Response Of Linear Systems Research Articles

Transfer-Matrix Approach to Determining the Linear Response of All-Fiber Networks of Cavity-QED Systems

A semiclassical model is presented for characterizing the linear response of elementary quantum optical systems involving cavities, optical fibers, and atoms. Formulating the transmission and reflection spectra using a scattering-wave (transfer matrix) approach, the calculations become easily scalable. To demonstrate how useful this method is, we consider the example of a simple quantum network, i.e., two cavity-QED systems connected via an optical fiber. Differences between our quasi-exact transfer matrix approach and a single-mode, linearized quantum-optical model are demonstrated for parameters relevant to recent experiments with coupled nanofiber-cavity-QED systems.

On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning.

Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow linear solution and a pure advective transport solution with different right-hand sides. The new solver was compared with other preconditioned iterative methods, the MODFLOW's GMG solver, and direct sparse solvers. Test problems include two- and three-dimensional benchmarks spanning homogeneous and highly heterogeneous and anisotropic formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. The algebraic multigrid preconditioner efficiency was preserved for the three dimensional heterogeneous and anisotropic problem unlike for the MODFLOW's GMG solver. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be Péclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for its routine application to large geological models. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning would remain competitive for the class of nonlinear and/or transient problems.

Random and interval uncertain symplectic methods for linear Birkhoff equations and their comparison study

With the increasing complexity and design requirement of engineering structures, the numerical computation plays an increasingly important role in the structural analysis. The symplectic algorithm for Birkhoffian systems has advantages over the traditional algorithm in accuracy and stability, and general mechanical systems can be transformed into Birkhoffian systems in theory. Additionally, the influence of uncertainties in practical engineering cannot be ignored. However, the research foundation of symplectic algorithms for Birkhoffian systems considering uncertainties is still weak. In this paper, the random and interval uncertain symplectic algorithms for linear Birkhoffian systems are proposed, respectively, which can be applied to the numerical calculation of the structural dynamic response with uncertainties. Furthermore, the compatibility between the two methods is studied. Based on the small parameter perturbation theory, the uncertain perturbation equation of the uncertain linear Birkhoffian system is established. According to different types of uncertainties, based on the probability theory and interval mathematical method, expressions of the mean and variance of random Birkhoffian systems, as well as the median value and radius of interval Birkhoffian systems are derived. By combining aforementioned methods with Birkhoffian symplectic algorithms, the random and interval perturbation methods for calculating the uncertain response of linear Birkhoffian systems are proposed, respectively. Since the uncertainty exists objectively, the uncertain features of the response should not be incompatible when characterization and analysis methods for uncertainties are different. Based on the Chebyshev inequality, this paper deduces the probabilistic and interval boundaries from the result calculated by proposed methods and the comparison between the two kinds of boundaries. It is mathematically proved that the probabilistic upper bound is less than the interval upper bound and the probabilistic lower bound is larger than the interval lower bound. Finally, examples are given to demonstrate the effectiveness of the proposed method in calculating the response of uncertain dynamics and its superiority over the traditional numerical methods.

Non-reciprocal transmission of microwave acoustic waves in nonlinear parity–time symmetric resonators

Acoustic waves have emerged as versatile on-chip information carriers with applications ranging from microwave filters to transducers. Nonreciprocal devices are desirable for the control and routing of high-frequency phonons. This is challenging, however, due to the linear response of most acoustic systems. Here, we leverage the strong piezoelectricity of lithium niobate to demonstrate fully tunable gain, loss, and nonlinearity for surface acoustic waves using electric circuitry. This allows the construction of a nonlinear acoustic parity-time-symmetric system and enables nonreciprocal transmission. We achieve a nonreciprocity of 10 decibels for a 200-MHz acoustic wave at a low input power of 3 $\mu$W and further demonstrate one-way circulation of acoustic waves by cascading nonreciprocal devices. Our work illustrates the potential of this piezoelectric platform for on-chip phononic processing and exploration of non-Hermitian physics.

A Modified Functional Observer-Based EID Estimator for Unknown Continuous-Time Singular Systems

This paper presents the design of a linear quadratic analog tracker (LQAT) based on the observer–Kalman-filter identification (OKID) method and the design of a modified functional observer-based equivalent input disturbance (EID) estimator for unknown square–non-square singular analog systems with unknown input and output disturbances. First, an equivalent mathematical model of the singular analog system is presented to simulate the time response of continuous-time linear singular analog systems to arbitrary inputs via the model conversion method. Then, for the unknown singular analog system, it constructs a linear quadratic analog tracker with state feedback and feed-forward gains based on the off-line OKID method. Furthermore, it extends the design methodology of the EID estimator for strictly proper regular systems with unknown matched–mismatched input and output disturbances to proper regular systems. It is important to mention that the newly developed modified functional observer for proper systems is used to estimate the unknown EID of singular analog systems and that the constraints on the dimensions of unknown disturbances can be eliminated by using the newly proposed EID estimation method. The contributions of this paper can be listed as follows: (1) based on both the OKID method and the discrete-to-continuous model conversion, the simulation of the time responses of the continuous-time linear singular models (which are not feasible using existing MATLAB toolboxes) become feasible; (2) for effective control of the unknown singular analog system, an off-line OKID method is proposed to design an LQAT with state feedback and feed-forward gains; and (3) based on the newly developed modified functional observer for the reduced-order proper regular system, the original EID estimator in the literature is newly extended to estimate the EID from the unknown strictly proper singular analog system, without the original dimensional constraints of the disturbances. It is important to mention that the disturbances of interest can be unknown matched–mismatched input and output disturbances.

Global Maximum Response of Linear Systems with Uncertain Damping to Irregular Excitation

AbstractIn the evaluation of the global maximum response of a structure subjected to its design load, damping effects must be included; however, the structure damping is often uncertain. This study...

New Scheme for Estimation of the First and Senior Moment Functions for the Response of Linear Delay Differential System Excited by Additive and Multiplicative Noises

The paper describes the theoretical apparatus and the algorithmic part of a scheme for stochastic examination of systems of linear stochastic delay differential equations perturbed by additive and multiplicative white noises. The presence of an efficient method of analyzing such problems, i.e., a method that can compete with the method of statistical simulation (Monte Carlo), is important both from the theoretical and applied points of view. The systems are substantial for modeling various objects and processes and can be the results of linearization of nonlinear stochastic systems with delay and multiplicative fluctuations. The importance of developing a procedure for calculating just the senior moment functions for the state vectors comes from the presence of multiplicative perturbations implying the inability to restrict the first moment functions as in the case of linear systems with Gaussian white noises as the input. To obtain ODEs for the first and senior moment functions without delays, we apply a new modification of our scheme combining the classical method of steps and extension of the system state space with the addition of the use of multidimensional matrices for the compact recording of the algorithm. The scheme realized in the environment of Wolfram Mathematica software package is demonstrated by an example devoted to an estimation the moment functions until the 4th order for a non-stationary stochastic response of the system with one degree of freedom.

Interval Predictors for a Class of Uncertain Discrete-Time Systems

This work presents set-valued algorithms to compute tight interval predictions of the state trajectories for a certain class of uncertain dynamical systems. Based on interval analysis and the analytic expression of the state response of discrete-time linear systems, non-conservative numerical schemes are proposed. Moreover, under some stability conditions, the convergence of the width of the predicted state enclosures is proved. The performance of the proposed set-valued algorithms are illustrated through two numerical examples and the results are compared to that obtained with an other method selected from the literature.

Co-digestión anaerobia en modo semi-continuo de residuos de vegetales y estiércol de vaca: un estudio de estabilidad de proceso

The anaerobic digestion of vegetable waste (VW) often shows the accumulation of fatty acids and low buffering capacity that promotes instability and low methane productivity. This work evaluated the anaerobic co-digestion of VW with cow manure (CM) as a strategy to improve the process stability. As a reaction system, a 4 L semi-continuous stirred tank reactor with an HRT of 20 days and fed with a substrate formulation of 40 g of VS was used in two periods: 34 days of VW mono-digestion and 26 days of VW:CM co-digestion. The mono and co-digestion processes were numerically evaluated through three analysis tools: a proposed co-digestion model embedded in the Anaerobic Digestion Model No. 1 structure, statistical process control theory, and modeling the pH dynamics as the response of a first-order linear system to an impulse manipulation. The mono-digestion process showed productivity of 0.381 L CH4 L digester-1 d-1, which increased by 14 % during co-digestion. The results also indicated that in VW:CM co-digestion, the pH dynamics presents a slower response to the daily feed induced by pulses, keeping the values of this parameter within the statistical stability range; as well as the early warning indicator IA/BA (ratio between intermediate and bicarbonate alkalinity) outside the failure thresholds. It was shown that the addition of CM to a mono-digestion of VW increases the buffer capacity of the system and the production of CH4, promoting a stable and efficient process.

Singularity Excitations and Initial Value Problem in Continuous LTI Systems

A modern challenge in electrical engineering education is to keep the math at a sufficient level, with a goal to find an optimal balance between calculus competence and operative skills needed for real-life technical applications. It is not uncommon that some gaps emerge during this quest, which makes it difficult for undergraduates to entirely understand topics related on prior knowledge. This paper aims to draw attention to several important moments concerning total response of Continuous Linear Time Invariant systems, which are superficially or incorrectly explained in many textbooks, and to offer logical arrangement which can be easily understood and accepted by students. The base of discussion relies on classical calculus background, particularly on Picard’s theorem on existence and uniqueness. This theorem is rarely mentioned in signals and systems textbooks. However, mathematical models of many types of signals don’t satisfy the condition for continuity, which can easily produce difficulties in the learning process. It is shown that some reported disagreements and issues related to initial conditions, can be easily cleared out by using the smooth transition from classical calculus to mathematics used in system theory. It is also shown that the classical method is always the primary tool, even for determining the impulse response, while the impulse response is unnecessary or sufficient to determine the total system response, regardless of whether the convolution integral is used.

Laplace-Time Domain Method for Computing Dynamic Response of Linear Systems to Arbitrary Intermittent Loadings

AbstractIn evaluating of the response of linear systems to arbitrary intermittent loadings, traditional methods have been exclusively conducted in the time domain where the time resolution must be ...

Effect of the high frequency components of near-fault ground motions on the response of linear and nonlinear SDOF systems: A moving average filtering approach

In this study, the effect of the high frequency components of near fault ground motions (NFGM) with forward rupture directivity effect (FRDE) on the seismic response of elastic and inelastic SDOF regular (non-isolated) and seismic isolated structures is studied. For this purpose, Moving Average filtering method is used to remove the high frequency content of the NFGM at various filtering levels. The key motive for this effort is to evaluate the appropriateness of representing the NFGMs by decomposed signals or mathematical pulse waveforms. Then, elastic and inelastic SDOF structures with various properties are subjected to the original and filtered NFGM and the responses are compared via elastic and inelastic response spectra. In addition, the efficiency of several pulse models in simulating the actual effect of NFGM on the seismic response of elastic and inelastic SDOF structures is investigated. The analyses results revealed that the high frequency content of NFGM has a significant effect on short period elastic structures and inelastic structures with high yield strength subjected to NFGM with short pulse periods. Furthermore, it is found that popular pulse models available in the literature failed to simulate the effect of the actual NFGM on the response of elastic and inelastic structures.

Dynamic linear response quantum algorithm

The dynamic linear response of a quantum system is critical for understanding both the structure and dynamics of strongly-interacting quantum systems, including neutron scattering from materials, photon and electron scattering from atomic systems, and electron and neutrino scattering by nuclei. We present a general algorithm for quantum computers to calculate the dynamic linear response function with controlled errors and to obtain information about specific final states that can be directly compared to experimental observations.

Major Parameters Affect the Non-Liner Response of Structure Under Near-Fault Earthquakes

Near-fault ground motion can be identified by the presence of a predominant long duration pulse in the velocity traces mainly due to directivity effect. This pulse exposes the structure to high input energy at the beginning of the earthquake which leads to a higher response in comparison with the ordinary ground motions. This paper investigates 79 earthquake records with different properties to achieve three goals: the first aim is to compare between the linear and nonlinear response of SDOF systems under near-fault and far-fault earthquakes. While the second objective is to examine the parameters that control the characteristics of near-fault earthquakes. Two factors have been studied which is PGV/PGA ratio and pulse period. Finally, the seismic code provisions related to the near-fault earthquakes were evaluated in term of the elastic acceleration response spectrum, the evaluation is adopted for American Society of Civil Engineers code ASCE 7 and Uniform Building Code UBC. The results lead to the following conclusions: with respect to a specific PGA, the near-fault earthquake imposed higher response in comparison with far-field earthquakes. The near-fault earthquakes become severe as the PGV/PGA and pulse period increase. The interested seismic codes can cover the actual behavior based on the average response of a certain amount of data, while it may become non-conservative relative to an individual record.

Linear response theory for quantum Gaussian processes

Fluctuation dissipation theorems (FDTs) connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a FDT for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

Influence of structure on the linear response rheology of colloidal gels

We study the linear response rheology, structure, and dynamics of colloidal gels formed by arrested phase separation with a combination of experiments and dynamic simulation, with a view toward understanding the influence of bond strength, volume fraction, and network morphology on the viscoelastic moduli. A rescaling of the data to remove the direct, equilibrium hydrodynamic, and entropic effects enables a direct comparison of experiment and simulation; the strong agreement shows that attractive forces and Brownian motion dominate relaxation, where hydrodynamic interactions play a simpler role that can be scaled out. Morphology transitions from thick, blobby strands with large solvent pores to particle-size solvent pores surrounded by concave surfaces when volume fraction increases. Unsurprisingly, generalized Stokes–Einstein relations make a poor predictor of rheology from particle dynamics. Models that connect bond dynamics to elasticity or that connect cluster dynamics to elasticity show better agreement. Prediction of age-stiffening requires a model that includes the effects of age-coarsening; surprisingly, age-stiffening is set primarily at high frequency by the dominant network length scale. A Rouse-like theory that connects dominant network length scale to elasticity provides good predictions for all volume fractions and ages, although there is an interplay between volume fraction and structural length scales. The linear viscoelastic response of the experimental system is thus well represented in a simpler computational model in which wall effects, hydrodynamics, explicit depletant molecules, and rejuvenation were neglected, suggesting that the connections between morphology, dynamics, and rheology are encoded primarily by volume fraction, attraction strength, Brownian motion, and age.

Phase driven study for stochastic linear multi-dofs dynamic response

Abstract This work addresses the computation of dynamic responses of stochastic linear systems using polynomial chaos expansion. As is now well known, polynomial chaos does not offer an accurate representation of dynamic response around resonances when the responses are evaluated for several frequency values. A new parametrization of the frequency response function is then proposed: instead of considering the frequency as the main parameter, a “total phase” parameter is defined and used to define the dynamical system to be solved. It is shown via two applications that this approach offers very accurate results when conjugated to polynomial chaos with low degree.

Recursive Decomposition of Electromyographic Signals With a Varying Number of Active Sources: Bayesian Modeling and Filtering.

This paper describes a sequential decomposition algorithm for single-channel intramuscular electromyography (iEMG) generated by a varying number of active motor neurons. As in previous work, we establish a hidden Markov model of iEMG, in which each motor neuron spike train is modeled as a renewal process with inter-spike intervals following a discrete Weibull law and motor unit action potentials are modeled as impulse responses of linear time-invariant systems with known prior. We then expand this model by introducing an activation vector associated with the state vector of the hidden Markov model. This activation vector represents recruitment/derecruitment of motor units and is estimated together with the state vector using Bayesian filtering. Non-stationarity of the model parameters is addressed by means of a sliding window approach, thus making the algorithm adaptive to variations in contraction force and motor unit action potential waveforms. The algorithm was validated using simulated and experimental iEMG signals with varying number of active motor units. The experimental signals were acquired from the tibialis anterior and abductor digiti minimi muscles by fine wire and needle electrodes. The decomposition accuracy in both simulated and experimental signals exceeded 90%. The recruitment/derecruitment was successfully tracked by the algorithm. Because of its parallel structure, this algorithm can be efficiently accelerated, which lays the basis for its real-time applications in human-machine interfaces. The proposed method substantially broadens the domains of applicability of the algorithm.

Automated Epilepsy Diagnosis Using EEG With Test Set Evaluation.

Several electroencephalogram (EEG)-based predictive models for automated epilepsy diagnosis have been proposed over more than a decade. However, to the best of our knowledge, none have been evaluated on a holdout/test set. A vast majority of these studies have reported accuracies above 95% on a benchmark EEG dataset, but the dataset has been shown here to have certain limitations when used for building classifiers for epilepsy diagnosis. We implemented two previously reported classifiers trained on the benchmark dataset whose accuracies were observed to drop sharply when evaluated on a test set. We propose a feature, engineered specifically, for epilepsy diagnosis that attempts to characterize the neuronal synchronization using scalp EEG by extending the concept of the impulse response of linear time-invariant systems to matrices. This feature was tested on the EEG of 50 epileptics and 50 healthy subjects and yielded an area under the curve (AUC) of 0.87. It outperforms the existing models implemented by us that gave the AUC of 0.80 when trained and tested on scalp EEG data, thereby, setting the new benchmark for automated epilepsy diagnosis on test set evaluation. The feature has also been shown to have statistical consistency across time and vigilance states with robustness against EEG artifacts.

LSTperiod software: spectral analysis of multiple irregularly sampled time series

Irregularly sampled time series are common in several different areas, such as astronomy, meteorology, biology, oceanography, cyclostratigraphy, and others. The periodogram is a primary tool to extract meaningful information from irregularly spaced and noisy time series. It is an element of decision theory, meaning the periodogram usually transforms the data, and its ordinates are subsequently submitted to a statistical test compared to a population originating from a known stochastic model (white Gaussian noise). If some ordinate f 0 (usually a local maximum, a peak) fails in this test, we declare that it is a ‘periodicity’ at a frequency f 0 . Besides its full usage, this method until now suffer from numerous theoretical difficulties in adapting to real case situations and shows lack of usefulness for very poorly sampled and high noise cases. All of it implies low usefulness for applying in most sedimentary sequences at our disposal nowadays. The LSTperiod is an application, written in Matlab, conceived to perform spectral analysis of multiple irregularly sampled time series. It combines information from Lomb-Scargle periodogram estimates over different time series sampling the same phenomenon , enabling the recovering of signals from very poorly sampled and noisy time series. The software comprises a set of four Graphical User Interfaces (GUIs) that allow the user to: (1) Have broad choices of the frequency-domain range and density for spectral estimation; (2) Select possible spectral features (i.e., pick T ) for testing as a model [ A ∗ sin ( 2 π t −θ )] T through the visualization of several goodness-of-fit statistics; (3) Visualize the fitting residuals in the time domain, for each time series, for the chosen sinusoidal model. These tools help the user to identify and analyze any suspected feature in the estimated spectra through its related linear system responses. All estimated parameter can be saved on worksheets and the visualizations in several different figure formats. We illustrate the use of the software with a set of Ocean Drilling Program (ODP) data series that show long-period Milankovitch-related spectral features and demonstrate its performance using synthetic time series.