Switching Surface Research Articles

Nonadiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation.

In this article, the nonadiabatic excited-state Molecular dynamics (NEXMD) package is linked with the SANDER package, provided by AMBERTOOLS. The combination of these software packages enables the simulation of photoinduced dynamics of large multichromophoric conjugated molecules involving several coupled electronic excited states embedded in an explicit solvent by using the quantum/mechanics/molecular mechanics (QM/MM) methodology. The fewest switches surface hopping algorithm, as implemented in NEXMD, is used to account for quantum transitions among the adiabatic excited-state simulations of the photoexcitation and subsequent nonadiabatic electronic transitions, and vibrational energy relaxation of a substituted polyphenylenevinylene oligomer (PPV3-NO2) in vacuum and methanol as an explicit solvent has been used as a test case. The impact of including specific solvent molecules in the QM region is also analyzed. Our NEXMD-SANDER QM/MM implementation provides a useful computational tool to simulate qualitatively solvent-dependent effects, like electron transfer, stabilization of charge-separated excited states, and the role of solvent reorganization in the molecular optical properties, observed in solution-based spectroscopic experiments.

Decoherence ensures convergence of non-adiabatic molecular dynamics with number of states.

Non-adiabatic (NA) molecular dynamics (MD) is a powerful approach for studying far-from-equilibrium quantum dynamics in photophysical and photochemical systems. Most NA-MD methods are developed and tested with few-state models, and their validity with complex systems involving many states is not well studied. By modeling intraband equilibration and interband recombination of charge carriers in MoS2, we investigate the convergence of three popular NA-MD algorithms, fewest switches surface hopping (FSSH), global flux surface hopping (GFSH), and decoherence induced surface hopping (DISH) with the number of states. Only the standard DISH algorithm converges with the number of states and produces Boltzmann equilibrium. Unitary propagation of the wave function in FSSH and GFSH violates the Boltzmann distribution, leads to internal inconsistency between time-dependent Schrödinger equation state populations and trajectory counts, and produces non-convergent results. Introducing decoherence in FSSH and GFSH by collapsing the wave function fixes these problems. The simplified version of DISH that omits projecting out the occupied state and is applicable to few-state systems also causes problems when the number of states is increased. We discuss the algorithmic application of wave function collapse and Boltzmann detailed balance and provide detailed FSSH, GFSH, and DISH flow charts. The use of convergent NA-MD methods is highly important for modeling complicated quantum processes involving multiple states. Our findings provide the basis for investigating quantum dynamics in realistic complex systems.

The fewest switches surface hopping as an optimisation problem

Several ways of defining the probabilities of quantum state transitions in nonadiabatic trajectory surface hopping simulations have been proposed and successfully applied to date. Despite their success, there is a question about the uniqueness of the ways to define such probabilities – some formulations require mathematically-motivated but still ad hoc assumptions to resolve the otherwise under-determined problem. In this work, I present a new approach (termed FSSH-3) to define the hop proposal probabilities. Unlike other approaches, it does not require any ad hoc assumptions and is based on the least squares optimisation of certain functionals combined with particular choices of initial conditions for the target variables. A comprehensive comparative study of several established surface hopping methodologies is conducted using several multiple-state model Hamiltonians. The recently reported formulation of the FSSH-2 method is extended to the case of multiple states and validated. It is demonstrated that the performance of all studied methods, including the new FSSH-3 (in two variants) is robust with respect to integration time step used but only if local diabatisation approach is used. Under such conditions, all methods yield nearly identical results, in excellent agreement with fully quantum simulations, even with sufficiently large integration time steps.

Ultrafast photochemistry and electron diffraction for cyclobutanone in the S2 state: Surface hopping with time-dependent density functional theory.

We simulate the photodynamics of gas-phase cyclobutanone excited to the S2 state using fewest switches surface hopping (FSSH) dynamics powered by time-dependent density functional theory (TDDFT). We predict a total photoproduct yield of 8%, with a C3:C2 product ratio of 0 trajectories to 8 trajectories. One primary S2 → S1 conical intersection is identified involving the compression of an α-carbon-carbon-hydrogen bond angle. Excited state lifetimes computed with respect to electronic state populations were found to be 3.96ps (S2 → S1) and 498fs (S1 → S0). We also generate time-resolved difference pair distribution functions (ΔPDFs) from our TDDFT-FSSH dynamics results in order to generate direct comparisons with ultrafast electron diffraction experiment observables. Global and target analysis of time-resolved ΔPDFs produced a distinct set of lifetimes: (i) a 0.548ps decay and (ii) a 1.69ps decay, both resembling the S2 minimum, as well as (iii) a long decay that resembles the S1 minimum geometry and the fully separated C2 products. Finally, we contextualize our results by considering the impact of the most likely sources of significant errors.

Dynamics of a stockless market through piecewise smooth models

Markets play a crucial role in the economic activity of any country, serving as fundamental drivers of growth, development, and employment. Given their significance, understanding the dynamics of markets is essential. In this study, we present a mathematical model to characterize the behavior of a stockless market. The model is formulated using a system of ordinary differential equations defined with piecewise smooth functions. We conduct a mathematical analysis of the model, particularly focusing on the behavior of trajectories as they approach switching surfaces using Filippov’s analysis. Furthermore, we provide numerical simulations to visually illustrate the model’s dynamics and a insights a brief study of bifurcations is done.

Naturally biocompatible melanin based iron-complex nanoparticles for pH-responsive magnetic resonance imaging

The sensitivity and diagnostic accuracy of magnetic resonance imaging mainly depend on the relaxation capacity of contrast agents (CAs) and their accumulated amount at the pathological region. Due to the better biocompatibility and high-spin capacity, Fe-complexes have been studied widely as an alternative to replace popular Gd-based CAs associated with potential biotoxicity. Compared with a variety of Fe complex-based CAs, such as small molecular, macrocyclic, multinuclear complexes, the form of nanoparticle exhibits outstanding longitudinal relaxation, but the clinical transformation was still limited by the inconspicuous difference of contrast between tumor and normal tissue. The enhanced effect of contrast is a positive relation as relaxation of CAs and their concentration in desired region. To specifically improve the amount of CAs accumulated in the tumor, pH-responsive polymer poly(2-ethyl-2-oxazoline) (PEOz) was modified on melanin, a ubiquitous natural pigment providing much active sites for chelating with Fe(III). The Fe(III)-Mel-PEOz we prepared could raise the tumor cell endocytosis efficiency via switching surface charge from anion to cation with the stimuli of the decreasing pH of tumor microenvironment. The change of pH has negligible effect on the r 1 of Fe(III)-Mel-PEOz, which is always maintained at around 1.0 mM−1s−1 at 0.5 T. Moreover, Fe(III)-Mel-PEOz exhibited low cytotoxicity, and satisfactory enhancement of positive contrast effect in vivo. The excellent biocompatibility and stable relaxation demonstrate the high potential of Fe(III)-Mel-PEOz in the diagnosis of tumor.

FSSH-2: Fewest Switches Surface Hopping with Robust Switching Probability.

This study introduces the FSSH-2 scheme, a redefined and numerically stable adiabatic Fewest Switches Surface Hopping (FSSH) method for mixed quantum-classical dynamics. It reformulates the standard FSSH hopping probability without using nonadiabatic coupling vectors and allows for numerical time integration with larger step sizes. The advantages of FSSH-2 are demonstrated by numerical experiments for five different model systems in one and two spatial dimensions with up to three electronic states.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

Robust Tracking Control of Wheeled Mobile Robot Based on Differential Flatness and Sliding Active Disturbance Rejection Control: Simulations and Experiments.

This paper proposes a robust tracking control method for wheeled mobile robot (WMR) against uncertainties, including wind disturbances and slipping. Through the application of the differential flatness methodology, the under-actuated WMR model is transformed into a linear canonical form, simplifying the design of a stabilizing feedback controller. To handle uncertainties from wheel slip and wind disturbances, the proposed feedback controller uses sliding mode control (SMC). However, increased uncertainties lead to chattering in the SMC approach due to higher control inputs. To mitigate this, a boundary layer around the switching surface is introduced, implementing a continuous control law to reduce chattering. Although increasing the boundary layer thickness reduces chattering, it may compromise the robustness achieved by SMC. To address this challenge, an active disturbance rejection control (ADRC) is integrated with boundary layer sliding mode control. ADRC estimates lumped uncertainties via an extended state observer and eliminates them within the feedback loop. This combined feedback control method aims to achieve practical control and robust tracking performance. Stability properties of the closed-loop system are established using the Lyapunov theory. Finally, simulations and experimental results are conducted to compare and evaluate the efficiency of the proposed robust tracking controller against other existing control methods.

Stabilization of Semi-Markovian Jumping Uncertain Complex-Valued Networks with Time-Varying Delay: A Sliding-Mode Control Approach

This paper pays close attention to the stabilization issue for delayed uncertain semi-Markovian jumping complex-valued networks via sliding mode control. The concerned corresponding transition rates depend on a positive constant, i.e., sojourn-time, which is not required to obey the general exponential distribution. Combine the generalized Dynkin’s formula with Lyapunov stability theory as well as the characteristics of cumulative distribution functions, a few sufficient criteria are proposed to ascertain the stochastic stability of the obtained sliding mode dynamical system. In addition, design a novel sliding mode controller to ensure all state trajectories of the potential closed-loop system can reach the synthesized sliding mode switching surface in a finite time and maintain there in the subsequent time. In the end of paper, one simple example is presented to verify superiority and feasibility of the provided controller design scheme.

Surface Hopping with Reliable Wave Function by Introducing Auxiliary Wave Packets to Trajectory Branching.

It is well-known that the widely utilized fewest switches surface hopping method suffers from the severe overcoherence problem, and thus adiabatic populations calculated by wave functions are generally inferior to those based on active states. More importantly, to achieve a complete description of nonadiabatic dynamics, the density matrix is essential. In this paper, we present an auxiliary branching corrected surface hopping (A-BCSH) method that introduces auxiliary wave packets (WPs) on the adiabatic potential energy surfaces for trajectory branching. Both rapid and gradual separation of WP components on different surfaces are characterized, and thus the correct decoherence time along each trajectory is captured. As demonstrated in the three standard Tully models, A-BCSH exhibits excellent internal consistency. Namely, close adiabatic populations are obtained based on both wave functions and active states. In particular, A-BCSH successfully obtains a reliable time-dependent spatial distribution of the density matrix, which relies only on electronic wave functions. Due to its high performance, our A-BCSH method provides a new and highly promising perspective on further development of more consistent surface hopping with reliable wave function.

Projective synchronization for distinct fractional-order neural networks consist of inconsistent orders via sliding mode control

The present study delves into the projective synchronization for distinct fractional-order neural networks consist of inconsistent orders, employing the principles of sliding mode control and incorporating fractional operators within the controller. Firstly, incorporating the fractional-order derivative into the controller facilitates the derivation of a synchronous error system, and a well-suited integral-type sliding switching surface is subsequently constructed, along with the development of an appropriate sliding mode controller, thereby ensuring the existence of sliding movement derived from the principle of sliding mode control. Then through the application of the Lyapunov direct method, it is shown that the sliding mode controller steers the evolution of error system towards the designated sliding switching surface and maintains therein indefinitely, meanwhile, novel criteria for achieving projective synchronization for distinct fractional-order neural networks consist of inconsistent orders is established. Lastly, to exemplify the efficacy and practical applications of the proposed approach, simulations with two types of distinct fractional-order neural networks are carried out utilizing a continuous frequency distribution model.

Satellite Attitude Control Using Faulty Double Gimbal Variable Speed Control Moment Gyroscope

A rigid satellite attitude control requires stable finite-time attitude convergence in the presence of rotation unwinding, external disturbances, and actuator faults. To achieve this, a new nonsingular fast fixed-time sliding mode controller is proposed to ensure finite-time convergence independent of the initial conditions of the system. Rotation unwinding is addressed using the body and shadow pair of the Modified Rodrigues Parameters (MRPs). Convergence behavior of the states errors in the neighborhood of the MRPs switching surface is also addressed. Attitude control is achieved using a double-gimbal variable-speed control moment gyro (DGVSCMG). For the first time, a DGVSCMG having all possible electrical and mechanical faults is considered for control design. A novel nonsingular fast fixed-time anti-unwinding fault-tolerant sliding control using a new sliding surface is proposed. This eliminates switching of the sliding surfaces and minimizes control chattering. Four new propositions are proposed and proved to establish fast fixed-time global stability of the system for tracking maneuver in fault and fault-free conditions with anti-unwinding. Simulation results are presented and compared with existing fixed-time sliding control approaches. The results show superiority of the proposed anti-unwinding fault-tolerant fast fixed-time control for the tracking maneuver in terms of convergence time, energy efficiency, and fault tolerance.

Nonadiabatic Molecular Dynamics of Water Cluster Dissociation by Vacuum Ultraviolet Absorption or Electron Impact Excitation.

After five decades of investigation since the 1970s, the nature of photon-induced or electron-induced water dissociation is still largely studied only in the gas phase, with a notable absence of dynamics studies of water clusters and bulk water. We study the problem with density functional theory and the nonadiabatic fewest switches surface hopping technique considering both singlet and triplet excited states to study the dissociation of water clusters leading mainly to OH + H. For clusters of 40 water molecules, the mean dissociation time was found to be <10 fs, and the threshold energy was ∼6 eV. Dissociation is almost exclusively associated with the cluster surface due to the lower energy of surface water excited states relative to the bulk. Recombination plays a major role in vacuum ultraviolet dissociation. O + H2 is found as a minor product in the dissociation and is mostly produced in "roaming" trajectories.

Acceleration-Based Switching Surfaces for Impulsive Trajectory Design Between Cislunar Libration Point Orbits

A method is proposed to generate an initial guess for impulsive trajectory design in the circular restricted three-body problem. The method uses acceleration-based switching surfaces to obtain near-impulsive solutions. A numerical continuation is performed on the maximum acceleration value to find near-impulsive solutions. A nonlinear programming problem is formulated by providing primer vector based analytical gradients. The solution space is narrowed down to aid the optimizer with the use of the near-impulsive solutions. The proposed method is used for the trajectory design of four different maneuvers between L1 and L2 Halo orbits in the Earth–Moon system. The results demonstrate the utility of the proposed method in generating extremal impulsive trajectories.

Adaptive prescribed performance based on recursive nonsingular terminal sliding mode control for quad-rotor systems under uncertainty and disturbance: Real-time validation

In this paper, at the aim of the fast trajectory-following control of the Unmanned Aerial Vehicle (UAV) systems subject to uncertainty and disturbance, the adaptive prescribed performance control based recursive nonsingular terminal sliding mode control is suggested. Afterward, for the fast trajectory-following control of the uncertain and perturbed quad-rotor system, a recursive nonsingular terminal sliding mode strategy is recommended. Since the better transient and steady-state response of the sliding mode surface is of the utmost importance in the design of the controller, the prescribed performance control scheme is proposed in which the transformed prescribed form of the previously proposed recursive nonsingular terminal sliding surface is obtained to prove that the recursive nonsingular terminal sliding surface can converge to a preset region. Whereas unknown bounded uncertainty and disturbance always exist in the UAV system's dynamical model which decreases its performance and efficiency, the adaptive mechanism is applied to approximate uncertain bounds of uncertainty and disturbance to advance the implementation of the UAV system. Later, quick reachability of the prescribed form switching surface is demonstrated using Lyapunov concept. Ultimately, simulation results using MATLAB/Simulink over a quad-rotor system and real-time simulation using the Speedgoat Real-Time Target Machine platform are conducted to validate the feasibility and performance of the proposed method.

Impact time guidance law for arbitrary lead angle using sliding mode control

PurposeThis paper aims to investigate a novel impact time control guidance (ITCG) law based on the sliding mode control (SMC) for a nonmaneuvering target using the predicted interception point (PIP).Design/methodology/approachTo intercept the target with the minimal miss distance and desired impact time, an estimation of time-to-go is introduced. This estimation results in a precise impact time for multimissiles salvo attack the target at the same time. Even for a large lead angle, the desired impact time is achieved by using the sliding mode and Lyapunov stability theory. The singularity issue of the proposed impact time guidance laws is also analyzed to achieve an arbitrary lead angle with the desired impact time.FindingsNumerical scenarios with desired impact time are presented to illustrate the performance of the proposed ITCG law. Comparison with the state-of-art impact time guidance laws proves that the guidance law in this paper can enable the missile to intercept the target with minimal miss distance and final impact time error. This method enables multiple missiles to attack the target simultaneously with different distances and arbitrary lead angles.Originality/valueAn ITCG law based on sliding mode and Lyapunov stability theory is proposed, and the switching surface is designed based on a novel estimation time-to-go for the missile to intercept the target with minimal miss distance. To intercept the target with initial arbitrary lead angles and desired impact time, the authors analysis the singular issue in SMC to ensure that the missile can intercept the target with arbitrary lead angle. The proposed approach for a nonmaneuvering target using the PIP has simple forms, and therefore, they have the superiority of being implemented easily.

Constant Power Load Stabilization With Fast Transient Boundary Control for DAB-Converters-Based Electric Drive Systems

Due to the negative incremental impedance of constant power loads (CPLs), many undesirable issues such as the oscillations or even possible collapse of the main dc bus voltage may occur, which may significantly degrade the system stability of Electrical Vehicles (EVs). This paper presents a natural-switching-surface (NSS) fast-transient-boundary-control (FTBC) based stabilization solution for EVs with dual-active-bridge (DAB) converters as the main power interface. Based on the mathematical models of multiple natural switching surfaces (NSS) and characteristics of CPL, the proposed FTBC control can achieve stable operation of DAB converters feeding CPLs and fast dynamic response irrespective operating stages such as the startup, sudden voltage and power reference changing conditions. Compared with other strategies such as load shedding, the proposed FTBC has no additional requirements for hardware, which is cost-effective. The analytical derivation of the proposed algorithm under the CPL condition is presented together with simulation and experimental evaluations, which validate that the proposed FTBC is capable of achieving 2 times faster start-up process and at least 33% dynamic response improvement compared with proportional integrator (PI) closed-loop control while eliminating the dc-bias current and guaranteeing the CPL stability by regulating the dynamic trajectories of DAB converters in the geometric domain.

On the integrability of hybrid Hamiltonian systems

A hybrid system is a system whose dynamics are controlled by a mixture of both continuous and discrete transitions. The integrability of Hamiltonian systems is often identified with complete integrability or Liouville integrability, that is, the existence of as many independent integrals of motion in involution as the dimension of the phase space. Under certain regularity conditions, Liouville–Arnold theorem states that the invariant geometric structure associated with Liouville integrability is a fbration by Lagrangian tori, on which motions are linear. In this paper, we study an extension of the Liouville–Arnold theorem for hybrid systems whose continuous dynamics is given by a Hamiltonian vector field and we state conditions on the impact map and the switching surface under which a hybrid Hamiltonian system is, in a certain sense, completely integrable.

Robust State-Estimator-Based Control of Uncertain Semi-Markovian Jump Systems Subject to Actuator Failures and Time-Varying Delay

This note presents a reformed state-estimator-based adaptive control strategy for uncertain delayed semi-Markovian jump systems (DSMJS) via sliding mode technique. In comparison to most literature results requiring exact prior knowledge of system time-delay, a linear state estimator not linking any control inputs is developed to cope with the case with unknown state delays. By virtue of the acquired state estimation, the establishment of both a new switching surface of linear-type and the involved adaptive controller is provided, and the devised controller could not only admit the assigned SSL's reachability in limited time but also operate on the DSMJS as desired despite the hidden actuator failures and unknowable time-delays. Also, a new sufficient stochastic stability criterion serving as a crucial solution to the control parameters of the resultant plant is inferred. The method also holds in a similar fashion for uncertain plants with no time-delays and/or no switching case. Eventually, the raised method is verified by numerical examples.