Damping Rate Research Articles

Laser cooling and magneto-optical trapping of molecules analyzed using optical Bloch equations and the Fokker-Planck-Kramers equation

We study theoretically the behavior of laser-cooled calcium monofluoride (CaF) molecules in an optical molasses and magneto-optical trap (MOT), and compare our results to recent experiments. We use multi-level optical Bloch equations to estimate the force and the diffusion constant, followed by a Fokker-Planck-Kramers equation to calculate the time-evolution of the velocity distribution. The calculations are done in three-dimensions, and we include all the relevant energy levels of the molecule and all the relevant frequency components of the light. Similar to simpler model systems, the velocity-dependent force curve exhibits Doppler and polarization-gradient forces of opposite signs. We show that the temperature of the MOT is governed mainly by the balance of these two forces. Our calculated MOT temperatures and photon scattering rates are in broad agreement with those measured experimentally over a wide range of parameters. In a blue-detuned molasses, the temperature is determined by the balance of polarization gradient cooling, and heating due to momentum diffusion, with no significant contribution from Doppler heating. In the molasses, we calculate a damping rate similar to the measured one, and steady-state temperatures that have the same dependence on laser intensity and applied magnetic field as measured experimentally, but are consistently a few times smaller than measured. We attribute the higher temperatures in the experiments to fluctuations of the dipole force which are not captured by our model. We show that the photon scattering rate is strongly influenced by the presence of dark states in the system, but that the scattering rate does not go to zero even for stationary molecules because of the transient nature of the dark states.

Two-level system damping in a quasi-one-dimensional optomechanical resonator

Nanomechanical resonators have demonstrated great potential for use as versatile tools in a number of emerging quantum technologies. For such applications, the performance of these systems is restricted by the decoherence of their fragile quantum states, necessitating a thorough understanding of their dissipative coupling to the surrounding environment. In bulk amorphous solids, these dissipation channels are dominated at low temperatures by parasitic coupling to intrinsic two-level system (TLS) defects, however, there remains a disconnect between theory and experiment on how this damping manifests in dimensionally-reduced nanomechanical resonators. Here, we present an optomechanically-mediated thermal ringdown technique, which we use to perform simultaneous measurements of the dissipation in four mechanical modes of a cryogenically-cooled silicon nanoresonator, with resonant frequencies ranging from 3 - 19 MHz. Analyzing the device's mechanical damping rate at fridge temperatures between 10 mK - 10 K, we demonstrate quantitative agreement with the standard tunneling model for TLS ensembles confined to one dimension. From these fits, we extract the defect density of states ($P_0 \sim$ 1 - 4 $\times$ 10$^{44}$ J$^{-1}$ m$^{-3}$) and deformation potentials ($\gamma \sim$ 1 - 2 eV), showing that each mechanical mode couples on average to less than a single thermally-active defect at 10 mK.

Kinetic treatment of acoustic waves in a four‐component dusty plasma

A kinetic formulation is developed to investigate low‐frequency dust ion acoustic waves (DIAWs) and dust acoustic waves (DAWs) as well as numerically for a four‐component, collisionless, unmagnetized dusty plasma, using the linearized Vlasov–Poisson model for species obeying the Maxwellian distribution. In particular, the dynamics of low‐frequency DIAWs is investigated by considering two cases. In the first case, ions and positive dust particles are assumed to be dynamically adiabatic while the negative dust particles are static in the background. In second case, the ions are taken adiabatic, while both positive and negative dust particles are static in the background. For DAWs, the ions are assumed to be isothermal, while both positive and negative dust species are considered adiabatic. Electrons are assumed to be isothermal in all cases. The linear characteristics and Landau damping rates for DIAWs and DAWs are investigated with effects of the dust particle concentrations and different temperature ratios. It is noted that for higher values of positive dust concentration, DIAWs (DAWs) are less (more) damped. It is also observed that the damping rate increases (decreases) as Ti approaches Te for DIAWs (DAWs). It is worth adding here that the theoretical results presented here are supported by numerical analyses and illustrations. The relevance of the study to laboratory and cosmic plasmas is also pointed out.

Chordwise wing flexibility may passively stabilize hovering insects.

Insect wings are flexible, and the dynamically deforming wing shape influences the resulting aerodynamics and power consumption. However, the influence of wing flexibility on the flight dynamics of insects is unknown. Most stability studies in the literature consider rigid wings and conclude that the hover equilibrium condition is unstable. The rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. Here, we show that a flapping wing flyer with flexible wings exhibits stable hover equilibria. The free-flight insect flight dynamics are simulated at the fruit fly scale in the longitudinal plane. The chordwise wing flexibility is modelled as a linear beam. The two-dimensional Navier-Stokes equations are solved in a tight fluid-structure integration scheme. For a range of wing flexibilities similar to live insects, all eigenvalues of the system matrix about the hover equilibrium have negative real parts. Flexible wings appear to stabilize the unstable mode by passively deforming their wing shape in the presence of perturbations, generating significantly more horizontal velocity damping and pitch rate damping. These results suggest that insects may passively stabilize their hover flight via wing flexibility, which can inform designs of synthetic flapping wing robots.

Reducing noise for PIC simulations using kernel density estimation algorithm

Noise is a major concern for Particle-In-Cell (PIC) simulations. We propose a new theoretical and algorithmic framework to evaluate and reduce the noise level for PIC simulations based on the Kernel Density Estimation (KDE) theory, which has been widely adopted in machine learning and big data science. According to this framework, the error on particle density estimation for PIC simulations can be characterized by the Mean Integrated Square Error (MISE), which consists of two parts, systematic error and noise. A careful analysis shows that in the standard PIC methods, noise is the dominant error, and the noise level can be reduced if we select different shape functions that are capable of balancing the systematic error and the noise. To improve, we use the von Mises distribution as the shape function and seek an optimal particle width that minimizes the MISE, represented by a cross-validation function. It is shown that this procedure significantly reduces the noise and the MISE for PIC simulations. A particle-wise width adjustment algorithm and a width update algorithm are also developed to further reduce the MISE. Simulations using the examples of Langmuir wave and Landau damping demonstrate that relative to the standard PIC methods, the KDE algorithm developed in the present study reduces the noise level on density estimation by 98% and gives a much more accurate result on the linear damping rate. To achieve the same accuracy, the KDE algorithm is 40% faster.

Non-normal amplification of stochastic quasicycles

Stochastic quasi-cycles for a two species model of the excitatory-inhibitory type, arranged on a triangular loop, are studied. By increasing the strength of the inter-nodes coupling, one moves the system towards the Hopf bifurcation and the amplitude of the stochastic oscillations are consequently magnified. When the system is instead constrained to evolve on specific manifolds, selected so as to return a constant rate of deterministic damping for the perturbations, the observed amplification correlates with the degree of non normal reactivity, here quantified by the numerical abscissa. The thermodynamics of the reactive loop is also investigated and the degree of inherent reactivity shown to facilitate the out-of-equilibrium exploration of the available phase space.

Predicting responses to inhibitory synaptic input in substantia nigra pars reticulata neurons.

The changes in firing probability produced by a synaptic input are usually visualized using the poststimulus time histogram (PSTH). It would be useful if postsynaptic firing patterns could be predicted from patterns of afferent synaptic activation, but attempts to predict the PSTH from synaptic potential waveforms using reasoning based on voltage trajectory and spike threshold have not been successful, especially for inhibitory inputs. We measured PSTHs for substantia nigra pars reticulata (SNr) neurons inhibited by optogenetic stimulation of striato-nigral inputs or by matching artificial inhibitory conductances applied by dynamic clamp. The PSTH was predicted by a model based on each SNr cell's phase-resetting curve (PRC). Optogenetic activation of striato-nigral input or artificial synaptic inhibition produced a PSTH consisting of an initial depression of firing followed by oscillatory increases and decreases repeating at the SNr cell's baseline firing rate. The phase resetting model produced PSTHs closely resembling the cell data, including the primary pause in firing and the oscillation. Key features of the PSTH, including the onset rate and duration of the initial inhibitory phase, and the subsequent increase in firing probability could be explained from the characteristic shape of the SNr cell's PRC. The rate of damping of the late oscillation was explained by the influence of asynchronous phase perturbations producing firing rate jitter and wander. Our results demonstrate the utility of phase-resetting models as a general method for predicting firing in spontaneously active neurons and their value in interpretation of the striato-nigral PSTH. NEW & NOTEWORTHY The coupling of patterned presynaptic input to sequences of postsynaptic firing is a Gordian knot, complicated by the multidimensionality of neuronal state and the diversity of potential initial states. Even so, it is fundamental for even the simplest understanding of network dynamics. We show that a simple phase-resetting model constructed from experimental measurements can explain and predict the sequence of spike rate changes following synaptic inhibition of an oscillating basal ganglia output neuron.

Tuning of 3-tap bandpass filter during acceleration for longitudinal beam stabilization at FAIR

During acceleration in the heavy-ion synchrotrons SIS18/SIS100 at GSI/FAIR longitudinal beam oscillations are expected to occur. To reduce longitudinal emittance blowup, dedicated LLRF beam feedback systems are planned. To date, damping of longitudinal beam oscillations has been demonstrated in SIS18 machine experiments with a 3-tap filter controller (e.g. [1]), which is robust in regard to control parameters and also to noise. On acceleration ramps the control parameters have to be adjusted to the varying synchrotron frequency. Previous results from beam experiments at GSI indicate that a proportional tuning rule for one parameter and an inversely proportional tuning rule for a second parameter is feasible, but the obtained damping rate may not be optimal for all synchrotron frequencies during the ramp. In this work, macro-particle simulations are performed to evaluate, whether it is sufficient to adjust the control parameters proportionally (inversely proportionally) to the change in the linear synchrotron frequency, or if it is necessary to take more parameters, such as bunch-length and synchronous phase, into account to achieve stability and a considerable high damping rate for excited longitudinal dipole beam oscillations. This is done for single- and dual-harmonic acceleration ramps.

Tuning of 3-tap Bandpass Filter During Acceleration for Longitudinal Beam Stabilization at FAIR

During acceleration in the heavy-ion synchrotrons SIS18/SIS100 at GSI/FAIR longitudinal beam oscillations are expected to occur. To reduce longitudinal emittance blowup, dedicated LLRF beam feedback systems are planned. To date, damping of longitudinal beam oscillations has been demonstrated in SIS18 machine experiments with a 3-tap filter controller (e.g. [1]), which is robust in regard to control parameters and also to noise. On acceleration ramps the control parameters have to be adjusted to the varying synchrotron frequency. Previous results from beam experiments at GSI indicate that a proportional tuning rule for one parameter and an inversely proportional tuning rule for a second parameter is feasible, but the obtained damping rate may not be optimal for all synchrotron frequencies during the ramp. In this work, macro-particle simulations are performed to evaluate, whether it is sufficient to adjust the control parameters proportionally (inversely proportionally) to the change in the linear synchrotron frequency, or if it is necessary to take more parameters, such as bunch-length and synchronous phase, into account to achieve stability and a considerable high damping rate for excited longitudinal dipole beam oscillations. This is done for single- and dual-harmonic acceleration ramps.

Obliquely propagating magnetosonic waves in a plasma modeled by bi-anisotropic Cairns distribution

Waves and instabilities have very often been an object of fascination since the introduction of non-Maxwellian features in space plasmas. To date, the dispersion relation, including real frequency, damping, and growth rates of magnetosonic waves has been studied in many different types of non-Maxwellian distributions. However, these characteristics have been overlooked in the temperature bi-anisotropic Cairns distribution, characterized by the free parameter Λ. By employing the linearized Vlasov–Maxwell system in homogeneous plasma, the dispersion relation is analytically solved. It is found that the non-Maxwellian features, Λ ≠ 0 along with electron temperature anisotropy, notably modify the real frequency, damping, and growth rates—both in the hydrodynamic as well as in the kinetic regimes. Interestingly, the growth rate in the kinetic regime is entirely due to the correlation of Λ with the electron temperature anisotropy which is otherwise absent in the Maxwellian distribution. Due to their relevance, the results are applicable to solar wind plasma.

High-Frequency Quasi-Potential Waves in the Plasma Formed under Tunnel Ionization of Atoms

The dispersion law and collisionless damping rate of quasi-potential waves in the plasma formed upon tunnel ionization of gas atoms in the field of a short pulse of circularly or linearly polarized radiation are found. It is shown how the frequency and damping rate of quasi-potential waves depend on the wave propagation direction relative to the symmetry axis of the photoelectron distribution. It is established that, in plasma with a toroidal photoelectron velocity distribution, weakly damped waves with a linear dispersion law and frequency above the electron plasma frequency can propagate in a wide range of angles. In the case of a bi-Maxwellian photoelectron distribution, the frequency of weakly damped waves is comparable with the electron plasma frequency and the anisotropy of electron motion manifests itself in relatively small corrections to the dispersion law.

Critical collapse of ultrarelativistic fluids: Damping or growth of aspherical deformations

We perform fully nonlinear numerical simulations to study aspherical deformations of the critical self-similar solution in the gravitational collapse of ultra-relativistic fluids. Adopting a perturbative calculation, Gundlach predicted that these perturbations behave like damped or growing oscillations, with the frequency and damping (or growth) rates depending on the equation of state. We consider a number of different equations of state and degrees of asphericity and find very good agreement with the findings of Gundlach for polar $\ell = 2$ modes. For sufficiently soft equations of state, the modes are damped, meaning that, in the limit of perfect fine-tuning, the spherically symmetric critical solution is recovered. We find that the degree of asphericity has at most a small effect on the frequency and damping parameter, or on the critical exponents in the power-law scalings. Our findings also confirm, for the first time, Gundlach's prediction that the $\ell = 2$ modes become unstable for sufficiently stiff equations of state. In this regime the spherically symmetric self-similar solution can no longer be recovered by fine-tuning to the black-hole threshold, and one can no longer expect power-law scaling to hold to arbitrarily small scales.

Mixed finite elements for global tide models with nonlinear damping

We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy accumulation. We also give rates of damping in unforced systems and various continuous dependence results on initial conditions and forcing terms. A priori error estimates for the momentum and free surface elevation are given in $$L^2$$ as well as for the time derivative and divergence of the momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.

Coordinated Tuning of the Parameters of PSS and POD Controllers Using Bioinspired Algorithms

This paper presents a technique based on the novel bat algorithm (NBA) for the design of the parameters of power system stabilizers and the generalized Unified power flow controller-power oscillation damping in a multimachine power system. The objective is to ensure minimal damping rates to low-frequency electromechanical oscillation modes. Simulations were carried out on the New England system to compare the performance of the NBA with three other techniques: particle swarm optimization, bacterial foraging optimization oriented by particle swarm optimization, and the bat algorithm. For the cases analyzed in this paper, the NBA produced results superior to other techniques. Moreover, the proposed methodology was able to obtain solutions with high damping levels, which showed to be robust when a wide range of loading conditions of the power system were considered.

Landau damping of dust acoustic waves in a nonthermal plasma

By employing the kinetic theory, the linear dispersion relation and Landau damping rate of dust-acoustic waves (DAWs) in a nonthermal dusty plasma are presented. The real frequency and the Landau damping rate of the mode are calculated by using the Cairns distribution function. It is demonstrated that by changing the spectral index α (index involved in the Cairns distribution), significant changes occur in the damping rate of the DAWs. In the limit α→0, the non-Maxwellian function approaches to the classic Maxwellian distribution and hence the DAWs reduce to Maxwellian results. A detailed examination of the various relevant plasma parameters on the real frequency and damping rate of DAWs is conducted.

Modelling linewidths of Kepler red giants in NGC 6819

We present a comparison between theoretical, frequency-dependent, damping rates and linewidths of radial-mode oscillations in red-giant stars located in the open cluster NGC 6819. The calculations adopt a time-dependent non-local convection model, with the turbulent pressure profile being calibrated to results of 3D hydrodynamical simulations of stellar atmospheres. The linewidths are obtained from extensive peakbagging of Kepler lightcurves. These observational results are of unprecedented quality owing to the long continuous observations by Kepler. The uniqueness of the Kepler mission also means that, for asteroseismic properties, this is the best data that will be available for a long time to come. We therefore take great care in modelling nine RGB stars in NGC 6819 using information from 3D simulations to obtain realistic temperature stratifications and calibrated turbulent pressure profiles. Our modelled damping rates reproduce well the Kepler observations, including the characteristic depression in the linewidths around the frequency of maximum oscillation power. Furthermore, we thoroughly test the sensitivity of the calculated damping rates to changes in the parameters of the nonlocal convection model.

Theory of Electromagnetic Surface Waves in Plasma with Smooth Boundaries

A theory of nonpotential surface waves in plasma with smooth boundaries is developed. The complex frequencies of surface waves for plasma systems of different geometries and different profiles of the plasma density are calculated. Expressions for the rates of collisionless damping of surface waves due to their resonance interaction with local plasma waves of continuous spectrum are obtained. The influence of collisions in plasma is also considered.

A Novel Approach to Resonant Absorption of the Fast Magnetohydrodynamic Eigenmodes of a Coronal Arcade

Abstract The arched field lines forming coronal arcades are often observed to undulate as magnetohydrodynamic waves propagate both across and along the magnetic field. These waves are most likely a combination of resonantly coupled fast magnetoacoustic waves and Alfvén waves. The coupling results in resonant absorption of the fast waves, converting fast wave energy into Alfvén waves. The fast eigenmodes of the arcade have proven difficult to compute or derive analytically, largely because of the mathematical complexity that the coupling introduces. When a traditional spectral decomposition is employed, the discrete spectrum associated with the fast eigenmodes is often subsumed into the continuous Alfvén spectrum. Thus fast eigenmodes become collective modes or quasi-modes. Here we present a spectral decomposition that treats the eigenmodes as having real frequencies but complex wavenumbers. Using this procedure we derive dispersion relations, spatial damping rates, and eigenfunctions for the resonant, fast eigenmodes of the arcade. We demonstrate that resonant absorption introduces a fast mode that would not exist otherwise. This new mode is heavily damped by resonant absorption, travelling only a few wavelengths before losing most of its energy.

Acoustic methods for regionalizing an impact force acting on a structure

It is often desired to know the location and magnitude of a force acting on a structure. Unfortunately, it is not always possible to install a sensor at the force location, particularly when that location is unknown. A structure subjected to an impact has many different vibrational modes that are excited to different levels based on the excitation location. These vibrations decay with time depending on their different rates of modal damping and the associated acoustic radiation characteristics. In this work, acoustic signatures for a number of structure impact locations were measured, normalized relative to the force magnitude, and processed to examine the ability to correlate the acoustic signal to the force impact location. Various processing techniques, such as the Short Time Fourier Transform, were considered. A primary interest focused on the ability of single-number metrics to aid in identifying the force location. For the experiments, a football helmet structure was used and multiple impact locatio...

A parameter quantifying radiation damping of bay oscillations excited by incident tsunamis

The transient response of a bay with a narrow mouth to incident tsunamis is interpreted as the convolution of the input signal with the impulse response obtained by an inverse Fourier transform of the response curve of the oscillatory system with one degree of freedom. The rate of radiation damping associated with energy escaping seaward through the bay mouth is expressed in terms of the quality factor Q, which determines the decaying envelope of the impulse response. The value of Q of the resonant peak is approximated by the ratio of the resonant frequency ω0 to the bandwidth between frequencies at which the power spectral density of sea level within the bay drops to half of the peak value. Since the shape of the frequency power spectrum during the tsunami event is almost similar to that in the normal state in the neighborhood of ω0, Q can be estimated from sea level datasets in the normal state. Although the amplitude and phase of the impulse response need to be adjusted using the first crest or trough of the observed leading wave, this approach proves to work well in examining the transient responses of Miyako Bay and Kushimoto Bay on the Japanese Pacific coast to incident tsunamis.