Equivalent Realizations Research Articles

Quantization of pseudo-hermitian systems

This work is a generalization of (Raimundo et al 2021 Phys. Rev. A 103 022201) to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization maps canonically related pseudoclassical theories to equivalent quantum realizations in arbitrary dimensions. We apply the formalism to the problem of two coupled spins with Heisenberg interaction.

Realization of synchronized modulations by stator flux trajectory tracking for low‐carrier‐ratio induction motor drives

SummaryCompared with asynchronous voltage modulations, the synchronous space vector modulation (Syn‐SVPWM) can suppress current harmonics for high‐power induction motors (IM) by generating symmetrical voltage pulses. However, it is difficult to build a high‐performance current regulator based on Syn‐SVPWM because of the requirements of fixed voltage phases and the nonsymmetrical switching sequences in Syn‐SVPWM. Therefore, this manuscript proposes the equivalent realization of Syn‐SVPWM by the concept of stator flux trajectory tracking (SFTT). The new method controls the stator flux vector to move along evenly distributed flux samples in the complex plane. Then, the synchronization and symmetries of voltage pulses are maintained by organizing the switching sequence between adjacent flux samples. Meanwhile, the torque can be changed by online updating the control period based on the inverse torque model. Consequently, the proposed method can provide fast torque response with Syn‐SVPWM in a simple manner because it does not have to compensate the phase contradiction and to extract the fundamental of sampled current. Both simulations and experiments have verified the effectiveness of proposed method.

Standard of Coherence in the Translated Texts: A Textlinguistic Contrastive Analysis

Translation Studies and practices currently face some procedural challenges which are summarizable into problems of Text reception and analyses, transfer of text meaning, assessment of translation text, and realization of textual equivalence. Translation practice have also witnessed a number of theories and approaches aimed at solving these problems. Textlinguistics has recently been considered a pragmatic touchstone for the analysis and assessment of translated texts. Textlinguists have made a strong case for the principle of Textuality (and its standards) as an effective tool in text creation and analysis as well as determinant of textuality in a natural text. Coherence as one of the seven standards of textuality therefore deals basically with the internal semantic structure of text. It is a textual procedure in which cognitive elements are activated to create and recover conceptual relations in a text. It also forms the basic features by which text world and its conceptual relations are characterised. This paper therefore aims to provide information on Coherence as one of the seven standards of textuality, expose its concepts and elements, and demonstrate its relationship with Translation. it also attempts at transforming Coherence standard into an effective cognitive theoretical framework for the analysis and assessment of translated text. Two political reports (Source and Target Texts) were selected from two (non-) governmental organizations for textual analysis and assessment. The paper concluded on the note that any translation process that is done on the basis of standard of coherence will enable translator to identify the extent of his success in producing a coherent, equivalent and communicative translated text.

Q-Markov Covariance equivalent realizations for unstable and marginally stable systems

An observer-based q-Markov Covariance equivalent realization (QMC) formulation is presented in the paper. It is shown that by inserting an observer in the input–output relationship associated with the dynamical system, a QMC approach can be developed that is applicable to systems with marginally stable or unstable equilibrium points. A system of equations governing all linear state-space realizations, along with the corresponding observers, is derived from matching a set of Markov and Covariance parameters. The solution to this equation system is shown to parameterize all state-space realizations that match the pre-specified correlation functions. Four numerical examples are used to show the utility of the proposed approach. The numerical results show that the observer-based QMC presented in the paper can identify linear SISO and MIMO systems with stable, marginally stable, and unstable characteristics.

An Efficient q-Markov Covariance Equivalent Realization Approach to System Identification

An efficient q-Markov covariance equivalent realization (QMC) formulation is presented in this paper. This efficient solution matches all Markov and Covariance parameters of a finite-dimensional system using a finite amount of data. The frequency responses of that system is also matched by the efficient QMC solution. The existence condition of this efficient QMC solution and its parametrization is given in this paper. Then, a generalized algorithm for system identification using the efficient QMC is given. The example is set up by a cantilever beam. Results show that the efficient QMC fully captures Markov and covariance parameters and frequency responses of the cantilever beam.

BonnLogic: Delay optimization by And-Or Path restructuring

We present BonnLogic, a timing optimization framework that replaces critical paths by logically equivalent realizations with less delay. Our tool allows to revise early decisions on the logical structure of the netlist in late physical design. The core routine of our framework is a new algorithm that constructs delay-optimized circuits for alternating And-Or paths with prescribed input arrival times. It is a sophisticated dynamic programming algorithm which is a common generalization of the previously best approaches. In contrast to all earlier methods, we avoid fixing the structure of sub-solutions before deciding on how to combine them, significantly expanding the search space of the algorithm. Our algorithm provably fulfills the best known approximation guarantees, almost always computes delay-optimum solutions, and empirically outperforms all previous approaches. In addition, we show how any algorithm for And-Or paths optimization which is restricted to integral arrival times can be generalized to fractional arrival times with the same guarantees on the delay. The reduction to And-Or path optimization allows us to optimize general combinatorial paths of arbitrary length in our logic restructuring framework BonnLogic. The framework is applied successfully as a late step in an industrial physical design flow. Experiments demonstrate the effectiveness of BonnLogic on industrial 7 nm instances.

Cycle-based LQG knock control using identified exhaust temperature model

Spark ignition engines are often desired to be operated close to their knock borderline when MBT (maximum brake torque) cannot be achieved for optimizing combustion efficiency. Under this circumstance, a calibrated baseline spark timing, along with other control parameters such as intake and exhaust valve timings, is found for the engine control system to maximize fuel economy, and a stochastic scheme can be used for the control based on a large number of history data. However, cycle-to-cycle combustion variations still exist, resulting in a relatively conservative baseline control. To reduce cycle-to-cycle combustion variations, a real-time cycle-wised knock compensation is required. The correlation between exhaust temperature at the current cycle and knock intensity at the next cycle was found in our earlier research. In this paper, a cycle-to-cycle spark timing compensation scheme is developed based on the measured exhaust temperature when the engine is operated close to its knock borderline. To make model-based control possible, [Formula: see text]-Markov COVER (COVariance Equivalent Realization) system identification was used to obtain a linearized engine exhaust system model from incremental spark timing to associated exhaust temperature and knock intensity. Accordingly, a Linear–Quadratic–Gaussian (LQG) controller is designed, based on the identified model, to minimize the knock intensity fluctuations based on incremental exhaust temperature variation. The LQG control strategy was integrated with the existing entire knock control architecture, where the baseline spark timing is generated based on the offline machine training with an online updating scheme developed earlier, and demonstrated experimentally. Note that the cycle-based compensation only adds incremental spark timing to the baseline control so that knock combustion variations can be reduced. Three test scenarios are used to demonstrate the effectiveness of the proposed cycle-to-cycle compensation scheme when the engine is knock-limited. With the help of cycle-to-cycle based compensation, it was demonstrated that engine spark timing can be further advanced about one crank degree while maintaining the same knock intensity up-limit due to reduced knock combustion variations. Note that this is corresponding to 0.5%–1.0% fuel economy for this engine when it is operated under knock condition.

Stochastic Modeling Approach to Identify Uncertainties of Karst Conduit Networks in Carbonate Aquifers

AbstractThe characterization of the karst conduit network is an essential task to understand the complex flow system within karst aquifers. However, this task is challenging and often associated with uncertainty. Equivalent porous media approaches for modeling flow in karst aquifers fall short of capturing the hydraulic effect of individual karst features, while process‐oriented karst evolution models imply major computational efforts. In this study, we apply the Stochastic Karst Simulator (SKS) developed by Borghi et al. (2012) to generate karst conduit networks at a regional scale of a highly karstified carbonate aquifer located in the Eastern Mediterranean region and extensively used for water supply. The SKS generates conduit network geometries reasonably quick, using a mathematical proxy that mimics conduit evolution. The conduit simulation is based on a conceptual model of the genesis of the aquifer, consisting of different karstification phases. The stochastic approach of the algorithm enables us to generate an ensemble of conduit network realizations and to represent the uncertainties of these simulations in a Karst Probability Map. With only soft input information to constrain conduit evolution, multiple equivalent realizations yield similar resulting network geometries, indicating a robust approach. The presented methodology is numerically efficient, and its input can be easily adjusted. Subsequently, the resulting stochastic spatial distribution of conductivities can be employed for the parametrization of regional karst groundwater models.

Molecular Dynamics Predictions of Shock‐Induced Pore Collapse in (010)‐Oriented β‐HMX: Effects of Sample Thickness and Transverse Orientation, and Run‐To‐Run Variability among Statistically Equivalent Samples

AbstractUsing shock‐induced quasi‐2D pore collapse in β‐HMX as a specific case study, we address three practical questions that arise when designing and interpreting molecular dynamics (MD) simulations of explicit shock wave propagation in crystals. How sensitive are the overall results to sample thickness perpendicular to the (quasi) plane of the problem? For impacts on a given crystal surface, how much does the transverse orientation of the sample matter? And, for a given sample size and orientation, how much run‐to‐run variability exists among results for independent but statistically equivalent realizations of the shock? The first and second questions are interrelated but pertain individually to assessing the roles of finite‐size and crystal anisotropy effects, respectively, on the simulated collapse mechanisms and associated local thermo‐mechanical states in the sample during and after collapse. The third addresses the confidence with which the results of individual simulations can be regarded as representative. All three questions become particularly important if the MD predictions are intended to serve as “ground truth” for validation of continuum mesoscale models. Here, quasi‐2D samples of (010)‐oriented single‐crystal β‐HMX (β‐1,3,5,7‐tetranitro‐1,3,5,7‐tetrazocane) containing a cylindrical pore were subjected to reverse‐ballistic impacts, resulting in explicit, supported shock propagation initially along [010], for impact speeds =1.0 and 0.5 km s−1. The individual samples differed in either the thickness perpendicular to the sample plane or the transverse crystal orientation normal to [010] in the quasi‐2D cell. Three independent realizations of the shock were performed for a selected case to assess run‐to‐run variability. Comparisons of qualitative features of the collapse, temperature and pressure distributions in the samples, and time scales for pore collapse suggest that there is little sensitivity to sample thickness for the same crystal orientation and moderate sensitivity to transverse crystal orientation for samples of the same thickness. Run‐to‐run variability is evident to the eye in side‐by‐side system observations. However, overall mechanisms of collapse, distributions for temperature and pressure in the samples, and time scales for collapse are in near‐quantitative agreement among the realizations.

Polarimetric method of generating full Poincaré beams within a finite extent

A novel polarimetric method of generating a variety of Poincaré beams such as half Poincaré beams and full Poincaré beams using doubly inhomogeneous wave plates ( d -plates) is proposed. In this method, every input state of polarization (SoP) through such a d -plate generates a unique Poincaré beam, thereby giving access to a potentially infinite number of them. Furthermore, the generation of full Poincaré beams is presented here as an instance of the geometrical problem of mapping the surface of a sphere onto a plane, and this insight allows one to design d -plates that convert the input SoP to every possible SoP, within a finite region of the beam. A gadget composed of three singly inhomogeneous wave plates for an equivalent realization of these d -plates is also presented.

Parameter fault diagnosis in heat exchange networks with distributed time delay

This paper deals with parameter fault diagnosis in heat exchange networks (HENs) with joining and splitting connections where the change in the heat transfer coefficient is considered as fault. The fault diagnosis oriented model of the HEN elements was developed based on the equivalent LTI realization of distributed delay models. The Signed Directed Graph (SDG) method is used to derive the fault observability conditions. The presence of faults induces bilinear fault-input terms into the system model. Thus, a nonlinear adaptive observer was proposed for fault diagnosis. To verify and validate the proposed method, a case study is presented. The simulation results show that the observers are successfully detecting and estimating the faults and unknown system states.

Realizations of Isostatic Material Frameworks

This article studies the set of equivalent realizations of isostatic frameworks and algorithms for finding all such realizations. It is shown that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. The complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions is enumerated and the impact of boundary length on the emergence of these realizations is studied. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints, alternative methods—based on constraint reduction and distance‐based covering map or Cayley parameterization of the search space—are presented. The application of these methods is studied on atomic clusters, a model of 2D glasses and jamming.

Classical-quantum correspondence for two-level pseudo-Hermitian systems

In this work, a classical-quantum correspondence for two-level pseudo-Hermitian systems is proposed and analyzed. We show that the presence of a complex external field can be described by a pseudo-Hermitian Hamiltonian if there is a suitable canonical transformation that links it to a real field. We construct a covariant quantization scheme which maps canonically related pseudoclassical theories to unitarily equivalent quantum realizations, such that there is a unique metric-inducing isometry between the distinct Hilbert spaces. In this setting, the pseudo-Hermiticity condition for the operators induces an involution which guarantees the reality of the corresponding symbols, even for the complex field case. We assign a physical meaning for the dynamics in the presence of a complex field by constructing a classical correspondence. As an application of our theoretical framework, we propose a damped version of the Rabi problem and determine the configuration of the parameters of the setup for which damping is completely suppressed. The experimental viability of the proposal is studied within a specific context. We suggest that the main theoretical results developed in the present work could be experimentally verified.

How accurately can we measure the baryon acoustic oscillation feature?

ABSTRACT Baryon acoustic oscillations (BAOs) represent one of the cleanest probes of dark energy, allowing for tests of the cosmological model through the measurement of distance and expansion rate from a 3D galaxy distribution. The signal appears at large scales in the correlation function where linear theory applies, allowing for the construction of accurate models. However, due to the lower number of modes available at these scales, sample variance has a significant impact on the signal, and may sharpen or widen the underlying peak. Therefore, equivalent mock realizations of a galaxy survey present different errors in the position of the peak when uncertainties are estimated from the posterior probability distribution corresponding to the individual mocks. Hence, the posterior width, often quoted as the error in BAO survey measurements, is subject to sample noise. A different definition of the error is provided by the asymptotic variance of the maximum likelihood estimator, which involves the average over multiple realizations, and is not subject to sample noise. In this work, we reanalyse the main galaxy survey data available for BAO measurements and quantify the impact of the noise component on the error quoted for BAO measurements. We quantify the difference between three definitions of the error: the confidence region computed from a single posterior, the average of the variances of many realizations, and the Fisher matrix prediction assuming a Gaussian likelihood. We also explore the impact of a ‘detectability prior’ based on the significance of the BAO detection.

Initial Sensitive Dynamics in Memristor Synapse-coupled Hopfield Neural Network

The initial sensitive dynamics in a Hopfield Neural Network (HNN) with three neurons under the action of electromagnetic induction current is reported. A simple 4-D memristive HNN is constructed by using a non-ideal memristor synapse to imitate the electromagnetic induction current caused by membrane potential difference between two adjacent neurons. By means of theoretical analyses and numerical simulations, the complex dynamical behaviors under different coupling strengths of the memristor synapse are researched, and special phenomena closely related to the initial values are revealed. Finally, the analog equivalent realization circuit of the memristive HNN model is designed, and the correctness of MATLAB numerical simulation is verified by PSIM circuit simulations.

The influence of connected heterogeneity on groundwater flow and salinity distributions in coastal volcanic aquifers

Geological heterogeneity is a key factor affecting rates and patterns of groundwater flow and the evolution of salinity distributions in coastal aquifers. The hydrogeologic systems of volcanic aquifers are characterized by lava flows that can form connected geologic structures in the subsurface. Surface-based geostatistical techniques were adopted to generate geologically-realistic, statistically equivalent model realizations of a hydrogeologic system based on that of the Big Island of Hawaii (conduit models). The density-dependent groundwater flow and solute transport code SEAWAT was used to perform 3D simulations to investigate subsurface flow and salt transport through these random realizations. Statistically equivalent geological systems generated with sequential indicator simulation (SIS) and equivalent homogeneous systems were also simulated for comparison. Simulation results show that conduit realizations tend to have more complex salinity distributions with larger mixing zones for which the center of mass is farther offshore compared to homogeneous and SIS realizations. The zone of groundwater discharge is also farther offshore than for homogeneous and SIS models, with higher point fluxes of both fresh and saline water and greater spatial variability. This highlights the importance of the geometry of geologic features in coastal groundwater flow and solute transport processes in highly heterogeneous aquifers. It also points to the importance of preferential flow, with implications for both coastal groundwater resource management and solute fluxes to the ocean.

Design and Realizations of Networked Estimators: A Descriptor Model Approach

This paper addresses the design and realization of a networked estimator, which requires further digital implementation using several subsystems. Implementation on a digital process entails finite word length effects on the coefficients’ representation, and a multiple-subsystem architecture also introduces internal time delays in the information interaction. Dealing with these intrinsic defects requires finding a resilient realization. A corresponding descriptor model-based approach is thus constructed to describe the internal time delays and equivalent realizations with finite word length effects in a unifying framework, which enables simultaneous consideration of design and realization. Based on the obtained descriptor model, a stability analysis condition is deduced and a design method for the estimator is further obtained. An algorithm is also proposed for finding the optimal realization requiring the minimum word length for stabilization. Finally, a simulation with two cooperative robots is considered to illustrate the effectiveness of the results.

Linear-Quadratic Tracking Control of a Commercial Vehicle Air Brake System

This article proposes to utilize linear-quadratic tracking (LQT) control to reduce the air brake system response time and vehicle stopping distance, and hence, to significantly improve the system performance of a commercial vehicle air brake system equipped with electro-pneumatic proportional valve actuators. The nonlinear dynamic model of the air brake system, consisting of a control actuator (a proportional valve) and braking actuator (the brake chamber), is developed and linearized using the q-Markov COVariance Equivalent Realization (q-Markov Cover) method in our early work. Based on the linearized dynamic model, an infinite horizon LQT controller is designed along with Kalman state estimation at each linearized operational condition. To apply the LQT control law over a wide operational range to track the target pressure, the designed controller was interpolated between the neighboring controllers to have a control law cover the entire operational range. To validate this control law, the control scheme is implemented into a dSPACE unit and validated through bench tests under different supply and reference pressures. The LQT control performance is also compared with the PID (proportional-integral-derivative) one. The bench test results confirm the effectiveness of the proposed control scheme.

Borel complexity up to the equivalence

We say that two classes of topological spaces are equivalent if each member of one class has a homeomorphic copy in the other class and vice versa. Usually when the Borel complexity of a class of metrizable compacta is considered, the class is realized as the subset of the hyperspace K([0,1]ω) containing all homeomorphic copies of members of the given class. We are rather interested in the lowest possible complexity among all equivalent realizations of the given class in the hyperspace.We recall that to every analytic subset of K([0,1]ω) there exists an equivalent Gδ subset. Then we show that up to the equivalence open subsets of the hyperspace K([0,1]ω) correspond to countably many classes of metrizable compacta. Finally we use the structure of open subsets up to equivalence to prove that to every Fσ subset of K([0,1]ω) there exists an equivalent closed subset.

Wave Field Propagation in Extended Highly Anisotropic Media

AbstractThe theory propagation in the Earth's ionosphere is well established. However, with the advent of Global Navigation Satellite System measurements, new demands are being placed on satellite system performance evaluation and diagnostic measurements. Propagation simulations are essential for system performance evaluation and they provide guidelines for interpreting diagnostic measurements. This paper presents simulations of propagation in extended highly anisotropic media obtained with split‐step integration of the parabolic wave equation. This requires three‐dimensional realizations of the electron density structure. A new configuration‐space model is used to generate realizations as summations of striations, which are local to field lines with defined scales and peak densities. The scale and peak densities can be selected to generate specified power law spectral density functions. An analytic three‐dimensional expectation spectral density function provides a parameterized ionospheric structure model. The simulations results show that replacing the extended structure with an equivalent phase screen placed at the center of the structured region provides statistically equivalent realizations of observation‐plane measurements at propagation distances greater than the layer extent. The equivalence is independent of the propagation direction relative to the magnetic field direction, although there is some variation for the extreme propagation disturbances caused by field‐aligned propagation. We also investigate the interpretation of in situ and path‐integrated diagnostic measurements and two‐dimensional propagation models, which are being used to model diagnostic measurements directly.