Time Constant Of System Research Articles

Comment on “Heat capacity, time constant, and sensitivity of Earth's climate system” by S. E. Schwartz

[1] In a recent paper, Schwartz [2007] (hereinafter referred to as S07) estimated climate sensitivity using globally averaged observed time series. He estimated the planet’s effective heat capacity and ‘‘pertinent time constant’’ from ocean heat content and observed global temperature records, assuming that the latter can be modeled as a firstorder Markov (AR(1)) process after removing the trend due to climate forcing by subtracting a linear trend. [2] As S07 correctly states, the autocorrelation of an AR(1) process at lag Dt follows the simple relation

Comment on “Heat capacity, time constant, and sensitivity of Earth's climate system” by S. E. Schwartz

[1] Schwartz [2007] recently evaluated the time constant of Earth’s climate system. However, his methodology yields to a significant underestimation of the value of t and obscures a much more interesting property of the system. Schwartz found t = 5 ± 1 years. Herein, by using an improved methodology I find that for short time scales from 0 to 2 years t is of the order of a several months and for larger time scales, at least up to 20 years, t is at least 70% larger than what Schwartz estimated. [2] Schwartz [2007] hypothesized (his equation (17)) that the climate system behaves as a first-order autoregressive process plus a linear trend. The implicit idea seems that the linear trend represents the effect of the external forcings on climate while the temperature signal, detrended of the above linear component, represents the internal variability of the same. This internal variability is assumed to be described by an AR(1) process whose autocorrelation function, r(Dt), decays as an exponential function of the lag time Dt with a given time constant t: r(Dt) = exp( Dt/t). [3] Although in physics using simple models is useful, the one suggested by Schwartz [2007], with a single time constant, is an oversimplification and, as I will prove below, it is inconsistent with the analysis. In fact, it is very well known that climate is the combination, coupling and superposition of several phenomena. Some phenomena respond quickly as the atmosphere, others as the deep ocean respond very slowly. Thus, each climate component responds with its own time constant that might range from a few months to several years or decades. [4] Given the length limitation of the temperature data herein analyzed (approximately 125 years) the analysis is limited to time scales below 20 years with a monthly resolution and I look for two time constants. The climate model I suggest is

A Circuit Coupling Method Based on a Temporary Linearization of the Energy Balance of the Finite Element Model

In this paper, a versatile method for modeling coupled magnetic field and circuit problems is presented. The field problem is solved by applying the finite element (FE) method. The nonlinear circuit equations are solved by applying the Newton-Raphson method. The finite element model and the circuit are solved separately, which in turn gives the possibility of considering different time constants for each domain. The idea is to extract values of the slowly varying lumped parameters describing the finite element model in the circuit equations at a rate related with the time constant of the finite element system, and to use them to iterate the circuit equations between two updates with a time step adapted to the significantly smaller time constant of the electric system. Contrary to the widely used numerically strong coupled methods, this paper introduces a different approach by applying an energy-based parameter identification.

Numerical instability of deconvolution operation via block pulse functions

Abstract This paper characterizes oscillations found in block pulse function (BPF) domain identification of open loop first-order systems with step input. A useful condition for occurrence of such oscillations is presented mathematically. For any positive value of ‘ah’, oscillations are observed to occur, where h is the width of BPF domain sub-interval and 1 / a is the time constant of the first-order system under consideration.

Heat capacity, time constant, and sensitivity of Earth's climate system

The equilibrium sensitivity of Earth's climate is determined as the quotient of the relaxation time constant of the system and the pertinent global heat capacity. The heat capacity of the global ocean, obtained from regression of ocean heat content versus global mean surface temperature, GMST, is 14 ± 6 W a m−2 K−1, equivalent to 110 m of ocean water; other sinks raise the effective planetary heat capacity to 17 ± 7 W a m−2 K−1 (all uncertainties are 1‐sigma estimates). The time constant pertinent to changes in GMST is determined from autocorrelation of that quantity over 1880–2004 to be 5 ± 1 a. The resultant equilibrium climate sensitivity, 0.30 ± 0.14 K/(W m−2), corresponds to an equilibrium temperature increase for doubled CO2 of 1.1 ± 0.5 K. The short time constant implies that GMST is in near equilibrium with applied forcings and hence that net climate forcing over the twentieth century can be obtained from the observed temperature increase over this period, 0.57 ± 0.08 K, as 1.9 ± 0.9 W m−2. For this forcing considered the sum of radiative forcing by incremental greenhouse gases, 2.2 ± 0.3 W m−2, and other forcings, other forcing agents, mainly incremental tropospheric aerosols, are inferred to have exerted only a slight forcing over the twentieth century of −0.3 ± 1.0 W m−2.

Cardiovascular haemodynamics and ventriculo‐arterial coupling in an acute pig model of coronary ischaemia–reperfusion

Although reperfusion after coronary occlusion is mandatory for myocardial salvage, reperfusion may trigger a cascade of harmful events (reperfusion injury) adding to myocardial injury. We investigated effects of reperfusion on left ventricular (LV) haemodynamics and ventriculo-arterial (VA) coupling in pigs following acute myocardial ischaemia induced by coronary artery occlusion. Experiments were performed in six animals, with measurements of cardiac and arterial function at baseline, after 60 min of ischaemia (T60) and after 2 (T180) and 4 h of reperfusion (T300). Ventriculo-arterial coupling was assessed using the ventriculo-arterial elastance ratio of paper, as well as using a 'stiffness coupling' and 'temporal coupling' index. Reperfusion following ischaemia (T180 versus T60) induced a progressive decline in cardiovascular function, evidenced by a decrease in mean arterial blood pressure, cardiac output and ejection fraction which was not restored at T300. Although reperfusion also induced an increase in slope of the end-systolic pressure-volume relationship (ESPVR), the ESPVR curve shifted to the right, associated with a depression of contractile function. Histology demonstrated irreversible myocardial damage at T300. The ventriculo-arterial elastance ratio and the 'stiffness coupling' index were unaffected throughout the protocol, but the 'temporal coupling' parameter indicated a relative shift between heart period and the time constant of the arterial system. It is unlikely that these alterations are attributable to ischaemic injury alone. The combination of both the stiffness and temporal coupling index may provide more information when studying ventriculo-arterial coupling than the more commonly used ventricular end-systolic stiffness/effection arterial elastance (E(es)/E(a)) ratio.

Dynamic models for substrate coupling in mixed-mode systems

In modern monolithic integrated circuits, substrate coupling is a major concern in mixed-mode systems design. Verification of such systems implies the availability of accurate and simulation-efficient substrate coupling models. Traditionally, for frequencies up to a few gigahertz, pure resistive models have been considered sufficient. However, with increasing frequencies of operation, dynamic models become mandatory. The authors motivate the use of dynamic resistive-capacitive (RC) models of substrate coupling as a natural extension to the standard purely resistive models. They propose an extraction methodology that starts with information about the process parameters and circuit's contact layout, and leads to a contact-to-contact RC element model. The underlying algorithm is based on a finite difference discretisation of the substrate, leading to a large tridimensional mesh which is reduced by means of a fast multigrid algorithm. Unlike standard model order reduction algorithms which can produce models of similar accuracy to state-space descriptions, the proposed method leads to a realisable RC model that can trivially be incorporated into circuit simulation tools. As a first approximation, such a model is shown to correspond to a single time-constant system. Furthermore, it is shown that this time constant can be computed from knowledge of the conductivity and permittivity of a single dominant layer. It is verified that this formulation can accurately model substrate coupling effects for frequencies up to several tens of gigahertz.

Design and Control of a Piezoelectric Driven Fatigue Testing System for Electronic Packaging Applications

Failure of solder joints for electronic packaging is an important issue for controlling the reliability of semiconductor devices. However, the complicated coupling between mechanical stressing and temperature and time dependent material properties makes it difficult to explore the fundamental failure control mechanisms using the existing accelerated thermal cycling methods. In addition, the testing speed is also severely restricted by the thermal time constant of the characterization system. In order to decouple the mechanical stress effect from other factors as the first step toward exploring the control mechanisms of failure, a piezoelectric-based fatigue characterization system is developed to replace the thermal cycling and provide fast and purely mechanical stressing cycles. A self-tuning based (STR) adaptive controller is also developed to provide accurate process control during experiments for compensating stiffness variation due to fatigue crack growth. It is found that this STR regulator is more robust than the traditional PID controller. The bandwidth of the system is approximately 70 Hz and is currently restricted by the equivalent time constant of the piezoelectric material. Nevertheless, this speed is sufficient for conducting a successful fatigue testing of solder joints. Finally, preliminary fatigue experiments have been performed on Sn63Pb 37 solders and the reduction of stiffness due to crack growth is clearly visible while the actuation performance is consistent and stable during the entire testing period. In the future, it is possible to operate in conjunction with a temperature control unit and a creep testing scheme to explore both the temperature and time dependent nature of solders in order to fully understand the failure control mechanisms of packaging

Cellular confinement of tunnel sections between two air curtains

This paper compares and discusses the efficiency of various air curtains designed to ultimately operate a bilateral aeraulic confinement of a short section of a tunnel or corridor-like geometry. The tested arrangements include single- and twin-jet air curtain systems with and without air return ducts. Jet opening ratios equal to 10 and 20 are considered, with air discharge velocities ranging from 1 to 10 m/s. The facility and the experimental approach used in this work are described and justified in many details. Results are presented in terms of leakage flow rates. Information is also provided about relevant air change rates and system time constants. The global efficiency of an air curtain is greatly improved by the adjunction of an air recirculation circuit due to enhanced system stability. A critical jet exit velocity corresponding to transition from the laminar to the turbulent regime of the channel flow inside the air curtain diffuser was found. For discharge velocities larger than this critical velocity an asymptotic behaviour is observed for every air curtain tested. At the lower nozzle exit velocities, the non-recirculated twin-jet system exhibits a weird behaviour. Unexpectedly, the results show that a single jet with a given opening ratio may perform better than a twin-jet of same height with a lower opening ratio. However, the results show that the performance of an air curtain is much dependant of the conditions under which this air curtain is operated demonstrating therefore that great care should be exercised in any attempt of comparison.

Determining the dispersion characteristics of rivers from the frequency response of the system

A new method of determining the parameters of an aggregated dead zone model (ADZ) to predict longitudinal dispersion in rivers is presented. The method is based on the frequency response analysis (FRA) of observed field tests, which consist of tracer injections (input) and measurement of tracer in downstream sampling points (output) located downstream from the injection point. The ADZ is a combination of plug and completely mixed flow compartments. The ADZ parameters (number of compartments, mean residence time, and delay time) are evaluated by means of Bode plots that give the system order (number of compartments), gain, time constant (mean residence time of each compartment) and delay time. The FRA‐ADZ method was checked with tracer data runs in two Spanish rivers, the Tagus and the Ebro rivers. The experimental tracer concentration versus time distributions were compared with the ADZ predicted curves, which were calculated using parameters obtained from the FRA method, and with curves predicted by several classical models. The residence time of several reaches within the two studied rivers was predicted by the FRA‐ADZ method with a relative error lower than 10%. The method is generally applicable to ideal and nonideal inputs and is particularly well suited to arbitrary‐shaped initial source concentration distributions.

The physiological basis of respiratory support

The complex interplay between the characteristics of the respiratory system, its changes as a result of respiratory disease and the effects of mechanical ventilation makes it important to analyse the physiology of the respiratory system in any given clinical situation. Key variables to be considered are the elastic recoil, resistance and time constant of the respiratory system, as well as the characteristics of the respiratory pump. The effects of respiratory support on the intrathoracic organs and lung perfusion must be taken into account. Respiratory support modes can then be tailored to provide maximum benefit and a minimum of negative effects. When the relatively few basic principles that underlie the mechanical behaviour of the respiratory system in most circumstances are kept in mind, the challenge of optimal support seems solvable for most children with respiratory insufficiency.

Null-Space Square-Root Information Filtering and Smoothing for Singular Problems

A new algorithm that does square-root information filtering and fixed-interval smoothing has been developed for singular discrete-time estimation problems. Singular measurements arise if one uses a Markov measurement error model or if one uses the quaternion normalization constraint in an attitude determination problem. The dynamics model becomes singular if delay states are included or if a system time constant is short compared to the sample interval. The new algorithm uses the lower-triangular/orthonormal factorization null-space method to deal with the estimation problem's linear equality constraints. This method is applied recursively and transforms the estimated quantities into components that are exactly determined by the constraints and components in the null space of the constraints. These latter components are estimated using linear least-squares techniques, which is the standard approach of square -root information filtering and smoothing methods. The new algorithm uses more computation and more memory than the only known competitor that can solve similar problems, but it has superior numerical stability. This improvement is demonstrated using an example one-dimensional tracking problem that includes Markov models and dynamics and measurement singularities. The new algorithm's computations nearly achieve machine precision even when the competing algorithm produces meaningless results.

Hybrid Flexure Pivot-Tilting Pad Gas Bearings: Analysis and Experimental Validation

Gas film bearings offer unique advantages enabling successful deployment of high-speed microturbomachinery. Current applications encompass micro power generators, air cycle machines, and turbo expanders. Mechanically complex gas foil bearings are in use; however, their excessive cost and lack of calibrated predictive tools deter their application to mass-produced oil-free turbochargers, for example. The present investigation advances the analysis and experimental validation of hybrid gas bearings with static and dynamic force characteristics desirable in high-speed turbomachinery. These characteristics are adequate load support, good stiffness and damping coefficients, low friction and wear during rotor startup and shutdown, and most importantly, enhanced rotordynamic stability at the operating speed. Hybrid (hydrostatic/hydrodynamic) flexure pivot-tilting pad bearings demonstrate superior static and dynamic forced performance than other geometries as evidenced in a high-speed rotor-bearing test rig. A computational model including the effects of external pressurization predicts the rotordynamic coefficients of the test bearings and shows good correlation with measured force coefficients, thus lending credence to the predictive model. In general, direct stiffnesses increase with operating speed and external pressurization, whereas damping coefficients show an opposite behavior. Predicted mass flow rates validate the inherent restrictor-type orifice flow model for external pressurization. Measured coast-down rotor speeds demonstrate very low-friction operation with large system time constants. Estimated drag torques from the gas bearings indirectly validate the recorded system time constant.

Transient analysis of gaseous electron‐ion recombination in the environmental scanning electron microscope

Most of the work carried out in relation to contrast mechanisms and signal formation in an environmental scanning electron microscope has yet to consider the time dependent aspects of image generation at a quantitative level. This paper quantitatively describes gaseous electron-ion recombination (also known as 'signal scavenging') in an environmental scanning electron microscope at a transient level by utilizing the dark shadows/streaks seen in gaseous secondary electron detector images of alumina (Al2O3) immediately after a region of enhanced secondary electron emission is encountered by a scanning electron beam. The investigation firstly derives a theoretical model of gaseous electron-ion recombination that takes into consideration transients caused by the time constant of the gaseous secondary electron detector electronics and external circuitry used to generate images. Experimental data of pixel intensity versus time of the streaks are then simulated using the model enabling the relative magnitudes of (i) ionization and recombination rates, (ii) recombination coefficients and (iii) electron drift velocities, as well as absolute values of the total time constant of the gaseous secondary electron detection system and external circuitry, to be determined as a function of microscope operating parameters such as gaseous secondary electron detector bias, sample-electrode separation, imaging gas pressure, and scan speed. The results revealed, for the first time, the exact dependence that the effects of secondary electron-ion recombination on signal formation has on reduced electric field and time in an environmental scanning electron microscope. Furthermore, the model implicitly demonstrated that signal loss as a consequence of field retardation due to ion space charges, although obviously present, is not the foremost phenomenon causing streaking in images, as previously thought.

Minimizing manoeuvre advantage requirements for a hit-to-kill interceptor

Hit-to-kill requires extremely high intercept accuracies. Such performance places severe demands on interceptor manoeuvrability and flight control response time constant when engaging targets that are intentionally or unintentionally manoeuvring. A well-known guidance law for use against a manoeuvring target is augmented proportional navigation (APN). It is an optimal guidance law under various assumptions including a constant-lateral-acceleration target. It is also effective when used against other target manoeuvres provided that the lateral acceleration capabilities of the interceptor is significantly greater than the lateral acceleration capabilities of the target, and if the time constant of the interceptor flight control system is small. The advantage of using a new guidance algorithm for a hit-to-kill interceptor against a manoeuvring target in two dimensions is demonstrated in this paper. A large manoeuvre advantage is not required, and it is effective with time constants that would otherwise degrade the performance of APN. Results are based on a two-dimensional non-linear model with the target performing a weave manoeuvre. The new algorithm can achieve increased intercept accuracy under minimal manoeuvre advantage requirements over a wide range of initial conditions with reasonable levels of angle noise and target manoeuvre estimation error.

Non-invasive monitoring of left ventricular contractility and ventilatory mechanics.

The maximum left ventricular elastance (Emax<inf>iv</inf>) is a valuable index of ventricular contractility. However, conventional methods for its measurements are too invasive for routine use. We propose a non-invasive technique for tracking changes in Emax<inf>iv</inf>by mathematically determining the dynamic coupling between beat-to-beat fluctuations in instantaneous lung volume and arterial blood pressure measured during random-interval breathing. The mathematical technique also provides an estimate of the dominant time constant of the ventilatory system (), which is equal to the product of the airway resistance and lung compliance. We then describe a theoretical evaluation of the technique with respect to realistic beat-to-beat variability generated by a cardiovascular simulator. Our results show that the technique is able to detect actual changes in the Emax<inf>iv</inf>and values of the simulator. With successful experimental testing, the technique may ultimately be employed to help guide therapy in heart failure patients.

Changes in lung function and tidal airflow patterns after increasing extrathoracic airway resistance

The aim of this study was to determine what changes occur in previously described tidal expiratory flow patterns when extrathoracic resistance is added. A total of 16 subjects with normal lung function and 15 patients with chronic COPD, were studied. The following measurements were made before and after the addition of an extrathoracic expiratory resistance (EER; 0.89 kPa/L s at a flow of 0.5 L/s) during uncoached tidal breathing: expiratory time (tE), frequency (f), expiratory time to maximum flow/total expiratory time (tPTEF/tE), tidal maximum expiratory flow (PEF(TIDAL)), and time constant of the respiratory system calculated from the passive portion of tidal expiration (trs(TIDAL)). Post peak profiles were categorized as convex, linear or concave and time for flow to fall to 80% and 20% of maximum (t80 and t20) were measured. Tidal indices tE, f and PEF(TIDAL), were similar in the two groups, but tPTEF/tE was greater and trs(TIDAL) was less in the normal subjects than in the COPD patients. Addition of EER in both groups caused PEF(TIDAL) to decrease and trs(TIDAL), t80 and the percentage of convex profiles to increase. tPTEF/tE increased in the COPD patients but was unchanged in the control group. After addition of EER during tidal breathing, expiratory flow in COPD patients resembled that seen in normal subjects.

Determination of the location and magnitude of synaptic conductance changes in spinal motoneurons by impedance measurements.

The relation between impedance change and the location and magnitude of a tonic synaptic conductance was examined in compartmental motoneuron models based on previously published data. The dependency of motoneuron impedance on system time constant (tau), electrotonic length (L), and dendritic-to-somatic conductance ratio (rho) was examined, showing that the relation between impedance phase and rho differed markedly between models with uniform and nonuniform membrane resistivity. Dendritic synaptic conductances decreased impedance magnitude at low frequencies; at higher frequencies, impedance magnitude increased. The frequency at which the change in impedance magnitude reversed from a decrease to an increase-the reversal frequency, F(r)-was a good estimator of electrotonic synaptic location. A measure of the average normalized impedance change at frequencies less than F(r), cuDeltaZ, estimated relative synaptic conductance. F(r) and cuDeltaZ provided useful estimates of synaptic location and conductance in models with nonuniform (step, sigmoidal) and uniform membrane resistivity. F(r) also provided good estimates of spatial synaptic location on the equivalent cable in both step and sigmoidal models. Variability in relations between F(r), cuDeltaZ, and conductance location and magnitude between neurons was reduced by normalization with rho and tau. The effects on F(r) and cuDeltaZ of noise in experimental recordings, different synaptic distributions, and voltage-dependent conductances were also assessed. This study indicates that location and conductance of tonic dendritic conductances can be estimated from F(r), cuDeltaZ, and basic electrotonic motoneuron parameters with the exercise of suitable precautions.

비분산 적외선 분광법을 이용한 Co2농도 고속 분석기의 Sampling Module 특성에 관한 실험적 연구

A fast response analyzer for measuring carbon dioxide concentration has been developed for transient characteristic and researches tested on internal combustion engine. The analyzer uses the well known NDIR(Non-Dispersive Infrared) method with miniaturized detection system, giving a time constant of approximately 30 microsecond, and sampling module consists of capillary tube. Since the transit time and the time constant of the sampling system depend on the sampling conditions, it is necessary to investigate the characteristics of sampling system before applied to exhaust gas measurement in engine. A unique method was designed to study the influence of the diameter of transfer sample line and operating conditions of the FRNDIR on transit time and time constant. A database of transit time and time constant was built up for different measured and simulated pressure conditions. The database can be used for correcting eventual concentration measurement.

Adaptive phase measurement system for surface profile measurement

A hybrid phase measuring system is described which is an adaptive development of traditional phase locked loops. It is based around a digital delay line. The target application is a slope-measuring continuous wave lidar designed to determine surface profiles at shallow angles of incidence. The lidar unit, of which the phase shifter is a key element, is a pioneering system designed to obtain a vector field representation of propagating deep water ocean gravity waves. The application of the system is in the new discipline of deterministic sea wave prediction (DWSP) and is intended to operate in fixed time mode. In the normal tracking mode, the phase difference to be estimated is much less than /spl pi//2, but however, due to the nature of the physical situation, sudden large jumps of several times /spl pi/ are possible. The system time constants adapt to such jumps, producing an evolving compromise between phase error and the time taken to recover the tracking mode.