Time-dependent Force Research Articles

Time-dependent vaccine efficacy estimation quantified by a mathematical model.

In this paper we calculate the variation of the estimated vaccine efficacy (VE) due to the time-dependent force of infection resulting from the difference between the moment the Clinical Trial (CT) begins and the peak in the outbreak intensity. Using a simple mathematical model we tested the hypothesis that the time difference between the moment the CT begins and the peak in the outbreak intensity determines substantially different values for VE. We exemplify the method with the case of the VE efficacy estimation for one of the vaccines against the new coronavirus SARS-CoV-2.

An absolute-zero-stiffness vibration isolator for continuously varying mass: Theoretical design and numerical simulation

Nonlinear quasi-zero-stiffness (QZS) vibration isolators can provide low dynamic but high static stiffness, and thus attract much attention in the fields of vibration isolation and reduction. However, it seems difficult for QZS isolators to protect continuously varying mass from the surrounding vibratory disturbance of relatively large amplitude. In this article, an adjustable absolute-zero-stiffness vibration isolator is designed by updating the classical QZS isolator in two steps. First, each hinged constraint in the QZS isolator that connects the oblique spring with the outer rigid framework, is released and replaced by a sliding constraint supported on an additional vertical linear side-spring. Second, the two oblique springs in the QZS isolator are further replaced by two identical oblique cam-roller-spring units, which can synthetically provide a constant negative-stiffness at will in the vertical direction. Once the stiffness ratios among the main-spring (as in the QZS isolator), side-springs and oblique-units of the new isolator are rationally determined, for a target object with any weight to be protected, absolute zero stiffness and transmittance can always be achieved by appropriately exerting an additional time-independent vertical force on each sliding constraint. The validity and efficiency of the theoretical design are fully verified by numerical simulations for both fictitious loads and real seismic spectra. This work provides a possible means for nonlinear vibration isolations of continuously varying mass.

Destabilization mechanism of the collisional microtearing mode in magnetized slab plasmas

The destabilization mechanism of the collisional microtearing mode driven by an electron temperature gradient is studied using theoretical analyses and gyrokinetic simulations including a comprehensive collision model, in magnetized slab plasmas. The essential destabilization mechanism of the microtearing mode is the lag of the parallel inductive electric field behind the magnetic field owing to the time-dependent thermal force and inertia force induced by the velocity-dependent electron–ion collisions. Quantitative measurements of the collision effects enable us to identify the unstable regime against collisionality and reveal the relevance of the collisional microtearing mode with existing toroidal experiments. A nonlinear simulation demonstrates that the microtearing mode does not drive magnetic reconnection with the explosive release and conversion of the magnetic energy.

Inferring equilibrium transition rates from nonequilibrium protocols

We develop a theory for inferring equilibrium transition rates from trajectories driven by a time-dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution function in terms of the equilibrium distribution function and the excess dissipation, we formulate a nonequilibrium transition state theory to estimate the rate enhancement over the equilibrium rate due to the nonequilibrium protocol. We demonstrate the utility of our theory in examples of pulling of harmonically trapped particles in one and two dimensions, as well as a semiflexible polymer with a reactive linker in three dimensions. We expect our purely thermodynamic approach will find use in both molecular simulation and force spectroscopy experiments.

Moment Lyapunov exponents and stochastic nonstability of a circular cylindrical shells

The paper investigates the stochastic stability conditions of circular cylindrical shells, compressed by time-dependent stochastic membrane forces. The main contribution of the paper is the determination of the moment Lyapunov exponents of the linear cylindrical shell for the first time. The moment and almost-sure stochastic stability of a three-degree-of-freedom coupled continuous system, under parametric excitation of white noise, are investigated. It is assumed that the system possesses a small damping. This type of a shell structure model requires a specific scheme for determining the moment Lyapunov exponents. The system of stochastic differential equations of motion is decoupled by using the contact transformation method with the obtained appropriate symplectic matrix of the system. Then a scheme for determining the moment Lyapunov exponents is presented which contains an analytical procedure. The largest Lyapunov exponent is calculated through its relation with the moment Lyapunov exponent. The moment and almost-sure stability boundaries are obtained analytically. These results are important and useful in engineering applications as an example of a procedure for dynamic analysis of mechanical systems with coupled stochastic oscillators.

One-Step Electrochemical Synthesis of AlO x -Passivated Twisted-Phosphorene Nanosheets for Potentially Stable Energy Storage Devices.

Black phosphorus (BP), a promising 2D material for electronics, energy storage, catalysis, and sensing, has sparked a research boom. However, exfoliated thin-layered BP is unstable and can easily be degraded under environmental conditions, severely limiting its practical applications. In this context, a simple and cost-effective method has been proposed that involves electrochemically exfoliating BP and simultaneously electrochemically depositing aluminum oxide (AlO x ) for passivation of the exfoliated BP. The ambient stability of the exfoliated BP is studied using a time-dependent atomic force microscope (AFM). The AlO x capping layer significantly improves the environmental stability of BP compared to uncapped BP. The thermal stability of the resulting BP is evaluated using power-dependent Raman spectroscopy. The results show that the AlO x -passivated BP has increased thermal stability, with only a slight shift in peak position toward higher Raman power intensity. These properties can make the material suitable for stable energy storage devices. Interestingly, the electrochemical exfoliation and passivation processes resulted in the BP with a twist angle (9.86°), which is expected to exhibit unique electronic properties similar to those of graphene with a twist angle.

Multi-valued random dynamics of partly dissipative reaction–diffusion system with discontinuous nonlinearity on

This paper is devoted to studying a system consisting of a reaction–diffusion equation with multi-valued right-hand side and an ordinary differential equation in absence of dissipation term, which is defined on the whole space . The system is driven by time-dependent forces and coloured noise with nonlinear diffusion. We first establish the global existence of strong/mild solutions for initial-value problems. The measurability of solution map with respect to sample points and initial values is then obtained via the upper semicontinuity, which indicates that these solutions define a (non-autonomous) multi-valued random dynamical system. Finally, we prove the existence of pullback attractor for the dynamical system.

Hyperdissipative Navier–Stokes Equations Driven by Time-Dependent Forces: Invariant Manifolds

We consider the incompressible hyperdissipative Navier–Stokes equations \begin{align}\left \{\begin{array}{l} u_t+\epsilon (-\Delta )^\alpha u+(u\cdot \nabla )u+\nabla p=f,\\ \nabla \cdot u=0, \end{array} \right .\end{align} on a two- or three-dimensional periodic torus, where the power and the forcing function is time-dependent. We intend to reveal how the fractional dissipation and the time-dependent force affect long-time dynamics of weak solutions. More precisely, we prove that with certain conditions on , there exists a finite-dimensional Lipschitz manifold in the -space of divergent-free vector fields with zero mean. The manifold is locally forward invariant and pullback exponentially attracting. Moreover, the compact uniform attractor is contained in the union of all fibers of the manifold. In our result, no large viscosity is assumed. It is also significant that in the three-dimensional case the spectrum of the fractional Laplacian does not have arbitrarily large gaps.

Probability inequalities for direct and inverse dynamical outputs in driven fluctuating systems.

When a fluctuating system is subjected to a time-dependent drive or nonconservative forces, the direct-inverse symmetry of the dynamics can be broken so inducing an average bias. Here we start from the fluctuation theorem, a cornerstone of stochastic thermodynamics, for inspecting the unbalancing between direct and inverse dynamical outputs, here called "events," in a bidirectional forward-backward setup. The occurrence of an event might correspond to the realization of a quantitative output, or to the realization of a sequence of acts that compose a complex "narrative." The focus is on mutual bounds between the probabilities of occurrence of direct and inverse events in the forward and backward mode. The inspection is made for systems in contact with a thermal bath, and by assuming Markov dynamics on the uncontrolled degrees of freedom. The approach comprises both the case of systems under a time-dependent drive and time-independent external forces. The general formulation is then used to derive (or re-derive) specialized results valid for finite-time processes, and for systems taken into steady conditions (either periodic steady states or steady states) starting from equilibrium. Among the results, we find already known forms of "generalized" thermodynamic uncertainty relations, and derive useful constraints concerning the work distribution function for systems in steady conditions.

Upper semicontinuity of pullback attractors for nonclassical diffusion equations with delay

In this paper, we mainly study the upper semicontinuity of pullback D-attractors for a nonclassical diffusion equation with delay term b ( t , u t ) which contains some hereditary characteristics. Under a critical nonlinearity f, a time-dependent force g ( t , x ) with exponential growth and a delayed force term b ( t , u t ), using the asymptotic a priori estimate method, we prove the upper semicontinuity of pullback D-attractor { A ε ( t ) } t ∈ R to equation (1.1) with ε ∈ [ 0 , 1 ].

Different effects of external force fields on aging Lévy walk.

Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time ta for aging anomalous diffusion processes. This paper pays more attention to how an external force field affects the aging Lévy walk. Based on the Langevin picture of the Lévy walk and the generalized Green-Kubo formula, we investigate the quantities that include the ensemble- and time-averaged mean-squared displacements in both weak aging ta≪t and strong aging ta≫t cases and compare them to the ones in the absence of any force field. Two typical force fields, constant force F and time-dependent periodic force F(t)=f0sin⁡(ωt), are considered for comparison. The generalized Einstein relation is also discussed in the case with the constant force. We find that the constant force is the key to causing the aging phenomena and enhancing the diffusion behavior of the aging Lévy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging Lévy walk are verified by both theoretical analyses and numerical simulations.

Penalty function method for FEM dynamic analysis of trusses with nonlinear multi-node constraints under harmonic load

This work introduces the establishment of the FEM model for investigating the dynamic behavior of trusses, subjected to multi-node constraints, under harmonic excitation based on utilizing the method of Penalty function. The technique for treating the nonlinear relationship of multi-node constraints is developed by using the Penalty function to extremum the Hamiltonian augmented potential energy function and to convert the multi-node constrained relation. The method of Newmark integration is utilized to convert dynamic differential equations of a truss system having multi-node boundary constraints subjected to a time-dependent harmonic force to incremental equations. The incremental-iterative algorithm had been developed based on the Newton-Raphson method, used for solving the dynamic incremental equation of motion for the truss system. Utilizing the constructed algorithm, the Matlab program is written to compute the investigated truss system’s internal force-time response and displacement-time response subjected to harmonic load. The advice for choosing the weight value of the Penalty function is proposed based on analyzing numerical results.

Qualitative analysis of a mechanical system of coupled nonlinear oscillators

In this paper we investigate nonlinear systems of second order ODEs describing the dynamics of two coupled nonlinear oscillators of a mechanical system. We obtain, under certain assumptions, some stability results for the null solution. Also, we show that in the presence of a time-dependent external force, every solution starting from sufficiently small initial data and its derivative are bounded or go to zero as the time tends to + ∞ , provided that suitable conditions are satisfied. Our theoretical results are illustrated with numerical simulations.

Time-dependent force in high-speed liquid droplet impacting on a wet wall

Recent research (Fujisawa, 2022a) has shown that the time-dependent force exerted on a droplet during high-speed [O (100 m/s)] impact on a planar rigid wall is quite different from that of low-speed [O (1 m/s)] impact case owing to the compressibility of the droplet. Here, we consider a more general case of a high-speed liquid droplet impacting a wall where a liquid film is present on the wall surface. Three-component Euler simulations were performed to determine the characteristics of the time-dependent force exerted on the droplet during high-speed liquid droplet impact on a planar rigid wet wall. Several initial liquid film thicknesses were considered. The strength of the force exerted on the droplet decreases in magnitude as the liquid film thickness increases, whereas the total force increases with increasing liquid film thickness owing to the presence of a water hammer shock that is reflected inside the liquid film.

Scrutinization of Stefan suction/blowing on thermal slip flow of ethylene glycol/water based hybrid ferro-fluid with nano-particles shape effect and partial slip

This study is aimed to examine thermal slip flow of mixture based hybrid ferro-fluid with shape effect of nano-particles and partial slip under the constant influence of Stefan suction/blowing impacts. Thermal slip flow is magnetized with applied time-dependent magnetic force in transverse direction of flow. Partial slip impact is considered on magnetized hybrid ferro-fluid. Additionally, spherical shaped nano-particles have been accounted to constitute the desired hybrid ferro-fluid whereas distinct shape nano-particle effect is analyzed and discussed for heat transfer efficiency. The flow governing highly nonlinear equations are transformed into ordinary differential equations using suitable similarity transform. Furthermore, motion and temperature profile for spherical shaped nano-particles of hybrid ferro-fluid are analyzed and discussed under the impression of suction and blowing effect. It is observed that in the event of mass suction S=1 and partial slip 0.2≤Sf≤0.6 reduced shear stress rates and high rates of heat transfer are obtained. It is concluded that high Lorentz force under suction/blowing effect contract thermal boundary of flow. Laminar shape nano-particle increase temperature profile when compared with other shapes of nano-particles.

Nonlinear Force Affecting Stock Market Volatility

We transform stock price time series to the time dependent force parameters using Newton’s second law (a kind of the information filtering). The force acts on a point in the space of data. One of ten force parameters, if its value in a short time interval is extremely large, announces increasing of the time series uncertainty. This delayed effect of the nonlinear force we interpret as sensitivity to initial conditions, for chaos combined with stochasticity, considering the time series generated by nonlinear differential equations with fluctuating function included. Our aim is to improve understanding and rough prediction of processes in complex systems.

Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime

Systems consisting of confined, interacting particles doing overdamped motion admit an effective description in terms of nonlinear Fokker-Planck equations. The behavior of these systems is closely related to the S power-law entropies and can be interpreted in terms of the S-based thermostatistics. The connection between overdamped systems and the S measures provides valuable insights on diverse physical problems, such as the dynamics of interacting vortices in type-II superconductors. The S-thermostatistical approach to the study of many-body systems described by nonlinear Fokker-Planck equations has been intensively explored in recent years, but most of these efforts were restricted to systems affected by time-independent external potentials. Here, we extend this treatment to systems evolving under time-dependent external forces. We establish a lower bound on the work done by these forces when they drive the system during a transformation. The bound is expressed in terms of a free energy based on the S entropy and is satisfied even if the driving forces are not derivable from a potential function. It constitutes a generalization, for systems governed by nonlinear Fokker-Planck equations involving general time-dependent external forces, of the H-theorem satisfied by these systems when the external forces arise from a time-independent potential.

Origin of eclipsing time variations in post-common-envelope binaries: Role of the centrifugal force

Eclipsing time variations in post-common-envelope binaries were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics performed with the PENCIL CODE. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of ∼10−4 is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.

Terahertz radiation generation in doped semiconductor interacting with femtosecond pulse in constant magnetic field

The generation of terahertz (THz) radiation in a doped semiconductor with a sufficiently large bandgap interacting with a femtosecond pulse of IR range has been investigated. Generation occurs due to the simultaneous effect on the conduction electrons of a constant magnetic field and time-dependent ponderomotive force. The spectral composition, total energy and shape of the THz radiation pulse are found.

The Kostin Equation, the Deceleration of a Quantum Particle and Coherent Control

Fifty years ago Kostin (J Chem Phys 57(9):3589–3591, 1972. https://doi.org/10.1063/1.1678812) proposed a description of damping in quantum mechanics based on a nonlinear Schrödinger equation with the potential being governed by the phase of the wave function. We show for the example of a moving Gaussian wave packet, that the deceleration predicted by this equation is the result of the same non-dissipative, homogeneous but time-dependent force, that also stops a classical particle. Moreover, we demonstrate that the Kostin equation is a special case of the linear Schrödinger equation with three potentials: (i) a linear potential corresponding to this stopping force, (ii) an appropriately time-dependent parabolic potential governed by a specific time dependence of the width of the Gaussian wave packet and (iii) a specific time-dependent off-set. The freedom of the width opens up the possibility of engineering the final state by the time dependence of the quadratic potential. In this way the Kostin equation is a precursor of the modern field of coherent control. Motivated by these insights, we analyze in position and in phase space the deceleration of a Gaussian wave packet due to potentials in the linear Schrödinger equation similar to those in the Kostin equation.