Time-dependent Force Research Articles

Classical and quantum harmonic oscillators subject to a time dependent force

Classical and quantum harmonic oscillators subject to a time dependent force

An Approach for Reconstructing the Time-Dependent Force Acting on a Thin Plate from Particle Velocity Measurements

An Approach for Reconstructing the Time-Dependent Force Acting on a Thin Plate from Particle Velocity Measurements

Mathematical modelling of atrial and ventricular pressure–volume dynamics and their change with heart rate

This paper presents mathematical models that can simulate the cardiovascular system of a healthy sheep under normal resting conditions in which the heart rate changes significantly. The models include several new modelling features that are introduced progressively. The contraction of the cardiac chambers is modelled using a time-dependent muscle force with constant elasticity instead of time dependent elasticity. A new hypothesis about the mechanical contraction of the atria generates realistic pressure volume (PV) loops. The inter-ventricular interaction is modelled as well. Additionally, hysteresis is incorporated in the aortic valve to produce an end-systolic reverse (negative) flow. Most of the model parameter values are based on previous literature data while time periods of delay, atrial and ventricular contraction are derived using experimental data from 14 sheep. We provide new relationships between contraction time and delay as a function of heart period. The effects of different aspects of our modelling on the mean cardiac output, stroke volume, ejection time, ejection fraction and PV loops are studied. Model outputs are compared with published experimental results where possible, and are within a wide range of physiological observations.

Reconstruction of time-dependent forces acting on a vibrating structure from pressure measurements.

This paper proposes an approach to reconstruct the time-dependent forces acting on a vibrating structure from pressure measurements. In the approach, the pressures measured in the near field of the structure are related to the exciting forces at the reconstruction points by the transfer functions determined in an experimental way, whereupon the time-dependent forces can be reconstructed with these pressures as inputs. In the reconstruction process, an additional regularization with a mixed lp , q-norm term is introduced to resolve the ill-posed inverse problem, which is able to take advantage of the prior knowledge of space and time characteristics of the forces. A numerical simulation of reconstructing the time-dependent forces acting on a plate and two experiments of reconstructing the impact forces acting on a semi-cylindrical shell and an elliptically shaped structure are carried out. The results demonstrate the feasibility of the proposed approach for reconstructing the forces in both temporal and spatial domains from pressure measurements. The proposed approach provides a non-contact and real-time way to identify the locations of forces and reconstruct their time histories, which can be further used to reveal the mechanical cause of the radiated noise.

Numerical investigation on postulated aircraft crash to tokamak building

Nuclear structures, systems and components important to safety should be adequately protected against diverse internal and external hazards. As part of the effort, a few comprehensive guidelines to deal with human-induced events were established and individual researches to assess fissile plant containment buildings under plausible aircraft colliding conditions were carried out. In relation to developing fusion plants, soundness of major structures as a barrier should also be ensured to prevent disaster due to potential external hazards as well as internal hazards like the leakage of radioactive material and electromagnetic waves. The objective of this study is to examine structural integrity of postulated tokamak building taking into account dynamic loading derived from aircraft collision process. The numerical models of aircraft and reinforced concrete structure were made in use of smoothed-particle hydrodynamics and finite element methods. Appropriateness of time-dependent impact force and impulse histories was verified through comparison between preliminary analysis data for a rigid wall and those obtained from Riera method. Systematic analyses of aircraft crash onto the tokamak building were performed under hypothetical scenarios with different variables such as impact velocities, angles and rebar diameters. As results, basic engineering parameters such as stresses and strains of the rebar were calculated, and damage of the concrete was estimated. Further sensitivity analyses were performed and effects of each numerical input were discussed in terms of the significant.

Two-atom van der Waals forces with one atom excited: The identical-atom limit

We compute the conservative van-der-Waals forces between two atoms, one of which is initially excited, in the limit of identical atoms. Starting with the perturbative calculation of the interaction between two dissimilar atoms, we show that a time-dependent approach in the weak-interaction approximation is essential in considering the identical atoms limit in the perturbative regime. In this limit we find that, at leading order, the van-der-Waals forces are fully-resonant and grow linearly in time, being different upon each atom. The resultant net force upon the two-atom system is related to the directionality of spontaneous emission, which results from the violation of parity symmetry. In contrast to the usual stationary van-der-Waals forces, the time-dependent conservative forces cannot be written as the gradients of the expectation values of the interaction potentials, but as the expectation values of the gradients of the interaction potentials only.

Effect of impact velocity on time-dependent force and droplet pressure in high-speed liquid droplet impingement

In this study, the effect of the impact velocity of a droplet on the time-dependent force exerted on the droplet and droplet pressure during high-speed [O (100 m/s)] liquid droplet impingement (LDI) on a planar rigid wall is numerically investigated. The force exerted on the droplet and droplet pressures are computed as a function of time, and its frequency spectrum is analyzed to explain the physical mechanisms that occur during high-speed LDI. The results show that high-speed LDI involves the formation of a water hammer shock and its reflection on the free surface of the droplet and wall, resulting in sustained reverberation inside the droplet. Therefore, the force curve shows oscillatory behavior and is quite different from that of the low-speed [O (1 m/s)] impact case. Finally, the force and the droplet pressure are computed for various impact velocities of the droplet.

Species extinction at the various environmental forcing in a stochastic ecosystem model

This paper considers a stochastic multi-species single resource population model. The stochastic model is obtained from perturbing the supply of resource by a time dependent force. We use analytical investigations and numerical simulations to study the dynamics of our model under chaotic and periodic environmental oscillations, and show that the stochastic dynamics of our model exhibits a strong dependence on initial parameters.

Phenomenon of double entropic stochastic resonance with recycled noise

The double entropic stochastic resonance (DSR) phenomenon for a Brown particle moving in a confined geometry driven by a time-dependent force in the declining direction subject to additive master noise and recycled noise is investigated in this paper. Under the adiabatic approximation condition, based on two-state theory and linear response theory, the expression for the system linear response (LR) is derived. Stochastic resonance (SR) and periodic SR behavior is observed when the LR changes with the feedback coefficient and with the time-delay of the recycled noise. DSR phenomenon appears when the LR varies with the constant component and with the fluctuation noise intensity of the force in the declining direction. Tradition SR occurs on the curve of the LR when the LR varies with the intensity of the master noise. The non-monotonous effect of the parameters of the confined structure on the LR is discussed.

Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems.

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

Soft impact of an elongated elasto-plastic missile

Motivated by the grave consequences of an aircraft impact into robust engineering structures like nuclear power plants, we investigate the time-dependent reaction force during the impact of a crushing, elongated elasto-plastic missile into a robust elastic target. We derive a set of partial differential equations on a time-dependent domain to describe the impact. The simplest case of a homogeneous, cylindrical aircraft fuselage impacting a rigid target is solved analytically by using conformal mapping. After developing a numerical scheme for the case of an elastic target, we find that a simple dimensionless number, the damage potential, gives an accurate prediction of the impact force. The peak reaction force during the impact is found to exceed the initial impact force by up to 20%; hence the often applied strategy to estimate the peak force as the initial impact force is not a conservative approach. This effect is due to a resonant vibration in both the missile and the target. Predicted and computed parameters at which this counter-intuitive, resonance-like behavior occurs are shown to agree well.

Statistical Floquet prethermalization of the Bose-Hubbard model

The manipulation of many-body systems often involves time-dependent forces that cause unwanted heating. One strategy to suppress heating is to use time-periodic (Floquet) forces at large driving frequencies. For quantum spin systems with bounded spectra, it was shown rigorously that the heating rate is exponentially small in the driving frequency. Recently, such exponential suppression of heating has been observed in an experiment with ultracold atoms, realizing a periodically driven Bose-Hubbard model. This model has an unbounded spectrum and, hence, is beyond the reach of previous theoretical approaches. Here, we study this model with two semiclassical approaches valid, respectively, at large and weak interaction strengths. In both limits, we compute the heating rates by studying the statistical probability to encounter a many-body resonance, and obtain a quantitative agreement with the exact diagonalization of the quantum model. Our approach demonstrates the relevance of statistical arguments to Floquet perthermalization of interacting many-body quantum systems.

Hysteresis loop area scaling exponents in DNA unzipping by a periodic force: A Langevin dynamics simulation study.

Using Langevin dynamics simulations, we study the hysteresis in unzipping of longer double-stranded DNA chains whose ends are subjected to a time-dependent periodic force with frequency ω and amplitude G keeping the other end fixed. We find that the area of the hysteresis loop, A_{loop}, scales as 1/ω at higher frequencies, whereas it scales as (G-G_{c})^{α}ω^{β} with exponents α=1 and β=1.25 in the low-frequency regime. These values are same as the exponents obtained in Monte Carlo simulation studies of a directed self-avoiding walk model of a homopolymer DNA [R. Kapri, Phys. Rev. E 90, 062719 (2014)10.1103/PhysRevE.90.062719], and the block copolymer DNA [R.K. Yadav and R. Kapri, Phys. Rev. E 103, 012413 (2021)2470-004510.1103/PhysRevE.103.012413] on a square lattice, and differs from the values reported earlier using Langevin dynamics simulation studies on a much shorter DNA hairpins.

Preliminary design of bionic flapping wing vehicle

This paper deals with the preliminary design of bionic flapping wing vehicle. The design is driven by its requirement and objective namely the maximum weight should be less than 0.5 kg with 1.5 m wingspan. In the conceptual design, the wing planform, wing structures and system of flapping mechanism will be considered to find the initial configuration and then continued the sizing of the flapping vehicle. The analysis of designed flapping vehicle is increasingly complex due to firstly the generation of time-dependent aerodynamic forces and moments from unsteady flow around the flapping wing, secondly, flexible wing structure which generates higher thrust may cause a structure failure and thirdly, a flapping mechanism system generating differential flapping motion for the vehicle maneuver. The aerodynamic analysis for given flapping motion model is carried out using Computational Fluid Dynamics method based the solution of unsteady Reynold Averaged Navier-Stokes equations and the structure analysis is conducted with the input of aerodynamic loads using Finite Element method to find critical stresses that may cause a structure failure. As a solution of differential flapping two controlled servos are used. The architecture of electrical system is made to analysis of the distribution of data signal and power. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The selection of system components is performed by considering weight constraint. The flight maneuver is achieved by changes in flapping frequency and sweeping angle. The wing platform has elliptical shape with airfoil maximum camber of 6% chord at a quarter chord. The outer body and wing are made of foam laminated by glass fibre with the foam density of 0.045 g/cm3. The horizontal tail is made of mylar film with density of 1.38 g/cm3 and its area of 168.3 cm2. As simulated results, the amount of total lift is 4.18 Newton generated at 6 Hz flapping frequency.

Typical transient effects in a piezoelectric semiconductor nanofiber under a suddenly applied axial time-dependent force

Based on the mechanical motion equation, Gauss’s law, and the current continuity condition, we study a few typical transient effects in a piezoelectric semiconductor (PS) fiber to realize the startup and turning-off functions of common piezotronic devices. In this study, the transient extensional vibration induced by a suddenly applied axial time-dependent force is examined in a cantilevered n-type ZnO nanofiber. Neither the magnitude of the loadings nor the doping concentration significantly affects the propagation caused by disturbance of the axial displacement. However, both of the factors play an important role in the propagation caused by disturbance of the electron concentrations. This indicates that the electromechanical coupling effect can be expected to directly determine the electronic performance of the devices. In addition, the assumption of previous simplified models which neglect the charge carriers in Gauss’s law is discussed, showing that this assumption has a little influence on the startup state when the doping concentration is smaller than 1021 m−3. This suggests that the screening effect of the carriers on the polarized electric field is much reduced in this situation, and that the state is gradually transforming into a pure piezoelectric state. Nevertheless, the carriers can provide a damping effect, which means that the previous simplified models do not sufficiently describe the turning-off state. The numerical results show that the present study has referential value with respect to the design of newly multifunctional PS devices.

The Navier\u2013Stokes equations on the plane with time-dependent external forces

We are concerned with the non-stationary Navier–Stokes equations on the whole plane with external forces which are non-decaying in time, and give a sufficient condition on the external forces for the existence of a solution which exists for whole time. Typical examples are time-periodic solutions and solutions almost periodic in time. The stability under perturbation is also verified.

Unconstrained slip mechanics and stepping reactions depend on slip onset timing

Slips can occur at any time during stance. Accordingly, time-dependent tangential ground reaction forces likely produce a diverse range of slipping foot mechanics when traction is lost, thus requiring flexible recovery strategies to prevent falls. However, previous research has focused on slip onset in early stance, often with experimental anteroposterior constraints on the slipping foot, despite the diversity of environmental slips and falls. This study aimed to determine the effects of slip onset time on slip direction, severity (distance and velocity), and compensatory stepping responses. Ten young adults received slipping perturbations at different times during the stance phase of walking via a wearable device that reduces available friction while allowing the slipping foot to slide freely within the horizontal plane. Slip direction, distance, and peak velocity, compensatory step direction and distance, and upper body angular momentum magnitude and plane of rotation were derived from kinematic data. All outcome measurements significantly correlated with the time of slip onset. Slip direction and the plane of rotation of angular momentum deviated widely from the sagittal plane, exhibiting laterally-directed components exceeding those in the anteroposterior direction. As slip onset occurred later in stance, slip severity decreased while compensatory steps became longer and progressed from a posterior to anterior placement. These results provide insight into critical times within stance when slips are most severe, and into the diversity of slipping mechanics caused by changes in slip onset time.

A Hopf Bifurcation in the Planar Navier\u2013Stokes Equations

We consider the Navier–Stokes equation for an incompressible viscous fluid on a square, satisfying Navier boundary conditions and being subjected to a time-independent force. As the kinematic viscosity is varied, a branch of stationary solutions is shown to undergo a Hopf bifurcation, where a periodic cycle branches from the stationary solution. Our proof is constructive and uses computer-assisted estimates.

Antiresonant driven systems for particle manipulation.

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

The Measurement of Information and Free Energy in Mechanical-Force-Driven Coil-Globule Transitions.

We study the role of information (the relative entropy) for polymers undergoing coil-globule transitions driven by a time-dependent force. Pulling experiments at various speeds are performed by Brownian dynamics simulations. We obtain the work distributions for the forward and time-reversed backward processes and information stored at the end of the nonequilibrium pulling processes. We present the systematic method to measure the information from the pulling experiments and extract the information by analyzing slowly relaxing modes. When the information is incorporated, the work distributions modified by the information allow access to the proper free energy via the formulation of the generalized fluctuation theorems even if the initial states of the forward and time-reversed backward processes are out of equilibrium. This demonstrates that the work-information conversion works well for a single-molecule system with many degrees of freedom.