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.     

Surface charge estimation on hemispherical dielectric samples from EFM force gradient measurements

A numerical model capable of estimating the surface charge density(σ_S) and the dielectric constant(k_e) of a hemispherical sample from force gradient measurements is proposed. Force gradients are commonly detected by a biased conductive tip during electrostatic force microscopy(EFM) probing but provide limited quantitative assessment of the charge in the sample. The proposed model gives an analytical solution for the force exerted over a biased conical tip. Theoretical numerical results, presented in the form of multitraces of minimum force gradients for fixed bias voltages and tip-sample distances allow the translation of EFM force gradient measurements into functions of σ_S and k_e.     

An overlooked electrostatic force that acts on a non-charged asymmetric conductor in a symmetric (parallel) electric field

Usually, when a material that has charge Q is placed in an electric field E, an electrostatic force F = QE acts on the material. This force does not act on a non-charged material. Nevertheless, when a non-charged material is placed in a convergent field, another electrostatic force acts. This force is called the gradient force. If the material is small and the shape is a sphere, the gradient force can be calculated by an approximate formula, but it cannot be calculated for other shapes. In this paper the gradient force that acts on a symmetric rod conductor in a convergent (asymmetric) field was simulated by an axis symmetry finite difference method.Under same simulation conditions without the next two points, the shape of the conductor and the form of the field were reversed. The shape of the conductor was changed into an asymmetric shape (e.g. bat shape), and the form of the field was changed into a symmetric (parallel) one. The electrostatic force that acts on the asymmetric conductor in the symmetric (parallel) field was simulated. It was found that approximately the same intensity force as in the first simulation also acts on this conductor. This force is thought to be an overlooked electrostatic force. I provisionally call it the asymmetric force in this paper.The asymmetric force with differently shaped conductors was simulated and it was found that the asymmetric force was maximized for a cup shaped conductor.Finally, the asymmetric force with the cup shaped conductor in normal and reversed parallel (symmetric) fields was simulated, and it was confirmed that the asymmetric force remains the same in both fields.     

Analysis of the electrostatic force on a dielectric particle with partial charge distribution

This paper presents the analysis of the electrostatic force acting on a charged dielectric particle on a grounded plane. The force has been determined by a numerical field calculation method to make clear the effect of particle dielectric constant and charge distribution on the particle surface. The charge is treated to be distributed in three ways: (a) uniformly over entire surface, (b) partially on the upper, or (c) on the lower part of a particle. The calculation results show that, if a particle with dielectric constant ?_p = 3 is partially charged on the lower part by a zenith angle π/2, π/4 and π/8, the force shall be higher by 0.7, 4.3 and 20 times, respectively, than that for a uniform charging with the same charge amount. On the other hand, the force becomes weaker when charge is on the upper part. The effect of the particle dielectric constant is found to be dependent on the charge distribution. With charge uniform on the entire surface or on the upper part, the force always increases with the dielectric constant. However, when surface charge is restricted to a small area at the lower part of the particle (θ_q < π/4), the force may decrease with increasing the dielectric constant.     

Maximum pull out force on DNA hybrids

We discuss theoretically the force F between two colloidal particles, each of them carrying one single strand DNA. The two strands are complementary only on a finite sequence of (ℓ) consecutive base pairs. We define an adjustment length ϰ⁻¹ (a few base pairs); in the adjustment regions near both ends of the paired region, the tension is still mainly on one single strand. But in the central part (for ℓ>ϰ⁻¹) the two backbones are equally loaded. This leads to a rupture force F_c increasing linearly with ℓ for ℓϰ<1, and saturating for ℓϰ>1.     

Transverse (lateral) instantaneous force of an acoustical first-order Bessel vortex beam centered on a rigid sphere

In a recent report [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724], it has been found that the instantaneous axial force (i.e. acting along the axis of wave propagation) of a Bessel acoustic beam centered on a sphere is only determined for the fundamental order (i.e. m = 0) but vanishes when the beam is of vortex type (i.e. m > 0, where m is the order (or helicity) of the beam). It has also been recognized that for circularly symmetric beams (such as Bessel beams of integer order), the transverse (lateral) instantaneous force should vanish as required by symmetry. Nevertheless, in this commentary, the present analysis unexpectedly reveals the existence of a transverse instantaneous force on a rigid sphere centered on the axis of a Bessel vortex beam of unit magnitude order (i.e. |m| = 1) not reported in [F.G. Mitri, Z.E.A. Fellah, Ultrasonics 51 (2011) 719-724]. The presence of the transverse instantaneous force components of a first-order Bessel vortex beam results from mathematical anti-symmetry in the surface integrals, but vanishes for the fundamental (m = 0) and higher-order Bessel (vortex) beams (i.e. |m| > 1). Here, closed-form solutions for the instantaneous force components are obtained and examples for the transverse components for progressive waves are computed for a fixed and a movable rigid sphere. The results show that only the dipole (n = 1) mode in the scattering contributes to the instantaneous force components, as well as how the transverse instantaneous force per unit cross-sectional surface varies versus the dimensionless frequency ka (k is the wave number in the fluid medium and a is the sphere’s radius), and the half-cone angle β of the beam. Moreover, the velocity of the movable sphere is evaluated based on the concept of mechanical impedance. The proposed analysis may be of interest in the analysis of transverse instantaneous forces on spherical particles for particle manipulation and rotation in drug delivery and other biomedical or industrial applications.     

Three-dimensional Casimir piston for massive scalar fields

We consider Casimir force acting on a three-dimensional rectangular piston due to a massive scalar field subject to periodic, Dirichlet and Neumann boundary conditions. Exponential cut-off method is used to derive the Casimir energy. It is shown that the divergent terms do not contribute to the Casimir force acting on the piston, thus render a finite well-defined Casimir force acting on the piston. Explicit expressions for the total Casimir force acting on the piston is derived, which show that the Casimir force is always attractive for all the different boundary conditions considered. As a function of a - the distance from the piston to the opposite wall, it is found that the magnitude of the Casimir force behaves like 1/a⁴ when a→0⁺ and decays exponentially when a→∞. Moreover, the magnitude of the Casimir force is always a decreasing function of a. On the other hand, passing from massless to massive, we find that the effect of the mass is insignificant when a is small, but the magnitude of the force is decreased for large a in the massive case.     

Vibrational properties of the adsorbed monolayer on face-centered cubic crystals

Calculations of mean-square displacements 〈u²〉 of the atoms in adsorbed monolayers on fcc crystals are presented and compared with LEED experimental results. This text is restricted to the case of a C(2 × 2) adsorbed layer on a (100) surface [experimental case of Ni(100) with adsorbed sulfur, sodium, cesium or oxygen]. 〈u²〉's perpendicular to and parallel to a (100) surface are calculated for the adsorbed atoms and the atoms of the first surface layer of the crystal. The values obtained are compared with those for a clean (100) surface and the volume of the crystal. Every possibility for force constants between adsorbate and substrate atoms is examined. It is shown that the measurement of 〈u²〉 perpendicular to the (100) surface yields the adsorbate-substrate force constants and that 〈u²〉 parallel to the (100) surface yields the adsorbate-adsorbate force constants.     

Effect of overlapping Debye spheres on structures of 2D dusty plasmas

In dusty plasmas, overlapping Debye spheres around dust grains could produce an attractive force between them. Its effects on static structures of two-dimensional (2D) dusty plasmas are studied here by using molecular dynamics simulations. Results, in terms of the equilibrium radial distribution function, are compared with those deduced from purely repulsive Debye-Hückel or Yukawa potential for different Coulomb-coupling and screening parameters. The effect of the attractive force is found quite noticeable for usual experimental conditions, and becomes more pronounced for larger screening parameter κ. In particular, it is observed that for large κ the attractive force is dominant, and dust grains tend to aggregate and form patterns with scattering voids.     

Bistability of radiation force on N-atom system

We consider a system with N two-level atoms in a cavity, interacting with an external radiation field. Using Ehrenfest's theorem the radiation force on the N-atom system is studied as a function of the external radiation field. In a certain parameter region we are able to show that the radiation force can be bistable     

Using capillary forces to estimate the adhesion strength of Magnaporthe grisea spores on glass

The Magnaporthe grisea is a fungus whose spores strongly adhere to plant leaves, and to solid surfaces in general. In this note, we give an estimate of the adhesion force, F_det, of a spore on a glass surface, in water. F_det is defined as the force to be applied to a spore to pull it out from the surface. In our experiments, spores are detached from the glass in a few milliseconds by means of a capillary force. The latter is provided by a water/air or a water/oil interface, in contact with the spore body. We thus find F_det of the order of 10⁻⁶ N.     

Influence of the spatial rotation of a polarization plane on the radiative friction force in light fields with polarization gradients

Simple atomic models (1/2→1/2 and 1/2→3/2 transitions) were taken as an example to consider, in the sub-Doppler cooling approximation, influence of the spatial rotation of a polarization plane on the radiative friction force at arbitrary field configurations of dimensionality D<1. Spatial gradients of the angles determining this rotation additionally contribute to the friction force. This contribution is comparable in magnitude with other forces if the detuning δ is on the order of the radiative relaxation constant γ. For the j→j+1 transitions, the contribution promotes sub-Doppler cooling at δ<0, whereas for the j→j transitions (half-integer j) it induces anisotropic heating and cooling processes.     

Spin dynamics of qqq wave function on light front in high momentum limit of QCD: Role of qqq force

The contribution of a spin-rich qqq force (in conjunction with pairwise qq forces) to the analytical structure of the qqq wave function is worked out in the high momentum regime of QCD where the confining interaction may be ignored, so that the dominant effect is Coulombic. A distinctive feature of this study is that the spin-rich qqq force is generated by a ggg vertex (a genuine part of the QCD Lagrangian) wherein the 3 radiating gluon lines end on as many quark lines, giving rise to a (Mercedes-Benz type) Y-shaped diagram. The dynamics is that of a Salpeter-like equation (3D support for the kernel) formulated covariantly on the light front, a la Markov-Yukawa Transversality Principle (MYTP) which warrants a 2-way interconnection between the 3D and 4D Bethe-Salpeter (BSE) forms for 2 as well as 3 fermion quarks. With these ingredients, the differential equation for the 3D wave function ? receives well-defined contributions from the qq and qqq forces. In particular a negative eigenvalue of the spin operator iσ₁ · σ₂ × σ₃ which is an integral part of the qqq force, causes a characteristic singularity in the differential equation, signalling the dynamical effect of a spin-rich qqq force not yet considered in the literature. The potentially crucial role of this interesting effect vis-a-vis the so-called ‘spin anomaly’ of the proton, is a subject of considerable physical interest.     

Electron drag of dislocations in thin metal plates

The electron force dragging dislocations in a thin metal plate of thickness d has been calculated and the dependence of the drag force F on the parameter $\text{d}\text{l}$ (l is the electron free path length) determined for the cases $\text{d}\text{l ? 1}$ and $\text{d}\text{l ? 1}$. With d ? l, the drag force depends upon the nature of electron scattering on the plate surface. The drag force dependence on the sample size has also been considered for a d.c. magnetic field H parallel to the plate faces. In the case of diffuse scattering the second derivative of F(H) reveals a square root singularity at the value of the magnetic field where the electron orbit diameter is equal to the plate thickness.     

Ab initio study of the force constants of inorganic molecules ONF and NF3

The force constants of ONF and NF₃ have been determined from Hartree-Fock ab initio wavefunctions by the force method. Three different Gaussian basis sets, ranging from 7s3p augmented with functions on the bonds to 5s2p, were used for ONF. Only the smallest basis was applied to NF₃. The results show remarkable agreement with experiment, especially for the coupling constants. The NF stretching force constant is greatly overestimated in calculations with the 5s2p basis. The calculated force field makes it possible to exclude sets of force constants which are unphysical but compatible with the experimental data. The results show that even calculations with 5s2p basis sets can contribute to the determination of force fields.The experimental value of the $\text{ON}\text{β}$ coupling constant in ONF ranges between 0.27 and 0.54 mdyn; our calculations corroborate the higher value. An estimation of the calculated molecular geometries is given.     

Simulation of ultrasound influence on melt convection for the growth of GaxIn1−xSb and Si single crystals by the Czochralski method

The flow simulation for Ga_xIn_1−xSb and Si melts was conducted for quasi-steady conditions. The maximum velocity was under the solid–liquid interface near periphery of the crystals. An introduction of ultrasound into the liquid formed a standing wave channel under the solid–liquid interface, which acted on melt particles. The calculations of convective and ultrasonic forces acting on the particles in the melt showed that the ultrasonic force is much higher than the convective force.     

Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid

Mixed convection flow of Cu–water nanofluid inside a lid-driven square cavity with adiabatic horizontal walls and sinusoidal heating on sidewalls has been investigated numerically. The effects of increase in shear force for a fixed buoyancy force and effects of increase in buoyancy force for a fixed shear force were investigated. Effects of variations of Richardson number, phase deviation of sinusoidal heating, and volume fraction of nanoparticles on flow and temperature field were studied. The obtained results showed that for a constant Grashof number at all Richardson numbers, a clockwise eddy was developed inside the cavity, also the rate of heat transfer increases with decrease in Richardson number and increase of volume fraction of nanoparticles. For a constant Reynolds number the clockwise eddy is observed up to Ri = 1. For Ri = 10 a multicellular flow pattern is formed inside the cavity. Moreover it was found that when the Reynolds number is kept constant, the rate of heat transfer increases with increase in Richardson number.     

Orientational effect of the dynamical interaction of circular dislocation loops with a moving edge dislocation

The glide of an edge dislocation in a crystal containing circular dislocation loops is studied theoretically. An analytical expression is obtained for the drag force exerted on a dislocation by various types of dislocation loops, and it is shown that this force depends significantly on the orientation of the Burgers vector of immobile dislocation loops with respect to the gliding dislocation line. The F _‖/F _⊥ ratio of the drag force for the parallel orientation of the Burgers vectors of the loops with respect to the gliding dislocation line (F _‖) and the drag force for the perpendicular orientation (F _⊥) is equal to K(v/c)², where v is the velocity of the dislocation; c is the velocity of acoustic waves in the crystal; and K is a dimensionless coefficient, whose value is of the order of the ratio of the concentrations of dislocation loops with parallel and perpendicular orientations of the Burgers vector.     

Towards a statistical theory of solid dry friction

Wearless dry friction of an elastic block of weight N, driven by an external force F over a rigid substrate, is investigated. The slider and substrate surfaces are both microscopically rough, interacting via a repulsive potential that depends on the local overlap. The model reproduces Amontons’s laws which state that the friction force is proportional to the normal loading force N and independent of the nominal surface area. In this model, the dynamic friction force decays for large velocities and approaches a finite static friction for small velocities if the surface profiles are self-affine on small length scales.     

Correlations between potentials and observables in the NN interaction

We study the effects of the components of the soft-core and velocity-dependent Paris nucleon-nucleon potential on the scattering observables for laboratory energies, T_L, between 10 and 350 MeV. Knowledge of these correlations is useful to indicate constraints on components of the nucléon-nucléon force. The velocity-dependent component, attractive at low energy and repulsive at high energy, plays a role at all energies. The polarisation P, the depolarisation D and the parameters D_t, A, R, C_KP and C_NN are good tests for the tensor, spin-orbit and, to a smaller extent, quadratic spin-orbit forces. The isovector tensor force contribution is important at low energy and that of the isovector spin-orbit at high energy. The isoscalar tensor force effect is large at all energies and that of the isoscalar spin-orbit force rather small. The potential without quadratic spin-orbit term reproduces well the experimental data for T_L < 150 MeV.