Search

In general, mechanical energy monotonically decreases in a physically consistent system, constructed with conservative force and dissipative force. This feature is important in designing a particle method, which is a discrete system approximating continuum fluid with particles. When the discretized system can be fit into a framework of analytical mechanics, it will be a physically consistent system which prevents instability like particle scattering along with unphysical mechanical energy increase. This is the case also in incompressible particle methods. However, most incompressible particle methods do not satisfy the physical consistency, and they need empirical relaxations to suppress the system instability due to the unphysical energy behavior. In this study, a new incompressible particle method with the physical consistency, moving particle full-implicit (MPFI) method, is developed, where the discretized interaction forces are related to an analytical mechanical framework for the systems with dissipation. Moreover, a new pressure evaluation technique based on the virial theorem is proposed for the system. Using the MPFI method, static pressure, droplet extension, standing wave and dam break calculations were conducted. The capability to predict pressure and motion of incompressible free surface flow was presented, and energy dissipation property depending on the particle size and time step width was studied through the calculations.

The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the effects of the Winkler coefficient, Pasternak coefficient and damping coefficient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary differential equations with variable coefficients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verified through two numerical examples. The influences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with different taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.

Considering static radial eccentricity, a Jeffcott rotor model is established for the rotor system of the permanent magnet synchronous motors in electric vehicles. The system conservative force, including unbalanced magnetic pull, which results in nonlinearity is analyzed, and center manifold theorem and Lyapunov method are used to determine the stabilities of multiple equilibrium points. This analysis shows that static eccentricity spoils the symmetry of the equilibrium points, although they are distributed in the line along the direction of the static eccentricity. This asymmetry leads to the pitchfork bifurcation of equilibrium points to a generic bifurcation with a defect. This analysis provides two stability conditions for the rotor system. Furthermore, the effect of the asymmetry on the dynamic characteristics that can induce backward whirling motion coupled with forward whirling motion is quite different from the case without static eccentricity. These characteristics are investigated by multi-scale method. As a result, the analytical solution of the system at steady state is obtained. The frequency characteristics of the main resonance are analyzed, and the stability of the solution is determined using Routh–Hurwitz criterion and the geometric constraint of the rotor whirling motion. The characteristics reveal that a globally unstable frequency band appears due to the geometric constraint. However, this frequency band narrows and even vanishes with increases in damping and electromagnetic stiffness and decreases in mass imbalance, mechanical stiffness and static eccentricity. The analysis by multi-scale method is based on the assumption of the time invariance of the forward and backward whirling amplitudes, which is validated by the numerical method. The results of the two methods agree well, which indicates that this assumption and the analysis are reasonable.

The fluid-solid interaction force has a decisive influence on the flow characteristics of micro-nano scale. Based on the dissipative particle dynamics (DPD) method, static and flow simulations of fluid in typical shale slits were carried out. The Lennard-Jones (LJ) potential function of 96X was applied to characterize the fluid-solid interaction force. The slit width ranged 3–10nm, the wall material was quartz, the fluid was n-hexane, and the driving force of the flow simulation ranged 1–20kcal/(mol·A). The results show that due to the attraction of solid wall, the aggregation of fluid molecules near the wall was enhanced, fluid density there increased, and the diffusion coefficient there was significantly lower than that in the middle of the slit. The fluidity of the fluid near the wall is significantly reduced. In the flow model, when the fluid-solid interaction force was ignored, the flow profile was piston-like, and the velocity gradient at the edge of the slit was extremely large, showing the characteristics of slip flow. When the fluid-solid interaction force was taken into account, the velocity was reduced significantly, and the profile was parabolic. When the LJ96X was replaced by LJ126X potential function to characterize the fluid-solid interaction force, the attractive force from the wall on the fluid near the wall decreased, the fluidity was enhanced, and the velocity profile increased. When the conservative force parameter of fluid was changed, enhancing the wettability of oil phase, the affinity between fluid and solid was increased, and the velocity profile was reduced.

In many problems of multidimensional dynamics, systems appear whose state spaces are spheres of finite dimension. Clearly, phase spaces of such systems are tangent bundles of these spheres. In this paper, we examine nonconservative force fields in the dynamics of a multidimensional rigid body in which the system possesses a complete set of first integrals that can be expressed as finite combinations of elementary transcendental functions. We consider the case where the moment of nonconservative forces depends on the tensor of angular velocity.

A many-body dissipative particle dynamics simulation is applied here to pave the way for investigating the behavior of mesoscale droplets after impact on horizontal solid substrates. First, hydrophobic and hydrophilic substrates are simulated through tuning the solid–liquid interfacial interaction parameters of an innovative conservative force model. The static contact angles are calculated on homogeneous and several patterned surfaces and compared with the predicted values by the Cassie’s law in order to verify the model. The results properly evaluate the amount of increase in surface superhydrophobicity as a result of surface patterning. Then drop impact phenomenon is studied by calculating the spreading factor and dimensionless height versus dimensionless time and the comparisons made between the results and the experimental values for three different static contact angles. The results show the capability of the procedure in calculating the amount of maximum spreading factor, which is a significant concept in ink-jet printing and coating process.

Interaction potential plays a vital role on the friction. Potential energy of two contacts directly determines on the friction force. However, many mathematic models proposed, always abandon the instantaneous status during sliding to devote to a weighted average over lateral force, which might miss some information about friction behavior. In this work, the relation among potential energies, separation distances of two contracts, and positions in the sliding direction are studied to evaluate the instantaneous friction characteristics. Two hydrogenated diamond surfaces are used as the examined model. The results show that a watershed between positive and negative friction forces locates at the position with the minimum adsorption energy. A rapid decrease in potential energy occurs near the 2.5 nN external force, where the friction coefficient approaches zero at each position in the sliding direction. Therefore, a novel method may be developed to greatly reduce the friction coefficient between two surfaces by adjusting the contract pressure.

Non-force and force electromagnetic fields, their generation, and application for an explanation of some physical effects well-known for a long time are considered.

In this paper, a parametric study of fluid–solid interaction for single-particle dissipative particle dynamics (DPD) model is conducted to describe the hydrodynamic interactions in a large range of particle sizes. To successfully reproduce the hydrodynamics for different particle sizes, and overcome the problem that effective radius of solid sphere does not match its real radius, the cut-off radius and conservative force coefficient of single-particle DPD model have been modified. The cut-off radius and conservative force coefficient are related to the drag force and radial distribution function, so that, for each particle size, they can be determined by DPD simulations. Through numerical fitting, two empirical formulas as a function of spherical radius are developed to calculate the cut-off radius and conservative force coefficient. Numerical results indicate that the single-particle DPD model is, indeed, capable of capturing low Reynolds number hydrodynamic interactions for different particle sizes by selecting these model parameters reasonably. Specifically, the model can not only insure that drag force and torque are quantitatively consistent with theoretical results, but also guarantee the effective radius matches well its real radius. In addition, the shear dissipative force is the major part of drag force and should not be ignored. This study will help to improve the application range of single-particle DPD model to make it suitable for different particle sizes and provide parameter guidance for studying fluid–solid interaction using single-particle DPD model.

This paper is a survey of integrable cases in the dynamics of a five-dimensional rigid body under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean. The problem of the search for complete sets of transcendental first integrals of systems with dissipation is quite topical; a large number of works are devoted to it. We introduce a new class of dynamical systems that have a periodic coordinate. Due to the existence of nontrivial symmetry groups of such systems, we can prove that these systems possess variable dissipation with zero mean, which means that on the average for a period with respect to the periodic coordinate, the dissipation in the system is equal to zero, although in various domains of the phase space, either energy pumping or dissipation can occur. Based on the facts obtained, we analyze dynamical systems that appear in the dynamics of a five-dimensional rigid body and obtain a series of new cases of complete integrability of the equations of motion in transcendental functions that can be expressed through a finite combination of elementary functions.

Discrete element simulations are used to model a two-dimensional gravity-free granular sample, which is trapped between two smooth sidewalls and one bottom rough wall while being subject to a constant shearing velocity at the top under a given confinement pressure. This system, inspired by conventional fluid mechanics, is called a granular lid-driven cavity. Attention is firstly paid to the time-averaged dynamics of the grains once a steady-state is reached. Strong spatial heterogeneities associated with a large-scale vortex formed within the whole volume of the lid-driven cavity are observed. The mean steady force on the sidewall facing the shearing velocity is then investigated in detail for different cavity lengths, shearing velocities and confinement pressures at the top. The ratio of the force on the latter wall to the top confinement pressure force is not constant but depends on both the shearing velocity and the confinement pressure. Above a critical value of the cavity length relative to the wall height and over a wide range of both shearing velocity and top confinement pressure, all data merge into a one-to-one relation between the mean force scaled by the top pressure force and the macroscopic inertial number of the lid-driven cavity. This result reveals the key role played by the inertial rheology of the granular material in the granular force transmission.

We have investigated the effect of scan velocity on atomic friction force in a Prandtl–Tomlinson model at finite temperature. We use a nonsinusoidal substrate potential with variable shape to capture surface features. The velocity dependence of atomic friction force is classified into two regimes: thermal and athermal regimes. We numerically find turning velocity between these two regimes, and its shape parameter dependence is determined. Furthermore, we have studied the torsional oscillation effect on a cantilever. We show that friction force can be reduced by controlling the frequency and the amplitude of the superimposed torsional oscillation at low scan velocity. The numerical calculations have shown that the substrate shape strongly affects the occurrence of resonances, so the torsional resonance frequency dependence of the shape parameter is established.

Steady dissipation of energy is a crucial property that distinguishes active particles from Brownian particles. However, it is not straightforward to explicitly model the dissipative property of existing active particles driven by a vibrating plate. We present a novel active particle that can be explicitly modeled by Newtonian dynamics of a conservative force field plus two asymmetrical dissipative terms. The particle is a dimer consisting of two ping-pong balls connected by a rigid rod, and its two balls are filled with granular particles of the same total mass but of different grain size. This dimer placed on a vibrating plate exhibits 3 types of motion – by tuning the frequency and the amplitude of the vibration, the dimer undergoes either a directed motion toward the small (or large) grain-filled side or an unbiased random motion. We investigate the various modes of motion both experimentally and numerically and show that the directed motion is a result of the asymmetric damping due to the size difference in the filling grains. Furthermore, the numerical simulation reveals that the dimer’s dynamics in either directed motion mode resembles a limit cycle attractor that is independent of its initial condition.

This paper is a survey of integrable cases in dynamics of two-, three-, and four-dimensional rigid bodies under the action of a nonconservative force field. We review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean.

The average force acting on a cylindrical or spherical body placed near the boundary of cylindrical cavity filled with liquid and executing rotational vibrations is experimentally studied. The repulsive lift force acting on solid is found and measured using the method of body suspension in the gravity field. In horizontal cavity the repulsive force provides steady state of light cylinder near the upper boundary at a distance comparable with the thickness of the Stokes layer. The heavy sphere which hangs on thread repulses from the wall of vertical cylindrical cavity under torsional vibration. The dependence of the average lift force on the amplitude and frequency of vibrations and on distance between the body and the boundary has been investigated. Results are presented on the plane of dimensionless parameters. In the examined frequency range the lift force acting on cylinder decreases exponentially with distance from the boundary. Lift force acting on sphere decreases with distance and strongly depends on dimensionless frequency of vibration. Conclusion that lift force is generated by body oscillations excited by its viscous interaction with the oscillating boundary is done. The found phenomenon is important for control of inclusions under microgravity conditions.

We clarified underlying physics and thereby developed threshold voltage model of a fast-moving ball actuator (FMBA) for reflective electronic paper display. The proposed threshold voltage model starts from considering all the related forces of Coulomb force, dielectrophoretic (DEP) force, frictional force, and adhesion caused by van der Waals force, where frictional force consists of vertical Coulomb and DEP forces, buoyance, and gravity. Considering 3-dimensional geometric effect, Coulomb and DEP forces were analyzed through numerical simulations while all the remaining forces were analytically modeled. As a result, DEP force, buoyance, and gravity were concluded negligible compared to Coulomb force and van der Waals force. With the simplified threshold voltage model, the required driving voltage of 39.54 V was obtained, which matched well to the measured voltage of 40 V.

A class of macroscopic systems is described which have the remarkable feature that they can sustain undamped compressional radial oscillations. They consist of an arbitrary number of particles confined by a harmonic potential and interacting among themselves through conservative forces scaling as the inverse cube of distances. The radial oscillation leads to a variation of the thermodynamic quantities characterizing the system. The system therefore does not approach equilibrium, since the (macroscopic) amplitude of the oscillation does not decrease as time goes to infinity. The oscillation is harmonic and isochronous, that is, its frequency is fixed and independent of the initial condition. These results hold independently of the dimension of the system and are also valid in the quantal context.

This study provides a novel insight into the study of static friction force. From numerical simulations with a simplified sliding model in which the friction force between an elastic slider with a split contact interface and a rigid base block with a smooth surface was analyzed, it was found that the existence of the stop–restart motion works to increase static friction force, while the stop–inversion motion reduces static friction force. Thus, the numerical simulations in this study demonstrated that the magnitude of static friction force varies with different types of tangential loading sequences. Furthermore, it was found from an analytical discussion that the magnitude of this tangential loading history effect is characterized by the dispersion level of the threshold lengths for the onset of slip motion at each contact point and also by the ratio of kinetic friction coefficient to static friction coefficient at the contact interface. Through the previously mentioned analytical approaches, this study emphasizes that the sequence of tangential loading is an important factor for characterizing the magnitude of static friction force.

The microstructures of magnetic fluids are simulated using a dissipative particle dynamics (DPD)-based method and are fundamentally important for controlling the macroscopic properties of magnetic fluids and understanding the corresponding rheological behaviors in diverse engineering applications. The cubic polynomial spline function often used as smoothing function in smoothed particle hydrodynamics (SPH) is employed as the conservative force potential function, which can provide a stronger conservative force weight function than the conventional weight function by choosing properly the cutoff radius between the dissipative particles. By employing the above method, the desired results are obtained for both stronger and weaker magnetic particle-particle interaction under the condition of varying the mass of the dissipative particles. In addition, the influences of the magnetic particle-particle interaction and of the magnetic particle area fraction on the microstructure of magnetic fluids are also investigated, respectively, and the obtained results agree qualitatively well with those in the literature obtained by other numerical approaches and experiments. The numerical solutions of the mean equilibrium velocities of the magnetic and dissipative particles are also calculated and approximate the corresponding theoretical values very well. Therefore the employed DPD-based method is highly effective in the simulation of the microstructure of magnetic fluids.

We discuss how to derive a force or a force density from a measured velocity field. The first part focuses on the integral force a fluid exerts on a body, e.g. lift and drag on an airfoil. Obtaining the correct pressure is crucial; however, it cannot be measured within the flow non-intrusively. Using numerical and experimental test cases, we compare the accuracy achievable with three methods: pressure reconstruction from velocity fields via (1) the differential momentum equation, or (2) the Poisson equation, furthermore, (3) Noca’s momentum equation [Noca, JFS 13(5), 1999], which does not require pressure explicitly. The latter gives the best results for the lift, whereas the first or second approach should be used for the drag. The second part deals with obtaining the distribution of a body force density generated by an actuator. Using a stream function ansatz, we obtain a Laplace equation that allows us to compute the solenoidal part of the force distribution; however, the irrotational part is lost. Furthermore, the wall pressure must be known. We validate this approach using numerical data from a wall jet flow in a rectangular box, driven by a fictitious, solenoidal body force. Reconstructing the force distribution yields an error of less than 10−2 for most of the domain.

Dynamic stability behavior of the shear-flexible composite beams subjected to the nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of the laminated composite beam is presented based on kinematic assumptions consistent with the Timoshenko beam theory, and the shear stiffness of the thin-walled composite beam is explicitly derived from the energy equivalence. An extended Hamilton’s principle is employed to evaluate the mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction stiffness matrices. Evaluation procedures for the critical values of divergence and flutter loads of the nonconservative system with and without damping effects are then briefly introduced. In order to verify the validity and the accuracy of this study, the divergence and flutter loads are presented and compared with the results from other references, and the influence of various parameters on the divergence and flutter behavior of the laminated composite beams is newly addressed: (1) variation of the divergence and flutter loads with or without the effects of shear deformation and rotary inertia with respect to the nonconservativeness parameter and the fiber angle change, (2) influence of the internal and external damping on flutter loads whether to consider the shear deformation or not.

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.

The electro-magnetic control of vortex-induced vibration (VIV) of a circular cylinder is investigated numerically in the exponential-polar coordinates attached on the moving cylinder for Re=150 in the paper. Compared with the fixed cylinder, the vibration of cylinder leads to the shift of stagnation point, the shear layer strength and the inertial force, which affects the hydrodynamic forces on the cylinder. The effects of the instantaneous wake geometries and the corresponding cylinder motion on the hydrodynamic forces for one entire period of vortex shed are discussed in the drag-lift phase diagram. The Lorentz force for controlling the vibration cylinder is classified into the field Lorentz force and the wall Lorentz force. The field Lorentz force decreases the lift oscillation, and in turn, suppresses the VIV, whereas the wall Lorentz force has no effect on the lift.

The interaction forces between a permanent disk and a superconductor disk are calculated for a cylindrical system by using the Anderson–Kim model. Model calculations show that both the vertical force and the stability exhibit a peak-like behavior in the repulsive branch. These peaks in the calculations are dependent on the model parameter and the ratio between the penetration and the applied fields, Hp/Hm. The features of hysteretic force and magnetic stiffness are discussed.

In this paper, the effects of Lorentz force on drag reduction for a circular cylinder have been studied experimentally and numerically. Based on its effects on drag reduction, the Lorentz force is found to be classified into two parts: one acts directly on the cylinder, named as the wall Lorentz force, and the other called the field Lorentz force acts on the fluid inside the boundary layer. The wall Lorentz force leads to the generation of a thrust, whereas the field Lorentz force results in drag increase. Since the former dominates the drag variation, the drag would reduce accordingly and even turn into negative (thrust) with the application of Lorentz force.

Friction between a nanoscale tip and a reconstructed Au(111) surface is investigated both by atomic force microscopy (AFM) and molecular statics calculations. Lateral force AFM images exhibit atomic lattice stick–slip behavior with a superstructure corresponding to the herringbone reconstruction pattern. However, the superstructure contrast is not primarily due to variations in the local frictional dissipation (which corresponds to the local width of the friction loop). Rather, the contrast occurs primarily because the local centerline position of the friction loop is periodically shifted from its usual value of zero. Qualitatively, similar behavior is reproduced in atomistic simulations of an AFM tip sliding on the reconstructed Au(111) substrate. In both simulations and experiments, this centerline modulation effect is not observed on unreconstructed surfaces. Similarly, using a topographically flat surface as a hypothetical control system, the simulations show that the centerline modulation is not caused by variations in the reconstructed surface’s topography. Rather, we attribute it to the long-range variation of the local average value of the tip-sample interaction potential that arises from the surface reconstruction. In other words, surface atoms located at unfavorable sites, i.e., in the transition between face-centered-cubic (FCC) and hexagonal-close-packed (HCP) regions, have a higher surface free energy. This leads to a varying conservative force which locally shifts the centerline position of the friction force. This demonstrates that stick–slip behavior in AFM can serve as a rather sensitive probe of the local energetics of surface atoms, with an attainable lateral spatial resolution of a few nanometers.

Contact force of Multi-body dynamics (MBD) system can be classified two parts. First is a normal force and the other is a tangential force called friction force. And the friction force can be represented by two states such as stick and slip. The stick-slip phenomenon is simply described as a simple contact model which is a rigid body contacted on a sloped surface. If the calculated friction coefficient between the body and sloped surface is less than the static friction coefficient, the body should be stuck. If the calculated friction coefficient is greater than the static friction coefficient, the body will be sliding along the surface. The phenomenon is called as stick and slip state of friction, respectively. Usually many researchers and commercial MBD software used a coulomb friction force model which is defined with an only function of relative velocity. This kind of friction force model will be called a conventional friction force model in this paper. A big problem of the conventional model can not describe a stick state of friction phenomenon. In the case of conventional friction force model, the body will be sliding even though friction state is stick. Because, the relative velocity must have a non-zero value in order to generate the friction force. To solve this kind of problem, we propose a stick-slip friction force model including a spring like force. In the case of stick-slip friction force model, the body can be stuck on the sloped surface because the friction force will be a non-zero value, even though the relative velocity approaches zero. We defined a relative displacement variable called stiction deformation. In this paper, the stick-slip friction model is proposed and applied in the contact algorithm of MBD system. And then two friction models are compared with numerical examples. With the proposed stick-slip friction model, more realistic results are achieved.

The void fraction profile and distributing mechanism of small bubbles were investigated in detail by using the Euler–Lagrange two-way model. The continuous phase is simulated by using direct numerical simulations in Euler frame of reference. Bubble trajectories are tracked by solving the Newton equations of motion with considering forces including gravity force (buoyant force), drag force, lift force, wall lift force, pressure gradient force, virtual mass force, and inertia force in Lagrange frame of reference. Results show that the void fraction profile of small bubbles exhibits double peak values, which is caused by different interphase forces dominating over bubble movements at different bubble places, and paths of bubbles are directly related to their injection places.

The 3-D lattice Boltzmann method is applied to evaluate the forces exerted on a stationary spherical particle in current and wave boundary layer flow in order to analyze the forces contributing to the incipient motion of the sediment particle. Results indicate that for current, the forces reach statistically steady finally at a relative low particle Reynolds number (less than 40). The streamwise drag force is the main driven force while the effect of the spanwise force can be ignored. The reason that results in the phenomenon is also discussed. As for the wave, the cyclical nature of the flow makes the evolution of drag and lift forces become quasi-periodic. The streamwise drag force is still the main driven force, but it changes direction with the flow. Meanwhile, the spanwise vorticity and the pressure around the particle show asymmetric distribution. The influence of spanwise force on the particle can not be neglected.

The paper deals with problem of critical states in single-support rods and cylindrical shells under axial follower forces and centrifugal inertial forces due to rotation. It is shown that depending on the relationship between these forces, loss of stability may be quasistatic or dynamic

We present a new method for simulation of inextensible cloth subjected to a conservative force (e.g., the gravity) and collision-free constraint. Traditional algorithms for cloth simulation are all physically-based in which cloth is treated as an elastic material with some stiffness coefficient(s). These algorithms break down ultimately if one tries to set this stiffness coefficient to infinite which corresponds to inextensible cloth. The crux of the method is an algorithm for interpolating a given set of arbitrary points or space curves by a smooth developable mesh surface. We formulate this interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, e.g., a planar figure, to a final mesh surface that interpolates the given points (called anchor points). During the deformation process, all the triangle elements in the intermediate meshes are kept isometric to their initial shapes, while the potential energy due to the conservative force is reduced gradually. The collision problem is resolved by introducing dynamic anchor points owing to the collision during the deformation. Notwithstanding its simplicity, the proposed method has shown some promising efficacy for simulation of inextensible cloth.

The effect of a magnetic field on thermal instability in mixed convection flow on a heated rotating convex surface is studied in this paper. The onset position characterized by the Goertler number G δ depends on the Grashof number, the rotational number, the Prandtl number, the magnetic field parameter, and the wave number. The buoyancy force, the centrifugal force, the Lorentz force, and the Coriolis force are found to significantly affect the flow structure and heat transfer of the flow. Negative rotation (clockwise) destabilizes the boundary layer flow on a convex surface. However, the Lorentz force stabilizes the flow. Numerical data in this study show the same order of magnitude like experimental data.

Large ΔV amounts are often required to maintain the relative geometry which is needed to implement a formation flying concept. A wise use of the orbital environment makes the orbit keeping phase easier, reducing the overall propellant consumption. A first important step in this direction is the selection of formation configurations and orbits which, while still satisfying the mission requirements, are less subject to perturbations resulting naturally in closed relative motion. Within this frame, a number of studies have been recently carried out in order to identify possible sets of invariant relative orbits under the effects of the Earth oblateness, a conservative force commonly referred to as J2 which is also the most important perturbation for Low Earth Orbit. These efforts clearly marked the difficulties connected with achieving genuine periodic relative motion under J2 effect, but they also showed the existence of a set of conditions on the orbital parameters which allow for quasi-periodic J2 trajectories. This paper presents these particular trajectories, by means of deeper theoretical explanations, showing the dependency of the shape of the relative configurations on the orbital inclination. Since the quasi-periodic trajectories cannot be written analytically, and moreover, they are very sensitive with respect to the initial conditions, difficulties arise when trying to exploit these paths as reference for the control of a formation. This paper proposes a novel approach to find, from the actual quasi periodic natural trajectories, minimal control periodic reference trajectories. Next, it evaluates quantitatively the amount of propellant which is needed to control a spacecraft formation along these paths. The choice of Hill’s classical circular projected configuration as a nominal trajectory is considered as a comparison, showing the clear advantages of the proposed guidance design, which assumes low-perturbed periodic reference orbits as nominal trajectories.

Based on the theoretical model describing the saltation of sand particles in the coupled wind-sand-electricity fields, the numerical simulations of the forces acting on saltating particles, such as the aerodynamic drag force, Magnus effect, Saffman force and electrostatic force, are analyzed in comparison to the gravity force of the particles in the steady windblown sand movement. Furthermore, the laws of the above forces vary with the friction velocity, the diameter of the sand particle, the initial angular velocity and the lift-off velocity are discussed.

We analyze the motion of a particle governed by a generalized Langevin equation with nonlocal dissipative force, linear external force and a constant load force. We consider the dissipative memory kernel consisting of two terms. One of them is described by the Dirac delta function which represents a local friction, whereas for the second one we consider two types: the exponential and power-law functions which represent nonlocal dissipative forces. For these cases, one can obtain exact results for the relaxation function. Then, we obtain the first moments and variances of the displacement and velocity. The long-time behaviors of these quantities are also investigated.

International audience; We report on an experimental device that makes it possible to assess the frictional properties of the contact between a slider and a horizontal surface, and to study the resulting trajectories of the slider when pulled across the surface by means of a flexible link. First, we show experimentally that, when the frictional properties are anisotropic, the slider is subjected, in addition to the dissipative frictional force oriented along the trajectory, to a force, perpendicular to the trajectory, which thus does not contribute to energy dissipation. Therefore, the slider does not necessarily moves in the pulling direction. Second, we show that the trajectories of the slider, when in continuous motion, in absence of inertial effects, can be recovered by assuming that, at all time, the friction force compensates the pulling force. We point out that we prove experimentally that the normal component of the friction force is given as the derivative, with respect to the sliding direction, of the tangential component. This result is particularly interesting as the relation between the normal and the tangential components is compatible with " the maximum of energy release rate " criterion used in the theory of fracture.

A method based on the energy dissipation mechanism of an Independent Oscillator model is used to calculate the frictional force and the friction coefficient of interfacial friction. The friction work is calculated with considering the potential change of contact surfaces during sliding. The potential change can be gained by a universal adhesive energy function. The relationships between frictional force and parameters of a tribo-system, such as surface energy and microstructure of interfacial material, are set up. The calculation results of the known experimental data denote that the frictional force is nearly proportional to the surface energy of the material, nearly inversely proportional to the scaling length, and independent of the lattice constant. The results agree with that of adhesion friction equations. They also agree with the experimental results performed with an atomic-force microscope under the ultra high vacuum condition.

Lubrication theory is applied to derive an expression for the drag force on a particle approaching a directionally solidified interface. To the leading order in the Peclet number, the thermal and hydrodynamic problems are uncoupled. The former yields an equation for the front’s curvature, the solution of which gives the interface profile. The drag force is obtained by solving the lubrication equations in the gap between the particle and the interface. In the absence of shrinkage flow, the force is due solely to the particle’s movement. The dependence of the drag on the parameters, such as the thermal gradient, the latent heat of fusion, and the ratio of the particle’s thermal conductance to that of the melt. α, is explicitly depicted. We find that the drag increases with α, so that perfectly insulated particles experience less drag than highly conducting particles. The variation of the drag force with the thermal gradient also depends on the thermal conductance ratio α. Furthermore, it is noted that the fluid drag force derived here resembles the Taylor’s lubrication force that resists the approach between two rigid surfaces.

As is well known, the existence of geometrically similar orbits for a particle moving under a central conservative force is a consequence of the fact that the corresponding potential energy is a homogeneous function of the co-ordinates. In this paper, we consider a particular non-homogeneous potential of the form V = U + W, where U and W are homogenous functions of degrees −1 and −2, respectively, because, for this potential, the search of closed orbits, for discrete values of the angular momentum, is straightforward. We focus our attention on these daisy-like charming orbits and graphically show the consequences of the impossibility of geometrical similarity.

We outline our Lorentz-force approach to the description of dispersion forces (see also C. Raabe and D.-G. Welsch, Phys. Rev. A 71:013814, 2005; Phys. Rev. A 73:063822, 2006). It is based on the ground-state Lorentz force density that acts on the charge and current densities attributed to the polarization and magnetization in linearly, locally, and causally responding media. Application of the theory to dielectric systems yields very general formulas for the Casimir force on dielectric bodies or parts of them. It is shown that well-known expressions for the Casimir-Polder force on a single atom and for the van der Waals force between atoms are also contained in our formula. The theory may thus be viewed as providing a unified basis for the calculation of dispersion forces from a macroscopic point of view.

In this paper we propose and derive expressions for the drag and lift forces in a two-phase particulate mixture. The analysis is limited to two-dimensional laminar flows. In the Section after the Introduction, a brief review of the single particle approach is provided; it is then shown that in most multiphase flow problems some generalization of these forces acting on a single particle is used. We then describe a different way of defining the lift force and the drag force, an approach used in non-Newtonian fluid mechanics. In the following Section, the essential equations of Mixture Theory are provided and the specific approach of [1] is used. In this scheme, the lift force is part of the interaction mechanisms, which are to be modeled as constitutive parameters. In the final Section, we derive an expression for the lift force, whereby it is shown that the normal component of the force acting on the body, obtained by integrating the traction vector of the mixture acting on a single isolated particle, will give us the desired expression for the lift force in multi-component flows.

It is known that for the magnetic force due to a closed circuit, the Weber force law can be identical to the Lorentz force law. In this investigation it is shown that for both the electric and the magnetic force of the quasi-static case, the Riemann force law can be identical to the Lorentz force law, while the former is based on a potential energy depending on a relative speed and is in accord with Newton's law of action and reaction.

Consideration is given to problems associated with modeling of the motion of a condensed particle in a channel with injection with allowance for the action of different force factors (the hydrodynamic-drag force, the Saffman lift force, and the thermophoresis force). From the results of the numerical modeling, the author draws conclusions on the degree of influence of different force factors on the pattern of motion of the particle.

This paper presents the approximate general solution of the triple well, double oscillator non-linear dynamical system. This system is non-integrable and the approximate general solution is calculated by application of the Last Geometric Theorem of Poincare (Birkhoff, 1913, 1925). The original problem, known as the Duffing one, is a 1 degree of freedom system that, besides the conservative force component, includes dumping and external forcing terms (see details in the web site: http://www.uncwil.edu/people/hermanr/chaos/ted/chaos.html). The problem considered here is a 2 degree of freedom, autonomous and conservative one, without dumping, and of axisymmetric potential. The space of permissible motions is scanned for identification of all solutions re-entering after from one to nine oscillations and the precise families of periodic solutions are computed, including their stability parameter, covering all cases with periods T corresponding to 4osc/T. Seven sub-domains of the space of solutions were investigated in detail by zooming, an operation that proved the possibility to advance the accuracy of the approximate general solution to the level permitted by the integration routine. The approximation of the general solution, although impressive, provides clear evidence of the complexity of the problem and the need to proceed to larger period families. Nevertheless, it allows prediction of the areas where chaos and order regions in the Poincare surfaces of section are to be expected. Examples of such surfaces of sections, as well as of types of closed solutions, are given. Two peculiar points of the space of solutions were identified as crossing, or source points from which infinite families of periodic solutions emanate. The morphology and stability of solutions of the problem are studied and discussed.

The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the fluctuation--dissipation theorem to far from equilibrium systems in a steady state which reduces to the usual Green-Kubo (GK) relation in the limit of small external non conservative forces. FR is a theorem for smooth uniformly hyperbolic systems, and it is assumed to be true in all dissipative ``chaotic enough'' systems in a steady state. In this paper we develop a theory of finite time corrections to FR, needed to compare the asymptotic prediction of FR with numerical observations, which necessarily involve fluctuations of observables averaged over finite time intervals T. We perform a numerical test of FR in two cases in which non Gaussian fluctuations are observable while GK does not apply and we get a non trivial verification of FR that is independent of and different from linear response theory. Our results are compatible with the theory of finite time corrections to FR, while FR would be observably violated, well within the precision of our experiments, if such corrections were neglected., Comment: Version accepted for publication on the Journal of Statistical Physics; minor changes; two references added

The constants of motion of the following systems are deduced: a relativistic particle with linear dissipation, a no-relativistic particle with a time explicitly depending force, a no-relativistic particle with a constant force and time depending mass, and a relativistic particle under a conservative force with position depending mass. The problem of getting the Hamiltonian for these systems is determined by getting the velocity as an explicit function of position and generalized linear momentum, and this problem can be solved a first approximation for the first above system.

The present work presents an experimental study on a free-falling rigid sphere in a quiescent incompressible newtonian fluid, placed in an oscillating frame. The goal of this investigation is to examine the effect of the history force acting on the sphere at small Reynolds numbers (Re≤2.5) and finite Strouhal numbers (1≤Sl≤20). The particle trajectory is measured by using a high-speed video camera and modern techniques of image processing. The average terminal velocity, the oscillation magnitude, and the phase shift with the oscillating frame are measured and compared with those obtained from theoretical approaches. The comparison is made by solving the equation of motion of the sphere with and without the history force. In addition to the significant role that this force plays in the momentum balance, it was found that the correction of the added mass force and the history force by the empirical coefficients of Odar and Hamilton (J Fluid Mech 18:302–314, 1964; J Fluid Mech 25:591–592, 1966) are not necessary in our Re and Sl ranges. The added mass is the same as that obtained by the potential flow theory and the history force is well predicted by the Basset expression (Treatise on hydrodynamics, 1888).

The question of the nature of the force, usually referred to as the “Lorentz force” experienced by vortices in superconductors has arosen new attention in the last years. This paper contains some observations that may help understand the nature of this force, at least for stationary, pinned vortices. One observation is that the force is not proportional to the electromagnetic coupling constant, i.e. the electric charge. This points to the importance of kinematical analysis in discussing it. A second observation refers to the fact that in the London limit, kinetic energy dominates over magnetic energy in the formation energy of a vortex. We give an exact derivation of the force using the London model. We indicate that in the Ginzburg–Landau theory the same result obtains. Our derivation shows also the origin of additional forces experienced by the vortex near the sample surface.

The appearance of the time derivative of the acceleration in the equation of motion (EOM) of an electric charge is studied. It is shown that when an electric charge is accelerated, a stress force exists in the curved electric field of the accelerated charge, and in the case of a constant linear acceleration, this force is proportional to the acceleration. This stress force acts as a reaction force which is responsible for the creation of the radiation (instead of the “radiation reaction force” that actually does not exist at low velocities). Thus the initial acceleration should be supplied as an initial condition for the solution of the EOM of an electric charge.

In this Letter, we study generalized relativistic billiards: as a particle reflects from the boundary of the domain, its velocity is transformed as if the particle underwent an elastic collision with a moving wall, considered within the framework of the special theory of relativity. Inside the domain, the particle moves under the influence of some gravitational and nongravitational force fields.