Linear Oscillator Model Research Articles

Resilience-as-process: Negative affect, stress, and coupled dynamical systems.

Resilience is often considered both a trait and a process. The current study proposes a new way to conceptualize resilience-as-process based on dynamical systems modeling, which allows researchers to capture the process of stress management in real time. Coupled damped linear oscillator models succinctly describe daily stress and negative affect in terms of developmental forces (e.g., velocity, acceleration). Models were fit to 56-day daily response data from 42 aging adults (M(age) = 78.8 years; SD(age) = 6.6 years) to observe and understand linkages between daily stress and affect. It was speculated that individuals with greater resilience would experience stress as less coupled to changes in negative affect (less stress reactivity), and would recover their affective equilibrium more quickly following a given exogenous stressor (greater stress recovery). To identify resilience resources related to reliable interindividual differences in coupling and damping between stress and negative affect, we examined possible protective factors. Aspects of personality and social support predicted both the strength and nature of this coupling, such that higher levels of these resources resulted in greater protection from the cost to negative affect from stress, as observed in damping of negative affect and decreased coupling between systems.

Capturing the Ebb and Flow of Psychiatric Symptoms With Dynamical Systems Models

Psychiatric symptoms play a crucial role in psychology and psychiatry. However, little is known about how dimensions of symptoms--other than symptom level--relate to psychiatric outcomes. Until recently, methods for measuring dynamic aspects of symptoms have not been available to clinicians or researchers. The authors sought to test whether systematic patterns of change in psychiatric symptoms can be recovered across weekly assessments of individuals at high risk for violence. A secondary objective was to explore whether dynamic features of symptoms (specifically, oscillation speed and dysregulation) are concurrently associated with violence, an important indicator of functional impairment for these individuals. Participants (N=132) were drawn from a sample of patients evaluated at the emergency room of an urban psychiatric hospital. Patients actuarially classified as being at high risk for violence were eligible for participation in the study. Participants and collateral informants were interviewed weekly for 26 weeks following an acute psychiatric evaluation. Psychiatric symptoms were assessed using the Brief Symptom Inventory. Measures of symptom fluctuation and regulation were derived using dynamical systems models. Involvement in violence was assessed using self, informant, and official reports. Individuals' symptom dynamics were recovered by a linear oscillator model that described how quickly symptoms oscillated and whether symptoms were amplifying or moving back toward equilibrium across time. Patterns of rapid symptom fluctuation and symptom amplification were concurrently associated with violence. Psychiatric researchers and clinicians have long been interested in adopting more dynamic approaches to understanding symptom change. This study is the first to demonstrate that systematic fluctuations in symptom patterns may be captured by dynamic models. Moreover, the concurrent association between symptom dynamics and violence suggests avenues for future research to test how features of symptom fluctuation could affect behavior.

Modeling Individual Damped Linear Oscillator Processes with Differential Equations: Using Surrogate Data Analysis to Estimate the Smoothing Parameter

Among the many methods available for modeling intraindividual time series, differential equation modeling has several advantages that make it promising for applications to psychological data. One interesting differential equation model is that of the damped linear oscillator (DLO), which can be used to model variables that have a tendency to fluctuate around some typical, or equilibrium, value. Methods available for fitting the damped linear oscillator model using differential equation modeling can yield biased parameter estimates when applied to univariate time series. The degree of this bias depends on a smoothing–like parameter, which balances the need for increasing smoothing to minimize error variance but not smoothing so much as to obscure change of interest. This article explores a technique that uses surrogate data analysis to select such a parameter, thereby producing approximately unbiased parameter estimates. Furthermore the smoothing parameter, which is usually researcher-selected, is produced in an automated manner so as to reduce the experience required by researchers to apply these methods. Focus is placed on the damped linear model; however, similar issues are expected with other differential equation models and other techniques in which parameter estimates depend on a smoothing parameter. An example using affect data from the Notre Dame Longitudinal Study of Aging (2004) is presented, which contrasts the use of a single smoothing parameter for all individuals versus use of a smoothing parameter for each individual.

Free v/s forced vibrations of a cylinder at low Re

Free vibrations of a circular cylinder of low non-dimensional mass are investigated at low Reynolds numbers. Computations are carried out for 5% blockage. Lock-in is observed for a range of Re and is accompanied with hysteresis at both lower as well as higher Re ends of the synchronisation/lock-in region. It is well known that the lock-in regime for free vibrations depends on the non-dimensional mass of the oscillator. The results from the present computations are compared with the data for forced vibrations from Koopmann (Journal of Fluid Mechanics, 28, 501–512, 1967) on a Y max/D vs. f* plot, where Y max is the maximum oscillation amplitude and f* is the ratio of cylinder vibration frequency to the vortex shedding frequency for a stationary cylinder. Good agreement is observed for the critical amplitude needed for onset of synchronisation between the forced and free vibrations. The results from the free vibrations are compared to the predictions from the linear oscillator model by assuming that the forces on the cylinder are unaffected as a result of vibrations. It is found that, for low mass oscillators, the modification of vortex shedding frequency and lift coefficient due to cylinder oscillations leads to the enhancement of the lock-in regime.

Measurement nonlinearity interpreted as material behavior in dynamic nanoindentation

This paper explores the errors that may arise in when interpreting dynamic nanoindentation measurements with a linear oscillator model. The work was motivated by an experimental observation that the system's primary resonance can be dramatically altered by changes in loading conditions. Investigations elucidate that different sources of nonlinearity can interact to alter the identified contact stiffness which will manifest itself as a change in the system's primary and secondary resonances. The errors associated with interpreting dynamic indentation measurements with a linear model are investigated through modeling, analysis, and numerical study. Theoretical efforts show that measurement nonlinearity can be falsely interpreted as material behavior. Hence, the common practice of applying a linear oscillator model is expected to sometimes lead to significant errors. These finding suggest that a nonlinear analysis may often be required to improve measurement interpretations.

Interspike interval densities of resonate and fire neurons

The subthreshold dynamics of a neuron can follow one of the two patterns: resonant neurons generate intrinsic subthreshold membrane potential oscillations, whereas in nonresonant neurons these oscillations are not observed. Here, we investigate how these subthreshold behaviors affect the suprathreshold response. Both types of neurons are described by a resonate and fire model, with the stable fixpoint being either a focus or a node. Using analytic expression for a linear oscillator model with threshold and reset, we calculate the multimodal interspike interval densities. We show that a change in model parameters induces qualitative changes in the interspike interval densities.

Emotional well-being in recently bereaved widows: a dynamical systems approach.

A dynamical systems approach was used to model the intraindividual variability in emotional well-being following conjugal loss. Well-being in a sample of 19 recently bereaved older adult widows was measured every day for 3 months. The pattern of variability of well-being was hypothesized to be an oscillating process that damps across time (i.e., large swings followed by a gradual damping). Results indicated that there was significant patterned variability in the emotional well-being adjustment that can be modeled by a linear oscillator model (R2=.77), in addition to an overall positive trend. Applying dynamical systems analyses to capture variability and subsequent well-being trajectories following spousal loss is an important step in delineating the complex adjustment to widowhood.

Static and Dynamical Properties of Single Poly(Ethylene Glycol) Molecules Investigated by Force Spectroscopy

Molecular recognition force spectroscopy was employed to probe the mechanical and dynamical features poly(ethylene glycol) (PEG). His6 was covalently coupled to AFM tips via PEG for the specific recognition of NTA on the surface. Force-extension profiles of single molecules obtained in force-distance cycles were fitted with an extended Worm Like Chain (WLC) model with a quality of the fit σdata-fit/σdata of 1.3. The fit revealed a persistence length LP of 3.8 ± 0.02 A and an enthalpic correction term K0 of 1561 ± 33 pN. Amplitude-distance cycles were recorded with dynamical force microscopy. Fitting with the damped linear oscillator model, using values for the persistence length and the nonlinear spring constant from force-distance cycles, yielded a fit quality σdata-fit/σdata of 1.5. Force-distance cycles calculated from amplitude-distance cycles by integration nicely agreed with simultaneously measured force-distance cycles, and even yielded an improved signal to noise ratio. This shows that no dissipative and irreversible processes occur and that the force extension profile of PEG is determined by purely elastic behavior.

Electron-lattice coupling parameters and oscillator strengths of cerium-doped lutetium oxyorthosilicate

Optical absorption of single-crystal, cerium-doped lutetium oxyorthosilicate has been carefully measured in the temperature interval 10-300 K. Prominent Gaussian absorption peaks occur at 3.432{+-}0.002 eV (peak a), 3.502{+-}0.002 eV (peak b), 4.236{+-}0.0002 eV (peak c), and 4.746{+-}0.0002 eV (peak d), in excellent agreement with previously reported excitation spectra. The second moments are well described by the usual linear model, yielding the Huang-Rhys parameter (S) and vibrational quantum energies for the individual peaks. All absorption bands are characterized by S>5 indicating strong coupling between the Ce{sup 3+} ion and lattice. Temperature dependence of the band centroids exhibits contrasting behavior that is dominated by higher-order coupling terms in the linear harmonic oscillator model or by crystal-field effects. Oscillator strengths of the 4f{yields}5d transitions are calculated from Smakula's formula and knowledge of the Ce{sup 3+} distribution between the two crystallographically inequivalent sites. Values for peaks b, c, and d range from approximately 0.003 to 0.004, and peak a spans magnitude approximately 0.012 to 0.018. From the known correlation between average Ce{sup 3+}-ion-ligand distance and oscillator strength, we tentatively conclude that peak a is correlated with the seven-oxygen-coordinated site, and peaks b, c, and d are associated with the six-oxygen-coordinated site. These results supportmore » the previously proposed two-activation-center model and identify the centers as the two crystallographically inequivalent substitutional sites. (c) 2000 The American Physical Society.« less

Diatomic metal encapsulates in fullerene cages: A Raman and infrared analysis of C84 and Sc2@C84 with D2d symmetry

Raman scattering and infrared absorption of the C84 and Sc2@C84 isomers 23:D2d were studied at room temperature and 95 K. The results are compared to the response of pristine and doped C60. According to the lower symmetry and the higher number of atoms C84 exhibits much more vibrational modes than C60, in particular at wave numbers above 500 cm−1. For lower energies the vibrational structure of C84 resembles a downshifted and split C60 spectrum. After the encapsulation of two scandium atoms the overall vibrational structure and the number of C84 modes was preserved as a result of the similar geometric structure. From the very good correlation of the C84 and Sc2@C84 cage modes metal to fullerene charge transfer induced shifts could be analyzed. The lines were found less shifted compared to the C60 modes in exohedral doped A6C60 (A=K,Rb,Cs). Increased line widths of low energy cage modes were attributed to an additional intramolecular relaxation channel related to the dynamics of the encapsulated scandium ions. A set of nine new lines with almost complementary Raman and infrared intensities was found for Sc2@C84 below 200, at 246 and at 259 cm−1, and attributed to Sc–C84 vibrations. These vibrations were further identified as Sc–C84 stretching and Sc–C84 deformation modes. The Sc–C84 valence force constant of 1.19 N/cm was derived with a linear three-mass oscillator model for Sc2@C84. Both, the charge transfer induced line shifts and the Sc–C84 valence force constant indicate an effective transfer of approximately two electrons per scandium to the carbon cage. This is in agreement with an electronic state (Sc2.2+)2@C844.4− previously proposed on the basis of x-ray powder diffraction, x-ray photoemission spectroscopy (XPS), and quantum chemical calculations. The unexpected high number of Sc–C84 vibrations is attributed to crystal field and factor group splitting.

A Dynamical Systems Analysis of Adolescent Substance Abuse

Models from dynamical systems theory were fit to the intraindividual variability In adolescent self-reported cigarette and alcohol use. A dampened linear oscillator model (potentially like a pendulum with friction) and a nonlinear oscillator model with two attractors were compared. The nonlinear oscillator model and two coupled oscillators for cigarette and alcohol use were rejected. Independent dampened linear oscillators for smoking and drinking provided high internal R2 but were unable to account for a substantial correlation between the acceleration in cigarette usage and alcohol usage; thus evidence was found for an intrinsic self-regulation mechanism in both smoking and drinking behavior, but the hypothesis was rejected that the intrinsic mechanism leading to increases in use in one substance directly predicted increased use in the other substance. Given the hypothesis of independent linear oscillators, the sign of the dampening parameter was found to be positive, indicating a system with dynamic instability; a self-regulation mechanism in which small changes in substance use lead to amplified changes after a short period of time.

Dielectric Theory of Collisional Absorption in Intense Laser Fields

AbstractCollisional absorption of superintense laser pulses in dense plasmas can be described by the classical linear dielectric theory in a wide range of parameters. For electron oscillation velocities largely exceeding their thermal motion a linear oscillator model is presented and nearly exact solutions in terms of Anger functions are given for the time‐averaged electron‐ion collision frequency. A possible extension of the dielectric theory into higher density and/or lower temperature regions is indicated and the need for time‐dependent collision frequencies is stressed.

Multiple resonances in the double-flash effect

When a single brief light pulse follows the offset of an inducer light field, the single pulse is seen as two (or more) flashes: this is the double-flash effect. Measurements of the strength of the effect as a function of the frequency of a flickering inducer field have revealed a high illuminance threshold and a strongly bandpass complex structure containing several peaks [ J. Opt. Sci. Am. A4, 746– 755 ( 1987)]. A linear-oscillator model may account for one peak but not for multiple peaks; furthermore, the high illuminance threshold is expected to introduce nonlinearity. We therefore base our analysis of the resonance structure on a nonlinear-oscillator model, and we argue that its leading term is cubic. The model accounts in a parsimonious way for all the double-flash results, it correctly predicts a shift in peak frequencies from ordinary threshold flicker effects, and, finally, it corroborates claims that the response of the visual system to suprathreshold stimuli is oscillatory rather than biphasic.

Non-linear effects in the vicinity of the resonant frequency of viscoelastic measurements devices

In previous work, an analysis was presented which permits the separation of unavoidable non-linear components from the frequency response curve in the oscillatory measurement of linear viscoelastic dynamic moduli. The remaining components show what can be labelled as a quasilinear behavior. It is believed they contain the measurable low-order non-linear corrections necessary in the first step in the design of a non-linear phenomenological model, which would be an extension of the standard linear oscillator model. This non-linear behavior might cause the existence of jump phenomena near the natural resonance frequency of torsion pendulum rheometers. Fine frequency scanning around resonance is suggested as a means to put it into evidence.

Human Operator Control of a Bilateral Teleoperator in Part-Simulation of Zero Gravity

An experimental investigation has been undertaken at the Jet Propulsion Laboratory to address issues associated with manual control of a teleoperated manipulator operated in an earth orbital environment (e.g., the Shuttle Remote Manipulator System (RMS)). Manual control of a teleoperator and the effect of microgravity on the operator's performance were examined using a force-reflecting hand controller (FRHC) and a gravity compensation system to simulate the effect of microgravity on the operator's arm. The kinematic and dynamic characteristics of the operator's arm and hand play a fundamental role in bilateral (backdriven) teleoperator control. Two control experiments were performed in this study: (a) verification of a linear damped harmonic oscillator model of human neuromotor control in trajectory formation and stability in standard one gravity (lg) operation, and (b) force tracking along simulated planes of resistance subject to unit pulse disturbance in simulated zero g operation. The results of the experiments verified the utility of the neuromotor model in teleoperator control performance and confirmed the existence of disturbance of human manual control performance associated with the micro-gravity condition. The results illustrate that compensatory techniques to return performance to a level commensurate with, or superior to, standard one gravity operation could be derived. These techniques are based on the human control model, and instituted through FRHC control parameter adjustment.

Identification of human lower extremity dynamics in torsion

A four degrees of freedom, damped, linear oscillator model of the lower extremity in torsion was identified through laboratory frequency response tests. The foot was rotated sinusoidally in the mediallateral plane through the 1–20 Hz frequency band at the constant amplitudes 2, 4 and 6 degrees. Weight bearing on the foot, muscle-induced bias torsion and knee flexion were also test variables. Identification was undertaken by minimizing the squared difference between the measured and predicted transfer functions of the pelvis and foot. The model specification and the laboratory identification procedures were the focus of this work. Variations greater than 30% in the identification stiffness, damping and inertia values were predicted over the test variable ranges. The transfer functions recorded in these tests indicated the lower extremity can be modeled as a compliance between a foot inertia and the pelvis-torso inertia. Joint compression, induced by weight bearing, and muscle contraction, measured by the bias torsional moment at the foot, increased the torsional stiffness of the knee, ankle and pelvis model elements, and they had an indeterminate influence on the hip stiffness. The model knee and hip stiffnesses and the model pelvis-torso inertia were maximized, and the model ankle stiffness was minimized at the maximum foot rotation amplitude.

Streamwise Oscillations of Cylinders

Slender structures, such as marine piles, have been observed to experience oscillations in a streamwise direction when exposed to an external flow under appropriate circumstances. This phenomenon is explored both theoretically and analytically with a view to explaining the basis of the phenomenon and of providing a method of calculating the response amplitude. The flow around a vibrating body, is assumed to be quasisteady. From this assumption a stability criterion, analogous to the Den Hartog criterion for transverse oscillation, is derived. This stability criterion indicates that instability is to be expected only over a range of Reynolds number near the critical value which corresponds to a sudden drop in the drag coefficient and an increase in the Strouhal number. Using a linear oscillator model for the body, an analysis is performed to seek solutions for the vibration amplitude. The results of this analysis are compared with observations of prototype oscillations of marine piles which occurred at Reynolds numbers high enough to be in the critical range.

The tree graphs theory for enzymatic reactions: A theorem for the reactions among the non-enzymatic species

The tree graphs theory may be usefully applied to the enzymatic reactions (1) by using the elimination rule for one of enzyme-complexes that by itself constitutes one knot, (2) building up separately the graph for the enzymatic reaction and, if there are any, the graph for the direct reactions among substrates, products and effectors; if only tree graphs belong to an enzymatic mechanism, then all its eigenvalues are real and strictly negatives and therefore each steady-state is stable. As examples we have analyzed the models of activated enzyme catalysis as a realization of a linear oscillator model (Seelig, 1971).

Photoinduced dichroism and vibronic relaxation of rhodamine dyes

Abstract The absorption anisotropy of rhodamine dye molecules in various solvents is measured on a picosecond time scale. The dye solutions are partially bleached with pump pulses and the dichroism is measured with delayed perpendicularly polarized probe pulses. The experimental results are compared with the linear oscillator model.

Activated enzyme catalysis as a possible realization of the stable linear chemical oscillator model

The stable linear chemical oscillator model of a preceding paper is reformulated in such a way that the action of the catalyst is expressed explicitly in terms of elementary reactions that are non-linear. It is shown that it is hardly possible to get a quasi-linear limiting case, if the substance produced on the feedback path is the catalyst itself. This can be achieved, if that substance is only an activator and the total amount of catalyst is constant. Thus, activated enzyme catalysis is a possible realization of the formally linear model. A further requirement is that the formation of the activated enzyme-substrate complex AES and the final reaction advances essentially over E + S ⇌ ES, ES + A ⇌ AES → P + A + E and that the enzyme is almost completely in the form ES. Fourier analysis of the results of computer simulations proves the high linearity in the essential substances even for cases of great amplitude in the limit cycle, while other parts, e.g. E, oscillate in a strongly non-linear way.