Non-conservative Forces Research Articles

Method of experimentally identifying the complex mode shape of the self-excited oscillation of a cantilevered pipe conveying fluid

The dynamics of a flexible cantilevered pipe conveying fluid have been researched for several decades. It is known that the flexible pipe undergoes self-excited vibration when the flow speed exceeds a critical speed. This instability phenomenon is caused by nonconservative forces. From a mathematical point of view, the system has a characteristic of non-selfadjointness and the linear eigenmodes can be complex and non-orthogonal to each other. As a result, such a mathematical feature of the system is directly related to the instability phenomenon. In this study, we propose a method of experimentally identifying the complex mode from experimentally obtained time histories and decomposing the linear mode into real and imaginary components. In nonlinear analysis, we show that the nonlinear effects of practical systems on the mode in the steady-state self-excited oscillation are small. The real and imaginary components identified using the proposed method for experimental steady-state self-excited oscillations are compared with those obtained in the theoretical analysis, thus validating the proposed identification method.

On (non-)conservative body forces, vorticity generation and energy conversion in ideal flows

Usually, the load on lifting bodies in incompressible, inviscid flow is determined by integration of the pressure on the body surface, once the flow is solved. Prandtl (Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch- Physikalische Klasse, vol. 1918, pp. 451–477) proposed an opposite method in which the body force field is the source term in the equation of motion to solve the flow. This force field method has not been used intensively but has regained importance in modern wind energy research. However, an analysis of which type of body force field generates vorticity and converts energy, and which body force field does not, is lacking. Prandtl's method is adopted here, but with the addition that the force field is allowed to be conservative or non-conservative. The relation between conservative/non-conservative body forces, vorticity generation, potential and kinetic energy and Helmholtz's vorticity theorems are derived. Similarly, the load on lifting bodies in two and three dimensions is classified as (non-)conservative, with some examples. To show that the force field method is consistent with the method where the load is output of an analysis, the expression for the Kutta–Joukowsky load and the relation between bound and trailing vorticity of a wing have been rederived using the force field method. The analysis confirms that this relation between bound and trailing vorticity is not governed by Helmholtz's theorems, as is often assumed, but by the non-conservative force field generating vorticity.

Optical trapping core formation and general trapping mechanism in single-beam optical tweezers

The working mechanism of single-beam optical tweezers is revisited using a recently established method. The optical force is split into conservative and nonconservative components, and these components are explicitly calculated for particles in the Rayleigh, Mie and geometrical optics regimes. The results indicate that optical trapping is attributable to the formation of an ‘optical trapping core’. Stable trapping is achieved when the conservative forces are larger than the nonconservative forces in the core region centered at the beam centers for all particle sizes. According to the conventional understanding, stability is a result of the conservative force overcoming the nonconservative force. In comparison, the concept of the optical trapping core more accurately illustrates the physical mechanism of optical trapping, for not only single-beam optical tweezers but also optical trapping settings.

Geometric decomposition of entropy production in out-of-equilibrium systems

Two qualitatively different ways of driving a physical system out of equilibrium, time-dependent and non-conservative forcing, are reflected by the decomposition of the system's entropy production into excess and housekeeping parts. We show that the difference between these two types of driving gives rise to a geometric formulation in terms of two orthogonal contributions to the currents in the system. This geometric picture in a natural way leads to variational expressions for both the excess and housekeeping entropy, which allow calculating both contributions independently from the trajectory data of the system. We demonstrate this by calculating the excess and housekeeping entropy of a particle in a time-dependent, tilted periodic potential.

The adaptive biasing force algorithm with non-conservative forces and related topics

We propose a study of the Adaptive Biasing Force method’s robustness under generic (possibly non-conservative) forces. We first ensure the flat histogram property is satisfied in all cases. We then introduce a fixed point problem yielding the existence of a stationary state for both the Adaptive Biasing Force and Projected Adapted Biasing Force algorithms, relying on generic bounds on the invariant probability measures of homogeneous diffusions. Using classical entropy techniques, we prove the exponential convergence of both biasing force and law as time goes to infinity, for both the Adaptive Biasing Force and the Projected Adaptive Biasing Force methods.

Analisis Perpindahan Besar Akibat Gaya Non-Konservatif

Structural applications based on large displacement analysis are widespread in various fields, such as the application of aircraft structures, membranes, cables, pipelines and risers. In this study, the author reviews the structural responses based on large displacement theory and non-conservative load models, assuming linear sections and materials. The parameters reviewed are the variation of the load factor and the variation of the slope angle of the load P at the end of the span. Solving non-linear differential equations with non-conservative force, using numerical integration method. The simulation results with the variation of the load factor with the angle of inclination, vertical and horizontal displacements are obtained, where the final orientation of the acting force corresponds to the deformation of the structure, and the maximum deformation occurs at a load angle of 90o, the deformation decreases for the angle orientation is getting smaller.

Long-time dynamics of a hinged-free plate driven by a nonconservative force

The first author is supported by the Thelam Fund (Belgium), Research proposal FRB 2019-J1150080. The second author is supported by PRIN from the MIUR and by GNAMPA from the INdAM (Italy). The third and fourth authors acknowledge support from the National Science Foundation from DMS-1713506 (Lasiecka) and NSF DMS-1907620 (Webster).

DYNAMIC PROCESSES ANALYSIS IN HIGH-SPEED SPINDLE ASSEMBLIES OF MACHINES TOOL WITH ACCOUNT DIFFERENT TYPES NONLINEARITY

The productivity and accuracy machine parts often depend on the dynamic processes during machine and cutting operation. The increase requirements for machining operation and quality machine parts leads to the need to evaluate and take into account all the capabilities of the technological processing system (TS) to ensure the stability of the cutting process and increase speed. One of the features emergence and existence of self-oscillating processes, the least studied and dangerous in terms of the effect on sustainability ТS is the nonlinearity parameters elastic system of the machine tool and the processes occurring during cutting operation. Therefore, to assess the conditions for implementation of the cutting process with a steady limited amplitude of oscillations, it is necessary to analyze and take into account the main nonlinearities dynamics of the TS. The article considers dynamic processes in high-speed processing systems on the example of high-precision spindle assemblies, with analysis and following review of their different types nonlinearity. The machine tool spindle unit for the case of high-speed processing according to the working conditions approaches the scheme of the rotor system which self-oscillations can be caused by the action of non-conservative circulation-type forces that are not associated with external periodic loads or any resonant relationships: internal friction forces, hydrodynamic forces in sliding bearings and seals, electrodynamic and electromagnetic forces in the electrical components of motor-spindles. It is shown that if the nonlinearity is associated only with internal external friction and coefficients of friction forces do not depend on frequency, the amplitude and frequency of self-oscillations (unlike linear system) will depend only on relationship of friction forces.

Dynamic stability of rotating cantilever meta-sandwich beam subjected to tangential tip non-conservative force

In this paper, stability problem of rotating tapered composite beams with metamaterial core subjected to tangential tip follower force is investigated. The governing equations of motion of the beam are derived on the basis of Timoshenko beam theory, and differential quadrature method is used to discretize the partial differential equations. By considering the five topologies of cellular metamaterial core, the critical flutter force is obtained. In order to confirm the validity and accuracy of the formulations, the numerical results are compared with the results reported in the literature. The effects of relative density and the topology of the core and rotating velocity on the stability characteristics are examined. The numerical results show that the meta-sandwich structure enhances the critical force of long beams. Also, rotation increases the critical flutter force of the beam.

A modified Jarzynski free-energy estimator to eliminate non-conservative forces and its application in nanoparticle-membrane interactions.

Computational methods to understand interactions in bio-complex systems are however limited to time-scales typically much shorter than in Nature. For example, on the nanoscale level, interactions between nanoparticles (NPs)/molecules/peptides and membranes are central in complex biomolecular processes such as membrane-coated NPs or cellular uptake. This can be remedied by the application of e.g. Jarzynski's equality where thermodynamic properties are extracted from non-equilibrium simulations. Although, the out of equilibrium work leads to non-conservative forces. We here propose a correction Pair Forces method, that removes these forces. Our proposed method is based on the calculation of pulling forces in backward and forward directions for the Jarzynski free-energy estimator using steered molecular dynamics simulation. Our results show that this leads to much improvement for NP-membrane translocation free energies. Although here we have demonstrated the application of the method in molecular dynamics simulation, it could be applied for experimental approaches.

March 24, 2022 Rémi Abgrall, Editor-in-Chiefcompatibility between Non-Conservative and Conservative Lorentz Forces for Energy Conservation

March 24, 2022 Rémi Abgrall, Editor-in-Chiefcompatibility between Non-Conservative and Conservative Lorentz Forces for Energy Conservation

Effects of basal clearance on the impact dynamics of dry granular flow against dual rigid barriers

A basal clearance is usually designed beneath barriers to enable sufficient discharge to minimise the maintenance work over service life. Current design guidelines for multiple barriers usually neglect the influence of basal clearance, resulting in either an overconservative or a nonconservative design impact force acting on the subsequent barriers. In this study, physical model tests were carried out to investigate the effects of basal clearance height (Hc) beneath first barrier on the interaction between dry granular flow and dual rigid barriers. A new approach based on the hydrodynamic equation is proposed to estimate the impact force on the second barrier exerted by the basal discharge and overflow from the first barrier. The basal discharge can attenuate the impact force exerted on the second barrier by dissipating the kinetic energy of landing flow and apportioning the load contributions from basal discharge and overflow. For the first barrier with a barrier height HB1 that was twice the flow depth h0, the impact force on the second barrier was governed by overflow when Hc/h0 ≤ 0.6 and was dominated by basal discharge when Hc/h0 ≥ 0.8. These two criteria provide a basis for optimising the impact forces for multiple-barrier systems with basal clearances.

Machine-learning nonconservative dynamics for new-physics detection.

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our neural new-physics detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and nonconservative components, which are represented by a Lagrangian neural network (LNN) and an unconstrained neural network, respectively, trained to minimize the force recovery error plus a constant λ times the magnitude of the predicted nonconservative force. We show that a phase transition occurs at λ=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846), and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms both an LNN and an unconstrained neural network for predicting the future of a damped double pendulum.

Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap

Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper, we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present the exact results for certain marginals of the full three-dimensional steady state probability distribution, in addition to results for the toroidal probability currents that are present in the steady state, as well as for the circulation of these currents. Our analytical results are confirmed by numerical solution of the steady state Fokker–Planck equation.

Optomechanical interaction between single-walled carbon nanotubes of various structures

We consider optomechanical interaction in an asymmetric structure of a carbon nanotubes dimer of different orientations and/or different atomic structures in the field of a plane wave or a focused Gaussian beam. Here we show that optical coupling in such the system can lead to nonreciprocal interactions between the constituents. We demonstrate that a non-conservative force is applied to the center of mass of an optically coupled nanotube dimer, resulting in an unexpected lateral action. The sign and magnitude of this force depend on abrupt phase transitions in the properties of the asymmetric dimer.

Chiral Thermodynamics in Tailored Chiral Optical Environments

We present an optomechanical model that describes the stochastic motion of an overdamped chiral nanoparticle diffusing in the optical bistable potential formed in the standing-wave of two counter-propagating Gaussian beams. We show how chiral optical environments can be induced in the standing-wave with no modification of the initial bistability by controlling the polarizations of each beam. Under this control, optical chiral densities and/or an optical chiral fluxes are generated, associated respectively with reactive vs. dissipative chiral optical forces exerted on the diffusing chiral nanoparticle. This optomechanical chiral coupling bias the thermodynamics of the thermal activation of the barrier crossing, in ways that depend on the nanoparticle enantiomer and on the optical field enantiomorph. We show that reactive chiral forces, being conservative, contribute to a global, enantiospecific, change of the Helmholtz free energy bistable landscape. In contrast, when the chiral nanoparticle is immersed in a dissipative chiral environment, the symmetry of the bistable potential is broken by non-conservative chiral optical forces. In this case, the chiral electromagnetic fields continuously transfer, through dissipation, mechanical energy to the chiral nanoparticle. For this chiral nonequilibrium steady-state, the thermodynamic changes of the barrier crossing take the form of heat transferred to the thermal bath and yield chiral deracemization schemes that can be explicitly calculated within the framework of our model. Three-dimensional stochastic simulations confirm and further illustrate the thermodynamic impact of chirality. Our results reveal how chiral degrees of freedom both of the nanoparticle and of the optical fields can be transformed into true thermodynamics control parameters, thereby demonstrating the significance of optomechanical chiral coupling in stochastic thermodynamics.

Reactive helicity and reactive power in nanoscale optics: Evanescent waves. Kerker conditions. Optical theorems and reactive dichroism

Considering time-harmonic optical fields, we put forward the complex helicity and its alternating flow, together with their conservation equation: the complex helicity theorem. Its imaginary part constitutes a novel law that rules the build-up of what we establish as the reactive helicity through its zero time-average flow. Its associated reactive flow and the imaginary Poynting momentum that accounts for the accretion of reactive power are illustrated in two paradigmatic systems: evanescent waves and fields scattered from magnetodielectric dipolar nanoparticles. As for the former, we show that its reactive helicity may be experimentally observed as we introduce a reactive spin momentum and a reactive orbital momentum in terms of which we express the imaginary field momentum, whose transversal component produces an optical force on a magnetoelectric particle that, as we illustrate, may surpass and can be discriminated from the known force due to the so-called extraordinary momentum. We also uncover a nonconservative force on such a magnetoelectric particle, acting in the decay direction of the evanescent wave, and that may also be discriminated from the standard gradient force; thus making the reactive power of the wavefield also observable. Concerning the light scattered by magnetoelectric nanoparticles, we establish two optical theorems that govern the accretion of reactive helicity and reactive power on extinction of incident wave helicity and energy. Like a nule total, i.e., internal plus external, reactive power is at the root of a resonant scattered power, we show that a zero total reactive helicity underlies a resonant scattered helicity. These reactive quantities are shown to yield a novel interpretation of the two Kerker conditions, which we demonstrate to be linked to an absence, or minimum, of the overall scattered reactive energy. Further, we demonstrate that the first Kerker condition, under which the particle becomes dual on illumination with circularly polarized light, amounts to a nule overall scattered reactive helicity. Therefore these two reactive quantities are shown to underly the directivity of the particle scattering and emission. In addition, we discover a discriminatory property of the reactive helicity of chiral light incident on a chiral nanoparticle by excitation of the external reactive power. This should be useful for optical near field enantiomeric separation, an effect that we call reactive dichroism.

Classical Hamiltonian Systems with balanced loss and gain

Classical Hamiltonian systems with balanced loss and gain are considered in this review. A generic Hamiltonian formulation for systems with space-dependent balanced loss and gain is discussed. It is shown that the loss-gain terms may be removed completely through appropriate co-ordinate transformations with its effect manifested in modifying the strength of the velocity-mediated coupling. The effect of the Lorentz interaction in improving the stability of classical solutions as well as allowing a possibility of defining the corresponding quantum problem consistently on the real line, instead of within Stokes wedges, is also discussed. Several exactly solvable models based on translational and rotational symmetry are discussed which include coupled cubic oscillators, Landau Hamiltonian etc. The role of -symmetry on the existence of periodic solution in systems with balanced loss and gain is critically analyzed. A few non--symmetric Hamiltonian as well as non-Hamiltonian systems with balanced loss and gain, which include mechanical as well as extended system, are shown to admit periodic solutions. An example of Hamiltonian chaos within the framework of a non--symmetric system of coupled Duffing oscillator with balanced loss-gain and/or positional non-conservative forces is discussed. It is conjectured that a non--symmetric system with balanced loss-gain and without any velocity mediated interaction may admit periodic solution if the linear part of the equations of motion is necessarily symmetric —the nonlinear interaction may or may not be -symmetric. Further, systems with velocity mediated interaction need not be -symmetric at all in order to admit periodic solutions. Results related to nonlinear Schrödinger and Dirac equations with balanced loss and gain are mentioned briefly. A class of solvable models of oligomers with balanced loss and gain is presented for the first time along with the previously known results.

The DeRisk database: Extreme design waves for offshore wind turbines

The estimation of extreme loads from waves is an essential part of the design of offshore wind turbines. Standard design codes suggest either to use simplified methodologies based on regular waves, or to perform fully-nonlinear computations. The former may not provide an accurate representation of the real extreme waves, while the latter is too computationally intensive for fast design iterations. Here, we address these limitations by using the fully-nonlinear solver OceanWave3D to establish the DeRisk database, a large dataset of extreme wave kinematics in a two-dimensional domain. From the database, which is open and freely available, a designer can easily extract fully-nonlinear wave kinematics for a wave condition and water depth of interest by identifying a suitable computation in the database and, if needed, by Froude-scaling the kinematics. This will ultimately enable quicker estimations of nonlinear wave loads, speeding up design evaluations. The database sea states cover a range of nondimensional depth of about h∗∈[3.0⋅10−3,6.5⋅10−2] and of nondimensional significant wave height of HS∗∈[1.0⋅10−3,8.0⋅10−3], where h∗=h/(gTP2)[−] and HS∗=HS/(gTP2)[−].The fully-nonlinear solver is validated against the DeRisk model-scale experiments, where a number of long-crested sea state realizations are generated at two different water depths, 33.0[m] and 20.0[m], and the induced force on a stiff monopile with a diameter of D=7.0[m] is measured.Comparison with the experiments shows that the database predicts maximum crest elevations at both depths very accurately. Predictions of the in-line force, obtained by application of the Rainey slender body force model with the database wave kinematics, are accurate for milder storms. However, for stronger storms, where slamming loads from breaking waves dominate, the force computations from the database kinematics provide slightly nonconservative force estimates compared with the standard methodologies such as the embedded stream function and the WiFi JIP model. This discrepancy is mainly due to the lack of a slamming load model in the applied force model. A procedure to add slamming loads to OceanWave3D and to the DeRisk database is currently being developed.

Cases of Integrability Which Correspond to the Motion of a Pendulum in the Three-dimensional Space

We systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies–pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system