Degree Of Freedom Model Research Articles

Thermal asperity trends

A thermo-mechanical model that predicts the changes in thermal asperities as a function of increasing areal density is described. Conceptually, the problem is divided into two portions: the collision and relative motion of an asperity along the slider, and the subsequent diffusion of thermal energy into the head in the vicinity of the read element. The former is treated using a quasi-static spring model for the various mechanical degrees of freedom; the later with a scaling model for the heat transfer. The thermal model was verified by using a focused fast laser pulse to simulate a thermal transient at the read element. The predictions of the full model were also compared with measured thermal asperities that were produced on a spin-stand. The results support one of the model's main predictions: a significant increase in the amplitude of worst case thermal asperity events can be expected in the next few years.

Tunnel Mover Guidance and Stability

SUMMARYThis paper describes the analytical work done for a new type of vehicle. The vehicle is to be used inside a tube. The simple analytical model shows a roll / lateral, and yaw degree of freedom. A relatively simple condition for motion stability has been developed. Divergent instability may occur when the c.g. lies behind the point half way between the front and rear axles. Large cornering stiffness of the tyres and small wheel suspension stiffness promotes instabilityAdditional degrees of freedom have been defined using an ADAMS model. In this model the effect of a steering degree of freedom was examined. The automatic guidance of the vehicle by the curved inner tube wall has been investigated and the design has been optimized. The findings of the simple linear two degree of freedom model could be verified and extensions regarding full vehicle non-linear behaviour could be given.Using the results of both models a physical prototype of the vehicle concept is built. Full scale test runs of this prototype are planned in november 1999.

Effects of Rider's Vibrational Characteristics on Straight-Running Stability of Motorcycles.

A six-degree-of-freedom model and a twelve-degree-of freedom model incorporating a rider's vibrational characteristics have been developed. The models include a mechanical model of the rider's body which consists of a leaning motion of the upper body and a lateral movement of the lower body. Damping properties and natural frequencies of weave and wobble modes were calculated using these models. Conclusions are drawn about effects of the rider's vibrational characteristics on the stability of motorcycles during straight running from the calculations in the six degree of freedom model. Implications for accurate modeling of motorcycle stability are derived from differences between the calculations in the twelve-degree-of-freedom model and running experiments.

BRACED FRAMES WITH HYSTERETIC DISSIPATIVE DEVICES: SEISMIC RESPONSE AND DESIGN CRITERIA

The seismic behaviour of elastic braced frames with hysteretic dissipative devices is investigated. The analysis is carried out using a simplified single degree of freedom model that is deduced on the basis of an equivalence criterion between one-storey and multi-storey braced frames. The criterion allows one to characterise the structure by means of a few global parameters, such as the fundamental period of vibration, the ratio between the fundamental period and that of the correspondent unbraced frame, and the behaviour factor. The combined effect of design values of structural parameters and the energy frequency content of the input is stressed by evaluating the power spectral density of the stationary phase of the response. Consistent energy, displacement and strength response spectra are shown. The results elucidate the different behaviour of short and medium period structures with respect to the predominant period of ground motion. For each of the two classes, design criteria and guidelines for choosing the optimal values of the structural parameters are summarised. Four design examples are presented in order to demonstrate the effectiveness of the proposed criteria.

Ride Control – A Two State Suspension Design for Cabs and Seats

ABSTRACTThis paper presents a computer-controlled suspension design for tractors and semi-trailers cabs and driver's seats. Two separate models representing the vehicle with a cab suspension and the seat with an operator modeled as a lumped mass system are presented. The vehicle is represented by an 8 degrees-of-freedom (DOF) model, which includes a 3-axle tractor semi-trailer and a separated cab with suspensions. The seat/operator system is modeled by a 6 DOF model to simulate the vertical dynamic response of the driver including the seat suspension. The cab is supported by a set of controllable suspensions at both of the front and rear ends of the cab. The seat is attached to the floor of the cab by another controllable suspension. Each controllable suspension is modeled by a set of linear spring and non-linear damper whose coefficient is time dependent. First, a sky-hook based semi-active controller was designed to seek optimum cab suspension. Then, the second state controller was used with the cab's velocity and displacement as input to minimize the parameters of the seat/operator model. The seat suspension parameters were optimized to yield the best ride quality under the prescribed input road conditions. The ride comfort is measured using the absorbed power under stochastic road excitation.

Phase Separation Induced by Orbital Degrees of Freedom in Models for Manganites with Jahn-Teller Phonons

The two-orbital Kondo model with classical Jahn-Teller phonons is studied using Monte Carlo techniques. The observed phase diagram is rich, and includes a novel regime of phase separation induced by the orbital degrees of freedom. Experimental consequences of our results are discussed. In addition, the optical conductivity $\sigma(\omega)$ of the model is presented. It is shown to have several similarities with experimental measurements for manganites.

SU(2) THEORY OF t– J TWO-LEG LADDERS

We present a low-energy effective model for the charge degrees of freedom in two-leg t– J ladders. Starting from the SU(2) mean-field theory, we find that, at low temperatures, the mean-field solution is the staggered-flux phase. Our analysis is applicable at low doping and in the `physical' range of parameters, t/ J∼3, where there is one massless mode in the charge sector and no massless modes in the spin sector. Low-lying charge excitations are described as bipolarons.

Bipolaronic charge excitations int−Jtwo-leg ladders

We present a low-energy effective model for the charge degrees of freedom in two-leg $t\ensuremath{-}J$ ladders. Starting from $\mathrm{SU}(2)$ mean-field theory, we exclude the spin degrees of freedom that have an energy gap. At low temperatures, the mean-field solution is the staggered-flux phase. For gapless charge excitations the effective theory is the Luther-Emery liquid. Our analysis is applicable at low doping and in the ``physical'' range of parameters $t/J\ensuremath{\sim}3$ where there is only one massless mode in the charge sector and no massless modes in the spin sector. Within our model we make predictions about correlation exponents and the superconductivity order parameter, and discuss the comparison with the existing numerical results.

Conformational Correlations in DNA. Molecular Dynamics Studies

A statistical, circular correlation model for conformational degrees of freedom in DNA is proposed. Correlation coefficients are computed for A and B DNA, as well as for transition processes between these forms, using microscopic MD simulation data. The correlations are interpreted and a minimal number of independent conformational degrees of freedom conserving basic static and dynamic properties of the right-handed DNA forms are found. The selected degrees of freedom form a hierarchical class and can constitute a base for a dynamical model using curvilinear degrees of freedom. In the most accurate representation one uses all backbone, torsional angles as well as pseudorotation parameters and glycosidic angles. In the second model one treats the backbone angles δi, and the glycosidic angles χi, as functions of the phases of pseudorotation, Pi. The third model assumes a functional dependence of other backbone angles ξi as functions of Pi.

Six degree of freedom joint power in stair climbing

Abstract In the past, joint power has most often been calculated as the product of the sagittal plane joint moment and the sagittal plane joint angular velocity, thus modelling the joint as a simple one degree of freedom (DOF) hinge. More recently three DOF power has been calculated by taking the scalar product of the net joint moment and the angular velocity of the joint, thus modelling the joint as a ball and socket joint. We introduce a six DOF approach for calculating joint power, an approach which allows three degrees of rotational freedom, as well as three degrees of translational freedom, thus implementing a rigorous definition of true mechanical power. We established that for the hip joint during stair ascent, three DOF power was significantly greater than six DOF power (by as much as 60 W/kg), while for stair descent, one DOF power was significantly less than six DOF power (by up to 45 W/kg). On the basis of the total work done in raising the body up a set of stairs (weight × height), the six DOF approach provided more accurate results than either the one or three DOF models. We also showed that six DOF power data were as repeatable as joint moments, with variance ratios between 0.13 and 0.20. While these findings are certainly not the definitive word, they do offer some guidance regarding the effect that certain assumptions have when calculating joint power in three dimensions.

Stick-Slip Motion of Frictionally Damped Turbine Airfoils: A Finite Element in Time (FET) Approach

A method is proposed for analyzing the periodic stick-slip motion of a single degree of freedom model of frictionally damped turbine blades. The method of finite elements in the time domain (FET) is based on a Hamilton’s weak principle, paralleling the variational methods in elastostatics. It permits a complete determination of the hysteretic friction force, and results in a set of highly structured system equations. The method has a number of unique features, which are utilized to provide a simple yet efficient approach for predicting the steady-state response. When applied to a number of example problems, including systems with static friction and the excitation of multiple discrete frequencies, the FET method is demonstrated to be an efficient and reliable alternative technique for nonlinear dynamic response analysis.

Domain pattern formation near phase transition – challenge for computer simulations

The principles of constructing a model with reduced number of degree of freedom, which allow to simulate the evolution of domain pattern of a displacive crystal, are overviewed. The model degree of freedom, related by the simple effective potential, must form modes consistent with symmetry of the primary and secondary order parameters of the studied crystal. The model potential and the procedure of finding the potential parameters are discussed.

Spin dynamics of SrCu2O3 and the Heisenberg ladder.

The $S=1/2$ Heisenberg antiferromagnet in the ladder geometry is studied as a model for the spin degrees of freedom of SrCu$_2$O$_3$. The susceptibility and the spin echo decay rate are calculated using a quantum Monte Carlo technique, and the spin-lattice relaxation rate is obtained by maximum entropy analytic continuation of imaginary time correlation functions. All calculated quantities are in reasonable agreement with experimental results for SrCu$_2$O$_3$ if the exchange coupling $J \approx 850$K, i.e. significantly smaller than in high-T$_c$ cuprates.

Dynamic Simulation of a Complex Human Figure Model with Low Level Behavior Control

Advances in computer hardware and software technology allow the simulation of natural phenomena in increasing levels of complexity. This research is concerned with simulating the articulated movements of humans using the laws of physical motion, and contributes to the fields of computer animation and biomechanics. A 90 degree of freedom model of a human figure is developed, and an efficient dynamic simulator is employed to create and analyze physically based, computer-generated motions. The foot of the simulated human figure has been modeled with a significant amount of kinematic complexity, with 28 degrees of freedom per foot. A joint-level control layer uses springs and dampers to control postures and movements. Inverse dynamics and inverse control can be used to calibrate the spring actuators to exactly achieve specified postural goals. A framework for higher level control is implemented, although specific tasks require tailored control strategies. Several example tasks are simulated and described, including a stable standing posture and the stepping phase of walking using passive dynamic effects to generate much of the motion. Together, the simulator and biomechanical model create a framework that can be used to address problems in computer animation and biomechanical research, and eventually, in a clinical setting, to assist doctors in analyzing the problems of specific patients.

Wave packet study of the Ne 2I 2 fragmentation dynamics: a four degrees of freedom model

We present a four degrees of freedom model that accounts for all possible fragmentation mechanisms in the vibrational predissociation of the Ne 2I 2 van der Waals cluster. Calculations are performed by wave packet propagation and results are interpreted in terms of an analytical sequential model leading to a good agreement with experimental data.

On the role of solvent electronic polarization in charge transfer reactions

The effect of a solvent’s electronic polarization on the rate of a charge transfer reaction is studied in both continuum and discrete solvent models. An effective system Hamiltonian that contains the equilibrium solvation from the solvent electronic polarization is obtained, and leads to an effective matrix element Veff coupling the charge transfer states that is smaller than the gas phase value. Both the effective Hamiltonian and Veff are dependent on the solvent’s instantaneous nuclear configuration, and liquid state theory is used to carry out the configuration average. The solvent electronic polarization reduces the transition rate for both adiabatic and nonadiabatic reactions. A standard relation between the equilibrium solvation energy of the reactants and the solvent reorganization energy is established that permits evaluation of the effect of a molecular solvent (using a Drude model for the electronic degrees of freedom) on the rate by evaluating a partition function. This permits use of a path integral formulation for the mixed quantum (electronic polarization) classical (slow nuclear configuration) solvent that leads to the information required for the rate constant. In a strong coupling regime, where the coupling between the charge-transfer species would be so large as to preclude reactant and product species, we show that a new mechanism for charge localization arising from the solvating effect of the electronic polarization may occur, and formulate a rate constant expression for this regime. It has the form of a quantum Kramers rate and shows that the solvent provides a friction effect that will reduce the rate relative to the no-friction rate.

Overturning Stability of Three Wheeled Motorized Vehicles

SUMMARY Three wheeled motorized vehicles are a major mode of public transport in many countries. These vehicles are prone to overturning even during normal turning and obstacle avoidance maneuvers. This paper presents a parametric analysis of a mathematical model of the vehicle and evolves guidelines for improving the overturning stability in terms of vehicle geometry and suspension properties. Differential equations governing the dynamic behavior of the vehicle are derived on the basis of a six degree of freedom model. The vehicle response to variations in steering, engine power and braking inputs is then numerically simulated. The effects of vehicle geometry and elasto-damping suspension coefficients on the vehicle stability are presented. The results indicate an optimum position of the center of gravity where the vehicle is most stable. While stiffer suspensions favour stability, there exists an optimum value of suspension damping for which the minimum wheel load is a maximum.

On equilibrium and primary variables in transport in porous media

Thermodynamic equilibrium, which involves mechanical, thermal, and chemical equilibria, in a multiphase porous medium, is defined and discussed, both at the microscopic level, and at the macroscopic one. Conditions are given for equilibrium in the presence of forces between the surface of the solid matrix and the fluid phases. The concept ofapproximate thermodynamic equilibrium is introduced and discussed, employing the definition of athermodynamic potential. This discussion serves as the basis for the methodology of determining the number of degrees of freedom in models of phenomena of transport (of mass, energy, and momentum) in porous media. Equilibrium and nonequilibrium cases are considered. The proposed expressions for the number of degrees of freedom in macroscopic transport models, represent the equivalent ofGibbs phase rule in thermodynamics.

Femtosecond Two-Dimensional Raman Spectroscopy of Liquid Water

Higher-order Raman spectra for water are calculated using the Brownian oscillator model for the nuclear degrees of freedom which is constrained to fit the spectral density obtained between 0 and 1000 cm-'. Assuming a static distribution, both fifth- and seventh-order processes are capable of distinguishing the homogeneous and inhomogeneous character of the spectral density. Through temperature-dependent heterodyne optical Kerr effect studies, an upper limit (150 f 30 fs extrapolated to 100 C) for the homogeneous lifetime in liquid water was established. The intermediate fifth-order case was analyzed to incorporate this dynamically evolving distribution of local environments and indicates that, even for a system as complex as water, higherorder field correlations can access information on its dynamic structure.

Simplification of the transition state concept in reactive island theory: Application to the HCN⇄CNH isomerization

The reactive island (RI) theory of chemical reaction rates is modified so that a precise knowledge of the transition state is not required. This revised form of the theory is applied to a realistic two (J=0) and three degree of freedom model (J≠0) of the isomerization HCN⇄CNH. The detailed reaction dynamics is examined and understood in terms of the cylindrical manifolds embedded in the molecular phase space. Of special interest we find a T-shaped conformer in addition to the HCN and CNH moieties at J=0. Rates of unimolecular decay are examined by numerical simulation and theory. Good agreement is found between theory and simulation except for a case where a substantial amount of phase space is consumed by regular motion. In all cases studied, the theory is a significant improvement over the Rice–Ramsperger–Kassel–Marcus (RRKM) theory, which is up to three orders of magnitude too large.