Search Results (624)

A model for the flow and thermal explosion of a micropolar gas is investigated, assuming the equation of state for a real gas. This model describes the dynamics of a gas mixture (fuel and oxidant) undergoing a one-step irreversible chemical reaction. The real gas model is particularly suitable in this context because it more accurately reflects reality under extreme conditions, such as high temperatures and high pressures. Micropolarity introduces local rotational dynamic effects of particles dispersed within the gas mixture. In this paper, we first derive the initial-boundary value system of partial differential equations (PDEs) under the assumption of spherical symmetry and homogeneous boundary conditions. We explain the underlying physical relationships and then construct a corresponding approximate system of ordinary differential equations (ODEs) using the Faedo–Galerkin projection. The existence of solutions for the full PDE model is established by analyzing the limit of the solutions of the ODE system using a priori estimates and compactness theory. Additionally, we propose a numerical scheme for the problem based on the same approximate system. Finally, numerical simulations are performed and discussed in both physical and mathematical contexts. Full article

Nuclei are self-bound systems in which the strong interaction (nuclear force) plays a dominant role, and the isospin is approximately a good quantum number. The isospin symmetry is primarily violated by electromagnetic interactions, namely Coulomb interactions among protons, the effects of which need be studied to understand the importance of the isospin symmetry. We investigate the effect of the Coulomb interaction on nuclear properties, especially quadrupole deformation and neutron drip line, utilizing the density functional method, which provides a universal description of nuclear systems in the entire nuclear chart. We carry out calculations of even–even nuclei with a proton number of $2\le Z\le 60$. The results show that the Coulomb interaction plays a significant role in enhancing quadrupole deformation across a wide range of nuclei. We also find that, after including the Coulomb interaction, some nuclei near the neutron drip line become stable against two-neutron emissions, resulting in a shift in the drip line towards larger neutron numbers. Full article

A new polymorph of N-(1,3-thiazol-2-yl)benzamide crystallises in the monoclinic space group Pc with four crystallographically independent molecules (Z′ = 4) in the asymmetric unit. Where the previously reported polymorphs exhibit two distinct hydrogen-bonded dimer geometries exclusively, the asymmetric unit of the new polymorph comprises both. Approximate symmetry was observed to relate the molecules of these dimers. These approximate symmetry elements combine to form a structure with distorted P2₁/c space group symmetry, rationalising the unexpectedly high number of crystallographically independent molecules. Full article

In this paper, we provide a novel extended mixed differential model that is appealing to users because of its numerous free parameters. The motivation of this research arises from the opportunity for a general investigation of some outstanding classical and novel dynamical models. The higher energy levels known in the literature can be governed by appropriately added correction factors. Furthermore, the different applications of the considered model can be achieved only after a proper parameter calibration. All these necessitate the use of diverse optimization and approximation techniques. The proposed extended model is especially useful in the important field of decision making, namely the antenna array theory. This is due to the possibility of generating high-order Melnikov polynomials. The work is a natural continuation of the authors’ previous research on the topic of chaos generation via the term ${x\left|x\right|}^{a-1}$. Some specialized modules for investigating the dynamics of the proposed oscillators are provided. Last but not least, the so-defined dynamical model can be of interest for scientists and practitioners in the area of antenna array theory, which is an important part of the decision-making field. The stochastic control of oscillations is also the subject of our consideration. The underlying distributions we use may be symmetric, asymmetric or strongly asymmetric. The same is true for the mass in the tails, too. As a result, the stochastic control of the oscillations we purpose may exhibit a variety of possible behaviors. In the final section, we raise some important issues related to the methodology of teaching Master’s and PhD students. Full article

Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems with bounded control range, we analyze when a unique control set (i.e., a maximal set of approximate controllability) with nonvoid interior exists, for the induced system on projective space. We use the system semigroup by considering piecewise constant controls and use spectral properties to extend the result to bilinear systems in ${\mathbb{R}}^d$. The contribution of this paper highlights the relationship between all the existent control sets. We show that the controllability property of a bilinear system is equivalent to the existence and uniqueness of a control set of the projective system. Full article

We analyze the high-order above-threshold ionization (HATI) process of a small polyatomic molecule with C₃ symmetry, which is induced by a bicircular strong laser field. This field consists of two coplanar, counter-rotating, circularly polarized components with frequencies $r\omega$ and $s\omega$ where r and s are integers. In our study, we use an improved molecular strong-field approximation to obtain electron energy-angle-resolved and momentum spectra of the BF₃ molecule. We analyze the contributions of individual atoms as well as the impact of molecular symmetries on these spectra. We find that these spectra are significantly affected by the characteristics of the molecule and the laser-field parameters. Furthermore, we observe pronounced interference minima in the HATI spectra. We demonstrate that these minima result from the destructive interference of rescattered wave packets from different atomic centers, and we determine the conditions under which they occur, including two-, three-, and four-center interference. Full article

Residual stress plays a crucial role in determining the structural reliability and mechanical performance of nano-multilayers. In the present study, nano-multilayers composed of ZrO_xN_y and V₂O₃ were deposited via magnetron sputtering, with the N:Ar flow ratio systematically varied during the process. Through the precise control of the deposition conditions, the compressive residual stress within the films was effectively reduced to approximately 0 GPa, thereby improving their mechanical robustness. It was observed that the optimization of the stress distribution was strongly influenced by the structural symmetry of the multilayer configuration. This symmetrical design not only mitigated stress accumulation but also ensured uniform mechanical response throughout the multilayer structure. The results from nanoindentation testing revealed a steady hardness value near 10.6 GPa. Furthermore, the maximum H³/E² and H/E ratios recorded were 0.054 GPa and 0.073, respectively, suggesting enhanced resistance to both plastic deformation and cracking. Full article

This study investigates the solution structure of the nonlinear Rayleigh oscillator equation through two widely used semi-analytical techniques: the Laplace–Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM). The Rayleigh oscillator exhibits inherent asymmetry in its nonlinear damping term, which disrupts the time-reversal symmetry present in linear oscillatory systems. Applying the LADM and HPM, we derive approximate solutions for the Rayleigh oscillator. Due to the absence of exact analytical solutions in the literature, these approximations are benchmarked against high-precision numerical results obtained using Mathematica’s NDSolve function. We perform a detailed error analysis across different damping parameter values ε and time intervals. Our results reveal how the asymmetric damping influences the accuracy and convergence behavior of each method. This study highlights the role of nonlinear asymmetry in shaping the solution dynamics and provides insight into the suitability of the LADM and HPM under varying conditions. Full article

This study addresses the long-standing difficulty of predicting the remaining useful life (RUL) of rolling bearings from highly non-stationary vibration signals by proposing WaveAtten, a symmetry-aware deep learning framework. First, mirror-symmetric and bi-orthogonal Daubechies wavelet filters are applied to decompose each raw signal into multi-scale approximation/detail pairs, explicitly preserving the left–right symmetry that characterizes periodic mechanical responses while isolating asymmetric transient faults. Next, a bidirectional sparse-attention module reinforces this structural symmetry by selecting query–key pairs in a forward/backward balanced fashion, allowing the network to weight homologous spectral patterns and suppress non-symmetric noise. Finally, the symmetry-enhanced features—augmented with temperature and other auxiliary sensor data—are fed into a long short-term memory (LSTM) network that models the symmetric progression of degradation over time. Experiments on the IEEE PHM2012 bearing dataset showed that WaveAtten achieved superior mean squared error, mean absolute error, and R² scores compared with both classical signal-processing pipelines and state-of-the-art deep models, while ablation revealed a 6–8% performance drop when the symmetry-oriented components were removed. By systematically exploiting the intrinsic symmetry of vibration phenomena, WaveAtten offers a robust and efficient route to RUL prediction, paving the way for intelligent, condition-based maintenance of industrial machinery. Full article

LK-99, with chemical formula Pb_10−xCu_x(PO₄)₆O, was recently reported to be a room-temperature superconductor. While this claim has met with little support in a flurry of ensuing work, a variety of calculations (mostly based on density-functional theory) have demonstrated that the system possesses some unusual characteristics in the electronic structure, in particular flat bands. We have established previously that within DFT, the system is insulating with many characteristics resembling the classic cuprates, provided the structure is not constrained to the P3(143) symmetry nominally assigned to it. Here we describe the basic electronic structure of LK-99 within self-consistent many-body perturbative approach, quasiparticle self-consistent GW (QSGW) approximation and their diagrammatic extensions. QSGW predicts that pristine LK-99 is indeed a Mott/charge transfer insulator, with a bandgap gap in excess of 3 eV, whether or not constrained to the P3(143) symmetry. When Pb₉Cu(PO₄)₆O is hole-doped, the valence bands modify only slightly, and a hole pocket appears. However, two solutions emerge: a high-moment solution with the Cu local moment aligned parallel to neighbors, and a low-moment solution with Cu aligned antiparallel to its environment. In the electron-doped case the conduction band structure changes significantly: states of mostly Pb character merge with the formerly dispersionless Cu d state, and high-spin and low spin solutions once again appear. Thus we conclude that with suitable doping, the ground state of the system is not adequately described by a band picture, and that strong correlations are likely. Irrespective of whether this system class hosts superconductivity or not, the transition of Pb₁₀(PO₄)₆O from being a band insulator to Pb₉Cu(PO₄)₆O, a Mott insulator, and multi-determinantal nature of doped Mott physics make this an extremely interesting case-study for strongly correlated many-body physics. Full article

Some properties on Banach spaces, such as the Radon–Riesz, Dunford–Pettis and approximation properties, allow us to better understand the naive details about the structure of space and the robust inhomogeneities and symmetries in space. In this work we try to examine such properties of vector-valued Schröder sequence spaces. Further, we show that these sequence spaces have a kind of Schauder basis. We also prove that ${\ell }_1\left(\mathcal{S},V\right)$ possesses the Dunford–Pettis property and demonstrate that ${\ell }_p\left(\mathcal{S},V\right)$ satisfies the approximation property for $1\le p<\infty$ under certain conditions and ${\ell }_{\infty }\left(\mathcal{S},V\right)$ has the Hahn–Banach extension property. Finally, we show that ${\ell }_2\left(\mathcal{S},V\right)$ has the Radon–Riesz property whenever V has it. Full article

This paper investigates the distributed state estimation problem for the linear system against non-Gaussian noise, where every sensor commutates information only within its adjacent sensors without the need for a fusion center. Correntropy is a similarity metric based on a kernel function that has symmetry. Symmetry means that for any two data points, the output value of the kernel function does not depend on the order of the data points. By adopting a correntropy cost function based on the rational quadratic kernel function approximation to restrain non-Gaussian heavy-tailed noise, a centralized maximum correntropy Kalman filter is first derived for the linear sens+or network system at first. Then the corresponding centralized maximum correntropy information filter is attained by employing the information matrices, which is a foundation for further designing distributed information algorithms under multi-sensor networks. Thirdly, the distributed rational quadratic maximum correntropy information filter and distributed adaptive rational quadratic maximum correntropy information filter are designed by exploiting the weighted census average to solve the non-Gaussian heavy-tailed noise interference in sensor networks. Finally, the performance of the proposed algorithms is illustrated through numerical simulations on the sensor network system. Full article

The disc-buckle scaffold system demonstrates significant advantages in prefabricated construction applications, particularly in terms of installation efficiency, load-bearing capacity, and standardization. Guangzhou Construction Group Co., Ltd., a leading enterprise in promoting prefabricated building development in Guangdong Province, China, has collaborated with the Guangdong University of Technology to develop an innovative disc-buckle scaffold system. The main difference between different scaffolds lies in the connection part of the joint. The mechanical behavior of scaffold joint plays a critical role in determining the structural integrity of the entire scaffolding system. So, the novel disc-buckle scaffold proposed in this paper is mainly new in the joint. Finite element simulation based on the test results is employed to study the performance of the novel scaffold joint in this paper. The results show that the newly developed scaffold joint exhibits superior mechanical performance, characterized by a bending stiffness of 34.5 kN·m/rad. The joint demonstrates maximum tensile and compressive bearing capacities of approximately 108 kN and 70 kN in the transverse direction, respectively. Furthermore, the joint’s maximum shear bearing capacity exceeds 180 kN, surpassing the buckling critical force of the vertical steel pipe and satisfying all strength requirements. The scaffold joint exhibits robust hysteresis characteristics, and the wedge-shaped connection mechanism maintains consistent stiffness and load-bearing symmetry under both positive and negative bending moments. The proposed disc-buckle steel scaffold joint features a minimal number of components, achieving an optimal balance between structural performance and economic efficiency. Full article

External fields modify the confinement potential and electronic structure in a multiple quantum well system, affecting the light–matter interaction. Here, we present a theoretical study of the modulation of the nonlinear optical response simultaneously employing an intense non-resonant laser field and an electric field. Considering four occupied subbands, we focus on a GaAs/AlGaAs symmetric multiple quantum well system with five wells and six barriers. By solving the Schrödinger equation through the finite element method under the effective mass approximation, we determine the electronic structure and the nonlinear optical response using the density matrix formalism. The laser field dresses the confinement potential while the electric field breaks the inversion symmetry. The combined effect of both fields modifies the intersubband transition energies and the overlap of the wave functions. The results obtained demonstrate an active tunability of the nonlinear optical response, opening up the possibility of designing optoelectronic devices with tunable optical properties. Full article