In this paper, we consider the Riemann problem of the Aw-Rascle traffic model with a damping term and the formation of delta shock waves in the limit of the Riemann solutions as gamma -> 1. By introducing a new variable and employing generalized characteristic analysis methods, we construct solutions to the Riemann problem of the inhomogeneous Aw-Rascle traffic model. Specially, for the case 0 < u(-) < u(+), we prove the existence of a critical value gamma(0) for gamma such that when 0 < gamma < gamma(0), the Riemann solutions contain no vacuum states; otherwise, a vacuum state emerges. Furthermore, we demonstrate that as gamma -> 1, the limit of the Riemann solutions with vacuum states aligns with the Riemann solutions to the inhomogeneous transport model under the same initial conditions, while the limit of solutions with shock waves converges to a curved delta shock solution. Notably, the weights supported on the delta shock solution differ from the Riemann solutions to the inhomogeneous transport model due to the influence of the damping term.

ABSTRACT Triboelectric nanogenerators (TENGs) offer a promising route for harvesting high‐entropy mechanical energy for self‐powered electronics, but their practical use is limited by highly variable electrical output and the mismatch between intermittent harvested power and the requirements of electronic loads. Here, we report an adaptive three‐stage power management circuit (ATS‐PMC) that integrates a rectification stage, an adaptive peak‐triggered energy extraction stage, and a dual‐mode output regulation stage. A self‐triggered switching unit autonomously tracks the voltage peak of the TENG output over a wide range of 30–300 V, thereby enabling efficient energy transfer with an energy conversion efficiency of 84%. The output control circuit adaptively switches between hysteresis mode and voltage‐regulated mode according to the balance between harvested power and load demand. Under insufficient input power, the hysteresis mode enables intermittent self‐triggered operation while suppressing static loss. Under sufficient input power, the regulation mode provides a stable DC output through closed‐loop feedback, with an ultralow ripple of 0.22%. The system further powers representative commercial IoT devices under random low‐frequency excitations of 0.2–5 Hz. This work provides a practical adaptive power management strategy for converting unstable triboelectric output into load‐compatible electrical power, thereby advancing the application of TENGs in self‐powered systems.

In this paper, we study the dissipative property of the first order 3x3 hyperbolic system with constant coefficients. For the corresponding n x n system, when the coefficients matrices are symmetric, it has been studied in [16] and the well-know Kawashima-Shizuta condition is obtained. When n = 3 and for asymmetric system, we give a sufficient condition for the system to be strictly dissipative.

We consider a Keller-Segel-Navier-Stokes system in a three-dimensional (3D) bounded domain and prove a logarithmic blow-up criterion of the local strong solutions. The Lp method, L infinity-method and the maximal regularity estimates of the parabolic equation are used.

In this paper, we delve into the following fractional Kirchhoff equation: a+b integral(3)(R)|(-Delta)s/2u|dx)(-Delta)(s)u+V(x)u+lambda u=|u|(q-2)u+K(x)|u|(p-2)u, x is an element of R-3 with prescribed mass integral (3)(R)|u|(2) dx=c(2), where s is an element of ( 3 /4 , 1), a, b, c > 0, p is an element of [1, 2), lambda is an element of R, V ( x ) equivalent to/ 0, K ( x ) equivalent to/ 0. This paper focuses on two cases. Firstly, under specific assumptions where the potentials satisfy V ( x )>= 0 and K ( x ) <= 0, we employ the linking geometry method to rigorously prove the existence of at least one L (2)-normalized solution ( u, lambda ) is an element of H (s) ( R (3) ) x R (+) to the equation. Secondly, shifting our focus to scenarios where the potentials adhere to V ( x ) <= 0 and K ( x ) >= 0, we demonstrate the existence of a mountain pass L 2- normalized solution with positive energy. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Triboelectric nanogenerators (TENGs) provide interpretable electrical signals to characterize mechanical motion processes during energy conversion, making them suitable sensors for applications in human-machine interaction, human motion characterization, and health monitoring. Nevertheless, the accurate characterization of the mechanical-electrical conversion process and improvement of sensor reliability necessitates the establishment of highly precise quantitative relationships between electrical signals and movement of TENGs. In this study, we propose a method for the accurate analysis of the continuous movement state of TENG, which allows for the successful reflection the mechanical-electrical conversion process of three types of TENG based on a unique charge detection circuit. The charge detection circuit, constructed from low-cost electronic components, is able to convert the weak charge signal from the TENG into a modest voltage signal, allowing seamless integration into a conventional electronic system. Subsequently, based on the method, we demonstrate the detection of charge output at the millimeter scale of TENG movement as well as the control of a manipulator by the electrical charge output generated by the finger. In addition, a portable multi-channel signal acquisition system was designed to enable the characterization of diversified gestures. This work not only provides an inexpensive and reliable solution for TENG-based sensing applications in the extraction of movement information but also promotes the engineering applications of triboelectric sensors to some extent.

The adoption of energy harvesting technology enables wireless sensor nodes to be self-powered, thereby significantly enhancing the deployment flexibility of wireless sensor networks (WSNs). While WSNs utilizing triboelectric nanogenerators (TENGs) are recognized for their immense potential, further development is required to ensure their suitability in real-world applications. In this study, we construct a wireless passive intelligent sensing system based on a highly stable TENG and an LC oscillator circuit, where the sensing information is modulated onto the transmitted signal frequency via fixed or variable capacitive modulation. The sensing system consists of three main components: self-powered signal transmitters, a receiving system integrating a single receiver with a signal processing module, and strong electrical applications. This configuration achieves three-layer physical isolation within the power system, thereby enhancing electrical safety. A self-charge-pumping TENG combined with a gas discharge tube switch is deployed to construct the self-powered signal transmitter, aiming to improve the system's output stability. Signals sent by different transmitters with varying frequencies are received and processed by the receiving system, allowing distinct switching operations and enabling centralized control over multiple electrical devices via a single receiving end. This sensing system holds significant potential for widespread applications in smart homes and the Internet of Things within modern commercial and industrial contexts.

In this paper, we consider the following fractional Choquard equation: (-Delta)(s)u+V(x)u+lambda u=(I-alpha*|u|(2)(alpha,s)*)|u|(2)(alpha,s)*-2u + mu|u|(q-2)u, x is an element of R-N, with prescribed mass integral(N)(R) |u|(2) dx = a(2), where s is an element of(0,1), mu >0, N/2 > s, 0 < alpha < min{N,4s}, I-alpha is the Riesz potential, V is an external potential vanishing at infinity and the parameter lambda is an element of R arises as Lagrange multiplier. The purpose of this paper is to establish the existence of solutions with prescribed norm to this class of nonlinear equations. Under some L-2 -subcritical, L-2 -critical and L-2 -supercritical perturbation mu|u|(q-2)u, respectively, we obtain several existence results. By limiting the range of mu, for q is an element of(q,2(s)*], we prove that there exists a positive ground state normalized solution for the above problem with a>0. Furthermore, for q is an element of(2,q), we prove that there exists a(0) > 0 such that the normalized solution with negative energy to the above problem can be obtained when a is an element of (0,a(0)).

In this paper, we delve into the following nonlinear fractional Kirchhoff-type problem (a+b||(−Δ)s2u||22)(−Δ)su+λu=g(u)+|u|2s*−2u in R3 with prescribed mass ∫R3|u|2dx=ρ>0, where s∈(34,1),λ∈R,2s*=63−2s. Under some general growth assumptions imposed on g, we employ minimization of the energy functional on the linear combination of Nehari and Pohoz˘aev constraints intersected with the closed ball in the L2(R3) of radius ρ to prove the existence of normalized ground state solutions to the equation. Moreover, we provide a detailed description for the asymptotic behavior of the ground state energy map.

Triboelectric nanogenerators (TENGs) based on lead-free piezoelectric materials have recently garnered significant attention for harvesting environment energy. However, conventional TENGs rely on interface effects to generate a limited surface charge density, which severely restricts their electrical performance. This study focuses on the (Ba0.838Ca0.162)(Ti0.9072Zr0.092)O3 (BCZTO) piezoelectric materials embedded in polydimethylsiloxane (PDMS) and employs a dielectrophoretic strategy to further enhance the surface charge potential of the triboelectric layer. By leveraging the piezoelectric and triboelectric coupling effects, the more effective stress transfer of ordered BCZTO demonstrates significantly improved charge transfer ability in the triboelectric layer. The piezoelectric charge coefficient (d33) of the ordered composite film is significantly higher than that of the traditional disordered BCZTO composite film, reaching 79 pC/N. Kelvin probe force microscopy results reveal that the embedded ordered BCZTO particles significantly and further enhance the surface charge potential of the PDMS matrix. The surface contact voltage of the ordered BCZTO composite film reaches -520 V, compared to -260 V and -18 V for the disordered BCZTO composite film and pure PDMS, as measured by the Trek-347. A surface charge density of 225 mu C/m2 is achieved, representing about 50 % enhancement over the 150 mu C/m2 observed for dispersed BCZTO composite films. The TENG exhibits excellent electrical output performance, reaching 2.1 W/m2, which is 75 % higher than that of dispersed BCZTO. This work demonstrates the potential of the developed power generator for high electric output in self-powered electronics and sensors.

In this paper, aim to synchronize uncertain fractional order chaotic systems with disturbances, a command filter adaptive fuzzy backstepping control method is proposed. A fractional order command filter is designed to solve the explosion of complexity problem in the backstepping framework. In particular, an error compensation signal is devised to reduce the filter error and improve the synchronization accuracy. Meanwhile, in the design of backstepping scheme, fuzzy logic systems are utilized to estimate unknown functions. Based on the Lyapunov stability criterion, the synchronization error can be ensured to ultimately converge to a small neighborhood near zero. Finally, a numerical simulation is given to verify the effectiveness and accuracy of the proposed scheme.

In this paper, the cooperative control of fractional-order multi-agent systems with time delay and unknown control direction is studied by combining frequency distributed model and event-triggered mechanism. The Nussbaum function is employed to address the unmeasured control direction. Then, through the event-triggered mechanism, a corresponding controller is designed, which can guarantee that all signals are bounded while saving resources. The proposed theme is convenient for analyzing the stability of fractional-order systems based on a transformation of frequency distributed model. In particular, in order to enhance the universality of the proposed scheme in the fractional-order system stability analysis, a generalized fractional-order generalized lemma with respect to the Nussbaum function is given. Finally, the availability of the proposed method is confirmed by a simulation example.

In this paper, a class of fractional Sturm–Liouville advection–dispersion equations with instantaneous and noninstantaneous impulses is considered, in particular, the nonlinearities discussed here include Caputo fractional derivatives. Since the nonlinear terms contain fractional derivatives, this problem does not directly have variational structure, we need to combine critical point theory and an iterative method to deal with such problems. Finally, the existence of at least one nontrivial solution is proved by the mountain pass theorem and the iterative method. At the same time, an example is given to illustrate the main result.

The combined vibrations of a top tensioned riser (TTR) excited by the waves and currents are investigated in this paper. The time-varying tension with two frequency components is considered and the time-varying characteristics of the currents are represented by the van der Pol oscillators. The effects of amplitude ratio of the fluctuating tension, the shedding frequency of the vortices and other parameters on the responses are investigated by the numerical method. The results show that some complicated responses can occur under the combined resonance.

In this paper, the effect of time delay is investigated on the system dynamics of a glucose-insulin model incorporating obesity. Treating the time delay as a bifurcation parameter, the stability switching on the positive equilibrium with global bifurcation is obtained. With the method of normal forms and central manifold theory, the direction and stability of limit cycles arising from Hopf bifurcation are analyzed. Using the method of multiple time scales, the normal form associated with non-resonant double Hopf bifurcation is derived. Moreover, the bifurcations are classified in the two-dimensional parameter plane near the critical point, and numerical simulations are presented to demonstrate the applicability of the theoretical results. Our results indicate that time delay in the glucose-insulin model can not only induce Hopf bifurcation and double Hopf bifurcation but also generate multiple stable periodic solutions. These results may help to understand the dynamical mechanism of glucose-insulin metabolic regulation systems, and to design control strategies for regulating and mitigating the occurrence of related diseases.

In this paper, a class of fractional advection-dispersion equations with instantaneous and non-instantaneous impulses and nonlinear SturmLiouville boundary conditions is considered. Firstly, based on the problem, we define an appropriate function space and construct corresponding variational structures. Then, under weaker conditions than the Ambrosetti-Rabinowitz condition, the existence and multiplicity of solutions to the equation are proven through the Mountain Pass Lemma and genus properties. Finally, an example is provided to illustrate the results obtained in this paper.

This paper considers a nonlinear impulsive fractional boundary value problem, which involves a ψ-Caputo-type fractional derivative and integral. Combining critical point theory and fractional calculus properties, such as the semigroup laws, and relationships between the fractional integration and differentiation, new multiplicity results of infinitely many solutions are established depending on some simple algebraic conditions. Finally, examples are also presented, which show that Caputo-type fractional models can be more accurate by selecting different kernels for the fractional integral and derivative.

Chaotic dynamics of the van der Pol-Duffing oscillator subjected to periodic external and para-metric excitations with delayed feedbacks are investigated both analytically and numerically in this manuscript.With the Melnikov method,the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically.The feature of the critical curves separating chaotic and non-chaotic regions on the ex-citation frequency and the time delay is investigated analytically in detail.The monotonicity of the critical value to the excitation frequency and time delay is obtained rigorously.It is presented that there may exist a special frequency for this system.With this frequency,chaos in the sense of Melnikov may not occur for any excitation amplitudes.There also exists a uncontrollable time delay with which chaos always occurs for this system.Numerical simulations are carried out to verify the chaos threshold obtained by the analytical method.

A coupling model representing the interactions between the riser and vortices is proposed, of which the time-varying top tension and the internal nonlinear axial force due to the bending of the riser are considered. In addition, the van der Pol oscillator is introduced to simulate the time-varying characteristic of the vortices. The motion equations are derived and the first-order mode approximation is obtained with the Galerkin approach. The multiple scale method is applied to study the steady-state solutions of the system. Effects of system parameters (the structural damping, nonlinearity, the amplitude ratio of the varying-tension, the shedding frequency) on the responses are investigated in detail. The synchronous and non-synchronous motions between the structure and wake oscillator are studied. The bifurcation diagrams for the responses in terms of the amplitude ratio and the nonlinear parameter are obtained in the large parameter ranges. The results show that responses with different topological properties including quasi-periodic, periodic and chaotic solutions can occur under different parameter conditions. A pair of chaotic attractors can be found for the large parameter range of the amplitude ratio. The joint effects of the amplitude ratio and the nonlinear parameter on the responses in the large parameter range are studied as well, which are further verified by the phase projections and Poincaré sections. The results show that the topological properties of responses can be controlled by the amplitude ratio. These results can be helpful to the dynamic design of the riser in practice.