Search Results (409)

The paper deals with the asymptotic behavior of a widely used correlation characteristic in large quantum systems. The correlation is quantum entanglement, the characteristic is entanglement entropy, and the system is an ideal gas of lattice fermions. If the one-body Hamiltonian of fermions is an ergodic finite difference operator with an exponentially decaying spectral projection, then the large-block form of the entanglement entropy is the so-called area law. However, the only class of one-body Hamiltonians for which this spectral condition was verified consists of discrete Schrödinger operators with random potential. In this paper, we prove the area law for several classes of Schrödinger operators whose potentials are ergodic but not random. We begin with quasiperiodic and limit-periodic operators and then move to a highly non-trivial case of potentials generated by subshifts of finite type. These arose in the theory of dynamical systems when studying chaotic phenomena. The corresponding asymptotic study requires involved spectral analysis, which therefore constitutes the bulk of the paper. Specifically, we prove uniform localisation of the eigenfunctions for the Maryland model and exponential decay of the eigenfunction correlator for various models. We believe these properties are of significant independent interest. Full article

This paper investigates a discrete-time fractional-order predator–prey model incorporating a double Allee effect in the prey population, derived from a fractional differential system via the piecewise constant argument method to capture both memory effects and density-dependent constraints. We establish the existence and local stability of all biologically meaningful equilibria and show that the interaction between fractional memory and the double Allee threshold significantly influences the stability of the coexistence state. Through the integration of linear stability analysis and center manifold reduction, we are able to obtain explicit conditions for Neimark–Sacker and period-doubling bifurcations. The system exhibits rich dynamics, including periodic oscillations, quasi-periodicity, and chaos. The double Allee effect plays a key role in shaping system stability. To suppress instability and chaotic behavior, feedback and hybrid control strategies are applied and shown to be effective. Numerical simulations are given to confirm the results obtained by the theoretical analysis and to show the transitions among different dynamical states, in which the fractional-order memory and multiple Allee effects play important roles. Full article

The increasing randomness of source–load fluctuations and the rapid proliferation of power-electronic devices have introduced wide dynamic ranges, fast time-varying behaviors, and strong stochastic characteristics into power signals, leading to severe measurement deviations in existing metering equipment. Conventional modeling and feature analysis methods based on fixed-frequency steady-state assumptions are inadequate for characterizing such non-stationary behaviors, making the underlying causes of metering deviations difficult to identify. To address this issue, we propose a modeling and dynamic time–frequency feature extraction method for complex non-stationary power signals. First, the operating characteristics of power equipment are analyzed to identify the fundamental non-stationary features of power signals, based on which a quasi-periodic harmonic signal model is established. Then, the scaling-basis chirplet transform is employed to intuitively represent the time–frequency structure, while a ridge detection algorithm is incorporated to quantitatively characterize the time–frequency trajectories and instantaneous amplitude features. Finally, to cope with the limited availability of power signal measurements, a non-stationary component reconstruction method based on cross-correntropy is developed. Experimental results from multiple datasets, including field-measured signals, demonstrate that the proposed method enables effective dynamic monitoring and reconstruction of non-stationary components, offering significant advantages in both time–frequency analysis capabilities and reconstruction accuracy. Full article

This study investigates the phenomenon of supratransmission in three-dimensional crystals with a B2 (CsCl) structure, employing classical molecular dynamics with β-Fermi–Pasta–Ulam–Tsingou potentials up to fourth-nearest neighbors. We analyze energy transfer from a harmonically driven surface into the crystal bulk across various frequency regimes relative to the phonon spectrum. While low-amplitude excitation results in energy transmission only within the phononic bands, high-amplitude driving triggers supratransmission in the phononic gap and above the optical band. Our results demonstrate that in these nonlinear regimes, energy is transported not by linear phonon waves but by discrete breathers (DBs) emitted quasi-periodically from the surface. A key finding is the distinct sublattice selectivity of these excitations: gap DBs propagate primarily along the heavy atom sublattice, whereas above-spectrum DBs travel along the light atom sublattice. We quantify the velocities and oscillation periods of these localized modes, revealing their critical role in bypassing linear spectral restrictions. These findings provide new insights into nonlinear energy transport in binary alloys and suggest potential applications for controlling heat flow and signal processing in crystals. Full article

We study a 1D model of a diffraction-mediated self-structuring instability which can occur when a Bose–Einstein condensate is illuminated by a pump laser and its reflection from a single feedback mirror. We carry out a linear stability analysis and, using numerical simulations, investigate the dynamics of the self-structuring process. Two dynamical regimes are identified: one in which the system behaves as a continuous space-time crystal oscillating between two states (one spatially uniform and one spatially periodic) and another where many condensate momentum states are involved and the condensate density develops chevrons which form and disperse quasi-periodically. We show the dependence of the pattern modulation depth and pattern formation time on pump saturation parameter and compare the simulation results with analytical expressions derived from a quantum Hamiltonian Mean Field model. The results show that this system offers a route to the first experimental realisation of the quantum Hamiltonian Mean Field model and of a continuous space-time crystal with a tunable spatial period. Full article

In the ElastoHydrodynamic Lubrication (EHL) meshing contact model for rough interfaces with convex–concave textured micro-asperities, the geometric morphology of the meshing interface exhibits pronounced multiscale characteristics: the macroscale manifests as the correlation between Interface-Enriched Lubrication (IEL) performance and meshing Anti-Scuffing Load-Bearing Capacity (ASLBC), while the microscale corresponds to the textured morphology of rough interfaces. In numerical simulations of EHL meshing contact, such cross-scale disparities necessitate solving large-scale systems of analytical solution equations. Assuming periodicity or quasi-periodicity at the microscale, various established methods enable decoupling the macroscopic and microscopic scales, such formalized approaches constitute homogenization theory. However, classical asymptotic assumptions may introduce considerable approximation errors. This study proposes a micro-texture-informed homogenized contact model based on multiscale characterization that incorporates the coupled effects of gear interface meshing forces and thermo-elastic deformations, effectively extending the applicability of classical asymptotic homogenization methods. Full article

This paper investigates the dynamics of a three-dimensional nonlinear model of the financial system and the conditions for the emergence of chaotic behavior. The well-known chaotic system with given parameters and initial conditions is considered as a basis. For the initial model, critical points are analyzed, two-dimensional and three-dimensional phase portraits are constructed, and Lyapunov exponents are calculated, which allow confirming the presence of chaos and assessing the degree of sensitivity to initial data. Next, a modification of the system is proposed, consisting of changing the degree of the variable in the second equation. For the group of models obtained, we considered the generalized form of the system, found its critical points, and classified them. At the next stage, a bifurcation analysis was performed: by changing the key parameters of the modified systems, bifurcation diagrams were constructed, and parameter regions corresponding to critical points, periodicity, quasi-periodicity, and chaos were identified. The results demonstrate that the nature of the dynamics depends significantly on both the parameters and the degree of nonlinearity and allow conclusions to be drawn about the mechanisms of chaos in the financial model under consideration. Full article

In this study, we develop and investigate a novel fractional discrete-time computer virus dynamics model in two dimensions with a memristive nonlinear coupling mechanism. The memristor introduces nonlinearity by having memory regulation that depends on the state and enhances the propagation dynamics of virus spread. By investigating both matching and non-matching fractional orders, it is then possible to derive useful knowledge with respect to cooperating roles in terms of fractional memory and memristive effects. The complexity behind it is confirmed via 3D phase portraits, bifurcation analysis with LE_max calculation, 0–1 chaos test, and SE complexity. Numerical results reveal rich dynamical phenomena, including periodic oscillations, quasi-periodicity, and strong chaos. In fact, positive LE_max values, Brownian-like trajectories, and high-complexity SE corroborate the chaotic nature of the regimes. Thereby, the fractional-order separation in noncommensurate conditions is a marker of chaotic motion, magnified in the emergently high-dimensional space introduced by the memristive element. As these results indicate that the derivative model proposed here provides an excellent fit for complex viruses present in scaffolds, it may prove to be a useful modeling tool. Full article

Theoretical studies of transonic accretion onto black holes reveal a wide range of possible solutions, broadly classified into smooth flows and flows featuring shocks. Accretion solutions that involve the formation of shocks are particularly intriguing, as they are expected to naturally produce observable variability features. However, despite their theoretical significance, time-dependent studies exploring the stability and evolution of such shocked solutions remain relatively scarce. To address this gap, we perform simulations of transonic accretion flows around a black hole in an ideal magnetohydrodynamic framework. Our simulations are initialized using boundary conditions derived from semi-analytical hydrodynamical models, allowing us to explore the stability of these flows under varying magnetic field strengths. Our results indicate that mildly magnetized flows in a uniform vertical magnetic field alter the accretion dynamics through magnetic pressure, with the resulting force imbalance driving oscillations in the shock front. Variations in the emitted luminosity arising from shock oscillations appear as quasi-periodic oscillations (QPOs), a characteristic feature commonly observed in accreting black holes. We find that the QPO frequency is determined by the radial position of the shock front: oscillations occurring closer to the black hole produce frequencies of tens of hertz, whereas shocks located farther out yield sub-hertz frequencies. Full article

We report six radio observations of four microquasars—SS 433, GRS 1915+105, Cyg X-3 and MAXI J1820+070—conducted between 2022 and 2025 with the Five-hundred-meter Aperture Spherical radio Telescope (FAST) using its pulsar backend, achieving a time resolution of 98.304 $\mathsf{\mu }$s across an effective feed range of 1.04–1.45 GHz. A major focus of this work is the development of a standardized calibration pipeline for microquasar observations, including RFI mitigation, flux density, and polarization calibration, as well as multi-beam correlation inspections. Using On–Off mode and cross-beam verification, radio activity was detected in SS 433, GRS 1915+105 and Cyg X-3, while MAXI J1820+070 remained inactive. Both SS 433 and GRS 1915+105 show low linear polarization degrees of only a few percent. No credible quasi-periodic oscillations (QPOs) were detected in the 0.01–100 Hz range, suggesting that radio QPOs within this frequency range are relatively rare compared to those observed in the X-ray band. We therefore highlight the importance of future monitoring with high–time-resolution and high–sensitivity radio telescopes such as FAST, which will be crucial for revealing the correlation between jet and accretion processes and for uncovering the physical origin of QPOs. Full article

Ground vortex formation beneath aeroengine intakes during near-ground operations represents an energy-related aerodynamic issue, as it degrades inlet flow quality, induces pressure distortion, and reduces the effective utilization of incoming kinetic energy. This study investigates the unsteady characteristics of ground vortex flow under headwind conditions and its influence on foreign object ingestion (FOI) in an aeroengine intake. Three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) simulations coupled with a Lagrangian Discrete Phase Model (DPM) are employed to resolve the interaction between intake-induced vortices and dispersed particles near the ground. The results indicate that the ground vortex rapidly develops into a quasi-periodic state, generating significant unsteady total pressure distortion at the intake face, with peak fluctuations reaching approximately 10% of the mean value. This flow non-uniformity reflects a deterioration of inlet energy distribution and is detrimental to downstream compression efficiency. Particle ingestion behavior is strongly dependent on particle density and diameter. Low-density and small particles are more readily entrained into the vortex core and ingested, whereas particles with higher density or larger size exhibit increased inertia and reduced sensitivity to vortex-induced energy transport. The ingestion region is biased toward the lower portion of the intake, consistent with the vortex core location. These findings provide insight into vortex-induced energy distortion and FOI mechanisms, offering guidance for improving aeroengine intake design and energy-efficient operation during near-ground conditions. Full article

We investigate the combined effects of spatial curvature and topology on the properties of the vacuum state for a charged scalar field localized on the (2 + 1)-dimensional Beltrami pseudosphere, assuming that the field obeys the quasiperiodicity condition with constant phase. As important local characteristics of the vacuum state, the vacuum expectation values (VEVs) of the field squared and energy–momentum tensor are evaluated. The contributions in the VEVs coming from geometry with an uncompactified azimuthal coordinate are divergent, whereas the compact counterparts are finite and are analyzed both numerically and asymptotically. For small values of the proper radius of the compactified dimension, the leading terms of topological contributions are independent of the field mass and curvature coupling parameter, increasing by a power law. In the opposite limit, the VEVs decay following a power law in the general case. In the special case of a conformally coupled massless field, the behavior is different. Unlike the VEV of field squared and vacuum energy density, the radial and azimuthal stresses are increasing by absolute value. As a consequence, the effects of nontrivial topology are strong for the stresses, in this case, at small values of the radial coordinate. Full article

This paper presents a detailed investigation of the deterministic and stochastic dynamics of a noise-driven forced nonlinear oscillator in a periodically driven framework. An overlap-mapping approach is used to compare multiple traveling-wave solutions and verify the structural consistency among distinct solution families. The qualitative behavior of the system is further characterized through geometric and stability-based analysis, supported by two- and three-dimensional phase portraits, time-series responses, and reconstructed three-dimensional attractors to examine periodic and chaotic regimes under varying parameters and initial conditions. The sensitivity to parameter perturbations is quantified and the distribution of final states is analyzed to identify chaotic regions in the phase space. The high-dimensional chaotic nature of the dynamics is rigorously confirmed through Lyapunov exponent estimation, Poincaré sections, and return-map analysis, collectively demonstrating strong sensitivity to initial conditions and systematic transitions induced by parameter variations. These results provide a comprehensive dynamical description of the nonlinear oscillator and contribute to a deeper understanding of noise-influenced nonlinear driven systems. Full article

In classical spectral theory, self-adjoint differential operators satisfy the relation $\sigma \left(L\right)=\sigma \left(L^{\ast }\right)$. However, this is not necessarily true for non-self-adjoint operators. In this study, we show that a similar spectral equality holds for non-self-adjoint with periodic PT-symmetric complex valued potential. These operators are often described in the literature as having self-adjoint-like spectral characteristics; however, here, we show that the reality of the spectrum depends on the isospectral relationship between the operator and its adjoint. Moreover, we prove that the adjoint operator $L^{\ast }$ inherits PT-symmetry and analyze its spectral properties under quasi-periodic boundary conditions, extending prior studies from the original operator to its adjoint. Full article

The problem of the dynamic quantization stabilization of the networked switched systems affected by denial-of-service (DoS) attacks is investigated. Firstly, a quasi-periodic logarithmic quantization strategy is proposed, which ensures the quantization accuracy of the quantizer under the premise of limited quantization levels. Secondly, the adjustment time and the update period of the quantizer are designed to avoid the saturation of the quantizer under DoS attacks. Subsequently, a quantized feedback controller is designed for the switched system under the influence of DoS attacks, and the sufficient conditions are obtained to ensure the global asymptotic stability of the closed-loop system. Finally, the effectiveness of the theoretical analysis is verified through a dual-tank system. Full article