scispace - formally typeset
Search or ask a question

Showing papers on "Linear approximation published in 2018"


Journal ArticleDOI
TL;DR: The proposed approach provides an explicit solution of the power flow equations system, which avoids the use of iterative methods, and enables to provide accurate results with very short processing times when real operating scenarios of dc power grids are analyzed.

89 citations


Journal ArticleDOI
TL;DR: Though this framework is completely algorithmic, it provides solutions with optimal statistical performances and controlled algorithmic complexity for a large family of nonconvex optimization problems.
Abstract: We propose a computational framework named iterative local adaptive majorize-minimization (I-LAMM) to simultaneously control algorithmic complexity and statistical error when fitting high dimensional models. I-LAMM is a two-stage algorithmic implementation of the local linear approximation to a family of folded concave penalized quasi-likelihood. The first stage solves a convex program with a crude precision tolerance to obtain a coarse initial estimator, which is further refined in the second stage by iteratively solving a sequence of convex programs with smaller precision tolerances. Theoretically, we establish a phase transition: the first stage has a sublinear iteration complexity, while the second stage achieves an improved linear rate of convergence. Though this framework is completely algorithmic, it provides solutions with optimal statistical performances and controlled algorithmic complexity for a large family of nonconvex optimization problems. The iteration effects on statistical errors are clearly demonstrated via a contraction property. Our theory relies on a localized version of the sparse/restricted eigenvalue condition, which allows us to analyze a large family of loss and penalty functions and provide optimality guarantees under very weak assumptions (For example, I-LAMM requires much weaker minimal signal strength than other procedures). Thorough numerical results are provided to support the obtained theory.

85 citations


Journal ArticleDOI
TL;DR: In this paper, a linear approximation of alternating current power flow (PF) considering the accuracy of the reactive load flows and transmission losses is investigated, and a linear PF (LPF) model involving tap changers and phase shifters is derived from the approximation analysis of general branch flows.
Abstract: Alternating current (ac) power flow (PF) presents difficulties for power system analysis and optimization due to its nonlinearity. Progress has been made to approximately linearize ac PF in recent decades. However, few studies have reported the simultaneous accurate approximation of reactive power and transmission losses. To bridge this gap, this paper investigates the linear approximation of ac PF considering the accuracy of the reactive load flows and transmission losses. Using the logarithmic transform of voltage magnitudes, a linear PF (LPF) model involving tap changers and phase shifters is derived from the approximation analysis of general branch flows. Transmission power loss and loss-concerned complex branch flow are also formulated. Cold-start and warm-start LPF calculation methods associated with injection compensation are also developed. Numerical simulations are performed to compare the proposed models and several state-of-the-art LPF models using 25 practical-scale test systems. The simulation results demonstrate the advantages of the proposed model over the other models for approximating voltage magnitudes, branch flows, and power losses. The effectiveness of using proper compensation injection in improving the solution accuracy is also verified.

81 citations


Journal ArticleDOI
TL;DR: The proposed method applies the SCA with enhanced chaotic map to explore and exploit the search space for obtaining optimized S-boxes on the basis of maximization of nonlinearity as fitness function to show the strength of proposed method for constructing bijective S- boxes of salient cryptographic features.
Abstract: This paper proposes a novel method of constructing strong substitution-boxes (S-boxes) of order n (4 ≤ n ≤ 8) based on a recent optimization algorithm known as sine-cosine algorithm (SCA). The paper also proposes a new 1D chaotic map, which owns enhanced dynamics compared to conventional chaotic map, for generating initial population of S-boxes and facilitating the optimization mechanism of SCA. The proposed method applies the SCA with enhanced chaotic map to explore and exploit the search space for obtaining optimized S-boxes on the basis of maximization of nonlinearity as fitness function. The S-box construction involves three phases such as initialization of population, optimization, and adjustment. The simulation and performance analyses are done using standard measures of nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, and autocorrelation function. The obtained experimental results are compared with some immediate optimization-based and other S-boxes to show the strength of proposed method for constructing bijective S-boxes of salient cryptographic features.

62 citations


Journal ArticleDOI
TL;DR: A linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system and the power spectrum of the unmodeled disturbances are identified to generate uncertainty bounds on the estimated model.
Abstract: This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be retrieved without a significant increase in the amount of measured data. 2) Next it is studied if it is safe to use a linear system identification approach, even if the presence of nonlinear distortions is detected. The properties of the linear system identification approach under these conditions are studied, and the reliability of the uncertainty bounds is checked. 3) Eventually, tools are provided to check how much can be gained if a nonlinear model were identified instead of a linear model. Addressing these three questions forms the outline of this article. The possibilities and pitfalls of using a linear identification framework in the presence of nonlinear distortions will be discussed and illustrated on lab-scale and industrial examples. In this article, the focus is on nonparametric and parametric black box identification methods, however the results might also be useful for physical modeling methods. Knowing the actual nonlinear distortion level can help to choose the required level of detail that is needed in the physical model. This will strongly influence the modeling effort. Also, in this case, significant time can be saved if it is known from experiments that the system behaves almost linearly. The converse is also true. If the experiments show that some (sub-)systems are highly nonlinear, it helps to focus the physical modeling effort on these critical elements.

61 citations


Journal ArticleDOI
TL;DR: The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady bluff body flows and describes the modal perturbation dynamics more accurately than the empirical Galerkin reduced-order model.
Abstract: A networked-oscillator-based analysis is performed to examine and control the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial proper orthogonal decomposition (POD) modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Tracking small energy inputs and using linear regression, a networked-oscillator model is constructed that reveals energy exchange among the modes. The model captures the nonlinear interactions among the modal oscillators through a linear approximation. A large collection of system responses is aggregated to capture the general network structure of oscillator interactions. The present networked-oscillator model describes the modal perturbation dynamics more accurately than the empirical Galerkin reduced-order model. The linear network model for nonlinear dynamics is subsequently utilized to design a model-based feedback controller. The controller suppresses the modal amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the proposed approach is demonstrated for a canonical example of two-dimensional unsteady flow over a circular cylinder. The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady bluff body flows.

45 citations


Journal ArticleDOI
TL;DR: The results show the efficiency of the linear approximation of the ( s, S ) policy at the strategic level to produce robust design solutions under uncertainty, and underline the sensitivity of the design solution to the demand type and the impact of the inventory holding costs and backorder costs, especially under non-stationary processes.

45 citations


Journal ArticleDOI
TL;DR: Experimental results show how the accuracy of the transducer under test is heavily degraded by nonlinear phenomena when low-order voltage harmonics are considered.
Abstract: Voltage instrument transformers are usually tested at the rated frequency. In order to assess their performance in measuring harmonic components, typically, the frequency response function (FRF) is evaluated. Therefore, this conventional characterization does not consider nonlinear effects that may have a nonnegligible impact on the accuracy, especially when the transducer under test is represented by an inductive voltage transformer (VT). In this paper, a simple procedure for the characterization of voltage instrument transformers is presented. The method is based on the concept of best linear approximation of a nonlinear system. It requires applying a class of excitation signals that resembles the typical voltage waveforms found in power systems. Results consist of the FRF that permits the best linear compensation of the transducer response, and sample variances that allow quantifying the impact of noise and nonlinearities on the accuracy. The method is presented and explained by means of numerical simulations. After that, it has been applied to the characterization of a conventional inductive VT. Experimental results show how the accuracy of the transducer under test is heavily degraded by nonlinear phenomena when low-order voltage harmonics are considered.

44 citations


Journal ArticleDOI
TL;DR: This paper proposes a novel level-set method named local approximation of Taylor expansion (LATE), which is a nonlinear approximation method to solve the nonconvex optimization problem of segmentation of images with severe intensity inhomogeneity.
Abstract: Intensity inhomogeneity is common in real-world images and inevitably leads to many difficulties for accurate image segmentation. Numerous level-set methods have been proposed to segment images with intensity inhomogeneity. However, most of these methods are based on linear approximation, such as locally weighted mean, which may cause problems when handling images with severe intensity inhomogeneities. In this paper, we view segmentation of such images as a nonconvex optimization problem, since the intensity variation in such an image follows a nonlinear distribution. Then, we propose a novel level-set method named local approximation of Taylor expansion (LATE), which is a nonlinear approximation method to solve the nonconvex optimization problem. In LATE, we use the statistical information of the local region as a fidelity term and the differentials of intensity inhomogeneity as an adjusting term to model the approximation function. In particular, since the first-order differential is represented by the variation degree of intensity inhomogeneity, LATE can improve the approximation quality and enhance the local intensity contrast of images with severe intensity inhomogeneity. Moreover, LATE solves the optimization of function fitting by relaxing the constraint condition. In addition, LATE can be viewed as a constraint relaxation of classical methods, such as the region-scalable fitting model and the local intensity clustering model. Finally, the level-set energy functional is constructed based on the Taylor expansion approximation. To validate the effectiveness of our method, we conduct thorough experiments on synthetic and real images. Experimental results show that the proposed method clearly outperforms other solutions in comparison.

42 citations


Journal ArticleDOI
TL;DR: The linear approximation method is formulated using the interval Taylor extension to help solve reactive power optimization problem and the affine arithmetic-based power flow calculation is used to solve the interval power flow equation instead of crude computation based on the interval arithmetic.
Abstract: Reactive power optimization is a special kind of optimal power flow for optimizing voltage profile and reactive power flow in the steady state based on deterministic sets of the demand load and generation values, thus minimizing the real power losses or improving the voltage quality of the power grid. However, the input data in power systems have a certain degree of uncertainty that requires the reactive power optimization be solved by means of uncertain nonlinear programming, as advocated in the literature. To address this problem, we represent the uncertain input data as intervals and establish a model of the reactive power optimization that incorporates the interval uncertainties to describe the problem. The linear approximation method is formulated using the interval Taylor extension to help solve this type of problem. To obtain more accurate intervals for the state variables, the affine arithmetic-based power flow calculation is used to solve the interval power flow equation instead of crude computation based on the interval arithmetic, and thus the modified linear approximation method is developed. The proposed methods are presented in detail and the numerical results are analyzed to demonstrate their effectiveness and applicability, especially in comparison to the previously proposed chance constrained programming method.

36 citations


Journal ArticleDOI
TL;DR: The proposed cryptographically strong S-box shows very low differential approximation probability as compared to other chaos-based S-boxes designed recently, while maintaining good cryptographic properties and high value of linear approximation probability.
Abstract: Substitution box is a vital and the only nonlinear component of modern encryption algorithm. S-box is introduced as a confusion component to resist against differential cryptanalysis. Chaos-based encryption is well liked because it exhibits similarity like cryptography. However, chaotic S-boxes possess high maximum differential approximation probability, measured using difference distribution table (DDT) for differential cryptanalysis. Therefore, this paper reports a systematic design methodology to generate chaotic S-box utilizing DDT and that can be used in multimedia encryption algorithms. DDT within the design loop is used to optimize differential approximation probability. The proposed S-box shows very low differential approximation probability as compared to other chaos-based S-box designed recently, while maintaining good cryptographic properties and high value of linear approximation probability. The strength of the proposed cryptographically strong S-box is vetted in the practical implementation of multimedia encryption.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new inverse optimization methodology for multi-objective convex optimization that determines a weight vector producing a weakly Pareto optimal solution that preserves the decision maker's trade-off intention encoded in the input solution.

Journal ArticleDOI
01 Jan 2018
TL;DR: In this article, the stability analysis of two-wheeled vehicles based on numerical definition of full range eigenvalues of a matrix linear approximation in the vicinity of the translation running is investigated.
Abstract: In this research it is investigated the stability analysis of two-wheeled vehicles based on numerical definition of full range eigenvalues of a matrix linear approximation in the vicinity of the translation running. The received result was checked by numerical integration of an initial equations system of the disturbed running in that model. Inadequacy of two analyses is explained by specialty of considered mathematical model in which two parts in a complex conjugate eigenvalues close to each other that explains the emergence of standard derivations calculating their numerical definition. The model is asymptotically stable in the range wider than an operational interval (with 100 m/s). In order to provide more intensive dampening of initial disturbances, it is possible to introduce a design to the wheel vehicle additional resilient and damping elements between trucks and the case that will parry yaw mode of trucks.

Journal ArticleDOI
TL;DR: In this paper, the radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed, where the fluid viscosity is considered temperature dependent.
Abstract: The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

Journal ArticleDOI
TL;DR: An improved full-discretization method (IFDM) based on the golden search is presented in this brief paper to predict stability lobe diagram (SLD).
Abstract: An improved full-discretization method (IFDM) based on the golden search is presented in this brief paper to predict stability lobe diagram (SLD). To begin with, the mathematical model of milling dynamics considering the regenerative chatter is expressed as a state space form. With the time delay being separated equally into a limited amount of elements, the time series expression is obtained by interpolating the integral nonhomogeneous term using linear approximation. Then, 2N order algorithm is adopted to resolve the exponential term into a real matrix, which avoids the exponential matrix that has to be calculated each time in scanning the plane comprised of axial cutting depth and spindle speed. Lastly, the golden search instead of traditional sequential search is applied to seek the crucial axial cutting depths corresponding to different spindle speeds, which can improve computational efficiency remarkably. The verifications with two classic benchmark examples demonstrate that the proposed method has higher computational efficiency.

Journal ArticleDOI
TL;DR: The objective of this paper is to design an embedding method that maps local features describing an image to a higher dimensional representation useful for the image retrieval problem and compares the proposed embedding methods with the state of the art in the context of image search.
Abstract: The objective of this paper is to design an embedding method that maps local features describing an image (e.g., SIFT) to a higher dimensional representation useful for the image retrieval problem. First, motivated by the relationship between the linear approximation of a nonlinear function in high dimensional space and the state-of-the-art feature representation used in image retrieval, i.e., VLAD, we propose a new approach for the approximation. The embedded vectors resulted by the function approximation process are then aggregated to form a single representation for image retrieval. Second, in order to make the proposed embedding method applicable to large scale problem, we further derive its fast version in which the embedded vectors can be efficiently computed, i.e., in the closed-form. We compare the proposed embedding methods with the state of the art in the context of image search under various settings: when the images are represented by medium length vectors, short vectors, or binary vectors. The experimental results show that the proposed embedding methods outperform existing the state of the art on the standard public image retrieval benchmarks.

Journal ArticleDOI
TL;DR: The problem is viewed from a new perspective and an algorithm called locally linear approximation (LLA) is proposed, which tries to keep the local structure of the data space while restoring the missing entries from row angle and column angle simultaneously.
Abstract: The matrix completion problem is restoring a given matrix with missing entries when handling incomplete data. In many existing researches, rank minimization plays a central role in matrix completion. In this paper, noticing that the locally linear reconstruction can be used to approximate the missing entries, we view the problem from a new perspective and propose an algorithm called locally linear approximation (LLA). The LLA method tries to keep the local structure of the data space while restoring the missing entries from row angle and column angle simultaneously. The experimental results have demonstrated the effectiveness of the proposed method.

Journal ArticleDOI
TL;DR: In this article, the validity of linear approximation for the oil film forces is discussed when the system operates under specific conditions, pointing out the influence of critical phenomena and dynamic parameters in rotordynamic analysis.
Abstract: The study of rotating machines is usually carried out taking into account linearized hydrodynamic forces, considering dynamic coefficients of stiffness and damping, although a high order of nonlinearity can be significantly present in the system. To solve the nonlinear problem, the solution of Reynolds equation is practically mandatory for each time step in the numerical integration procedure, leading to high computational costs that often can make its application unavailable. In this paper, the validity of linear approximation for the oil film forces is discussed when the system operates under specific conditions, pointing out the influence of critical phenomena and dynamic parameters in rotordynamic analysis. Experimental tests are compared to numerical simulations for linear and nonlinear models of bearings in laboratory test rig in order to validate the analysis. Afterward, several simulations were accomplished, in time domain, for a rotor configuration more susceptible to critical operation, comparing the results for linear and nonlinear models. The main focus is on the influence of internal damping, gyroscopic effects, journal eccentricities, and excitation forces. The results demonstrate that the excitation force plays a fundamental role in nonlinearity degree of response, namely in extreme operation conditions under high excitation forces, the linear approach fails in representing the hydrodynamic bearings.

Proceedings ArticleDOI
11 Jun 2018
TL;DR: This paper proposes a constraint generation algorithm that iterates between 1) using an optimization algorithm to identify a point that maximizes the error of the linearization at that iteration and 2) updating thelinearization to minimize the worst-case error among all points identified thus far.
Abstract: The power flow equations are at the heart of many optimization and control problems relevant to power systems. The non-linearity of these equations leads to computational challenges in solving power flow and optimal power flow problems (non-convergence, local optima, etc.), Accordingly, various linearization techniques, such as the DC power flow, are often used to approximate the power flow equations. In contrast to a wide variety of general linearization techniques in the power systems literature, this paper computes a linear approximation that is specific to a given power system and operating range of interest. An “adaptive linearization” developed using this approach minimizes the worst-case error between the output of the approximation and the actual non-linear power flow equations over the operating range of interest. To compute an adaptive linearization, this paper proposes a constraint generation algorithm that iterates between 1) using an optimization algorithm to identify a point that maximizes the error of the linearization at that iteration and 2) updating the linearization to minimize the worst-case error among all points identified thus far. This approach is tested on several IEEE test cases, with the results demonstrating up to a factor of four improvement in approximation error over linearizations based on a first-order Taylor approximation.

Journal ArticleDOI
Peter Andras1
TL;DR: It is found that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection and such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sampleof the data manifold.
Abstract: Approximation of high-dimensional functions is a challenge for neural networks due to the curse of dimensionality. Often the data for which the approximated function is defined resides on a low-dimensional manifold and in principle the approximation of the function over this manifold should improve the approximation performance. It has been show that projecting the data manifold into a lower dimensional space, followed by the neural network approximation of the function over this space, provides a more precise approximation of the function than the approximation of the function with neural networks in the original data space. However, if the data volume is very large, the projection into the low-dimensional space has to be based on a limited sample of the data. Here, we investigate the nature of the approximation error of neural networks trained over the projection space. We show that such neural networks should have better approximation performance than neural networks trained on high-dimensional data even if the projection is based on a relatively sparse sample of the data manifold. We also find that it is preferable to use a uniformly distributed sparse sample of the data for the purpose of the generation of the low-dimensional projection. We illustrate these results considering the practical neural network approximation of a set of functions defined on high-dimensional data including real world data as well.

Journal ArticleDOI
TL;DR: The enhanced oil recovery problem of ASP flooding with four injection wells and nine production wells is solved by the proposed method and a temporal difference (TD) learning algorithm is introduced to update the weight coefficients.

Journal ArticleDOI
TL;DR: In this paper, the authors study two broad classes of nonlinear time-varying continuous time systems with outputs, and propose a finite time observer for each of them, which provides exact values of the state at all times larger than a suitable finite time, and an approximate estimate when there are nonzero disturbances.
Abstract: We study two broad classes of nonlinear time-varying continuous time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance a↵ects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the ecacy of our methods.

Journal ArticleDOI
TL;DR: A linear approximation of the forward model of soft X-ray tomography, such that the reconstruction is solvable by standard iterative schemes, takes into account the three-dimensional point spread function of the optical system, which consequently enhances the reconstruction of data.

Journal ArticleDOI
TL;DR: In this article, the authors present practical examples where linear interpolation or linear approximation with respect to the parameters proves ineffectiv... (i.e., linear approximating a function that depends on a parameter).
Abstract: When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters proves ineffectiv...

Journal ArticleDOI
TL;DR: This paper presents a study on electro-hydraulic servo system for the purpose of position control using a compatible linear model, and proposes a procedure with less conservativeness and less restriction that has the fastest operation without any overshoot.
Abstract: This paper presents a study on electro-hydraulic servo system for the purpose of position control using a compatible linear model. The system has high level of nonlinearity and linearization introduces extra error in system model. In order to reduce this error several methods of linearization uncertainty are discussed. In spite of applying Taylor's series for all methods, several procedures are used for considering uncertainty on linearization constants. In the first procedure, a simple bound is considered for each linearization constant. In the second procedure, a polytope is extracted for the uncertainty by a graphical method. Finally, a procedure with less conservativeness and less restriction is proposed. This procedure is used to extract the linear model of the electro-hydraulic servo system for the task of position control. The resulting model is used to synthesize an output-feedback H∞ controller for the EHSS using a Linear Matrix Inequality (LMI)-based approach. The effectiveness of the proposed method is demonstrated by simulation and experimental results. The results showed that the procedure is less conservative and has the fastest operation without any overshoot.

Proceedings ArticleDOI
09 Jul 2018
TL;DR: D-DiLL is introduced, a deterministic refinement of DiLL with a D-exponential, for which it exhibits a cut-elimination procedure, and a categorical semantics.
Abstract: Differential Linear Logic (DiLL), introduced by Ehrhard and Regnier, extends linear logic with a notion of linear approximation of proofs. While DiLL is classical logic, i.e. has an involutive negation, classical denotational models of it in which this notion of differentiation corresponds to the usual one, defined on any smooth function, were missing. We solve this issue by constructing a model of it based on nuclear topological vector spaces and distributions with compact support.This interpretation sheds a new light on the rules of DiLL, as we are able to understand them as the computational principles for the resolution of Linear Partial Differential Equations. We thus introduce D-DiLL, a deterministic refinement of DiLL with a D-exponential, for which we exhibit a cut-elimination procedure, and a categorical semantics. When D is a Linear Partial Differential Operator with constant coefficients, then the D-exponential is interpreted as the space of generalised functions ψ solutions to Dψ = φ. The logical inference rules represents the computational steps for the construction of the solution φ. We recover linear logic and its differential extension DiLL particular case.

Journal ArticleDOI
TL;DR: This paper develops a nonlinear model predictive control (MPC) algorithm for dynamic systems represented by piecewise linear Hammerstein models that does not require the inversion of static nonlinearity and can directly cope with input constraints even in multivariable systems.
Abstract: This paper develops a nonlinear model predictive control (MPC) algorithm for dynamic systems represented by piecewise linear (PWL) Hammerstein models. At each sampling instant, the predicted output trajectory is linearized online at an assumed input trajectory such that the control actions can be easily calculated by solving a quadratic programming optimization problem, and such linearization and optimization may be repeated a few times for good linear approximation accuracy. A three-step procedure is developed to linearize a PWL function, where the derivatives of a PWL function are obtained by a computationally efficient look-up table approach. Unlike many existing MPC algorithms for Hammerstein systems, it does not require the inversion of static nonlinearity and can directly cope with input constraints even in multivariable systems. Two benchmark chemical reactors are studied to illustrate the effectiveness of the proposed algorithm.

Journal ArticleDOI
TL;DR: A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean-Kawasaki equation describing density fluctuations in colloidal systems, which can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.
Abstract: Spatiotemporally correlated motions of interacting Brownian particles, confined in a narrow channel of infinite length, are studied in terms of statistical quantities involving two particles. A theoretical framework that allows analytical calculation of two-tag correlations is presented on the basis of the Dean-Kawasaki equation describing density fluctuations in colloidal systems. In the equilibrium case, the time-dependent Einstein relation holds between the two-tag displacement correlation and the response function corresponding to it, which is a manifestation of the fluctuation-dissipation theorem for the correlation of density fluctuations. While the standard procedure of closure approximation for nonlinear density fluctuations is known to be obstructed by inconsistency with the fluctuation-dissipation theorem, this difficulty is naturally avoided by switching from the standard Fourier representation of the density field to the label-based Fourier representation of the vacancy field. In the case of ageing dynamics started from equidistant lattice configuration, the time-dependent Einstein relation is violated, as the two-tag correlation depends on the waiting time for equilibration while the response function is not sensitive to it. Within linear approximation, however, there is a simple relation between the density (or vacancy) fluctuations and the corresponding response function, which is valid even if the system is out of equilibrium. This non-equilibrium fluctuation-response relation can be extended to the case of nonlinear fluctuations by means of closure approximation for the vacancy field.

Journal ArticleDOI
TL;DR: In this paper, the authors considered general linear approximation spaces for periodic Besov spaces on the d-torus, including spaces of generalized and logarithmic smoothness, and obtained the exact asymptotic behavior of approximation and entropy numbers of embeddings of such spaces.
Abstract: We consider general linear approximation spaces $$X^b_q$$ based on a quasi-Banach space X, and we analyze the degree of compactness of the embedding $$X^b_q \hookrightarrow X$$ . Applications are given to periodic Besov spaces on the d-torus, including spaces of generalized and logarithmic smoothness. In particular, we obtain the exact asymptotic behavior of approximation and entropy numbers of embeddings of such Besov spaces in Lebesgue spaces and in Besov spaces of logarithmic smoothness.

Journal ArticleDOI
TL;DR: In this paper, the authors explore experimental methods to detect the internal structure of the system, using a black box approach, and compare two different strategies and the best combination of these is introduced.
Abstract: Block oriented model structure detection is quite desirable since it helps to imagine the system with real physical elements. In this work we explore experimental methods to detect the internal structure of the system, using a black box approach. Two different strategies are compared and the best combination of these is introduced. The methods are applied on two real systems with a static nonlinear block in the feedback path. The main goal is to excite the system in a way that reduces the total distortion in the measured frequency response functions to have more precise measurements and more reliable decision about the structure of the system.