Framework Of Linear System Theory Research Articles

Analytical and numerical modelling of the electrostatic behaviour of highly insulating materials in the time domain

The usual response of an insulator subjected to a voltage step involves time power laws. We present here mathematical tools allowing to calculate this time domain response in open circuit after an initial charge deposit, within the framework of linear systems theory, using linear fractional transfer functions. In the time domain, the inverse Laplace transform of the data taken from the frequency domain leads to Mittag-Leffler functions, generalizing the Debye exponential response to an extended fractional α-order response. The open-circuit boundary conditions are different from the closed-circuit ones. We nevertheless demonstrate that using a transfer function deduced from the Cole-Cole response in closed-circuit, a precise analytical formula of the potential decay after an initial charge deposit may be established, and a numerical computation of this decay may be performed using easily available software. Applying the superposition principle, the voltage return following a brief short circuit may also be deduced. Experimental results are presented and the limits of the superposition principle applied to real materials are discussed.

Analysis of non-Markovian passive quantum linear systems’ response to single-photon input fields*

In this paper, we analyze the response of passive quantum linear systems in a non-Markovian environment to single photon input fields. Based on an augmented modelling method for non-Markovian quantum systems, analytic forms of output intensity and output covariance function in steady-state are derived. These results allow us to quantitatively analyze the influence of non-Markovian environment on system response under a framework of linear system theory.

Response of Solar Irradiance to Sunspot-area Variations

Abstract One of the important open questions in solar irradiance studies is whether long-term variability (i.e., on timescales of years and beyond) can be reconstructed by means of models that describe short-term variability (i.e., days) using solar proxies as inputs. Preminger & Walton showed that the relationship between spectral solar irradiance and proxies of magnetic-flux emergence, such as the daily sunspot area, can be described in the framework of linear system theory by means of the impulse response. We significantly refine that empirical model by removing spurious solar-rotational effects and by including an additional term that captures long-term variations. Our results show that long-term variability cannot be reconstructed from the short-term response of the spectral irradiance, which questions the extension of solar proxy models to these timescales. In addition, we find that the solar response is nonlinear in a way that cannot be corrected simply by applying a rescaling to a sunspot area.

Physical-Perceptual Correspondence for Dynamic Thermal Stimulation.

Thermal displays have been applied in various haptic applications, from material simulation to interpersonal communication; however, there is insufficient knowledge about the temporal processing in human thermal sense to provide a knowledge basis for thermal display design. In this study, we investigated the physical-perceptual correspondence for dynamic thermal stimulation to shed a light on the temporal processing of human thermal sense. In the experiments, participants reported subjective timings of the temperature onset and temperature peak of continuous temperature changes applied to the thenar eminence. We found that the physical-perceptual correspondence was not consistent for warm and cold stimulations. For warm stimulation, the subjective experience always came after the corresponding physical event. On the other hand, for cold stimulation, while the subjective onset always lagged the physical onset, the subjective temperature peak preceded the physical temperature peak. We analyzed these results in the framework of linear systems theory. The results suggest that the senses of warmth and cold have distinct temporal filtering properties, with the sense of cold being more transient than the sense of warmth. These findings advance our knowledge regarding temporal processing in human thermal sense and serve as a basis for thermal display design.

Summary statistics for size over space and time.

A number of studies have investigated how the visual system extracts the average feature-value of an ensemble of simultaneously or sequentially delivered stimuli. In this study we model these two processes within the unitary framework of linear systems theory. The specific feature value used in this investigation is size, which we define as the logarithm of a circle's diameter. Within each ensemble, sizes were drawn from a normal distribution. Average size discrimination was measured using ensembles of one and eight circles. These circles were presented simultaneously (display times: 13-427 ms), one at a time, or eight at a time (temporal-frequencies: 1.2-38 Hz). Thresholds for eight-item ensembles were lower than thresholds for one-item ensembles. Thresholds decreased by a factor of 1.3 for a 3,200% increase in display time, and decreased by the same factor for a 3,200% decrease in temporal frequency. Modeling and simulations show that the data are consistent with one readout of three to four items every 210 ms.

Second-order processes in vision: introduction.

led to a radical reconceptualization ofthe nature of visual processing within the framework oflinear systems theory. Pattern adaptation and thresholdpattern-discrimination experiments provided dramaticevidence that human vision filters the retinal input into anumber of channels selectively tuned for spatiotemporalfrequency and orientation. These channels were concep-tualized as approximately linear, shift-invariant transfor-mations of the time-varying retinal input. It was hy-pothesized that these filters were realized byretinotopically organized arrays of neurons. The neu-rons in a given such array were all assumed to have thesame receptive field profile (typically modeled as a Gaborfunction of some specific spatial frequency and orienta-tion), and to monitor different locations in the stimulusfield: one neuron for each location. Thus the responsesof these neurons in a given channel array composed a‘‘neural image’’

Analysis of tracer transit in rat brain after carotid artery and femoral vein administrations using linear system theory

Determination of tissue perfusion rates by MRI bolus tracking methods relies on the central volume principle which states that tissue blood flow is given by the tissue blood volume divided by the mean tracer transit time (MTT). Accurate determination of the MTT requires knowledge of the arterial input function which in MRI experiments is usually not known, especially when using small animals. The problem of unknown arterial input can be circumvented in animal experiments by directly injecting the contrast agent into a feeding artery of the tissue of interest. In the present article the passage of magnetite nanoparticles through the rat cerebral cortex is analyzed after injection into the internal carotid artery. The results are discussed in the framework of linear system theory using a one-compartment model for brain tissue and by using the well characterized γ-variate function to describe the tissue concentration profile of the contrast agent. The results obtained from the intra-arterial tracer administration experiments are then compared with the commonly used intra-venous injection of the contrast agent in order to estimate the contribution of the peripheral circulation to the MTT values in the latter case. The experiments were analyzed using a two-compartment model and the γ-variate function. As an application perfusion rates in normal and ischemic cerebral cortex of hypertensive rats were estimated in a model of focal cerebral ischemia. The results indicate that peripheral circulation has a significant influence on the MTT values and thus on the perfusion rates, which cannot be neglected.

Study on the Influence of Time Varying Parameter Variations in Linear Systems Using Variational Expression

Parameters of the linear system in operation usually deviate from its nominal values used for the design. These deviations are generally time-varying and yield nonlinear effects even if the system is linear. Thus, it is difficult to deal with the time-varying parameter variations in the framework of linear system theory. In this paper, we give a variational expression for the output variation Δy (t) caused by the variable parameter term δμi (t) Dix (t) in the linear system. Using the expression, we can derive a necessary and/or sufficient condition for its first variation δy (t) to vanish in the open loop system, which are extended to the closed loop system with state feedback and reference input. This variational expression and derived conditions are useful for sensitivity analysis of structured parameter variations in linear systems.

An Introduction to the Theory of Linear Systems

Abstract : Until the past decade the term 'system' as used in the many disciplines of science and engineering conveyed a variety of meaning. Since the early 1960's theorists have been folding these varied impressions into the single, formidable conceptual framework of linear system theory. The discussions of this volume are intended to lend to this unification. Specifically, the intent is to draw on the conceptual ideas that are common to linear filters, linear time-invariant systems, Markov chains and quantum theory and present, in a non-rigorous manner, their respective similarities.

Nonobservable or Noncontrollable Analog Schemes for the Solution of a Special Class of Differential Equations

The analog computer solution of linear time invariant differential equations of the type p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> y + a <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</inf> p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</sup> y +...+ a <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> y = b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> u + b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</inf> p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</sup> u... + b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> u; (p=d/dt) is treated for the case in which the polynomials S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> + a <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</inf> S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</sup> +...+ a <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> and b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</inf> S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m-1</sup> + ... + b <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> have common roots. It is shown that the ``dummy variable'' [2] method of analog solution is not suitable if we want not only the ``forced'' solution, but also the ``free'' or ``homogeneous'' solution (corresponding to arbitrary initial conditions y(0), py(0) ... p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</sup> y(0)). It is in fact impossible to find the initial conditions x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> (0) ... x <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</inf> (0) at the output of the integrators in the analog scheme, corresponding to the ``dummy variable'' method. The reason is found in the framework of linear system theory, which shows that this scheme represents a non observable system. An intuitive explanation of this fact is shown at the end of the paper. Other analog computer schemes are shown which do not present this difficulty, and which give the ``free'' as well as the ``forced'' solution of our equation.