Approximate Model Research Articles

Second-order water wave properties over Roseau’s three-parameter bottom topography

Summary In his book Asymptotic Wave Theory (North-Holland 1976), Roseau develops the only known exact solution for linear wave propagation over a shoal. Remarkably, almost half a century later, the only properties of that solution which appear to have been used to validate more wide-ranging models are the limiting values of wave height in the far field. The primary aim of this work is to remedy this situation by providing a robust computational setting where the solution may be fully evaluated randomly both on the surface and the interior, speedily and to a high degree of accuracy. Such ‘benchmark’ solutions will facilitate a much more rigorous approach to validation of more general alternative approximation models. One such has some of its numerical results here examined and subsequently largely vindicated by the present calculations. Computation of the absolutely convergent solution integrals is supported by cubic spline approximation of an integrand component which satisfies a certain difference equation and the work is extended to cover bottom profiles with overhang including the extreme case where the overhang degenerates to a semi-infinite flat plate. The further development of solutions at second-order reveals details of mean Eulerian current and the attendant Stokes drift enabling mass transport computations; all illustrated through the entire depth with a range of contouring and arrows plots. The force field that drives a second harmonic component is calculated and shows excellent agreement with its equivalent in the more general modal expansion model applied to a non-identical but somewhat similar profile. This further validates the modelling approach and application described in that work.

Generative Modeling of Semiconductor Devices for Statistical Circuit Simulation

Statistical simulation is a necessary step in integrated circuit design since it provides a realistic picture of the circuit’s behavior in the presence of manufacturing process variations. When some of the circuit components lack an accurate analytical model, as is often the case for emerging semiconductor devices or ones working at cryogenic temperatures, an approximation model is necessary. Such models are usually based on a lookup table or artificial neural network individually fitted to measurement data. If the number of devices available for measurement is limited, so is the number of approximation model instances, which renders impossible a reliable statistical circuit simulation. Approximation models using the device’s physical parameters as inputs have been reported in the literature but are only useful if the end user knows the statistical distributions of those parameters, which is not always the case. The solution proposed in this work uses a type of artificial neural network called the variational autoencoder that, when exposed to a small sample of I-V curves under process variations, captures their essential features and subsequently generates an arbitrary number of similarly disturbed curves. No knowledge of the underlying physical sources of these variations is required. The proposed generative model trained on as few as 20 instances of a MOSFET is shown to precisely reproduce the period and power consumption distributions of a ring oscillator built with these MOSFETs.

Spatiotemporal Changes in the Slavery-Inequality Relationship: The Diffusion of the Legacy of Slavery.

Despite the persistence of relationships between historical racist violence and contemporary Black-White inequality, research indicates, in broad strokes, that the slavery-inequality relationship in the United States has changed over time. Identifying the timing of such change across states can offer insights into the underlying processes that generate Black-White inequality. In this study, we use integrated nested Laplace approximation models to simultaneously account for spatial and temporal features of panel data for Southern counties during the period spanning 1900 to 2018, in combination with data on the concentration of enslaved people from the 1860 census. Results provide the first evidence on the timing of changes in the slavery-economic inequality relationship and how changes differ across states. We find a region-wide decline in the magnitude of the slavery-inequality relationship by 1930, with declines traversing the South in a northeasterly-to-southwesterly pattern over the study period. Different paces in declines in the relationship across states suggest the expansion of institutionalized racism first in places with the longest-standing overt systems of slavery. Results provide guidance for further identifying intervening mechanisms-most centrally, the maturity of racial hierarchies and the associated diffusion of racial oppression across institutions, and how they affect the legacy of slavery in the United States.

Application of Sampling Methods for Constrained Space in Hull Form Optimization

Use of approximation models instead of direct application of CFD tools plays a crucial role in hull form optimization to enhance efficiency. The selection of sample points directly impacts the accuracy and cost of approximation models, and the effectiveness of hull form optimization. This paper presents a sampling method based on constrained space. The distribution pattern of the constrained space is initially analyzed, and its boundary is subsequently extracted by the Support Vector Machine (SVM), providing guidance for the subsequent sample selection. To ensure effective sampling within the constrained space, the maximum minimum distance criterion is employed. The proposed methodology is validated via a case study involving a 13,000DWT inland twin-screw bulk carrier. The Kriging approximation model is constructed to optimize the hull form while adhering to specific constraint conditions, thereby demonstrating the feasibility and efficacy of the proposed approach.

Hierarchical multinomial processing tree models for meta-analysis of diagnostic accuracy studies

Abstract Meta-analysis represents a widely accepted approach for evaluating the accuracy of diagnostic tools in clinical and psychological investigations. This article investigates the applicability of multinomial tree models recently suggested in the literature under a fixed-effects formulation for assessing the accuracy of binary classification tools, where the study specific disease prevalences are taken into account. The model proposed in this article extends previous results to a hierarchical structure accounting for the variability between the studies included in the meta-analysis. Interestingly, by exploiting the parameter separability of the complete likelihood function, the resulting hierarchical multinomial tree model is shown to coincide, in its interest parameter component, with the well-known bivariate random-effects model under an exact within-study distribution for the number of true positives and true negatives subjects. The proposal is in line with a latent-trait approach, where inference follows a frequentist point of view. The applicability of the proposed model and its performance with respect to its fixed-effects counterpart and to the approximate bivariate random-effects model based on normality assumptions commonly used in the literature is evaluated in a series of simulation studies. Methods are applied to a real meta-analysis about the accuracy of the confusion assessment method as delirium screening tool.

Research on Noise Reduction of Water Hydraulic Throttle Valve Based on RBF Neural Network and Multi-Island Genetic Algorithm

Excessive pressure drop within the internal flow channel of the water hydraulic throttle valve will generate severe noise. In order to reduce the noise of the throttle valve, in this paper, the model of the throttle valve was established, and the flow characteristics and acoustic characteristics of the valve were simulated. The simulation results showed that the parameters of the throat structure, such as the half angle, throat inlet angle and throat length, have a significant effect on the noise of the valve. Then, the three main structural parameters were used as optimization variables, and radial basis function (RBF) neural networks and multi-island genetic algorithms (MIGA) were used to reduce the noise of the valve. The approximate model of the relationship between the structural parameters of the valve and noise was established by RBF neural networks, and MIGA was used to optimize the approximate model. Finally, the optimal valve model was established based on the obtained optimal parameters, and its noise was analyzed through simulation and experiment. The research results indicated that the optimization method, which combines RBF Neural Network and MIGA, can effectively reduce the noise of hydraulic throttle valves.

Nonlinear dynamics of cantilevered hyperelastic pipes conveying fluid: Comparative study of linearelasticity and hyperelasticity

In light of the softness and lightweight characteristics, hyperelastic pipes are prone to large deformation. Intending to provide accurate predictions of their large deformation vibrations, the present study aims to establish a rotation-angle-based geometrically exact model for cantilevered pipes conveying fluid composed of hyperelastic materials. Additionally, given the presence of nonlinear geometric relations, it is imperative to assess the role of hyperelasticity in the nonlinear dynamics of fluid-conveying pipes in comparison to linearelastic pipes. The modeling process integrates the Mooney-Rivlin hyperelastic model with a geometrically exact description of the pipe. And the final governing equation is developed through energy analysis and the extended Hamilton's principle. Subsequently, Galerkin's method and the finite difference method are employed to address the governing equation. Following the verification of the proposed model, parametric studies are conducted in the form of planar oscillation diagrams, time histories, phase trajectories, and bifurcation diagrams. The findings of the present study highlight three critical insights. Firstly, the hyperelastic model introduces numerous complicated nonlinear terms as function of the rotation angle with high-order nonlinearity. In the present study, at least fifth-order nonlinear terms should be preserved to adequately predict large deformation vibrations. Secondly, the Mooney-Rivlin hyperelastic model imparts a hardening effect in comparison to the linearelastic model, significantly reducing vibration amplitudes. Lastly, the third-order approximate model is demonstrated to be inadequate in predicting large deformation vibrations at high flow velocity, as it contains the approximation on not only the geometric description but the hyperelasticity-related terms.

Nuclear structure properties and weak interaction rates of even–even Fe isotopes

Nuclear structure properties and weak interaction rates of neutron-rich even–even iron (Fe) isotopes (A = 50 – 70) are investigated using the Interacting Boson Model-1 (IBM-1) and the proton–neutron Quasiparticle Random Phase Approximation (pn-QRPA) model. The IBM-1 is used for the calculation of energy levels and the B(E2) values of neutron-rich Fe isotopes. Later their geometry was predicted within the potential energy formalism of the IBM-1 model. Weak interaction rates on neutron-rich nuclei are needed for the modeling and simulation of presupernova evolution of massive stars. In the current study, we investigate the possible effect of nuclear deformation on stellar rates of even–even Fe isotopes. The pn-QRPA model is applied to calculate the weak interaction rates of selected Fe isotopes using three different values of deformation parameter. It is noted that, in general, bigger deformation values led to smaller total strength and larger centroid values of the resulting Gamow–Teller distributions. This later translated to smaller computed weak interaction rates. The current finding warrants further investigation before it may be generalized. The reported stellar rates are up to 4 orders of magnitude smaller than previous calculations and may bear astrophysical significance.

Global fit of electron and neutrino elastic scattering data to determine the strange quark contribution to the vector and axial form factors of the nucleon

We present a global fit of neutral-current elastic (NCE) neutrino-scattering data and parity-violating electron-scattering (PVES) data with the goal of determining the strange quark contribution to the vector and axial form factors of the proton. Previous fits of this form included data from a variety of PVES experiments (PVA4, HAPPEx, G0, SAMPLE) and the NCE neutrino and anti-neutrino data from BNL E734. These fits did not constrain the strangeness contribution to the axial form factor GAs(Q2) at low Q2 very well because there was no NCE data for Q2<0.45 GeV2. Our new fit includes for the first time MiniBooNE NCE data from both neutrino and antineutrino scattering; this experiment used a hydrocarbon target and so a model of the neutrino interaction with the carbon nucleus was required. Three different nuclear models have been employed: a relativistic Fermi gas model, the superscaling approximation model, and a spectral function model. We find a tremendous improvement in the constraint of GAs(Q2) at low Q2 compared to previous work, although more data is needed from NCE measurements that focus on exclusive single-proton final states, for example from MicroBooNE. Published by the American Physical Society 2024

Using frequency domain analysis to elucidate travel time reliability along congested freeway corridors

Travel time reliability (TTR) is an essential measure of service for traffic performance management, especially for congested freeway corridors. This paper proposes a systematic analytical framework to analyze the predictable and unpredictable variations in route TTR in corridor networks. More specifically, the predictable variation in route TTR is estimated with a deterministic fluid-based polynomial arrival queue (PAQ) model, while the unpredictable variation in route TTR is analyzed through the residual induced by the PAQ estimation model. Based on the output of the PAQ estimation model, a frequency-domain approach is proposed to decompose the observed time-domain travel time into underlying unobserved factors in different temporal resolutions. With the discrete-time Fourier transform method and the Butterworth low-pass filtering technique, it is capable of analytically uncovering different temporal scales of predictable variations in TTR, including the trend of day-to-day variations, the dynamics of within-day variations, as well as the stochasticity of within-period variations. Connecting with the unpredictable variations represented by the residual due to the PAQ approximation model, we can comprehensively elucidate TTR for congested freeway corridors. Case studies are conducted to show the effectiveness of the proposed frequency-domain approach in elucidating and measuring different contributing elements in TTR, and more specifically, the four components, i.e., the trend of day-to-day variations, the dynamics of within-day variations, the stochasticity of within-period variations, and the residual induced by the PAQ estimation model, account for 64.9 %, 20.2 %, 1.2 %, 13.7 % of variations in the route travel time, respectively, based on a case study with the PeMS dataset.

Forward Starting Option Pricing under Double Fractional Stochastic Volatilities and Jumps

This paper aims to provide an effective method for pricing forward starting options under the double fractional stochastic volatilities mixed-exponential jump-diffusion model. The value of a forward starting option is expressed in terms of the expectation of the forward characteristic function of log return. To obtain the forward characteristic function, we approximate the pricing model with a semimartingale by introducing two small perturbed parameters. Then, we rewrite the forward characteristic function as a conditional expectation of the proportion characteristic function which is expressed in terms of the solution to a classic PDE. With the affine structure of the approximate model, we obtain the solution to the PDE. Based on the derived forward characteristic function and the Fourier transform technique, we develop a pricing algorithm for forward starting options. For comparison, we also develop a simulation scheme for evaluating forward starting options. The numerical results demonstrate that the proposed pricing algorithm is effective. Exhaustive comparative experiments on eight models show that the effects of fractional Brownian motion, mixed-exponential jump, and the second volatility component on forward starting option prices are significant, and especially, the second fractional volatility is necessary to price accurately forward starting options under the framework of fractional Brownian motion.

Simplified Strategy for Trajectory Tracking Application of a Passive Suspension Rover-Type Mobile Robot

In the present work, based on an approximate modelling of a rover-type robot and a proportional control law, a simplified trajectory tracking strategy for a passive suspension rover-type mobile robot was developed. This strategy achieves trajectory tracking and the autonomous displacement of a rover, of which its configuration involves complex kinematics and dynamics. All these lineaments reduce the complexity of the analysis, the number of electronic components to implement, the computational requirements and the energy consumption. The robotic system used is based on the Shrimp rover, which is a robot with a passive suspension that is capable of carrying out displacements over rough terrain. The tests were performed using numerical simulations with different desired trajectories, and also using experimental tests using a passive suspension rover-type mobile robot.

Variability propagation in manufacturing systems: the impact of the processing time distribution

ABSTRACT In manufacturing and service systems, the negative effects of variability propagation are usually addressed through approximation models and other tools, such as simulation and optimization algorithms. This paper investigates the conditions in which these approaches are ineffective, and considering only the mean and variance of the processing time distribution is misleading. A scenario analysis deepens the impacts of considering the entire processing time distribution (beyond its mean and variance) on the inter-departure times in balanced and unpaced lines modeled through Discrete Event Simulation. The results correlate the impacts on variability propagation of approximating the processing time distribution with system characteristics such as utilization levels, line sizes, and inter-arrival and processing time variability. Production planning approaches can benefit from these results to reduce variability propagation, particularly in flexible and reconfigurable manufacturing systems, largely adopted in Industry 4.0, that can highly influence processing time distributions by varying product mix and line configuration.

A multidimensional AI-trained correction to the 1D approximate model for Airborne TDEM sensing

The computational resources required to solve the full 3D inversion of time-domain electromagnetic data are immense. To overcome the time-consuming 3D simulations, we construct a surrogate model, more precisely, a data-driven statistical model to replace the 3D simulations. It is trained on 3D data and predicts the approximate output much faster. We construct a surrogate model that predicts the discrepancy between a 1D subsurface model and a deviation of the 1D assumption. The latter response is fastly computable with a semi-analytical 1D forward model. We exemplify the approach on a two-layered case. The results are encouraging even with few training samples. Given the computational cost related to the 3D simulations, there are limitations in the number of training samples that can be generated. In addition, certain applications require a wide range of parameters to be sampled, such as the electrical conductivity parameters in a saltwater intrusion case. The challenge of this work is achieving the best possible accuracy with only a few thousand samples. We propose to view the performance in terms of learning gain, representing the gain from the surrogate model whilst still acknowledging a residual discrepancy. Our works open new avenues for effectively simulating 3D TDEM data.

Electric dipole polarizability of magic nuclei

The correlations between the electric dipole polarizability and neutron skin thickness are studied by the magic nuclei 40,48Ca, 68,78Ni, 132Sn, and 208Pb. The strength distribution of the E1 transitions is calculated within the random phase approximation model based on the Skyrme nuclear energy density functional. A comparison with the experimental data has allowed us to constrain the value of the nuclear symmetry energy J = 30–37 MeV.

Hull form optimization research based on multi‐precision back‐propagation neural network approximation model

AbstractIn order to shorten the optimization cycle of ship design optimization and solve the time‐consuming problem of computational fluid dynamics (CFD) numerical calculation, this paper proposes a multi‐precision back‐propagation neural network (MP‐BP) approximation technology. Fewer high‐precision ship samples and more low‐precision ship samples were used to construct an approximate model, back‐propagation (BP) neural network was used to train multi‐precision samples. So that the approximate model is as close as possible to the real model, and achieving the effect of high‐precision approximation model. Subsequently, numerical verification and typical hull form verification are given. Based on CFD and Rankine theory, the multi‐objective design optimization framework for ship comprehensive navigation performance is constructed. The multi‐objective approximation model of KCS ship is constructed by MP‐BP approximation technology, and optimized by particle swarm optimization (PSO) algorithm. The results show that the multi‐objective optimization design framework using the MP‐BP approximation model can capture the global optimal solution and improve the efficiency of the entire hull form design optimization. It can provide a certain degree of technical support for green ship and low‐carbon shipping.

Electric response of a composite of topological insulator nanoparticles

The electric response of a composite of topological insulator (TI) nanoparticles is studied using approximate effective medium models focusing on the topological magneto-electric (TME) response of the system. Both the Maxwell-Garnett and the Bruggeman models are generalized to incorporate the axion coupling parameter. Such a response is studied in the electrostatic limit via a capacitor with the composite as the dielectric medium. Manifestation of the TME is highlighted to provide an alternative probing method of such an effect via electrostatics experiments.

Re-examination of effects of pairing gaps on charge-changing transitions

We re-examine the effects of pairing gaps on charge-changing transitions and the associated β-decay half-lives. Calculations are performed using the proton-neutron quasiparticle random phase approximation (pn-QRPA) model for 250 nuclei possessing astrophysical significance. Pairing gaps between like nucleons are key model parameters in the pn-QRPA approach. Three different values of empirically computed pairing gaps were used as input parameters in our nuclear model. Changing the pairing gap values significantly altered the Gamow-Teller distributions including the total strength and centroid values. The β-decay half-lives also changed substantially. The half-lives computed via the three-term pairing formula, based on separation energies of nucleons, were in best agreement with the measured data.

Energy and Z dependence of low velocity Nq+ ion induced M X-ray relative intensities for some heavy elements

The intensity ratios, IMk/IMn (exp)(k = ξ, γ, m1; n = total, αβ), for some heavy elements, 70Yb, 79Au, 81Tl, 82Pb and 83Bi induced by 1000 keV−1750 keV Nq+ (q = 4, 5) ions have been measured in order to investigate their dependence on the projectile energy and atomic number of the respective target elements. The measured intensity ratios have been compared with two sets of values calculated using the Mj (j = 1–5) sub-shell ionization cross sections based on the ECPSSR-UA model, the X-ray emission rates based on the Dirac-Hartree Slater (DHS) model, two sets of the fluorescence and Coster-Kronig yields based on the DHS model and those evaluated by McGuire employing non-relativistic Hartree-Slater model. Significant differences have been observed between the present measured IMk/IMαβ (exp) (k = ξ, γ, m1) intensity ratios and those calculated using independent particle approximation (IPA) models based single atomic vacancy state physical parameters.

Effect of parameter optimization on the flow characteristics of venturi-self-excited oscillation mixer based on response surface model and multi-island genetic algorithm

Effect of parameter optimization on the flow characteristics of venturi-self-excited oscillation mixer based on response surface model and multi-island genetic algorithm