Nonresonant Forces Research Articles

Non-contact non-resonant atomic force microscopy method for measurements of highly mobile molecules and nanoparticles

Atomic force microscopy (AFM) is nowadays indispensable versatile scanning probe method widely employed for fundamental and applied research in physics, chemistry, biology as well as industrial metrology. Conventional AFM systems can operate in various environments such as ultra-high vacuum, electrolyte solutions, or controlled gas atmosphere. Measurements in ambient air are prevalent due to their technical simplicity; however, there are drawbacks such as formation of water meniscus that greatly increases attractive interaction (adhesion) between the tip and the sample, reduced spatial resolution, and too strong interactions leading to tip and/or sample modifications. Here we show how the attractive forces in AFM under ambient conditions can be used with advantage to probe surface properties in a very sensitive way even on highly mobile molecules and nanoparticles. We introduce a stable non-contact non-resonant (NCNR) AFM method which enables to reliably perform measurements in the attractive force regime even in air by controlling the tip position in the intimate surface vicinity without touching it. We demonstrate proof-of-concept results on helicene-based macrocycles, DNA on mica, and nanodiamonds on SiO2. We compare the results with other conventional AFM regimes, showing NCNR advantages such as higher spatial resolution, reduced tip contamination, and negligible sample modification. We analyze principle physical and chemical mechanisms influencing the measurements, discuss issues of stability and various possible method implementations. We explain how the NCNR method can be applied in any AFM system by a mere software modification. The method thus opens a new research field for measurements of highly sensitive and mobile nanoscale objects under air and other environments.

On the Countering of Free Vibrations by Forcing: Part II—Damped Oscillations and Decaying Forcing

The present two-part paper concerns the active vibration suppression for the simplest damped continuous system, namely the transverse oscillations of an elastic string, with constant tension and mass density per unit length and friction force proportional to the velocity, described by the telegraph or wave-diffusion equation, in two complementary parts. The initial part I considers non-resonant and resonant forcing, by concentrated point forces or continuous force distributions independent of time, with phase shift between the forced and free oscillations, in the absence of damping, in which case the forced telegraph equation reduces to the forced classical wave equation. The present and final part II uses the forced wave-diffusion equation to model the effect of damping, both as amplitude decay and phase shift in time, for non-resonant and resonant forcing by a single point force, with constant magnitude or magnitude decaying exponentially in time at an arbitrary rate. Assuming a finite elastic string fixed at both ends, the free oscillations are (i) sinusoidal modes in space-time with exponential decay in time due to damping. The non-resonant forced oscillations at an applied frequency distinct from a natural frequency are also (ii) sinusoidal in space-time, with constant amplitude and a phase shift such that the work of the applied force balances the dissipation. For resonant forcing at an applied frequency equal to a natural frequency, the sinusoidal oscillations in space-time have (iii) a constant amplitude and a phase shift of π/2. In both cases, the (ii) non-resonant or (iii) resonant forcing dominates the decaying free oscillations after some time. Even by optimizing the forcing to minimize the total energy of oscillation, it remains below the energy of the free oscillation alone, but only for a short time—generally a fraction of the period. A more effective method of countering the damped free oscillations is to use forcing with amplitude decaying exponentially in time; by suitable choice of the forcing decay relative to the free damping, the total energy of oscillation over all time can be reduced to no more than 1/16th of the energy of the free oscillation.

Searching spin-mass interaction using a diamagnetic levitated magnetic-resonance force sensor

Axion-like particles (ALPs) are predicted to mediate exotic interactions between spin and mass. We propose an ALP-searching experiment based on the levitated micromechanical oscillator, which is one of the most sensitive sensors for spin-mass forces at a short distance. The proposed experiment tests the spin-mass resonant interaction between the polarized electron spins and a diamagnetically levitated microsphere. By periodically flipping the electron spins, the contamination from nonresonant background forces can be eliminated. The levitated microoscillator can prospectively enhance the sensitivity by nearly $10^3$ times over current experiments for ALPs with mass in the range 4 meV to 0.4 eV.

Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators

Beam lattice materials are characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. The dispersion properties governing the free dynamic propagation of elastic waves can be studied by formulating parametric discrete models of the cellular microstructure and applying the Floquet-Bloch theory. Within this framework, governing the wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical and applied interest. Specifically, the wave propagation can be inhibited by purposely designing the microstructural parameters to open stop bands in the material spectrum at target center frequencies. Based on these motivations, a general dynamic formulation is presented for determining the dispersion properties of mechanical metamaterials, modeled as locally resonant beam lattices with generic coordination number. The mechanism of local resonance is realized by tuning periodic auxiliary oscillators, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped waves is governed by a linear homogeneous system of integro-differential equations of motion. Therefore, differential equations of motion with frequency-dependent viscoelastic coefficients are obtained by applying the in-space Z-transform and in-time bilateral Laplace transform. The complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed for the beam lattice characterized by quadrilateral periodic cell. The spectral branches may exceed the model dimension, due to the occurrence of pure-damping spectral components. Particularly, the spectra corresponding to Laurent series approximations of the viscoelastic coefficients are investigated and the solution admissibility and convergence for increasing order series is analyzed. The standard dynamic equations with linear viscous damping are recovered at the first-order approximation. Low-order approximations are found to underestimate the real and imaginary parts of the spectrum, as well as the low-frequency stop bandwidth. Finally, the forced response to a harmonic mono-frequent external point excitation is investigated. The metamaterial responses to non-resonant, resonant and quasi-resonant external forces are compared and discussed from a qualitative and quantitative viewpoint.

Formation and dynamics of quantum hydrodynamical breathing-ring solitons

We show that exciton-polariton condensates may exhibit a new fundamental, self-localized nonlinear excitation not seen in other quantum hydrodynamical systems, which takes the form of a dark ring shaped breather. We predict that these structures form spontaneously and remain stable under a combination of uniform resonant and nonresonant forcing. We study single ring dynamics, ring interactions and ring turbulence, and explain how direct experimental observations might be made. We discuss the statistics of ring formation and propose an experimental scheme by which these structures may be exploited to study the smooth cross-over between equilibrium and non-equilibrium critical phase transitions. Finally, we present an alternative mechanism of formation for these topological breathers, in which they circumscribe Gaussian resonant pumps. The observation of a breathing ring soliton would represent the first fundamental breathing soliton within the broad field of quantum hydrodynamics.

Efficient nonresonant dipole force on molecules by a tightly focused laser

When a molecule is placed in a nonresonant laser field, the Stark interactions between the laser field and the induced molecular dipole result in a mechanical force on the molecule. This nonresonant dipole force is proportional to the intensity gradient of the laser, thus requiring a strong and focused pulsed laser for a sizable impact on the molecule. 36.4 mJ pulses of a 1064 nm Nd:YAG laser focused with a 17.5 cm focal length convex lens produced a 6.4 m/s change in the transverse velocity of a CS2 molecular beam. Using spherical mirrors with shorter focal lengths such as 10.0, 7.5, and 5.0 cm, dipole forces of similar magnitude were obtained with laser pulses of much lower energies. In particular the 5.0-cm focal length spherical mirror provided an 11.3 m/s change in the transverse velocity using 3.6 mJ laser pulses. This corresponds to 18-fold increase in the deflection efficiency, the ratio between the maximum velocity change and the pulse energy. From the improved efficiency, the nonresonant dipole force can be exerted with ease.

Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case

AbstractA computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of motion, for gravity-wave packets at large amplitudes. The governing parameter of this analysis had been the scale-separation ratio$\varepsilon $between the gravity wave and both the large-scale potential-temperature stratification and the large-scale wave-induced mean flow. A novel feature of the theory had been the non-resonant forcing of higher harmonics of an initial wave packet, predominantly by the large-scale gradients in the gravity-wave fluxes. In the test cases considered a gravity-wave packet is propagating upwards in a uniformly stratified atmosphere. Large-scale winds are induced by the wave packet, and possibly exert a feedback on the latter. In the limit$\varepsilon \ll 1$all predictions of the theory can be validated. The larger$\varepsilon $is the more the transfer of wave energy to the mean flow is underestimated by the theory. The numerical results quantify this behaviour but also show that, qualitatively, XWKB remains valid even when the gravity-wave wavelength approaches the spatial scale of the wave-packet amplitude. This includes the prevalence of first and second harmonics and the smallness of harmonics with wave number higher than two. Furthermore, XWKB predicts for the vertical momentum balance an additional leading-order buoyancy term in Euler and pseudo-incompressible theory, compared with the anelastic theory. Numerical tests show that this term is relatively large with up to$30\hspace{0.167em} \% $of the total balance. The practical relevance of this deviation remains to be assessed in future work.

Dynamical responses of oscillating yeast cell suspensions to periodic forcing.

Fermenting S. cerevisiae cells suspensions undergo synchronized metabolic oscillations whose amplitude and frequency depends on the population density. The asymptotic population-level dynamics is qualitatively and quantitatively accounted for by mathematical models describing the intracellular glycolytic oscillations and the coupling through the external medium. Such dynamical systems often display low-dimensional dynamics for the parameters that quantitatively fit the experimental observations. However, the high dimensionality of the chemical space and the possible existence of intermingled time scales can potentially support more complex dynamics, in particular when the system is perturbed by external forcings. Here, we explore experimentally and by means of numerical models the response of cellular populations to different kinds of periodic forcing: resonant forcing of diluted, nonoscillating populations and strongly nonresonant forcing of populations in oscillating regimes with different dynamical features. We show that, in all cases, low-dimensional semi-quantitative models reproduce the observed dynamics. Both a nonlinear analysis of the experimental time series and the models indicate that complex-looking time series correspond to quasiperiodic and not to chaotic regimes. The fact that low-dimensional dynamical systems are able to reproduce the response of biological populations in different regimes of external periodic forcing supports the use of theoretical models for inquiring the dynamical behaviour of collectively oscillating cells.

A test model for fluctuation–dissipation theorems with time-periodic statistics

The recently developed time-periodic fluctuation–dissipation theorem (FDT) provides a very convenient way of addressing the climate change of atmospheric systems with seasonal cycle by utilizing statistics of the present climate. A triad nonlinear stochastic model with exactly solvable first and second order statistics is introduced here as an unambiguous test model for FDT in a time-periodic setting. This model mimics the nonlinear interaction of two Rossby waves forced by baroclinic processes with a zonal jet forced by a polar temperature gradient. Periodic forcing naturally introduces the seasonal cycle into the model. The exactly solvable first and second order statistics are utilized to compute both the ideal mean and variance response to the perturbations in forcing or dissipation and the quasi-Gaussian approximation of FDT (qG-FDT) that uses the mean and the covariance in the equilibrium state. The time-averaged mean and variance qG-FDT response to perturbations of forcing or dissipation is compared with the corresponding ideal response utilizing the triad test model in a number of regimes with various dynamical and statistical properties such as weak or strong non-Gaussianity and resonant or non-resonant forcing. It is shown that even in a strongly non-Gaussian regime, qG-FDT has surprisingly high skill for the mean response to the changes in forcing. On the other hand, the performance of qG-FDT for the variance response to the perturbations of dissipation is good in the near-Gaussian regime and deteriorates in the strongly non-Gaussian regime. The results here on the test model should provide useful guidelines for applying the time-periodic FDT to more complex realistic systems such as atmospheric general circulation models.

Monochromatic waves induced by large-scale parametric forcing

We study the formation and stability of monochromatic waves induced by large-scale modulations in the framework of the complex Ginzburg-Landau equation with parametric nonresonant forcing dependent on the spatial coordinate. In the limiting case of forcing with very large characteristic length scale, analytical solutions for the equation are found and conditions of their existence are outlined. Stability analysis indicates that the interval of existence of a monochromatic wave can contain a subinterval where the wave is stable. We discuss potential applications of the model in rheology, fluid dynamics, and optics.

Dynamics of thermal Casimir-Polder forces on polar molecules

We study the influence of thermal Casimir-Polder forces on the near-surface trapping of cold polar molecules, with emphasis on LiH and YbF near an Au surface at room temperature. We show that for a molecule initially prepared in its electronic and rovibrational ground state, the Casimir-Polder force oscillates with the molecule-wall separation. The non-resonant force contribution and the evanescent part of the resonant force contribution almost exactly cancel at high temperature which results in a saturation of the (attractive) force in this limit. A dynamical calculation reveals how the spatial oscillations die out as thermalisation of the molecule with its environment sets in.

Nonlinear nonresonant forces by radio-frequency waves in plasmas

Nonresonant forces by applied rf waves in plasmas are analyzed. Along the background dc magnetic field, the force arises from the gradient of the ponderomotive potential. Only when the dc magnetic field is straight, however, is this parallel force completely consistent with that from the single particle picture, where the ponderomotive force depends on the gradients of rf fields only. Across the dc magnetic field, besides the ponderomotive force from the particle picture, additional Reynolds stress and polarization stress contribute to the total force. For waves with frequency much lower than the cyclotron frequency, the perpendicular forces from the particle and fluid pictures can have opposite signs. In plasmas with a symmetry angle (e.g., toroidal systems), nonresonant forces cannot drive net flow or current in the flux surface, but the radial force may influence macroscopic behavior of plasma. Moreover, nonresonant forces may drive flow or current in linear plasmas or in a localized region of toroidal plasmas.

Nonlinear ponderomotive force by low frequency waves and nonresonant current drive

The collisionless nonresonant force by low frequency waves has been thought to be capable of driving the nonresonant current. However, for a single particle, the ponderomotive force is in the direction of the gradient of the wave field energy. For cold plasmas, the Reynolds stress acting on the Lagrangian fluid element fully counteracts the nonresonant force offered by the quasilinear electromagnetic force. For hot plasmas, the collisionless nonresonant force is also cancelled by the nonlinear kinetic stress force. Therefore, in collisionless plasmas, none of the ponderomotive forces by low frequency waves can drive the nonresonant current.

Internal-wave reflection from uniform slopes: higher harmonics and Coriolis effects

Abstract. Weakly nonlinear reflection of internal waves from uniform slopes produces higher harmonics and mean fields; the expressions are here derived for constant stratification and with Coriolis effects fully included, i.e. the horizontal component of the earth rotation vector (referred to as "non-traditional'') is taken into account. Uniformity in one of the horizontal directions is assumed. It is shown that solutions can be as readily derived with as without ; hence there is no need to make the so-called Traditional Approximation. Examples of reflecting internal-wave beams are presented for super-inertial, inertial and sub-inertial frequencies. The problem of resonant and non-resonant forcing of the second harmonic is studied for single plane waves; unlike under the Traditional Approximation, the problem of reflection from a horizontal bottom no longer forms a singular case. Non-traditional effects are favourable to resonant forcing at near-tidal rather than near-inertial frequencies, and generally increase the intensity of the second harmonic. Strong stratification tends to suppress non-traditional effects, but a near-total suppression is only attained for high values of stratification that are characteristic of the seasonal thermocline; in most parts of the ocean, non-traditional effects can therefore be expected to be important.

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 3. The proton halo and dispersive waves

The kinetic shell model seeks to test the collisionless kinetic response of coronal hole protons to the quasi‐linear resonant cyclotron dissipation of outwardly directed, parallel propagating ion cyclotron waves, which is often invoked as the mechanism responsible for generating the fast solar wind. In this model, we make the approximation that the resonant cyclotron interaction proceeds much faster than any other process affecting the protons, so that the resonant portions of the distribution are maintained in a state of marginal stability with respect to this interaction. Under this approximation, the resonant protons are organized on nested shells of constant density in velocity space, defined by the condition that the proton energy is conserved in the rest frame moving with the phase speed of the resonant wave. These shells then evolve on the slower nonresonant timescale, responding to the shell‐averaged forces of gravity, charge‐separation electric field, mirror force, and an inertial force due to the fact that the waves are propagating in the accelerating plasma frame. Since these kinetic shell distributions are held in a marginally stable state, they cannot exchange any more energy with the waves than that taken to maintain that state. Thus their evolution corresponds to the effect of the maximum possible dissipation of outward propagating waves. Our earlier work was simplified in two major respects: we considered only dispersionless waves and we assumed that all the antisunward protons were resonantly interacting with self‐generated inward propagating waves. In this paper, we first present an improved treatment of the antisunward protons which yields more plausible speeds and temperatures than obtained previously. We then incorporate the effects of ion cyclotron dispersion into the model. Dispersion creates resonant shells which are broader in υ∥ than our previous dispersionless distributions. We find that the nonresonant forces acting on these dispersive shell distributions invariably produce only weak acceleration and result in perpendicular cooling rather than the heating that is generally required for fast solar wind speeds. These effects are attributed to the weaker inertial force on the sunward dispersive shells and are essentially independent of the behavior of the antisunward particles. Since these results correspond to the maximum possible dissipation by this mechanism, we conclude that the heating of coronal hole protons and the generation of the fast solar wind are not caused by the collisionless dissipation of parallel propagating ion cyclotron waves.

The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 2. Inward and outward propagating waves

We extend the kinetic shell model of the cyclotron resonant interaction between coronal hole protons and outward propagating ion cyclotron waves presented in the first paper of this series [Isenberg et al., 2001]. That work showed that the resonant dissipation of outward propagating waves produced proton distributions that were unstable to the generation of inward propagating waves. Here we include the kinetic shell interaction with the inward waves, assuming that both the wave generation and wave dissipation proceed much faster than all other processes in the collisionless coronal hole. In this case, the entire proton distribution will be resonant with one set of waves or the other and is thus composed of constant‐energy shells in both the sunward and antisunward regions of velocity space. The evolution of the distribution as the plasma flows away from the Sun is then described by following the motion of these shells under the action of the nonresonant forces in the coronal hole. We find that the distribution consists of a core population which circulates through velocity space and a halo which continually expands to higher energy. The halo population is shown to be essential to obtain acceleration of the bulk proton plasma through its response to the mirror force. We present an illustrative calculation of this system which assumes the waves to be dispersionless. We find for this case that the halo particles soon reach extremely high energies, leading to a continuous, rather than declining, acceleration of the plasma. We suggest that these properties are due to the dispersionless assumption and that an improved model incorporating wave dispersion may give more reasonable quantitative results.

Molecular lens applied to benzene and carbon disulfide molecular beams

A molecular lens of the nonresonant dipole force formed by focusing a nanosecond IR laser pulse has been applied to benzene and CS2 molecular beams. Using the velocity map imaging technique for molecular ray tracing, characteristic molecular lens parameters including the focal length (f ), minimum beam width (W), and distance to the minimum beam width position (D) were determined. The laser intensity dependence of the observed lens parameters was in good agreement with theoretical predictions. W was independent of the laser peak intensity (I0), whereas f and D varied linearly with 1/I0. The differences in lens parameters between the molecular species were well correlated with the polarizability per mass values of the molecules. A high chromatographic resolution of Rs=0.84 was achieved between the images of benzene molecular beams undeflected and deflected by the lens. The possibilities for a new type of chromatography are discussed.

Discrete coherent amplification of oscillations by nonresonant forcing

A new mechanism of generation of oscillations in a linear forced oscillatory system is found. Natural oscillations may be generated at a "sharp" pulse (rapid variation) of the natural frequency. In this process oscillations are generated by nonresonant forcing, e.g., by the action of a constant, nonperiodic or periodic force (with driving frequency much less than the natural one). Repetitive pulses of the natural frequency result in emergence of oscillations that interfere and may give a powerful resultant output. These phenomena relate to a basis of the theory of open linear oscillatory systems.

Optical deflection of molecules

When intense light interacts with a molecule it induces a force proportional to the gradient of the Stark shift. We use this nonresonant force to deflect ${\mathrm{I}}_{2}$ and ${\mathrm{CS}}_{2}$ molecules. We trace the direction of molecules in a molecular beam, showing that the molecules that pass near the center of a 1.06-\ensuremath{\mu}m or 10.6-\ensuremath{\mu}m laser beam will focus. We predict that Stark shifts on the order of 50 meV can be obtained for all small molecules and atoms while maintaining ionization rates below ${10}^{6}{\mathrm{s}}^{\mathrm{\ensuremath{-}}1}.$ Among the devices that can be based on the nonresonant Stark shift are molecular accelerators and molecular quantum wires.