Finite Time Research Articles

Dynamics of dissipative gravitational collapse in the Morris–Thorne wormhole metric: One scenario - several outcomes

We consider the dynamical Morris–Thorne metric with radiating heat flow. By matching the interior Morris–Thorne metric with an exterior Vaidya metric we trace out the collapse solutions for the corresponding spherically symmetric inhomogeneous distribution of matter. The solutions obtained are broadly of four different types, giving different end state dynamics. Corresponding to three of the solutions we elaborate the collapsing dynamics of the Morris–Thorne type evolving wormhole. We show that for all those cases where collapse upto zero proper volume is obtained in finite time, the ensuing singularity is always a black hole type. However our solutions can also show other end states, like oscillating wormhole-black hole pair or infinite time contracting universe or a conformal past matter dominated universe. In all the cases we have worked out the background dynamics and physics of the solution. All our solutions are illustrated with appropriate graphical descriptions.

A triple plasmon-induced transparency terahertz sensor based on graphene metamaterials

A metamaterial-based terahertz sensor design is presented in this paper. The metamaterial unit structure comprises a graphene cross and three sets of graphene strips, which collectively achieve a triple plasmon-induced transparency (PIT) in both polarization directions. The theoretical results based on the Lorentz resonance theoretical model are in good agreement with finite difference time domain (FDTD) simulations. The sensor is polarization-independent and changes in the angle of incidence between 0° and 10° have a negligible impact on the sensing performance. Furthermore, the sensor exhibits a notable slow-light effect, with a maximum sensitivity of 1.65 THz/RIU and a FOM value of 4.74/RIU for the triple PIT, which is superior to that of comparable devices.

Electromagnetic absorption properties of composite mortar with graphene and manganese-zinc ferrite

Electromagnetic wave absorption of building structures plays a crucial role in safeguarding information and mitigating electromagnetic radiation. This study delves into the absorption capabilities of composite mortar made with graphene (GR) and manganese-zinc ferrite (MFO) across frequencies of 1−18 GHz. The mechanical strength, microstructural examinations, and numerical simulations to elucidate the underlying mechanisms of wave absorption in the composite mortar are investigated. The results indicate that incorporating 30% MFO reduces the strength of mortar due to its low bonding capacity and diluting effects, whereas GR enhances the strength of mortar by facilitating cement hydration. Electromagnetic examinations reveal that MFO boosts the magnetic loss performance, while GR augments dielectric loss properties. In addition, the presence of needle, rod, mesh, and flake hydration products in the pores of composite mortar also contributes to increased wave depletion. According to the simulation of electromagnetic absorption based on the finite difference time domain (FDTD) method, the composite mortar with GR and MFO exhibits a superior performance of electromagnetic wave absorption. With the 25 mm thickness of composite mortar with 30% MFO, an absorption below -10 dB, covering a bandwidth of 1.68−4.34 GHz are obtained, with a peak reflection loss of -22.13 dB at 3.23 GHz. Thus, by combination magnetic loss of MFO, dielectric loss of GR, and the reflective capabilities of porous mortar, a composite mortar with a better electromagnetic wave absorption can be achieved.

Dynamical maps for accelerating detectors

We study the open quantum dynamics using the language of dynamical maps of a two-level particle detector that starts accelerating through Minkowski vacuum weakly coupled to a massless scalar field. We consider a detector with non-zero size and study its time evolution for the case where it is initially in inertial motion and subsequently a constant acceleration is switched on for a finite time. We study the dynamical maps that describe the evolution of such a system and show that the dynamics is not completely positive (NCP). The inertial motion prior to the acceleration can entangle the detector and field leading to the NCP dynamics. We examine the nature of the open dynamics during the accelerated phase as a function of the duration of prior inertial motion and the magnitude of the acceleration.

Colorimetric Fabry-Pérot Sensor with Hetero-Structured Dielectric for Humidity Monitoring.

A full-color colorimetric humidity sensor with high brightness is proposed by using a hetero-structured dielectric film in a metal-insulator-metal (MIM) resonator. A humidity-responsive polymer is designed to graft on top of a metal-organic frameworks (MOFs) thin film (MOFs-Polymer) as insulator layer in the resonator. Programmable tuning of reflected color is achieved by controlling the polymer thicknesses, and finite difference time domain simulation of light-matter interactions at subwavelength scales proves the dependence of the reflected wavelength on dielectric layer thickness of the resonator. Vivid full-color changing is realized during tracking humidity process due to swelling of the stimuli-responsive polymer. Ultrafast response (≈0.75 s) is achieved for tracking trace H2O from H2O/methanol mixture, which is ≈104 faster than that of the pure polymer-based MIM resonator. Meanwhile, the study observes significant spectral redshift because the porous MOFs film facilitates the preconcentration of external stimulus and improves the detection sensitivity of the resonator. Further, double-channel anti-counterfeiting multiplexing imaging is devised on the MIM resonator by photomask technology. Patterned encoding for security label is achieved on the MIM resonator by engineering humidity-tunable pixels of Au/MOFs-Polymer/Au and humidity-invalid pixels of Au/MOFs/Au.

Observer based finite-time adaptive fractional-order sliding mode control of DFIG wind turbines with unknown dynamic parameters

In this study, we investigate adaptive finite-time fractional-order sliding mode control (AFFSMC) of DFIG wind turbines (DWTs) under model uncertainty in finite time. A fractional-order sliding surface is first constructed to develop the concept. A robust terminal adaptive sliding mode controller is then designed for pitch angle control of wind turbine to achieve finite-time stability at high wind speeds to regulate the produced electric power in Zone III of the turbine’s working range. This is all with this assumption that there is no any information about the dynamics of the turbine due to the significant uncertainties. Through the use of a stable adaptive law, the vector of the wind turbine’s unknown dynamic parameters is approximated in this method. An observer is also proposed to estimate both turbine speed and external disturbances term. The closed-loop system’s finite-time stability study and the finite-time convergence of the turbine output were both carried out using the dynamic model of the system and the proposed Lyapunov theory. Some numerical examples are also presented together with a comparison to the standard integer sliding mode control to demonstrate the correctness of the control law.

Fractional‐order fast terminal sliding mode trajectory tracking control of quadrotor UAV based on finite time disturbance observer

AbstractIn this paper, a novel trajectory tracking control problem of the quadrotor UAV is addressed, which considers the system uncertainties and unknown external disturbances meanwhile. To ensure a rapid convergence rate of the states, fast terminal sliding mode control (FTSMC) algorithm is improved combining with a fractional order method. In addition, finite‐time observer is designed to handle disturbances and enhance the robustness of the system. The closed‐loop finite‐time stability of the quadrotor UAV system is established using Lyapunov theory in accordance with the novel control law. To evaluate the effectiveness of our proposed strategy, various simulations under different scenarios are conducted respectively. These simulation results clearly demonstrate the superiority of our control scheme, which we refer to as fractional‐order fast terminal sliding mode control (FOFTSMC).

Blow‐up of smooth solutions to the relaxed compressible Navier‐Stokes equations

In this paper, the full compressible Navier‐Stokes equations with Cattaneo's heat transfer law or revised Maxwell's law are considered. We present a loss of initial smoothness of smooth solutions within a finite time and give an upper bound of such time. It is not required that the initial data has compact support or contains vacuum in any finite regions. Moreover, the blow‐up result has no restriction about the specific heat ratio. The main approach is motivated by previous studies and constructing a differential inequality.

Relay Switching–Based Event‐Triggered Finite‐Time Tracking Control for Nonholonomic Systems: Theory and Experiment

ABSTRACTThis paper investigates the event‐triggered finite‐time trajectory tracking controller based on a type of chained‐form nonholonomic systems under unknown disturbances by utilizing relay switching technology. A key design idea is that the entire control design is grouped into two separated control stages to produce different finite‐time tracking controllers with correspondingly event‐triggered control rules. By using some nonlinear design methods, a relay switching–based event‐triggered finite‐time tracking control method is adopted to assure that the resulting closed‐loop tracking error system converges to an arbitrarily small neighborhood around zero within a finite time. All closed‐loop error system states keep bounded throughout the entire process. Simulation and experiment results demonstrate the rationality of the designed tracking control strategy.

Cloud droplet size distributions governed by condensation, collision–coalescence, and sedimentation. Part 2: Analytical expressions for size distribution shape and asymptotic behavior for large-droplet tails

Abstract Droplet growth via condensation and collision-coalescence has been investigated in the limit of very weak coalescence growth: a collector-mode approximation emerges for coalescence growth that consists solely of droplets in the tail collecting droplets near the main mode of the cloud droplet size distribution, and that does not deplete the mode. In this second part, the approximation is formalized, leading to a simplified form of the collision-coalescence term in the equation governing the evolution of the droplet size distribution. This form allows for analytical solutions for transient growth and for steady-state distributions representing a balance between condensation, collision-coalescence growth, and removal by sedimentation. The solutions lead to an expression for the drizzle growth time, formally, the finite time in which a droplet approaches infinite size. The drizzle growth time is related to a transition radius at which droplet growth switches from condensation-dominated to coalescence-dominated. The solutions also provide a dimensionless group that governs the steady-state distribution shape, which is referred to as the drizzle number. The solutions are checked by comparing to a Monte Carlo model developed in Part 1, and it is found that the analytical solution is excellent when the drizzle number is much greater than unity, which is the typical situation for the microphysical conditions achievable in a convection-cloud chamber. The steady-state size distribution has the form of a modified gamma distribution, with a transition to power-law tail at sufficiently large radius. The solutions are formally valid for a convection-cloud chamber, but can also be extended to shallow, mixed-layer clouds such as mixing fogs.

Asynchronous Sliding Mode Control of Networked Markov Jump Systems via an Asynchronous Observer Approach Based on a Dynamic Event Trigger

This paper explores the utilization of sliding mode control, which relies on an asynchronous observer, for Markov jump systems subject to external disturbances. Firstly, given that the system’s mode is not directly measurable and could potentially differ from the observer’s and controller’s mode, the paper constructs an asynchronous observer employing a hidden Markov model. Secondly, a sliding surface is designed to correspond with the asynchronous observer. Moreover, a multi-parameter event-triggered mechanism is incorporated into the observer design to alleviate bandwidth strain. Thirdly, by applying the integrated sliding mode control law, we ensure that the system state trajectories will reach the sliding surface within a finite time. Fourthly, the achievement of H∞ stability is realized by making use of the Lyapunov function. Lastly, a practical-oriented example is presented to illustrate the efficiency of the established method.

Optimized trajectory tracking control with disturbance resistance for wheeled mobile robot

When unavoidable disturbances exist in practical applications, the unicycle wheeled mobile robot (WMR) with non-holonomic constraint is challenging to be accurately controlled in finite time. An optimized dual closed-loop strategy is proposed in this paper to solve the trajectory tracking control problem of the unicycle WMR. The control strategy with fast time convergence and anti-disturbance properties consists of kinematic and dynamics controllers and an optimization algorithm. The kinematic controller is designed with an improved backstepping method to eliminate the non-holonomic constraints. The robust sliding mode control (SMC) method with fixed-time convergence is used to construct the dynamics controller. The optimization algorithm enhances the performance of the strategy and achieves accurate control. The global convergence and robustness of the strategy are theoretically demonstrated. The effectiveness of the strategy is verified by comparison in simulations.

On the blow-up for a Kuramoto–Velarde type equation

It is known that the Kuramoto-Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters γ1 and γ2 involved in the non-linear terms verify γ2=γ12 or γ2=0. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto-Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework γ2≠γ12 and γ2≠0, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. As a complement to it, we address an alternative result on the finite-time blow-up of smooth solutions by considering a virial-type estimate.

Design of sliding mode controller for servo feed system based on generalized extended state observer with reinforcement learning

Nonlinear friction, system uncertainty, and external disturbances have a significant impact on the performance of high-precision servo feed systems. In order to achieve higher tracking accuracy, a sliding mode controller based on a generalized extended state observer with the double critic deep deterministic policy gradient algorithm is designed. Firstly, a flexible two mass drive model (FTMDM) is established for the two-axis differential micro-feed system (TDMS). Next, a generalized extended state observer (GESO) is designed to estimate matched interference and mismatched interference. And it is proved that the observation error of GESO is bounded. A sliding mode controller based on GESO is further proposed. The stability of the controller has been proven through Lyapunov theory, and the error is bounded and converges to zero in finite time. The tuning process of controller parameters is simplified by using quadratic optimal control principle. Furthermore, a double critic deep deterministic policy gradient algorithm (DCDDPG) is proposed to achieve dynamic optimization of parameters about GESO. The simulation results show that GESO with DCDDPG can reduce the observation error of step signal and sinusoidal signal, and improve the observation accuracy of nonlinear friction significantly. Finally, experimental results show that the proposed control method achieves more accurate position tracking performance on TDMS.

On a drift‐diffusion model for perovskite solar cells

AbstractWe introduce a vacancy‐assisted charge transport model for perovskite solar cells. This instationary drift‐diffusion system describes the motion of electrons, holes, and ionic vacancies and takes into account Fermi–Dirac statistics for electrons and holes and the Fermi–Dirac integral of order for the mobile ionic vacancies in the perovskite. The free energy functional we work with corresponds to that choice of the statistical relations. To verify the existence of weak solutions, we consider a problem with regularized state equations and reaction terms on any arbitrarily chosen finite time interval. We motivate its solvability by time discretization and passage to the time‐continuous limit. A priori estimates for the chemical potentials that are independent of the regularization level ensure the existence of solutions to the original problem. These types of estimates rely on Moser iteration techniques and can also be obtained for solutions to the original problem.

Distributed finite-time sliding mode containment control for multi-unmanned surface vehicles with input and output quantization

To solve the containment control problem of multi-unmanned surface vehicles (USVs) with input and output quantization communication, we propose a distributed containment method using sliding mode control (SMC) technology. First, with only the quantized value of position information being available, a super-twisting algorithm (STA)-based observer is used to recover the unmeasured velocities of the follower USVs in a finite time. Second, based on the STA-based observer, a distributed SMC strategy is developed to guide the follower USVs closely into the convex hull formed by the leader USVs under quantized communication. Furthermore, the stability analysis is given to guarantee that sliding variables and containment position errors can converge to specified ranges related to the quantization parameters and the parameters of the STA-based observer. Finally, simulation results demonstrate the feasibility of the designed SMC approach.

New delay‐dependent finite‐time stabilization of Takagi–Sugeno fuzzy approaches for delayed nonlinear systems

AbstractIn this paper, the finite‐time stability and stabilization of nonlinear systems with delays is studied, via a Takagi–Sugeno approach. By using a novel Lyapunov–Krasovskii functional and introducing some fuzzy free‐weighting matrices, sufficient conditions are derived, for bounded and differentiable time‐varying delays in terms of an upper bound of the delay derivatives. Then, we achieve closed‐loop stabilization in finite time through an efficient parallel distributed compensation design. The sufficient conditions are formulated as linear matrix inequalities to achieve the desired performance. Finally, the proposed methodology is applied to various case studies, highlighting its significance.

Integrated substrate and adsorbent layer additive manufacturing for asymmetrically operating minichannel adsorbent bed

Adsorption heat pumps (AHP) have conventionally used packed bed design, making their operation sluggish leading to difficulty in using heat for the adsorbent regeneration. While thin adsorbent coatings improve the performance of AHPs when implemented in microscale geometries like minichannels, integrating the adsorbent coating procedure into the scaled-up adsorbent bed manufacturing has been impractical because of the finite time required for the coating process. Meanwhile, separately coated plates manifest sealing issues. This research details an innovative avenue to fabricate a unified adsorbent bed integrated with thin adsorbent coatings. Here, a compact adsorbent bed was fabricated through the integration of additive manufacturing using a fused deposition modeling (FDM) 3D printer for the substrate and resin curing for the MIL-101 (Cr) adsorbent layer. The multi-layered bed was designed to exchange heat between heat transfer fluid (HTF) and the passages through which the refrigerant vapor flows. The vapor channels were coated with a MIL-101 (Cr) adsorbent. The research incorporated both experiments and computational models to evaluate the operation of this adsorbent bed through the measurement of pressure during the adsorption and desorption stages for this component. Various HTF temperatures (80 °C − 90 °C) and flow rates (0.125 kg min−1 – 0.25 kg min -1) were tested. The findings revealed the much-desired asymmetrical operation with long adsorption (75–80 % of the cycle time) and short desorption stages (20 %-25 % of the cycle time), opening the possibility of employing a single bed in adsorption cooling systems to produce a near continuous cooling effect leading to more compact AHPs. The computational model developed for this test setup using MATLAB strongly aligned with experimental findings, with an error margin of 4–12 %.

Generalized hydrodynamics and approach to generalized Gibbs equilibrium for a classical harmonic chain

Abstract We study the evolution of a classical harmonic chain with nearest-neighbor interactions starting from domain wall initial conditions. The initial state is taken to be either a product of two Gibbs ensembles (GEs) with unequal temperatures on the two halves of the chain or a product of two generalized Gibbs ensembles (GGEs) with different parameters in the two halves. For this system, we construct the Wigner function and demonstrate that its evolution defines the generalized hydrodynamics (GHD) describing the evolution of the conserved quantities. We solve the GHD for both finite and infinite chains and compute the evolution of conserved densities and currents. For a finite chain with fixed boundaries, we show that these quantities relax as ∼ 1 / t to their respective steady-state values given by the final expected GE or GGE state, depending on the initial conditions. Exact expressions for the Lagrange multipliers of the final expected GGE state are obtained in terms of the steady-state densities. In the case of an infinite chain, we find that the conserved densities and currents at any finite time exhibit ballistic scaling while, at infinite time, any finite segment of the system can be described by a current-carrying non-equilibrium steady state (NESS). We compute the scaling functions analytically and show that the relaxation to the NESS occurs as ∼ 1 / t for the densities and as ∼ 1 / t 2 for the currents. We compare the analytical results from hydrodynamics with those from exact microscopic numerics and find excellent agreement.

Landing Guidance Control Combining Powered Descending with Nonlinear Optimization and Vertical Descending with Model Prediction

In this study, we propose a landing guidance control method for the Moon using two control methods. The landing of a spacecraft on the Moon is divided into two phases: the powered descending phase and the vertical descending phase. The powered descending phase aims to optimize the entire trajectory to satisfy the termination constraint, instead of allowing for a relatively long control period. This phase performs feedback control using trajectory updates via nonlinear optimization. The vertical-descending phase aims to achieve accurate control over a short control period. This phase applies nonlinear model predictive control for fast optimization on finite time intervals. First, the landing of a spacecraft on the Moon is modeled as a two-body problem of the Moon and spacecraft, and equations of motion are derived. Subsequently, we formulated an optimization problem for each phase and developed the proposed landing guidance method by combining the two control methods. Furthermore, numerical simulations based on the derived equations of motion were performed to confirm the effectiveness of the proposed method and to compare its performance with another optimization method, the successive convexification (SCvx) algorithm.