Nonconservative Force Field Research Articles

Comparison of complete integrability cases in dynamics of a two-, three-, and four-dimensional rigid body in a nonconservative field

We present complete results devoted to the study of the equations of motion of a dynamically symmetric four-dimensional rigid body in a nonconservative force field. The form of the body is taken from the dynamics of real two- or three-dimensional rigid bodies interacting with a resisting medium according to the streamline flow around laws under which a non-conservative pair of forces acts on the body and forces the body center of mass to move rectilinearly and uniformly.

Complete list of first integrals for dynamic equations of motion of a solid body in a resisting medium with consideration of linear damping

A new case of integrability in the spatial problem of motion for a solid body with consideration of the nonconservative moment of forces is discussed. A nonconservative force field of action of the medium on the body is constructed. Contrary to some previous author’s works, a linear dependence of this field on the angular velocity is taken into account, although the introducing of this dependence into the components of such a field is not obvious in advance.

Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems

This paper presents results concerning the geometric invariant theory of completely integrable Hamiltonian systems and also the classification of integrable cases of low-dimensional and high-dimensional rigid body dynamics in a nonconservative force field. The latter problems are described by dynamical systems with variable dissipation. The first part of the work is the basis for the doctorial dissertation of V. V. Trofimov (1953-2003), which was already published in parts. However, in the present complete form, it has not appeared, and we decided to fill in this gap. The second part is a development of the results presented in the doctoral dissertation of M. V. Shamolin and has not appeared in the present variant. These two parts complement one another well, which initiated this work (its sketches already appeared in 1997).

Nonconservative forcing and diffusion in refractive optical traps

Refractive optical trapping forces can be nonconservative in the vicinity of a stable equilibrium point even in the absence of radiation pressure. We discuss how nonconservative 3D force fields, in the vicinity of an equilibrium point, reduce to circular forcing in a plane; a simple model of such forcing is the refractive trapping of a sphere by a four rays. We discuss in general the diffusion of an anisotropically trapped, circularly forced particle and obtain its spectrum of motion. Equipartition of potential energy holds even though the nonconservative flow does not follow equipotentials of the trap. We find that the dissipated nonconservative power is proportional to temperature, providing a mechanism for a runaway heating instability in traps.

Integration of rotational algorithms into dissipative particle dynamics: modeling polyaromatic hydrocarbons on the meso-scale

Heavy crude oil consists of thousands of compounds, a significant fraction of which have fairly large molecular weights and complex structures. Our work aims at constructing a meso-scale platform to explore this complex fluid in terms of microstructure, phase behavior, stability and rheology. In the present study, we focus on the treatment of the structures of fused aromatic rings as rigid body fragments in fractions such as asphaltenes and resins. To derive the rotational motion of rigid bodies in a non-conservative force field, we conduct a comparison of three rigid body rotational algorithms integrated into a standard dissipative particle dynamics (DPD) simulation. The simulation results confirm the superiority of the Quaternion method. To ease any doubt concerning the introduction of rigid bodies into DPD, the performance of the Quaternion method was tested carefully. Finally, the aggregation dynamics of asphaltene in very diluted toluene was investigated. The nanoaggregates are found to experience forming, breaking up and reforming. The sizes of the asphaltene monomer and nanoaggregate are identified. The diffusion coefficient of diluted asphaltene in toluene is similar to that found experimentally. All these results verify the rotational algorithm and encourage us to extend this platform to study the rheological and colloidal characteristics of heavy crude oils in the future.

Tunable Brownian vortex at the interface

A general kind of Brownian vortices is demonstrated by applying an external nonconservative force field to a colloidal particle bound by a conservative optical trapping force at a liquid-air interface. As the liquid medium is translated at a constant velocity with the bead trapped at the interface, the drag force near the surface provides enough rotational component to bias the particle's thermal fluctuations in a circulatory motion. The interplay between the thermal fluctuations and the advection of the bead in constituting the vortex motions is studied, and we infer that the angular velocity of the circulatory motion offers a comparative measure of the interface fluctuations.

Classification of complete integrability cases in four-dimensional symmetric rigid-body dynamics in a nonconservative field

This work is a relatively final result in studying the equations of motion of a dynamically symmetric, four-dimensional rigid body in a nonconservative force field in two logically possible cases of its tensor of inertia. The form of the force field considered is taken from the dynamics of real three-dimensional rigid bodies interacting with a medium.

Direct Measurement of the Nonconservative Force Field Generated by Optical Tweezers

The force field of optical tweezers is commonly assumed to be conservative, neglecting the complex action of the scattering force. Using a novel method that extracts local forces from trajectories of an optically trapped particle, we measure the three-dimensional force field experienced by a Rayleigh particle with 10 nm spatial resolution and femtonewton precision in force. We find that the force field is nonconservative with the nonconservative component increasing radially away from the optical axis, in agreement with the Gaussian beam model of the optical trap.

Giant Enhanced Diffusion of Gold Nanoparticles in Optical Vortex Fields

We study the diffusion of a metal nanoparticle in the nonconservative force field of an optical vortex lattice. Radiation pressure in the vortex array is shown to induce a giant enhancement over the free thermal diffusion. Langevin dynamics simulations show that the diffusion coefficient of (50 nm radius) gold particles at room temperature is enhanced by 2 orders of magnitude at power densities of the order or smaller than those used to trap nanoparticles with optical tweezers.

Brownian vortexes

Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle's thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle's fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.

Quantum Wave Equation of Non-conservative System

It is well known that Schr\"{o}dinger's equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave equation is proposed, which can describe the particle in non-conservative force field. We think the new quantum wave equation can be used in many fields.

MECHANOCHEMICAL COUPLING OF MOLECULAR MOTORS WITH NONCONSERVATIVE FORCE

The biochemical process for coupling between hydrolysis of ATP and the performance of mechanical work involves a sequence of events. Here we present a two-dimensional ratchet model with a non-conservative impulsive force field. The non-conservative impulsive force that represents the chemical energy consumed in the conformation changing process provides a source of non-equilibrium fluctuation, which is a crucial factor for the Brownian motors and can lead to macroscopic motion.

TWO-DIMENSIONAL RATCHETS WITH NON-CONSERVATIVE IMPULSIVE FORCE

We discuss the directed motion of overdamped Brownian particles based on a two-dimensional ratchet model with a non-conservative impulsive force field. We consider the combined effects on the stationary current due to local spatial asymmetry in the longitudinal direction as well as the constrained harmonic force in the transverse direction. We notice that the current reversal is induced by the change of colored noise strength and the dynamics in the transverse direction influences the directed motion in the longitudinal direction significantly. The non-conservative impulsive force that represents the chemical energy consumed in the conformation changing process is a crucial factor to the directed motion of the Brownian motors.

Two-dimensional inverse problem of dynamics for families in parametric form

The two-dimensional inverse problem of dynamics is considered for nonconservative force fields, both in inertial and rotating frames. The families of curves are given in parametric form x = F(λ, b), y = G(λ, b), b varying along the monoparametric family of planar curves and λ being the parameter describing a specific curve. The special case of the force fields generated by a potential in an inertial field, already studied by Bozis and Borghero, is derived as well as the corresponding one in rotating frames.

Metaphors and time reversibility and irreversibility in economic systems

This paper deals with the way metaphors carried over from physical or biological systems condition the analysis of economic systems. The metaphors drawn from Newtonian mechanics, or from conservative fields of force, by neoclassical economists are discussed. Alternative metaphors which involve non-homeostasis and time irreversible processes are then outlined. Particular attention is paid to thermodynamics, evolutionary biology, and non-conservative or hysteretic force fields as sources of such metaphors. It is argued that these metaphors provide illumination to aspects of economic systems which are not consistent with the homeostatic, time reversible metaphors conventionally employed in economics.

The Characteristics of Ionic Wind and Its Effect on Electrostatic Precipitators

The ionic wind and turbulent flow field formed in a nonconservative electric force field have long been recognized to have a significant effect on an electrostatic precipitator (ESP). To simulate the flow field in an ESP, one should include the electric force term in the momentum equation. We considered the flow field in an ESP to be a turbulent flow and applied two- and three-dimensional models of k-e-A and k-e-E to close turbulence. The SIMPLE-C numerical scheme was applied to investigate the characteristics of the ionic wind and its influence on an ESP. The collecting efficiency of an ESP for a particle diameter of each grade was calculated to understand how the ionic wind interferes with the collecting efficiency. The results indicate that under normal operating conditions the effect of ionic wind is not pronounced. However, as the flow velocity becomes smaller, especially when the flow velocity is <0.6 m/s, the ionic wind becomes pronounced and has a significant influence on the flow field and the co...

Variational methods for the problems of nonconservative force fields in the micropolar elastodynamics

Based on the properties of the convolution and the convolute commutation, some quasi-variational principles for the problems of nonconservative force field in the micropolar elastodynamics are given and verified in this paper. The theorem given in this paper can be applied to the theories of the nonlocal elastic mediums and the nonlocal micropolar elastic mediums.

On linear rotor‐bearing dynamics

Dynamics of rotating machinery has long been an active field of study and research because of its importance to a wide variety of applications. Extensive analysis of complex machinery configurations is now a routine practice in many quarters as a result of advancements in computerized methods. However, basic physical insights are often obscured in the presence of enormous computational power. To a large extent, this is because certain fundamental properties of rotor‐bearing systems have not been sufficiently exposed in the literature, in contrast to computational methods and results. Specifically, the equations of motion for typical rotor‐bearing systems [MẌ, + CẊ + KX = F(t)l frequently result in nonsymmetric C and K matrices. Decomposition into symmetric and skew‐symmetric matrices can readily be shown to amount to a separation of conservative and non‐conservative interactive force fields [see M. L. Adams and J. Padovan, “Insights Into Linearized Rotor Dynamics,” J. Sound Vib. (in press)]. The skew‐symmetric portion of K embodies a nonconservative circulatory force field which is responsible for classical rotor‐bearing instability. The skew‐symmetric portion of C embodies a conservative force field which produces spectrum bifurcation, e.g., gyroscopic and fluid‐annulus inertia effects.

Circularly polarized electromagnetic waves in nonlinear dissipative media

Earlier time-sinusoidal progressive-wave and standing-wave solutions for nondissipative isotropic nonlinear dielectrics are generalized to allow for dissipation. Both dielectric and ferromagnetic media are considered. In the former case the waves are time-sinusoidal plane circularly polarized and transverse, while in the latter case the magnetic field intensity may have a spatially nonuniform longitudinal component. The problem of finding the spatial variation of the wave amplitude and phase is analogous to a problem of plane motion of a particle in a nonconservative force field.