Motion in a periodic potential driven by rectangular pulses

Exact solutions are found for the averaged velocity of an overdamped pendulum driven by a series of square pulses. The formalism developed can be applied to either periodic or random switching as well as cases intermediate between the two. The phenomenon known as phase locking can be shown to exist when periodic switching is used.     

Spreading of a drop on a contaminated substrate

Most wetting or spreading problems are treated with surface and interfacial free energies taken as constants for the system in question. We consider here the case where a two-dimensional drop (ribbon) is deposited on a solid substrate bearing a very fine layer of a contaminant which modifies the effective drop/solid interfacial free energy. As the contaminant diffuses into the drop, the interfacial free energy, and thus the capillary balance, evolve. This has strange effects on wetting behaviour, including causing a wetting `overshoot'. Possible applications are briefly discussed.     

Nonlinear vibrations of a charged drop in an electrostatic suspension

The problem of nonlinear vibrations of a charged drop of an ideal incompressible conducting fluid in an electrostatic suspension is analytically solved in an approximation quadratic in two small parameters: vibration amplitude and equilibrium deformation of the shape of the drop in an electrostatic field. To solve the problem analytically, the desired quantities are expanded in semiinteger powers of the small parameters. It is shown that the charge of the drop and the gravitational field influence the shape of the drop, nonlinear corrections to the vibration frequencies, and critical conditions for instability of the drop against the surface charge. At near-critical values of the charge, the shape of the nonlinearly vibrating drop falls far short of being a sphere or a spheroid, which should be taken into account in treating experimental data.     

Acoustic radiation from a drop due to its nonlinear vibrations

It is shown that the intensity of acoustic radiation from a vibrating drop depends mainly on the monopole and dipole components appearing only in the second order of smallness in vibration amplitude. The intensity of the quadrupole acoustic radiation generated by the vibration fundamental mode in the first order of smallness in amplitude turns out to be much weaker. This is associated with the fact that, if the acoustic wavelength is much larger than the drop characteristic size, their ratio becomes a governing small parameter, being lesser than the ratio of the drop vibration amplitude to the drop linear size. Analytical estimates of the amplitudes of monopole, dipole, and quadrupole components of the velocity field associated with the acoustic field of the drop.     

Analytical study of nonlinear vibrations of a charged viscous liquid drop

The generatrix of a nonlinearly vibrating charged drop of a viscous incompressible conducting liquid is found by directly expanding the equilibrium spherical shape of the drop in the amplitude of initial multimode deformation up to second-order terms. A fact previously unknown in the theory of nonlinear interaction is discovered: the energy of an initially excited vibration mode of a low-viscosity liquid drop is gradually (within several vibrations periods) transferred to the mode excited by only nonlinear interaction. Irrespectively of the form of the initial deformation, an unstable viscous drop bearing a charge slightly exceeding the critical Rayleigh value takes the shape of a prolate spheroid because of viscous damping of all the modes (except for the fundamental one) for a characteristic time depending on the damping rates of the initially excited modes and the further evolution of the drop is governed by the fundamental mode. In a high-viscosity drop, the rate of rise of the unstable fundamental mode amplitude does not increase continuously with time, contrary to the predictions of nonlinear analysis in terms of the ideal liquid model: it first decreases to a value slightly differing from zero (which depends on the extent of supercriticality of the charge and viscosity of the liquid), remains small for a while (the unstable mode amplitude remains virtually time-independent), and then starts growing.     

Nonlinear capillary vibrations of a charged drop placed in a dielectric medium: Single-mode initial deformation of the drop shape

The nonlinear vibrations of the equilibrium spherical shape of a charged drop placed in a perfect incompressible dielectric medium are asymptotically calculated in the second-order approximation in single-mode initial deformation of the drop surface. The drop is assumed to be a perfect incompressible liquid. It is shown that the nonlinear vibration amplitudes, as well as the energy distribution between nonlinearly excited modes, depend significantly on the parameter ρ, where ρ is the ratio of the environmental density to that of the drop. It is also demonstrated that an increase in ρ raises the amplitude of the highest of the vibration modes excited due to second-order nonlinear interaction. In the second order of smallness, the amplitude of the zeroth mode is independent of the density ratio. As ρ grows, the effect of the self-charge of the drop, the interfacial tension, and the permittivity of the environment on the nonlinear oscillations increases.     

On nonlinear resonant four-mode interaction between capillary vibrations of a charged drop

Energy transfer from higher modes of capillary vibrations of an incompressible liquid charged drop to the lowest fundamental mode under four-mode resonance is studied. The resonance appears when the problem of nonlinear axisymmetric capillary vibration of a drop is solved in the third-order approximation in amplitude of the multimode initial deformation of the equilibrium shape of the drop. Although the resonant interaction mentioned above builds up the fundamental mode even in the first order of smallness, its amplitude turns out to be comparable to a quadratic (in small parameter) correction arising from nonresonant nonlinear interaction, since the associated numerical coefficients are small.     

Motion of spiral tip driven by local forcing in excitable media

We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed： the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation.     

Nonlinear vibrations of a charged drop due to the initial excitation of neighboring modes

The asymptotic analysis of the nonlinear vibrations of a charged drop that are induced by a multi-mode initial deformation of its equilibrium shape is performed. It is shown that when two, three, or several neighboring modes are present in the initial deformation spectrum, the mode with the number one (translational mode) appears in the second-order mode spectrum. The excitation of the translational mode follows from the requirement of center-of-mass immobility and causes the dipole components (which are absent in the linear analysis) to appear in the spectra of the acoustic and electromagnetic radiation of the charged drop.     

Drying of a multicomponent solution drop on a solid substrate: Qualitative analysis

It is shown that, when a drop of a biological fluid dries out on a substrate, diffusion processes to a great extent suppress the transfer of the salt toward the periphery of the drop by capillary flows and still have a minor effect on the motion of colloid particles.     

Investigation of the shape and stability of a liquid drop on a rotating substrate

The shape and stability of a capillary-sized water drop sitting on a rotating substrate are studied both theoretically and experimentally. The theoretical and experimental data are found to be in good agreement. The results of the study may be used in fabricating self-assembled thin films by means of spin coating technology.     

Nonlinear vibrations of a charged drop in a third-order approximation in the amplitude of multimode initial deformation

A solution to the problem of nonlinear surface vibration of a charged ideal liquid drop is found in a third-order approximation in initial multimode deformation of the equilibrium spherical shape by the method of many scales. It is shown that the spectrum of modes that are responsible for the shape of the drop at an arbitrary time instant depends considerably on the spectrum of modes governing the initial deformation of the drop. The latter spectrum also has an effect on nonlinear corrections to the vibration frequencies and, consequently, on a nonlinear correction to the critical Rayleigh parameter, which specifies the stability of the drop against self-charge.     

Analysis of shape perturbations of a drop on a vibrating substrate for different wetting angles

An exact solution is obtained to the problem of axisymmetric normal modes and natural frequencies characterizing surface perturbations of a drop that sits with an arbitrary wetting angle on a substrate and experiences only gravity and surface tension. The resulting mode solutions are used to calculate and analyze different shapes of the perturbed surface for the same drop placed on a vibrating base. The distinctive feature of the present study is the explicit representation of the results in the form of calculated shapes of the surface of a vibrating drop, comparison of the parameters of actual drops with resonance frequencies, and comparison with experimental data.     

表面能梯度驱动下纳米水滴在不同微结构表面上的运动

近年来, 微观尺度下水滴在能量梯度表面上的运动情况受到了广泛关注, 然而通过实验进行研究尚存在困难. 本文利用分子动力学方法研究了不同微结构表面上纳米水滴在表面能梯度驱动下的运动情况. 结果表明: 槽状和柱状微结构可以明显提升纳米水滴在微结构表面上的运动效率, 钉状微结构会降低纳米水滴的运动效率, 尽管它具有稳定的疏水性; 结合槽状和钉状结构的混合状微结构兼具二者的优点, 不但可以有效地提高纳米水滴在粗糙表面上的运动效率, 而且具有比较高的疏水稳定性. 此外, 表面能的微小改变会明显影响水滴的运动效率.     

On the possibility of corona-discharge ignition in the vicinity of a weakly charged drop executing nonlinear vibrations

An analytic expression for the electric-field strength in the vicinity of a charged drop of an electrically conducting liquid is obtained for the case where the initial shape of the drop executing nonlinear vibrations is specified by a virtual excitation of an arbitrary single mode of capillary vibrations. It turns out that, even at small charges (such that the Rayleigh parameter for the drop is equal to one-tenth of the critical value associated with stability against the intrinsic charge), the electric-field strength at the drop surface in the case of an initial excitation of one of high modes is sufficient for the ignition of a corona discharge.     

Nonlinear capillary vibrations and stability of a highly charged drop under single-mode initial deformation of large amplitude

Nonlinear vibrations of a charged drop that are caused by a virtual initial perturbation of the equilibrium spherical shape of the drop were considered. The perturbation can be proportional to any of the free vibration modes. The spectrum and stability of the vibrations were studied correct to second order of smallness.     

On nonlinear vibrations of a charged drop in the third-order approximation in the amplitude of initial single-mode excitation

Nonlinear axisymmetric motions of the free surface of a charged drop of an ideal liquid under the single-mode initial deformation of its equilibrium shape is investigated in the third-order approximation in the initial perturbation amplitude. An analytical expression for the drop shape generatrix is derived. Nonlinear corrections to the vibration frequencies for the initial perturbation of an arbitrary mode are found for the first time. The effect of vibration nonlinearity on the instability of the drop against its self-charge is studied.     

Transitions driven by a missing frequency

We demonstrate an intricate combination of strong and weak interactions of a broadband half-cycle pulse with Rydberg atoms. A transition, which is resonant with a frequency that was taken out of the frequency spectrum, can be enhanced. In the experiment, the broadband ultrashort terahertz half-cycle pulse propagates through water vapor, which absorbs on discrete lines in the spectrum, thus removing frequencies from the spectrum. The resulting pulse interacts with a rubidium Rydberg atom, which has a resonant transition with one of the missing frequencies. Under certain conditions, the transition probability is enhanced although the associated frequency was missing in the spectrum.