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This slide-show presents analysis of spectrograms and the phase error of filtered noise in a signal. When the filtered noise is smaller than the signal amplitude, the phase error can never exceed 90{deg}, so the average phase error over many cycles is zero: this is called the capture effect because the largest signal captures the phase and frequency determination.
This paper investigates the tracking performance of a Costas loop in the presence of single and multiple in-band pulsed RFI signals and receiver additive noise. It is shown that the loop's tracking performance is very sensitive to the pulse durations of the RFI signals, as well as their repetition rates and peak powers relative to those of the desired signal. The presence of in-band RFI can affect the loop's tracking performance in basically three ways. 1) The loop tracks the composite phase of the RFI instead of the phase of the desired signal when the effective RFI power is greater than that of the signal. 2) When the effective RFI power is not sufficiently large to capture the loop, there still will exist static phase error biases which cause the loop to lock at a phase between that of the desired signal and the composite RFI. 3) There is an increase in the rms phase jitter over the nominal design. These latter two effects degrade the bit error probability performance of the receiver. More significantly, if the nominal loop bandwidth is not designed properly to account for the increase in jitter phenomenon, frequency cycle slipping may result.
We introduce an unbinned method for extracting the CKM angle $γ$ from the decay chain $B^\pm \to (D \to K_S π^+ π^-) K^\pm$ using normalizing flows (NFs). The NFs, trained on $D$ decay data, learn a faithful continuous representation of the amplitude and strong phase variation over the $D\to K_Sπ^+π^-$ Dalitz plot whose fidelity improves with increased data sample sizes. With this input, the $B$ decay data can be used to extract the parameters $r_B$, $δ_B$, and $γ$. We test the method on Monte Carlo generated data, where it successfully recovers the injected value of $γ$ within uncertainties. The present implementation propagates statistical uncertainties from finite training data via an ensemble of independently trained flows, and does not attempt to capture the effects of systematic experimental errors. We explore two versions of the method that differ in how the trigonometric constraint on phase variation is encoded, and comment on the possible extension to Bayesian NFs, which would provide direct uncertainty estimates on the learned densities without requiring ensemble training.
Quantum algorithms have been proposed to accelerate the simulation of the chaotic dynamical systems that are ubiquitous in the physics of plasmas. Quantum computers without error correction might even use noise to their advantage to calculate the Lyapunov exponent by measuring the Loschmidt echo fidelity decay rate. For the first time, digital Hamiltonian simulations of the quantum sawtooth map, performed on the IBM-Q quantum hardware platform, show that the fidelity decay rate of a digital quantum simulation increases during the transition from dynamical localization to chaotic diffusion in the map. The observed error per CNOT gate increases by $1.5{\times }$ as the dynamics varies from localized to diffusive, while only changing the phases of virtual RZ gates and keeping the overall gate count constant. A gate-based Lindblad noise model that captures the effective change in relaxation and dephasing errors during gate operation qualitatively explains the effect of dynamics on fidelity as being due to the localization and entanglement of the states created. Specifically, highly delocalized states that are entangled with random phases show an increased sensitivity to dephasing and, on average, a similar sensitivity to relaxation as localized states. In contrast, delocalized unentangled states show an increased sensitivity to dephasing but a lower sensitivity to relaxation. This gate-based Lindblad model is shown to be a useful benchmarking tool by estimating the effective Lindblad coherence times during CNOT gates and finding a consistent $2\unicode{x2013}3{\times }$ shorter $T_2$ time than reported for idle qubits. Thus, the interplay of the dynamics of a simulation with the noise processes that are active can strongly influence the overall fidelity decay rate.
Our purpose in examining this test problem is to measure directly the effect of mesh refinement and the resulting mesh interfaces on a known wave that is sensitive to phase errors, while concurrently being able to visually display a meaningful picture of the effects of the refinement induced error on the solution. The refined mesh must be able to adequately capture the diffraction behavior, so that the plane wave front bends as it passes through the slit. Given that the coarse and refined meshes are sufficiently accurate, the phase errors introduced during the problem solution will be a function of th sound speed on the two grids plus the coarse/refined grid interaction errors.
While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in BaTiO 3 , PbTiO 3 , and KNbO 3 , quantitative estimates of the transition temperatures (T C ) have errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of BaTiO 3 , PbTiO 3 , and KNbO 3 obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of T C , which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in T C originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of BaTiO 3 , PbTiO 3 , and KNbO 3 . We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.
To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale physics-guided data-driven approach, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. By defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.
To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale framework was proposed in this paper by applying a physics-guided data-driven approach. Instrumental to this framework, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. In this work, by defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.
Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.
Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.
Previous studies of the reaction ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ have mainly focused on providing the best central value and error bar for the S factor at solar energies. Experimental measurements of this capture reaction at higher energies, the ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering phase shifts, as well as properties of ${}^{7}\mathrm{Be}$ and its excited state, have been used to constrain the theoretical models employed for this purpose. Here we show that much more information than was previously appreciated can be extracted from angle-integrated capture data alone. We use the next-to-leading-order (NLO) amplitude in an effective field theory (EFT) for ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}\to {}^{7}\mathrm{Be}+\gamma $ to perform the extrapolation. At this order the EFT describes the capture process using an s-wave scattering length and effective range, the asymptotic properties of ${}^{7}\mathrm{Be}$ and its excited state, and short-distance contributions to the E1 capture amplitude. We extract the multi-dimensional posterior of all these parameters via a Bayesian analysis that uses capture data below 2 MeV. We find that properties of the ${}^{7}\mathrm{Be}$ ground and excited states are well constrained. The total S factor $S(0)\,={0.577}_{-0.016}^{+0.015}$ keV b, while the branching ratio for excited- to ground-state capture at zero energy, ${Br}(0)={0.406}_{-0.011}^{+0.013}$, both at 68% degree of belief. This S(0) is broadly consistent with other recent evaluations, and agrees with the previously recommended value $S(0)=0.56\pm 0.03\,\,\mathrm{keV}$ b, but has a smaller error bar. We also find significant constraints on ${}^{3}\mathrm{He}$–${}^{4}\mathrm{He}$ scattering parameters, and we obtain constraints on the angular distribution of capture gamma rays, which is important for interpreting experiments. The path forward for this reaction seems to lie with better measurements of the scattering phase shifts and S(E)'s angular dependence away from zero energy, together with better understanding of the asymptotic normalization coefficients of the ${}^{7}$Be bound states' wave functions. Lastly, data on these could further reduce the uncertainty on S(0).
We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.
Quantification of nuclear power plant safety risk requires a systematic and yet practical approach to identification of accident scenarios, assessment of their likelihood and consequences. Instrumental to this goal is risk-informed safety margin characterization (RISMC) framework, whose realization requires computationally robust and affordable methods for sufficiently accurate simulation of complex multi-dimensional physical phenomena, such as turbulent and multi-phase flow. The CFD-like correlation-based codes with 3D simulation capability (e.g., GOTHIC) ensure computational efficiency using coarse mesh size and the sub-grid phenomena in the boundary layer that can be captured by adequate constitutive correlations. However, the error sources and user effects on the selection of mesh size and models lead to unpredictable simulation error, while rich High-Fidelity (HF) data from experiments and numerical simulation using validated code or DNS are not fully explored. It would be useful to have a “smart” data-driven multi-scale framework in which the low-resolution models can be “taught” to emulate high-resolution models. The objective of this work is to develop and evaluate a physical-based data-driven mesh-model optimization approach (Optimized Mesh/Model Information System, OMIS) to estimate the simulation error and give advice on the optimized selection of coarse mesh size and Low-Fidelity (LF) models for System Thermal Hydraulic (STH) simulation to achieve accuracy comparable to that of HF models. This approach takes advantages of computational efficiency of coarse-mesh simulation and application of Machine Learning (ML) algorithms.
In this paper, a nonlinear analytical model based on the Magnetic Equivalent Circuit (MEC) method is developed for a double-sided E-Core Transverse Flux Machine (TFM). The proposed TFM has a cylindrical rotor, sandwiched between E-core stators on both sides. Ferrite magnets are used in the rotor with flux concentrating design to attain high airgap flux density, better magnet utilization, and higher torque density. The MEC model was developed using a series-parallel combination of flux tubes to estimate the reluctance network for different parts of the machine including air gaps, permanent magnets, and the stator and rotor ferromagnetic materials, in a two-dimensional (2-D) frame. An iterative Gauss-Siedel method is integrated with the MEC model to capture the effects of magnetic saturation. A single phase, 1 kW, 400 rpm E-Core TFM is analytically modeled and its results for flux linkage, no-load EMF, and generated torque, are verified with Finite Element Analysis (FEA). The analytical model significantly reduces the computation time while estimating results with less than 10 percent error.
Abstract Reactivity controlled compression ignition (RCCI) combustion has previously been proposed as a method to achieve high fuel conversion efficiency and reduce engine emissions. A single-fuel RCCI combustion strategy can have decreased fuel system complexity by using a reformate fuel for port fuel injection and the parent fuel (diesel) for direct injection. This paper presents a one-dimensional computational model of a compression ignition engine with single-fuel RCCI. A Wiebe function is used to predict the combustion process by representing the mass fraction burned (MFB) on a crank angle resolved basis. One single-Wiebe function (SWF) and two double-Wiebe functions(DWFs) were fitted to experimentally derive MFB data using the least-square method. The fitted results were compared with MFBs calculated from experimental data to verify the accuracy. The SWF did not fully capture the MFB curve with high fidelity while the detailed DWF captured the MFB curve within a root mean square error of 1.4%. The reduced double-Wiebe function (RDWF) also resulted in a predicted combustion profile with similar accuracy. Hence, the RDWF was used in a GT-power thermodynamic study to understand the effects of the low-temperature heat release (LTHR) fraction and combustion phasing on combustion characteristics. At optimum phasing of 5–10 crank angle degree after the top dead center, increasing the LTHR fraction from 20% to 60% resulted in the fuel conversion efficiency increasing from 39.5% to 41.1%, thus suggesting that the reformate fuel-based RCCI strategy is viable to unlock improved combustion performance.
Thermal hydraulic instability can challenge the control and the safety of nuclear reactors. This experimental research captures and investigates the instability in a low-pressure (1–10 atmospheres) natural circulation loop with an adiabatic chimney installed above the heated section. Direct transient local measurement of two-phase flow is performed at multiple axial locations along the flow channel with thermocouples and conductivity probes traversed by customized high-precision mechanisms. Based on the periodicity of oscillations, a post-processing method is proposed to align the data captured non-simultaneously to reconstruct the instability behavior in one representative period. The averaging operation over multiple oscillation cycles is performed to reduce the random errors. Cyclic phenomena are clearly demonstrated by the post-processed data, and rapid void fraction change induced by the flashing is observed to be significant in the driving mechanism for low pressure oscillations. Parametric effects of inlet subcooling, heat flux, inlet flow restriction and system pressure are studied within the experiment range, and qualitative results are explained and compared with existing literature. The ratio between the oscillation period and the travelling time of the fluid particle through the test section is compared with the theoretical value for the density wave oscillation. The new dataset contains directly measured transient multi-dimensional two-phase data along the flow channel for natural circulation under density wave oscillations. The generated dataset is valuable for the validation of system analysis codes and CFD codes in the simulation of natural circulation phenomena and dynamic two-phase flow.
The OpenSE Cookbook is an open-sourced collection of patterns, procedures, and best practices targeted for systems engineers who seek guidance on applying model-based and executable systems engineering (MBSE) using SysML. Its content has emerged from the system level modeling effort on the European Framework Program 6 (FP6) and the Thirty Meter Telescope (TMT). The TMT MBSE approach applied the Executable Systems Engineering Method (ESEM) and the open-source Engineering Environment (OpenMBEE) to specify, analyze, and verify requirements of TMT’s Alignment and Phasing System (APS) and the Narrow Field Infrared Adaptive Optics System (NFIRAOS). In these applications, implicit dependencies are made explicit in a formal model through the use of ESEM, OpenMBEE, and SysML modeling constructs. The value proposition for applying this MBSE approach was to establish precise requirements and fine-grained traceability to system designs, and to verify key requirements beginning early in development. The integration of ESEM and the OpenMBEE tooling infrastructure (providing linked-data and web-operability) is a significant added value for the MBSE approach. The APS is responsible for the overall pre-adaptive optics wavefront quality, using starlight to measure wavefront errors and align the TMT optics. In the formally integrated and executable SysML model, simulations are performed to analyze the impact of changed requirements and verify specified constraints for various operational scenarios. The APS team used several modeling patterns to capture information such as the requirements, the operational scenarios, involved subsystems and their interaction points, the estimated or required time durations, and the mass and power consumption. Adaptive optics systems are designed to sense real-time atmospheric turbulence and correct the telescope’s optical beam to remove its effect. The system model for the adaptive optics operational modes was developed to capture sequence behaviors and operational scenarios to run Monte-Carlo simulations for verifying acquisition time, observing efficiency, and operational behavior requirements. The model is particularly useful for investigating the effect of parallelization, identifying interface issues, and re-ordering sequence acquisition tasks. A former version of the Cookbook (which is now updated to MBSE challenges, goals, and lessons learned) included modeling guidelines and conventions for all system aspects, hierarchy levels, and views, which were developed during for the Active Phasing Experiment (APE), an opto-mechatronical system technology demonstrator for the Extremely Large Telescope (ELT). The Cookbook utilizes the above mentioned system models as real-world case-studies to demonstrate and document the applications of the recipes, providing also instructional examples and addressing the available tooling support. The Cookbook is accompanied by a number of SysML models and aodel libraries which facilitate model authoring and maintenance. The Cookbook covers the different aspects of Systems Engineering such as management of Requirements, Design (behavior and structure), Interfaces, Interdisciplinary Integration, Analysis, Trade Studies, and Technical Resources. This paper presents the background, motivation, architecture, and highlights some key content of the Cookbook. For example, interface management, error budget management, requirements verification, Monte Carlo driven analysis, and timing analysis of operational scenarios. The paper discusses how the capabilities of OpenMBEE contributed significantly to the adoption of executable systems engineering.
In this paper, a highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich–von Neumann–Döring (ZND) detonation wave, and Taylor–Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m / s , which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott–Stewart–Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting strategy, in conjunction with a nonlinear optimizer, a new set of reaction rate parameters improves the correlation of the model to experimental results. In conclusion, this new model is tested against two dimensional slabs as a validation test.