Underdamped Vibrations Research Articles

Role of Quantum Information in HEOM Trajectories.

Open quantum systems often operate in the non-Markovian regime where a finite history of a trajectory is intrinsic to its evolution. The degree of non-Markovianity for a trajectory may be measured in terms of the amount of information flowing from the bath back into the system. In this study, we consider how information flows through the auxiliary density operators (ADOs) in the hierarchical equations of motion. We consider three cases for a range of baths, underdamped, intermediate, and overdamped. By understanding how information flows, we are able to determine the relative importance of different ADOs within the hierarchy. We show that ADOs sharing a common Matsubara axis behave similarly, while ADOs on different Matsubara axes behave differently. Using this knowledge, we are able to truncate hierarchies significantly, thus reducing the computation time, while obtaining qualitatively similar results. This is illustrated by comparing 2D electronic spectra for a molecule with an underdamped vibration subsumed into the bath spectral density.

Dynamic embedding of effective harmonic normal mode vibrations in all-atomistic energy gap fluctuations: Case study of light harvesting 2 complex.

Environmental effects in excitation energy transfer have mostly been modeled by baths of harmonic oscillators, but to what extent such modeling provides a reliable description of actual interactions between molecular systems and environments remains an open issue. We address this issue by investigating fluctuations in the excitation energies of the light harvesting 2 complex using a realistic all-atomistic simulation of the potential energy surface. Our analyses reveal that molecular motions exhibit significant anharmonic features, even for underdamped intramolecular vibrations. In particular, we find that the anharmonicity contributes to the broadening of spectral densities and substantial overlaps between neighboring peaks, which complicates the meaning of mode frequencies constituting a bath model. Thus, we develop a strategy to construct a minimally underdamped harmonic bath that has a clear connection to all-atomistic dynamics by utilizing actual normal modes of molecules but optimizing their frequencies such that the resulting bath model can best reproduce the all-atomistic simulation results. By subtracting the underdamped contribution from the entire fluctuations, we also show that identifying a residual spectral density representing all other contributions with overdamped behavior is possible. We find that this can be fitted well with a well-established analytic form of a spectral density function or, alternatively, modeled as explicit time dependent fluctuations with muti-exponential or power law type correlation functions. We provide an assessment and the implications of these possibilities. The approach presented here can also serve as a general strategy to construct a simplified bath model that can effectively represent the underlying all-atomistic bath dynamics.

Linear stability analysis of the condition for vibration during frictional slip

Slip along a frictional contact between elastic bodies can be stable or unstable, leading to stick-slip motion. Frictional slip can also be associated with vibrations. The condition for these vibrations and their characteristics remains poorly understood. To address this issue, which is relevant to engineering and earth science, we carry out a linear stability analysis of a spring-and-slider system obeying rate and state friction. We first identify the solution space for the linearized equation and define the conditions for different slip modes from the real and imaginary parts of the solution. We then derive asymptotic equations for all boundaries between overdamped stable sliding, inertial/non-inertial underdamped oscillation, stick-slip, and harmonic vibration. Finally, we verified the conditions with numerical simulations. Our work provides rigorous criteria regarding the conditions for the various frictional slip modes and the emergence of vibrations. It can help design appropriate approaches for suppressing undesired vibrations in mechanical systems and investigate the mechanisms generating vibrations (tremor) associated with fault slip in nature.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer.

We elucidate the influence of the system-bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Characterization of Surface Topography Variation in the Ultra-Precision Tool Servo-Based Diamond Cutting of 3D Microstructured Surfaces.

Previous models of the relative tool-work vibration are not generalized to represent the surface generation mechanism in the ultra-precision tool servo-based diamond cutting (UTSDC) of three-dimensional (3D) microstructured surfaces. This is due to the fact that the tool-work vibration in UTSDC is no longer a steady harmonic vibration with a constant amplitude but is influenced by the tool motion along the thrust direction. In this paper, dynamic modeling of the cutting system is presented for the characterization of surface topography variation in UTSDC of a microlens array considering the tool-work vibration as an underdamped vibration. The natural frequency and damping ratio of the cutting system are determined by the data-dependent systems (DDS) method. Based on the analysis of the surface profile and cutting force signals, it is found that the tool-work vibration is significantly enhanced in the cut-in process when the cutting speed increases. The simulation results show that the proposed dynamic model can well-determine root-mean-squares values of the surface primary profile and the dynamic force acting on the force sensor. The dynamic model provides insight into the formation of the surface topography variation in UTSDC of 3D microstructured surfaces, and the model might be applied in self-optimized machining systems in the future.

Nonlinear wave in granular systems based on elastoplastic dashpot model

AbstractThe dynamic dashpot models are widely used in EDEM commercial software. However, most dashpot models suffer from a serious numerical issue in calculating the granular chain because the denominator of damping force includes the initial impact velocity. Moreover, the existing dynamic dashpot models extended from the original Hertz contact law overestimated the contact stiffness in the elastoplastic contact phase. These two reasons above result in most dynamic dashpot models confronting some issues in calculating the multiple collision of the granular chain. Therefore, this investigation aims to propose a new composite dynamic dashpot model for the dynamic simulation of granular matters. First, the entire contact process is divided into three different phases: elastic, elastoplastic, and full plastic phases. The Hertz contact stiffness is still used in the elastic contact phase when the contact comes into the elastoplastic or full plastic phase. Hertz contact stiffness in the dynamic dashpot model is replaced by linearizing the contact stiffness from the Ma‐Liu (ML) model in each time step. Second, the whole contact behavior is treated as a linear mass‐spring‐damper model, and the damping factor is obtained by solving the single‐degree‐freedom underdamped vibration equation. The new dynamic dashpot model is proposed by combining the contact stiffnesses in different contact phases and corresponding damping factors, which not only removes the initial impact velocity from the denominator of damping force but also updates the contact stiffness based on the constitutive relation of the contact body when the contact comes into the elastoplastic or full plastic phase. Finally, a granular chain is treated as numerical examples to check the reasonability and effectiveness of the new dynamic dashpot model by comparing it to the experimental data. The simulation shows that the solitary waves obtained using the new dashpot model are more accurate than the dashpot model used in EDEM software.

Cooperation between Excitation Energy Transfer and Antisynchronously Coupled Vibrations.

The effects of the environment in energy transfer systems have been continuously studied for decades. Here, we investigate how the energy transfer and the emergence of vibrational correlations cooperate with each other based on simulations with a few numerically approximate mixed quantum classical (MQC) methods. By adopting a two-state system with locally coupled underdamped vibrations that are resonant with the electronic energy gap, we observe prominent energy dissipations from the electronic system to the vibrations, rehighlighting the role of underdamped vibrations as a temporal electronic energy buffer. More importantly, this energy dissipation generates specific phase relations between the two vibrations. Namely, the vibrations become anticorrelated right after the initiation of the energy transfer but then synchronized as the transfer completes. These phase relations are interpreted as a selective activation of an anticorrelated motion of the vibrations and a subsequent deactivation by thermal energy redistribution. Furthermore, we show that a single vibration simultaneously coupled to the two electronic states with opposite phases induces a completely equivalent energy transfer dynamics as the two localized vibrations. Finally, we discuss how the vibrational energy dissipation dynamics is affected by the adopted MQC approaches and warn about the increased subtlety toward properly treating dissipation effects over having reliable population dynamics.

Low-Frequency Protein Motions Coupled to Catalytic Sites.

This review examines low-frequency vibrational modes of proteins and their coupling to enzyme catalytic sites. That protein motions are critical to enzyme function is clear, but the kinds of motions present in proteins and how they are involved in function remain unclear. Several models of enzyme-catalyzed reaction suggest that protein dynamics may be involved in the chemical step of the catalyzed reaction, but the evidence in support of such models is indirect. Spectroscopic studies of low-frequency protein vibrations consistently show that there are underdamped modes of the protein with frequencies in the tens of wavenumbers where overdamped behavior would be expected. Recent studies even show that such underdamped vibrations modulate enzyme active sites. These observations suggest that increasingly sophisticated spectroscopic methods will be able to unravel the link between low-frequency protein vibrations and enzyme function.

Quantifying non-Markovianity in underdamped versus overdamped environments and its effect on spectral lineshape.

Non-Markovian effects in open quantum systems are central to understanding spectral lineshape. Here, we quantify the non-Markovianity associated with both overdamped and underdamped vibrations in terms of information flow between the bath and the system and compare this with the broadening and ellipticity of two-dimensional spectra. Using the Breuer Laine Piilo (BLP) measure, we link the well-known stochastic models for spectral lineshape with modern quantum information theory. Specifically, we study the effect of non-Markovianity in a system in contact with underdamped vibrations and examine the differences observed on increasing the damping to the overdamped limit. The open quantum system dynamics are evolved using the hierarchical equations of motion, efficiently terminated with a Markovian cutoff, where separate hierarchies are derived for the underdamped and overdamped environments. It is shown that the BLP measure is quantitatively correlated with the ellipticity of two-dimensional spectra and memory effects are more pronounced in underdamped environments, due to the long-lived feedback of information between the system and its bath, compared to overdamped environments. Environmental signatures in spectral lineshapes emerge as a result of information flow from the bath back into the system.

Effect of Underdamped Vibration on Excitation Energy Transfer: Direct Comparison between Two Different Partitioning Schemes

We study excitation energy transfer (EET) in a model three-site system with a mixed-quantum classical dynamics method, by focusing on the effect of an underdamped vibration. We construct two types of models where the underdamped vibration mode is included either in the quantum subsystem or in the classical bath. We show that the two models yield practically equivalent results despite the different depictions of the vibration. In particular, both models consistently demonstrate accelerations of population relaxation induced by quasi-resonant vibration. This indicates that intricate features of EET dynamics that have been frequently ascribed to the quantal nature of vibrations, such as vibronic mixing, can be successfully reproduced by using physically equivalent but classically described bath modes. The mechanism behind the observed quantum-classical correspondence is proposed. We also systematically examine how the structure of the spectating continuum phonon modes affects the vibronic resonance and observe that phonon modes with different time scales influence the resonance in different manners.

Effect of an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions on excitation energy transfer.

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton-phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton-phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton-phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.

On the influence of underdamped vibrations on coherence and energy transfer times in light‐harvesting complexes

We study the quantum exciton dynamics in light‐harvesting complexes under the influence of underdamped vibrational molecular modes. We observe prolonged coherent population oscillations between different pigments due to an underdamped mode connected to the originally excited pigment. At the same time, an underdamped vibration at the exit site of the complex provides additional channels for the excitation energy transfer towards the reaction center which shortens the transfer times. image

Linear and third- and fifth-order nonlinear spectroscopies of a charge transfer system coupled to an underdamped vibration.

We study hole, electron, and exciton transports in a charge transfer system in the presence of underdamped vibrational motion. We analyze the signature of these processes in the linear and third-, and fifth-order nonlinear electronic spectra. Calculations are performed with a numerically exact hierarchical equations of motion method for an underdamped Brownian oscillator spectral density. We find that combining electron, hole, and exciton transfers can lead to non-trivial spectra with more structure than with excitonic coupling alone. Traces taken during the waiting time of a two-dimensional (2D) spectrum are dominated by vibrational motion and do not reflect the electron, hole, and exciton dynamics directly. We find that the fifth-order nonlinear response is particularly sensitive to the charge transfer process. While third-order 2D spectroscopy detects the correlation between two coherences, fifth-order 2D spectroscopy (2D population spectroscopy) is here designed to detect correlations between the excited states during two different time periods.

Vibronically coherent speed-up of the excitation energy transfer in the Fenna-Matthews-Olson complex.

We show that underdamped molecular vibrations fuel the efficient excitation energy transfer in the Fenna-Matthews-Olson molecular aggregate under realistic physiological conditions. By employing an environmental fluctuation spectral function derived from experiments, we obtain numerically exact results for the exciton quantum dynamics in the presence of underdamped vibrationally coherent quantum states. Assuming the prominent 180-cm(-1) vibrational mode to be underdamped, additional coherent transport channels for the excitation energy transfer open up and we observe an increase of the transfer speed towards the reaction center by up to 24%.

Development and control of a series elastic actuator equipped with a semi active friction damper for human friendly robots

Compliance is increasingly being incorporated in the transmission of robotics actuation systems to cope with unpredictable interactions, improve the robustness of the robot and in some cases its efficiency. However, compliance also introduces some drawbacks as e.g. reduced bandwidth of the controlled system and typically underdamped vibration modes which decrease the accuracy and stability margin of the controlled system. To tackle these issues, variable physical damping has recently been incorporated in such actuation systems. This paper presents the analysis, development, control, identification and experimental evaluation of a novel actuation system which embodies transmission characteristics such as passive compliance and variable physical damping. The first part of this paper introduces an analysis on how these two physical properties affect the performance of the actuation system with the second part analysing the mechatronic design and control in detail. Furthermore, a novel damping estimation method is presented. Results are presented to validate the results obtained in the analysis section advantages gained by employing such actuation approach and to show the effectiveness of the actuation unit in replicating and estimating desired mechanical impedance values.

Optimal design of fluid dynamic bearings to develop a robust disk-spindle system in a hard disk drive utilizing modal analysis

This research proposes an optimal design methodology for fluid dynamic bearings (FDBs) in a hard disk drive to improve the dynamic performance of the disk-spindle system. We solved equations of motion for the rigid rotor supported by FDBs with five degrees of freedom. Five modal damping ratios were selected as multi-objective functions. The constraint equations were the friction torque of the FDBs and the stiffness and damping coefficients related to under-damped vibration modes. Ten major design variables of the FDBs were chosen for this optimization problem. The steady-state whirl radius and the shock response at half-speed whirl of the rotating rigid spindle-bearing system were evaluated as RRO and NRRO, respectively. The RRO and NRRO of the optimal design were compared with those of the conventional design. Our results show that the proposed method effectively reduces RRO and NRRO.

Robust optimal design of the FDBs in a HDD to reduce NRRO and RRO

This research proposes a robust optimal design methodology of the FDBs in a HDD to reduce RRO and NRRO. The critical mass, which determines the dynamic behavior of rotor-bearing system, was selected as an objective function, and the constraint equations were the friction torque of the FDBs, and the stiffness and damping coefficients related with under-damped vibration modes. Ten major design variables of the FDBs were chosen in this optimization problem. The steady-state whirl radius and the shock response at half-speed whirl of the rotating rigid spindle-bearing system were evaluated as RRO and NRRO, respectively. RRO and NRRO of the optimal design were compared with those of conventional one, and it showed that the proposed method could effectively reduce RRO and NRRO.

Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms

We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction. Beside the universal screening search, we also analytically identify the best for the case of Drude dissipation and that for the Brownian oscillators environment without strongly underdamped bath vibrations. For the mechanistic study, we quantify the quantum nature of bath influence and further address the issue of localization versus delocalization. Proposed are a reduced system entropy measure and a state-resolved constructive versus destructive interference measure. Their performances on quantifying the correlated system-environment coherence are exemplified in conjunction with the optimized hierarchical equations of motion evaluation of the model system dynamics, at some representing bath parameters and temperatures. Analysis also reveals the localization to delocalization transition as temperature decreases.

Design Optimization of FDBs to Minimize Friction Torque

We proposed a design method to optimize the design variables of fluid dynamic bearings (FDBs) in a hard disk drive (HDD) in such a way as to minimize the friction torque while satisfying the constraints of robust dynamic performance of a rotating disk-spindle system. The objective function was defined as the friction torque of the FDBs and was calculated by integrating the shear stress determined from the Reynolds equation using the finite element method (FEM). Two kinds of constraints were used to satisfy the robust dynamic performance of a rotating disk-spindle system. For under-damped vibration modes of a rotating disk-spindle system, the critical mass was set to be greater than that of the conventional disk-spindle system; for over-damped vibration modes, the related direct stiffness and damping coefficients were set to be greater than those of conventional FDBs. A micro-genetic algorithm was applied to solve the proposed optimal design problem of the FDBs in a 3.5-in HDD, and it showed that the friction torque of the FDBs decreased by 9.5% with the better dynamic performances of the rotating disk-spindle system.

Neural-adaptive control using alternate weights

This paper proposes a novel robust neural-adaptive control method for controlling underdamped non-minimum phase system. Without robust modifications to the training rule, adaptive approximators experience weight weight drift which typically causes control chatter and excitation of the natural frequency. Popular robust modifications, like e-modification and deadzone, significantly reduce performance. In the proposed method, an alternate neural network, providing approximately the same output, guides the training. The proposed algorithm trains the alternate weights in a manner so as to avoid the weight drift caused by underdamped vibrations. Experimental results show dramatic improvement in performance over e-modification when controlling a flexible-joint robot.