A gas of Brownian particles in statistical dynamics

We consider a large number of particles on a one-dimensional latticel Z in interaction with a heat particle; the latter is located on the bond linking the position of the particle to the point to which it jumps. The energy of a single particle is given by a potentialV(x), x∈Z. In the continuum limit, the classical version leads to Brownian motion with drift. A quantum version leads to a local drift velocity which is independent of the applied force. Both these models obey Einstein's relation between drift, diffusion, and applied force. The system obeys the first and second laws of thermodynamics, with the time evolution given by a pair of coupled non linear heat equations, one for the density of the Brownian particles and one for the heat occupation number; the equation for a tagged Brownian particle can be written as a stochastic differential equation.     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001     

Harnack Inequalities and Discrete—Continuous Error Estimates for a Chain of Atoms with Two—Body Interactions

We consider deformations in ℝ³ of an infinite linear chain of atoms where each atom interacts with all others through a two-body potential. We compute the effect of an external force applied to the chain. At equilibrium, the positions of the particles satisfy an Euler–Lagrange equation. For large classes of potentials, we prove that every solution is well approximated by the solution of a continuous model when applied forces and displacements of the atoms are small. We establish an error estimate between the discrete and the continuous solution based on a Harnack lemma of independent interest. Finally we apply our results to some Lennard-Jones potentials.     

Dynamic simulation using a multipolar model of particles under dielectrophoretic force

This article presents the simulation of an electrorheological (ER) fluid system by using a multipole model that includes multipolar interactions between particles. The model uses the multipole re-expansion and the method of images for calculating electric field and force. The highest order of multipoles (N_mp) and the number of iterations (N_iter) used in the method of images can be chosen for the accuracy of the force approximation and the simulation time required. Study of a two-particle configuration shows that the force does not increase linearly with increasing N_mp and N_iter. The specific case N_mp=4 and N_iter=2 is chosen for dynamic simulation. We have performed the simulation of a system of 20 particles, and compared the formulation of particle chains with that obtained using the dipole model. The results imply that the response time for the change in viscosity of real-ER fluids is significantly shorter than that predicted by the dipole model.     

Radiation force exerted on nanometer size non-resonant Kerr particle by a tightly focused Gaussian beam

We calculate the radiation force that is exerted by a focused continuous-wave Gaussian beam of wavelength λ on a non-absorbing nonlinear particle of radius a ? 50λ/π. The refractive index of the mechanically-rigid particle is proportional to the incident intensity according to the electro-optic Kerr effect. The force consists of two components representing the contributions of the electromagnetic field gradient and the light scattered by the Kerr particle. The focused intensity distribution is determined using expressions for the six electromagnetic components that are corrected to the fifth order in the numerical aperture (NA) of the focusing objective lens. We found that for particles with a < λ/21.28, the trapping force is dominated by the gradient force and the axial trapping force is symmetric about the geometrical focus. The two contributions are comparable with larger particles and the axial trapping force becomes asymmetric with its zero location displaced away from the focus and towards the beam propagation direction. We study the trapping force behavior versus incident beam power, NA, λ, and relative refractive index between the surrounding liquid and the particle. We also examine the confinement of a Kerr particle that exhibits Brownian motion in a focused beam. Numerical results show that the Kerr effect increases the trapping force strength and significantly improves the confinement of Brownian particles.     

Particle drift in a resonance tube--a numerical study

The paper considers longitudinal drift of small particles in a resonance tube, caused by periodic shock waves, and its effect on particle agglomeration. It is found that depending on particle size, drift is caused by shock waves and/or gas acceleration and compression. It is also shown that the drift velocity and direction can be controlled by the frequency of the piston that causes gas oscillations in the resonance tube. The obtained numerical solutions indicate that particle drift in a resonance tube enhances aerosol agglomeration. An agglomeration kernel is derived for this case, accounting for particle drift, leading to an estimate of agglomeration time. The time predicted by present model is of the same order of magnitude as that obtained from experiments in the literature.     

Species segregation in one-dimensional granular-system simulations

We present one-dimensional molecular dynamics simulations of a two-species, initially uniform, freely evolving granular system. Colliding particles swap their relative position with a 50% probability allowing for the initial spatial ordering of the particles to evolve in time and frictional forces to operate. Unlike one-dimensional systems of identical particles, two-species one-dimensional systems of quasi-elastic particles are ergodic and the particles' velocity distributions tend to evolve towards Maxwell-Boltzmann distributions. Under such conditions, standard fluid equations with merely an additional sink term in the energy equation, reflecting the non-elasticity of the interparticle collisions, provide an excellent means to investigate the system's evolution. According to the predictions of fluid theory we find that the clustering instability is dominated by a non-propagating mode at a wavelength of the order 10πL/Nɛ , where N is the total number of particles, L the spatial extent of the system and ɛ the inelasticity coefficient. The typical fluid velocities at the time of inelastic collapse are seen to be supersonic, unless Nɛ ≲ 10π . Species segregation, driven by the frictional force occurs as a result of the strong temperature gradients within clusters which pushes the light particles towards the clusters' edges and the heavy particles towards the center. Segregation within clusters is complete at the time of inelastic collapse.     

Tip-surface interactions at redox responsive poly(ferrocenylsilane) (PFS) interface by AFM-based force spectroscopy

Poly(ferrocenylsilanes) (PFS) belong to the class of redox responsive organometallic polymers. Atomic force microscopy (AFM)-based single molecule force spectroscopy (SMFS) was used earlier to study single chain PFS response and redox energy driven single chain PFS molecular motors. Here we present further AFM investigations of force interactions between tip and a grafted PFS surface under potential control in electrochemical redox cycles. Typical tip-Au interaction is considered as reference in the force measurements. First the electrostatic component in the diffused double layer (DL) in NaClO₄ electrolyte environment was considered for a “grafted to” PFS, which dominated the interplay between the tip and sample surface. The DL forces can also hinder the physisorption of PFS chain onto the tip when the voltage was applied at −0.1 V. On the other hand, if the tip contacted the PFS surface prior to the electrochemical process, physisorption of PFS chains governed the overall interaction regardless of subsequently applied surface potential. In addition, prolonged contact time, t_c, may also contribute to the stability of tip-PFS bridging and detection of electrostatic forces between the tip-PFS interface. The results showed that tip-substrate interaction forces without PFS grafts have negligibly small force contributions under similar, electrochemically controlled, conditions used in single PFS chain based molecular motors.     

Optimal transport in a ratchet coupled to a modulated environment: The role of Levy walks

We consider a Brownian particle in a ratchet potential coupled to a modulated environment and subjected to an external oscillating force. The modulated environment is modelled by a finite number N of uncoupled harmonic oscillators. Superdiffusive motion and Levy walks (anomalous random walks) are observed for any N and for low values of the external amplitude F. The coexistence of left and right running states enhances the power α from the time dependence of the mean square displacement (MSD). It is shown that α is twice the average of the power of the separated left and right MSDs. Normal random walks are obtained by increasing F. We show that the maximal mobility of particles along the periodic structure occurs just before superdiffusive motion disappears and Levy walks are transformed into normal random walks.     

Mixing Properties for Mechanical Motion¶of a Charged Particle in a Random Medium

We study a one-dimensional semi-infinite system of particles driven by a constant positive force F which acts only on the leftmost particle of mass M, called the heavy particle (the h.p.), and all other particles are mechanically identical and have the same mass m < M. Particles interact through elastic collisions. At initial time all neutral particles are at rest, and the initial measure is such that the interparticle distances ξ _i are i.i.d. r.v. Under conditions on the distribution of ξ which imply that the minimal velocity obtained by each neutral particle after the first interaction with the h.p. is bigger than the drift of an associated Markovian dynamics (in which each neutral particle is annihilated after the first collision) we prove that the dynamics has a strong cluster property, and as a consequence, we prove existence of the discrete time limit distribution for the system as seen from the first particle, a ψ-mixing property, a drift velocity, as well as the central limit theorem for the tracer particle. Received: 22 March 2000 / Accepted: 8 December 2000     

Soft Dynamics simulation. 1. Normal approach of two deformable particles in a viscous fluid and optimal-approach strategy

Discrete simulation methods are efficient tools to investigate the behaviors of complex fluids such as dry granular materials or dilute suspensions of hard particles. By contrast, materials made of soft and/or concentrated units (emulsions, foams, vesicles, dense suspensions) can exhibit both significant elastic particle deflections (Hertz-like response) and strong viscous forces (squeezed liquid). We point out that the gap between two particles is then not determined solely by the positions of their centers, but rather exhibits its own dynamics. We provide the first ingredients of a new discrete numerical method, named Soft Dynamics, to simulate the combined dynamics of particles and contacts. As an illustration, we present the results for the approach of two particles. We recover the scaling behaviors expected in three limits: the Stokes limit for very large gaps, the Poiseuille-lubricated limit for small gaps and even smaller surface deflections, and the Hertz limit for significant surface deflections. We find that for each gap value, an optimal force achieves the fastest approach velocity. The principle of larger-scale simulations with this new method is provided. They will consitute a promising tool for investigating the collective behaviors of many complex materials.     

Convective motion and transfer of force by many-body hydrodynamic interaction

We consider hydrodynamic interactions between N rigid bodies of arbitrary shape immersed in an incompressible fluid. When the bodies are carried along by an incident flow without exerting forces or torques on the fluid then their translational and rotational velocities are linearly related to the incident flow velocity by convection kernels. In the absence of an incident flow, but with applied forces and torques, the force density acting on the fluid is linearly related to the forces and torques by transfer kernels. We show that the convection and transfer kernels are simply related by a symmetry relation. For freely moving bodies the force density exerted on the fluid is related to the incident flow by a convective friction kernel. We show that this kernel is symmetric.     

The radial force on a charged particle in superimposed magnetic fields on Schwarzschild spacetime

Following the approach of optical reference geometry we derive the expression for the total force in the radial direction acting on a charged particle in magnetic fields superimposed on the static Schwarzschild background and show the possible existence of bound orbits for particles in the field of ultra compact objects at distancesr?3m wherein the Lorentz force counterbalances both the gravitational and centrifugal forces.     

Thermophoresis as persistent random walk

In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between +v and −v. If v is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the model accounts readily for the particle's drift along the temperature gradient and recovers basic results of the conventional thermophoresis theory.     

Dynamics of an interacting Bose-Einstein condensate in a three-well potential

We study the dynamics of an ultracold interacting Bose-Einstein gas confined in a one-dimensional potential composed of three symmetrical wells. We numerically solve the time-dependent Schrödinger equation of the N-particle Hamiltonian for N = 50, 150, 500, 1000. We demonstrate that the quantum phase transition from a superfluid (SF) to a Mott insulator (MI) phase in the three-well potential depends on the strength of the interactions among the particles, the total number of particles, and the confining potential in which the particles move. We discuss the appearance of population revivals as a function of time and find that, even in the case when the interaction strength among the particles is very small, its effect has the consequence that the system never returns to the initial condition. A stationary state for long times is observed in the SF phase, while the particle population in each well remains almost equal to the initial condition in the MI phase.     

A power mode approach to estimating vibrational power transmitted by multiple sources

A power mode method for the estimation of the power transmitted to a flexible receiver by an array of point force excitations is described. The vibrational power transmitted by N discrete point forces is regarded as the power transmitted by N independent power modes following eigendecomposition of the mobility matrix of the receiving structure. Approximate expressions for the upper and lower bounds and the mean value of the transmitted power are then developed in terms of these power modes. The approach is extended to more general cases, including that where both force and moment excitations are applied to the structure and where there are velocity source excitations. Numerical examples are presented.     

Ground state of an impurity in a homogeneous system in the hypernetted chain approximation

The hypernetted chain theory of the ground state of a homogeneous N-particle medium NM with an impurity particle is presented. The N identical particles are fermions with spin-isospin degeneracy ν, or bosons (in the limit of ν → ∞). The ground-state wave-function of the system is assumed in the Jastrow form with central, state-independent correlation functions. Central, spin-isospin-dependent two-body interactions both in NM and between the impurity particle and the particles of NM are considered. Expressions for the ground-state energy of the system and for the separation energy of the impurity particle are derived. The simplified case of the chain approximation is also considered.     

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian-Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force-known as Basset-Boussinesq history force-and the non-Stokesian drag based on Schiller-Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor-Reynolds number, Re_λ?31, for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81-91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.     

Particle size reduction and enhanced diffusion of Fe and Pt atoms in FePt-C granular films by N addition

N-doped FePt-C nanocomposite films were fabricated using facing-target sputtering method under different N₂ partial pressures (P_N) at room temperature. Annealing at 650 °C turns the amorphous films into ordered structures. Nitrogen doping not only make the ordering of FePt particles easier than the ordering in FePt-C films, due to the enhanced diffusivity of Fe and Pt atoms, but also effectively limits the growth of the FePt particles during the thermal induced ordering, especially for the annealed films fabricated at P_N = 40%, where the average size of well-isolated FePt particles is only ∼8 nm. The particle size reduction and the enhanced diffusion of Fe and Pt atoms can be ascribed to the desorption of doped N atoms and dissociation of FeN bonds during annealing. The room-temperature coercivity of the samples decreases with the P_N due to the particle size reduction and thus the enhancement of the thermal agitation for small particles during the magnetizing procedure.