Current operational IBF indices, especially over the Indian region are empirical and do not necessarily consider the modal dynamics or their role in the impact of dry and moist heat-related discomfort. In this study, based on two large-scale intraseasonal modes of summer temperature variability, the driving mechanisms of dry and moist heat extremes over the Indian region are identified. The regional scale impact identified based on the Heat Index is driven by these two large-scale modes. The first mode represents the conditions conducive for the formation of the dry heat extremes. The second mode represents the regional circulation pattern that supports the moisture inflow towards the coastal states. This inflow combined with the modal temperature pattern drives the moist heat extremes over India. Based on the location of the principal components of these modes in the phase space, the heat-related health risk associated with the dominant modes is assessed. Warnings for different phases of dry and moist heat extremes occurring over the Indian region are also proposed for operational use. [ABSTRACT FROM AUTHOR]

In this work, the multistream quasiparticle model of collective electron excitations is applied to study the energy-density distribution of collective quantum excitations in an interacting electron gas with an arbitrary degree of degeneracy. Generalized relations for the probability current and energy density distribution are obtained which suggests a diffusive mechanism for plasmonic excitations of pure quasiparticle states at the microscopic level. The effect is applied to different cases of free quasiparticles, quasiparticles in an infinite square-well potential, and the analytic form of damping rate is obtained. The Wigner distribution and damping of excited states in phase space are also investigated. It is shown that plasmon excitations have the intrinsic tendency to decay into an equilibrium state with uniform energy density spatial distribution. It is found that plasmon levels of quasiparticles in a square-well potential are unstable decaying into an equilibrium state due to the fundamental property of collective excitations. The decay rates of pure plasmon states are determined analytically. The phase-space analysis reveals that there may be a close relation between the quantum diffusion and the Landau damping of quasiparticle states. Current research can have implications with applications in plasmonics and related fields. Current analysis can be readily generalized to include external potential, magnetic field, and electron correlation effects. [ABSTRACT FROM AUTHOR]

Key expansion plays an important role in symmetric block cipher. To generate desired number of round keys that satisfy irreversibility, parallelism and independence, we first constructed a 2D memristor-based discrete hyper chaotic map (2D-MDHCM), through adding a memristor to the 2D discrete hyper chaotic map (2D-DHCM), whose state point has ergodicity in phase space and good randomness in a sufficiently large parameter range. Took advantage of the irreversibility of the chaotic iteration, we designed an irreversible key expansion algorithm, which can generate the round keys in parallel with specified round and flexible length, what's more, each round key can be generated by the initial key independently. Experimental and analysis results demonstrated that the improved key expansion algorithm satisfied irreversibility, parallelism and independence, which enhanced the security of initial key greatly. [ABSTRACT FROM AUTHOR]

Density-functional theory (DFT) is utilized to study the crystal structure, geometry, and magnetic and electronic properties of the triple perovskites Ba3MRu2O9 (M = Fe, Co, and Ni) in hexagonal phase with space group P63/mmc. Generalized gradient approximation plus Hubbard potential is found to be an effective potential for the treatment of these perovskites. Spin-orbit coupling with Hubbard U (GGA+SOC+U) is also applied to analyze its effect on the understudy compounds. The optimized crystal structures and geometries are consistent with the experimental reported results. The stability of these perovskites is described by cohesive and formation energies. The antiferromagnetic (AFM) nature of all these perovskites is confirmed by stable magnetic phase energies and magnetic susceptibility. The electronic band profiles in the AFM phase and electrical resistivities confirm that these perovskites are metallic in nature. Metallicity as well as magnetism in these compounds is due to d-state electrons of the M and Ru atoms. The metallic AFM nature reveals that these compounds are promising materials for magnetic cloaking, high-speed switching devices, and spintronic applications. [ABSTRACT FROM AUTHOR]

We continue studies of the nonlocal erosion equation that is used as a mathematical model of the formation of a spatially inhomogeneous relief on semiconductor surfaces. We show that such a relief can form as a result of local bifurcations in the case where the stability of the spatially homogeneous equilibrium state changes. We consider a periodic boundary-value problem and study its codimension- bifurcations. For solutions describing an inhomogeneous relief, we obtain asymptotic formulas and study their stability. The analysis of the mathematical problem is based on modern methods of the theory of dynamical systems with an infinite-dimensional phase space, in particular, on the method of integral manifolds and on the theory of normal forms. [ABSTRACT FROM AUTHOR]

We explore the impact of the chameleon mechanism in scalar field Einstein-Gauss-Bonnet gravity on the dynamics of cosmological parameters. Conducting a thorough analysis of the phase space, we identify conditions under which the future attractor does not depict a singular universe. Our conclusion is that although Einstein-Gauss-Bonnet scalar field gravity offers an inflationary solution as a future attractor, it is unable to account for the late-time acceleration of the universe and it can not describe a universe similar to that provide by the -CDM model. On the other hand, when the matter source is described by a massless scalar field, then the de Sitter universe is a future attractor. However, the hyperbolic inflationary solution provided by the two scalar fields does not exist. [ABSTRACT FROM AUTHOR]

This article explores the characteristics of interacting new Tsallis agegraphic dark energy (NTADE) and Sharma-Mittal holographic dark energy (SMHDE) models in a flat FLRWuniverse within Rastall gravity (RG). To check the viability of thesemodels and to distinguish them, we develop important cosmological parameters including equation of state (EoS) parameter, deceleration parameter q, square speed of sound, statefinder pair and Om(z) diagnostic. By constraining the different parameters for both dark energy (DE) models, it is observed that: EoS parameter indicates phantomlike behavior, deceleration parameter is showing a phase transition from decelerating to accelerating phase. The (j, s) plane is indicating a rich behavior as it shows different DE eras like quintessence, phantom and Chaplygin gas for both models depending upon interacting term d², parameter δ and Rastall parameter λ. The ωD - ω -- D pair is indicating freezing region for NTADE but for SMHDE it initially falls in freezing region then move towards thawing region. We also check stability of NTADE/SMHDE models through the graphical interpretation of square speed of sound. [ABSTRACT FROM AUTHOR]

We elaborate on a model of nonassociative and noncommutative Einstein-Dirac-Maxwell, EDM, theory determined by star product R-flux deformations in string theory. Solutions for nonassociative EDMsystems and physical properties not studied in modern physics. For modifications of the four-dimensional, 4-d, Einstein gravity, we work on conventional nonassociative 8-d phase spaces modelled as star-deformed co-tangent Lorentz bundles. Generalizing the anholonomic frame and connection deformation method, the nonassociative EDM equations are decoupled and integrated in exact and parametric quasi-stationary forms. Corresponding generic off-diagonal metrics are described by nonlinear symmetries and encode nonassociative effective sources and generating functions depending on space and momentum-like coordinates. For respective nonholonomic parameterizations, such solutions describe nonassociative deformations of the Reissner-Nordström black holes. A variant of nonassociative phase spacewormhole solutionwith fermions possessing anisotropic polarized masses is also analyzed. We conclude that such phase space physical objects can't be charac-terized using the concept of Bekenstein-Hawking entropy and show how to compute another type (modified G. Perelman ones) nonassociative geometric and statistical thermodynamic variables. [ABSTRACT FROM AUTHOR]

Various physical properties of the ternary intermetallics CeTAl3 (T = Pd, Pt, Cu, Ag and Au) are investigated in tetragonal phase with space group I4 mm (No. 107) using generalized gradient approximation (GGA) along with Hubbard potential (U) in the domain of density functional theory (DFT). The calculated results show that the understudy intermetallics are stable in tetragonal symmetry and are found in good agreement with experiments. Magnetic optimization energies show that CePdAl3 is stable in G-type antiferromagnetic (G-AFM) phase, CeTAl3 (T = Cu and Au) are stable in A-AFM, CePtAl3 is spin glass (SG) and CeAgAl3 is stable in ferromagnetic (FM) phase and are confirmed through magnetic susceptibilities. The electronic band profiles, electrical resistivities and electronic thermal conductivities demonstrated the metallic nature of these intermetallics and CePtAl3 is good conductor among this series. The elastic properties show that all these intermetallics are mechanically stable, anisotropic and brittle in nature. The above mention properties make these intermetallics suitable for spintronics, storage and electronic devices. [ABSTRACT FROM AUTHOR]

The problem of multi-class classification is always a challenge in the field of EEG (electroencephalogram)-based seizure detection. The traditional studies focus on computing or learning a set of features from EEG to distinguish between different patterns. However, the extraction of characteristic information becomes increasingly difficult as the number of EEG types increases. To address this issue, a creative EEG classification technique is proposed by employing a principal component analysis network (PCANet) coupled with phase space reconstruction (PSR) and power spectrum density (PSD). We have introduced the PSR and PSD to prepare the inputs, where dynamic and frequency information are exposed from deep within PCANet. It is remarkable that a layered cascade strategy is designed to make a powerful deep learner according to the rule of one network vs one task (OVO). The proposed method has achieved greater effects than the individual models and shown superior performance in comparison with state-of-the-art algorithms, which present 98.0% of sensitivity, 99.90% of specificity, and 99.07% of accuracy. Our ensemble PCANet model works in an assembly line-like manner, obviating the need for hand-craft features. Results demonstrate that the proposed scheme can greatly enhances the accuracy and robustness of seizure detection from EEG signals. [ABSTRACT FROM AUTHOR]

We report a theoretical investigation of the ultrafast dynamics of electrons and phonons in strained monolayer WS2 following photoexcitation. We show that strain substantially modifies the phase space for electron-phonon scattering, unlocking relaxation pathways that are unavailable in the pristine monolayer. In particular, strain triggers a transition between distinct dynamical regimes of the non-equilibrium lattice dynamics characterized by the emission of chiral phonons under high strain and linearly-polarized phonons under low strain. For valley-polarized electronic excitations, this mechanism can be exploited to selectively activate the emission of chiral phonons – phonons carrying a net angular momentum. Our simulations are based on state-of-the-art ab-initio methods and focus exclusively on realistic excitation and strain conditions that have already been achieved in recent experimental studies. Overall, strain emerges as a powerful tool for controlling chiral phonons emission and relaxation pathways in multivalley quantum materials. [ABSTRACT FROM AUTHOR]