Dynamic Transfer Functions Research Articles

Numerical analysis of laminar velocity-forced premixed slit flames using modal decomposition techniques

The relation between Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Flame Transfer Functions (FTF) is explored to gain further insight into the dynamics of two-dimensional laminar slit flames externally forced by velocity perturbations. The application of POD to the heat release rate fields suggests that the resultant modes can be split into two groups: the ones that are related to the displacement of the reactive sheet in the normal direction with regards to the flame front, and the ones that contain the local flame front distortions. The latter modes show preferential frequencies associated to the phase values of π, 2π and 3π of the FTFs, which can be related to the maximum gain value depending on the case. Furthermore, the results of the modal analysis seem to support that the flame tip dynamics can be conceptually modelled as a set of standing waves whose joint response can reconstruct a propagation in the normal flame front direction, generating also the temporal fluctuations of the spatially-integrated heat release in the domain. The DMD analysis shows the existence of an interaction between the flame and the flow, and illustrates the fundamental role played by the velocity perturbations at the base for the motion of the reactive sheet. Thus, the analysis shows how data-based decomposition methods can be used to identify complex physical phenomena contained in the FTF graphs with different levels of detail, and extend the modal analysis to the physical space.Novelty and significance statementThis paper proves the potential of modal decomposition techniques like POD and DMD to infer the underlying physics of canonical flames and their relation to the FTF, validating also the hypotheses and methodology of other reduced-order models in the literature. A canonical configuration featuring a two-dimensional slit flame has been selected to analyse the flame dynamics using these methods. Hence, this work aims to set the foundations to elaborate data-driven reduced-order models based on modal decomposition techniques to support the analysis and the study of flame dynamics.

Mapping the dynamic transfer functions of eukaryotic gene regulation.

Biological information can be encoded within the dynamics of signaling components, which has been implicated in a broad range of physiological processes including stress response, oncogenesis, and stem cell differentiation. To study the complexity of information transfer across the eukaryotic promoter, we screened 119 dynamic conditions-modulating the pulse frequency, amplitude, and pulse width of light-regulating the binding of an epigenome editor to a fluorescent reporter. This system revealed tunable gene expression and filtering behaviors and provided a quantification of the limit to the amount of information that can be reliably transferred across a single promoter as ∼1.7 bits. Using a library of over 100 orthogonal chromatin regulators, we further determined that chromatin state could be used to tune mutual information and expression levels, as well as completely alter the input-output transfer function of the promoter. This system unlocks the information-rich content of eukaryotic gene regulation.

Evaluation of Lee etal.: Clarity and interpretation of mutual information in promoter transfer functions.

One snapshot of the peer review process for "Mapping the dynamic transfer functions of eukaryotic gene regulation" (Lee etal., 2021) appears below.

Mapping the Dynamic Transfer Functions of Epigenome Editing

Biological information can be encoded in the dynamics of signaling components which has been implicated in a broad range of physiological processes including stress response, oncogenesis, and stem cell differentiation. To study the complexity of information transfer across the eukaryotic promoter, we screened 119 dynamic conditions — modulating the frequency, intensity, and pulse width of light — regulating the binding of an epigenome editor to a fluorescent reporter. This system revealed highly tunable gene expression and filtering behaviors and provided the most comprehensive quantification to date of the maximum amount of information that can be reliably transferred across a promoter as ~1.7 bits. Using a library of over 100 orthogonal epigenome editors, we further determined that chromatin state could be used to tune mutual information and expression levels, as well as completely alter the input-output transfer function of the promoter. This system unlocks the information-rich content of eukaryotic epigenome editing.

Gradient-Induced Mechanical Vibration of Neural Interfaces During MRI.

Resonant vibrations of implanted structures during a magnetic resonance imaging (MRI) procedure pose a risk to the patient in the form of soft tissue irritation and degradation of the implant. In this paper, the mechanical behavior of implant structures in air, water, and viscoelastic materials was explored. The static and dynamic transfer functions of various test samples in air and immersed in both water and hydrogels were analyzed. The laser-based acquisition method allowed for high-angular-resolution (10 μDeg) and high-dynamic-range (0-6 kHz) measurements. Additional MRI experiments were conducted to investigate the dependence of vibration strength on magnetic resonance (MR) sequence parameters in combination with the obtained transfer functions. The largest forces were found to be in the micronewton to millinewton range, which is comparable to forces applied during implantation. Of additional concern was the damping introduced by viscoelastic tissue, which was less than expected, leading to an underdamped system. In contrast to current wisdom, the imaging experiments demonstrated drastically different vibration amplitudes for identical gradient slew rates, but different timing parameters TR, mainly due to resonant amplification. The results showed that a safe force-free MR procedure depends not only on the gradient slew rate, but also and more drastically on the choice of secure timing parameters. These findings delineate design improvements to achieve longevity of implants and will lead to increased patient safety during MRI. A prudent choice of mechanical characteristics of implanted structures is sufficient to avoid resonant excitation due to mismatched MR sequence parameters.

DESIGN OF THE CONTROL SYSTEM BY MOVEMENT OF ROBOTS MOBILE GROUP IN CONDITIONS OF UNCERTAINTY

Many controlled plants, in particular mobile robots, solve various tasks in a priori uncertain conditions. In this connection their mathematical models necessary for creation of qualitative control systems are unknown. Therefore development of design methods of adaptive control systems is actuality. The big uncertainty of this control problem makes application of adaptive systems with identification by the most expedient. In article the new analytical design method of adaptive control systems by movement of mobile robots group in the uncertainty conditions is offered. This method is focused on the decision of a task of identification of the current mathematical models of robots with the subsequent design of a control system by movement of each robot. The suggested method can be realized automatically as required. It is developed on a basis of the markov method of identification, the method of analytical design of systems with control on output and impacts, and also the standard normalized transfer functions are used. As a whole this method allows to design of the adaptive control systems with desirable qualitative properties. Trial step functions of the small intensity and the original method of digital processing of the information are used at identification. Property of system invariancy of the markov parameters and their direct connection with factors of the discrete dynamic systems transfer functions are a basis of the method of digital processing of the information. It is supposed, that the mobile robots are full or can be stabilized at all possible values of their order and parameters. The suggested method can be used for creation of control systems by the various technical plants functioning in conditions of uncertainty.

Frequency-domain modeling of time-periodic switched electrical networks: A review

Abstract Power networks are, in nature, nonlinear time-variant systems. Starting with synchronous machines, which function as generators, passing by transmission and distribution networks whose topologies are altered due to different switching actions in the network, and ending with uncontrolled loads, which depend to a large extent on customer behavior and their dynamics. Despite the aforementioned nature, power system analysis mainly relies on taking snap shots of the system to estimate its behavior under different conditions, e.g., normal operation load flow, short circuit analysis, etc. Nevertheless, the time-varying characteristic of modern power systems, e.g., time-periodic switching of power electronic converters, impacts the overall network behavior; such impact can be interpreted as overvoltages, waveform distortion, resonance conditions, and even instability. Here the need to account for time-varying nature in modeling of modern power networks. Frequency-domain (FD) provides a convenient domain to solve a set of differential equations that describes the system as algebraic equations for the aforementioned studies, though limited to linear systems. In performing power system studies, periodic nature of rotating machines is accounted for by Park's transformation, which is able to mask the time-periodic nature of the machine in a manner that does not compromise the simplicity of the solution. Yet, the introduction of converters sidestepped FD for network analyses to the favor of time-domain (TD) analysis tools, albeit their relative complexity and large computational times. However, since the inception of the need to analyze time-periodic (TP) systems in general, numerous techniques evolved with varying degrees of success to provide a practical tool for network studies. This paper provides a brief of those efforts. The paper discusses Floquet theory, Harmonic Domain Dynamic Transfer Functions, and Equivalent Signal theory as tools for analysis of TP power systems, putting special attention to switched networks. Also, the paper compares those tools from the points of view of: (i) computational effort for model preparation, (ii) possible applications to modern power networks, and (iii) suitability for integration with present network analysis tools.

Efficient Stochastic Rendering of Static and Animated Volumes Using Visibility Sweeps.

Stochastically solving the rendering integral (particularly visibility) is the de-facto standard for physically-based light transport but it is computationally expensive, especially when displaying heterogeneous volumetric data. In this work, we present efficient techniques to speed-up the rendering process via a novel visibility-estimation method in concert with an unbiased importance sampling (involving environmental lighting and visibility inside the volume), filtering, and update techniques for both static and animated scenes. Our major contributions include a progressive estimate of partial occlusions based on a fast sweeping-plane algorithm. These occlusions are stored in an octahedral representation, which can be conveniently transformed into a quadtree-based hierarchy suited for a joint importance sampling. Further, we propose sweep-space filtering, which suppresses the occurrence of fireflies and investigate different update schemes for animated scenes. Our technique is unbiased, requires little precomputation, is highly parallelizable, and is applicable to a various volume data sets, dynamic transfer functions, animated volumes and changing environmental lighting.

An Empirical Model for Reliable Spiking Activity.

Understanding a neuron's transfer function, which relates a neuron's inputs to its outputs, is essential for understanding the computational role of single neurons. Recently, statistical models, based on point processes and using generalized linear model (GLM) technology, have been widely applied to predict dynamic neuronal transfer functions. However, the standard version of these models fails to capture important features of neural activity, such as responses to stimuli that elicit highly reliable trial-to-trial spiking. Here, we consider a generalization of the usual GLM that incorporates nonlinearity by modeling reliable and nonreliable spikes as being generated by distinct stimulus features. We develop and apply these models to spike trains from olfactory bulb mitral cells recorded in vitro. We find that spike generation in these neurons is better modeled when reliable and unreliable spikes are considered separately and that this effect is most pronounced for neurons with a large number of both reliable and unreliable spikes.

Activity-Dependent Electrical Asymmetry of Dendrites as a Factor Determining the Repertoire of Intrinsic Firing Patterns of Neurons

Metrical asymmetry induced by the inequality of lengths and/or diameters of sister branches of dendrites is a common feature of complex dendritic arborizations in neurons of different types. A consequence of this structural feature is the electrical asymmetry, namely the inequality of passive electrical transfer along metrically asymmetrical branches and, correspondingly, different electrical states of those branches. In our previous studies, it was shown that, for any pair of dendrite branches with a given metrical asymmetry, the asymmetry of their passive transfer functions is characteristically modified with changes in the specific membrane conductance, which depends on the intensity of activation of dendritic synapses. We have investigated in detail the relationships of metrical asymmetry and synaptic activity-dependent transfer properties typical of the dendritic arborizations in different-type neurons (reconstructed pyramidal neurons of the neocortex and hippocampus, cerebellar Purkinje neurons, brainstem neurons, and spinal motoneurons), on the one hand, and the output discharge patterns generated by a given neuron when its dendrites receive synaptic signals of different intensities, on the other hand. In all examined neurons, the repertoire of output discharge patterns critically depended on synaptically induced dynamical changes in the electrical asymmetry of the dendritic arborization. These facts show that the parametric sensitivity of dynamic transfer functions of complex dendritic arborizations with active membrane properties plays a significant role in the formation of output discharge patterns. The latter can be determined by multiple metastable electrical states of metrically asymmetrical branches and sub-trees of the given arborization.

Propagation noise calculations in VVER-type reactor core

Neutron noise induced by propagating disturbances in VVER-type reactor core is addressed in this paper. The spatial discretization of the governing equations is based on the box-scheme finite difference method for triangular-z geometry. Using the derived equations, a 3-D 2-group neutron noise simulator (called TRIDYN-3) is developed for hexagonal-structured reactor core, by which the discrete form of both the forward and adjoint reactor dynamic transfer functions (in the frequency domain) can be calculated. In addition, both types of noise sources, namely point-like and traveling perturbations, can be modeled by TRIDYN-3. The results are then benchmarked in different cases. Considering the noise source as propagating perturbations of the macroscopic absorption cross sections, the induced neutron noise is calculated throughout the reactor core. For the first time, adjoint approach is applied and examined for modeling moving noise sources. Moreover, the space- and frequency-dependence of the propagation noise are investigated in this paper.

Discrete-Time, Robust Wiener Filtering with Non-Parametric Spectral Uncertainty

In this paper, a discrete-time, robust Wiener filtering problem is approached along the lines pursued in [4] for the continuous-time case. The robust, multivariate filtering problem considered here involves non-parametric spectral uncertainty defined by the so-called spectral band and generalized-variance constraints. The approach in question centers on computing upper and lower bounds on the minimum worst-case performance achieved with causal filters, together with filters which attain such bounds, on the basis of semi-definite linear programming problems (SDLP, for short). Upper bounds are obained from a Lagrangean duality formulation. Relying on finitedimensional, linearly-parametrized classes of dynamic multipliers and filter transfer functions, the computation of progressively tighter upper bounds together with causal filters which achieve them is reduced to solving SDLPs. Analogously, on the basis of the min-max theorem and relying on similar classes of rational power spectral densities, the computation of lower bounds together with the corresponding filters is also shown to be equivalent to solving SDLPs. Combining these results, causal filters can be obtained whose worst-case, least squares performance can be certified to be close to the optimal one, as illustrated in a simple numerical example.

The Green’s matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis.

Improved measurement of dynamic modulation transfer functions on display using pursuit camera method based on wavelet-denoising method

A new method was developed for studying dynamic modulation transfer functions (DMTFs) of liquid crystal display (LCD) based on the slanted edge method, improved wavelet-denoise (IWD) method, and Fourier transformation. Measurements were made for capturing the images of moving step-edge patterns on the display by a slightly tilted pursuit camera. The scanning-rate and contrast-dependent DMTFs of a LCD were demonstrated, and the corresponding parameters such as blurred edge width (BEW), spatial sharpness, and motion picture response time (MPRT) were calculated from the DMTF curves. A simple linear relationship between these parameters was found. The properties of a cathode ray tube (CRT) display were also measured for comparison with those of the LCD.

Dynamic relations for sparsely sampled Gaussian processes

In longitudinal studies, it is common to observe repeated measurements data from a sample of subjects where noisy measurements are made at irregular times, with a random number of measurements per subject. Often a reasonable assumption is that the data are generated by the trajectories of a smooth underlying stochastic process. In some cases, one observes multivariate time courses generated by a multivariate stochastic process. To understand the nature of the underlying processes, it is then of interest to relate the values of a process at one time with the value it assumes at another time, and also to relate the values assumed by different components of a multivariate trajectory at the same time or at specific times selected for each trajectory. In addition, an assessment of these relationships will allow to predict future values of an individual’s trajectories. Derivatives of the trajectories are frequently more informative than the time courses themselves, for instance, in the case of growth curves. It is then of great interest to study the estimation of derivatives from sparse data. Such estimation procedures permit the study of time-dynamic relationships between derivatives and trajectory levels within the same trajectory and between the components of multivariate trajectories. Reviewing and extending recent work, we demonstrate the estimation of corresponding empirical dynamical systems and demonstrate asymptotic consistency of predictions and dynamic transfer functions. We illustrate the resulting prediction procedures and empirical first-order differential equations with a study of the dynamics of longitudinal functional data for the relationship of blood pressure and body mass index.

Asymptotic expansion of slightly coupled modal dynamic transfer functions

In case of non-diagonal modal damping, normal modes of vibration do not decouple modal equations. The usual way to handle such a non-diagonal modal damping matrix is to neglect its off-diagonal elements. In this paper, we propose an approximate method based on an asymptotic expansion of the transfer function. It is intermediate between the classical decoupling approximation and the formal solution requiring a full matrix inversion. Indeed, on the one hand, it allows to partially account for modal coupling and, on the other hand, still allows the modal equations to be solved independently from each other. We first provide the mathematical background necessary to canvass the proposed method, then consider a benchmark against which the benefits of the method are measured.

Evolution of internal dynamics for neural network nodes

Most artificial neural networks have nodes that apply a simple static transfer function, such as a sigmoid or gaussian, to their accumulated inputs. This contrasts with biological neurons, whose transfer functions are dynamic and driven by a rich internal structure. Our artificial neural network approach, which we call state-enhanced neural networks, uses nodes with dynamic transfer functions based on n-dimensional real-valued internal state. This internal state provides the nodes with memory of past inputs and computations. The state update rules, which determine the internal dynamics of a node, are optimized by an evolutionary algorithm to fit a particular task and environment. We demonstrate the effectiveness of the approach in comparison to certain types of recurrent neural networks using a suite of partially observable Markov decision processes as test problems. These problems involve both sequence detection and simulated mice in mazes, and include four advanced benchmarks proposed by other researchers.

Hardware and software technologies for improvement of hearing characteristics of headphone reproduction

This report specifically describes commercialization technology of a headphone system with out-of-head localization applying dynamic head-related transfer functions (HRTFs) that can localize sound easily over a full 360 deg. A source image by output of conventional headphones is localized inside the listener’s head. However, the image can be localized outside the listener’s head by wearing headphones over a full 360 deg through accurate simulation of the listener’s HRTFs. Developments of headphone systems using signal processing technology for data correction have given rise to the static binaural reproduction system (SBRS). The first part of this speech describes its psychoacoustic characteristics and challenges. A rotating dummy-head that is synchronized with the listener’s head movement was produced experimentally to create the dynamic binaural reproduction system (DBRS). Using the DBRS, HRTFs synchronize with the listener’s head movement. Psychoacoustic characteristics and advantages of the system are also discussed in this report. Further developments were made to realize the commercialization of the DBRS in areas including piezoelectric gyroscope head-tracking technology, headphone technologies that can reproduce real sound characteristics, and simplification of HRTF signal processing employing a simulator with electronic circuits. Finally, future visions for these technologies will be touched upon.

Finite element frequency-domain acoustic analysis of open-cell plastic foams

A numerical method using an impulsive excitation to excite and collect the acoustic frequency response functions of corrugated open-cell plastic foams is presented in this study. In the study, the Biot's poroelasticity equations are first phrased in terms of solid and fluid displacements and then transformed into the Laplace domain. With the use of the general quadrilateral or triangular elements, the stiffness matrixes for the foams in the Laplace domain are then derived by the Galerkin-type finite element method. After solving and obtaining the dynamic stiffness transfer functions for the foams that are excited by an impulsive pressure on their upper surface, the Laplace transformed stiffness transfer functions are then transformed into frequency domain called dynamic stiffness functions, which can be further used in calculating the acoustic properties of foams. For validations, the proposed Laplace transformed finite element method (LTFEM) is first used to predict the acoustic properties of a planar and rigidly backed open-cell plastic foam with infinite width and permeable upper surface. Thereafter, the influences of the thickness, the width-to-thickness ratio, and the roller as well as fixed side edge restraints on the planar foams’ acoustic properties are examined. Furthermore, the use of LTFEM to predict the acoustic properties of corrugated foams are demonstrated and discussed. Without the use of the additional acoustic field that is required in the earlier studies, results predicted in the present study are in good agreement with either the exact solutions or the experimental data.

VALID STRAIN MEASUREMENTS FOR STRUCTURAL DYNAMICS TESTING. Part 2: Dynamic Strain Measurement System Transfer Functions and Linearity

VALID STRAIN MEASUREMENTS FOR STRUCTURAL DYNAMICS TESTING. Part 2: Dynamic Strain Measurement System Transfer Functions and Linearity