Approximate Model Research Articles

Bayesian optimization for state engineering of quantum gases

Abstract State engineering of quantum objects is a central requirement for precision sensing and quantum computing implementations. When the quantum dynamics can be described by analytical solutions or simple approximation models, optimal state preparation protocols have been theoretically proposed and experimentally realized. For more complex systems such as interacting quantum gases, simplifying assumptions do not apply anymore and the optimization techniques become computationally impractical. Here, we propose Bayesian optimization based on multi-output Gaussian processes to learn the physical properties of a Bose-Einstein condensate within few simulations only. We evaluate its performance on an optimization study case of diabatically transporting the quantum gas while keeping it in its ground state. Within a few hundred executions, we reach a competitive performance to other protocols. While restricting this benchmark to the well known Thomas-Fermi approximation for straightforward comparisons, we expect a similar performance when employing more complex theoretical models, which would be computationally more challenging, rendering standard optimal control theory protocols impractical. This paves the way for efficient state engineering of complex quantum systems including mixtures of interacting gases or cold molecules.

An improved circuit model for the estimation of the electromagnetic energy coupling throughout aperture into metallic enclosure

The development and exploration of approximate phenomenological models used to calculate the electromagnetic energy coupling throughout apertures into metallic enclosures is presented in this paper. An analytical approach has been established for the calculation of the electric and magnetic shielding effectiveness (SE, SM) a rectangular metallic enclosure with an aperture and conductor in it by means of Robinson's model. With the existence of inductive and capacitive obstacles, the modal technique is to complete the first one to estimate SE and SM exactly taking into consideration the maximum of propagating modes. The results of the SE and SM obtained by the analytical model are validated by the software CST/EMC and the Finite-Difference Time Domain method (FDTD). Very similar results are obtained between these methods.

Transient Thermal Analysis of a Kiln Using Different Numerical Approaches by Means of CFD

A transient study for the prediction of the temperature of hot gases inside a kiln loaded with bricks, using Computational Fluid Dynamics (CFD), is presented in this work. The prediction of transient thermal performance is obtained through four different approaches: the Properties Fitted to Temperature Polynomials (PFTP) model, the density changes according to the Boussinesq Approximation (BA) model with a Constant Thermal Expansion Coefficient (CTEC), the BA model with a Variable Thermal Expansion Coefficient (VTEC) and the density changes according to the Ideal Gas Law (IGL) model. Furthermore, the effects of a layer of ceramic fiber as insulation are investigated. The numerical results of the transient temperature of the hot gases inside the kiln were validated with experimental data. The mean relative error of the transient temperature was 5.0%, 32.6%, 26.4% and 4.4% for the PFTP model, BA model with a CTEC, BA model with a VTEC and IGL model, respectively. It was concluded that IGL model is the best approach to predict the transient temperature of the kiln. Finally, an increase in the temperature of the hot gases of 12.7% was obtained by applying the IGL model and using a layer of 0.07 m of ceramic fiber as insulation. The results of this work could be helpful to improve the design and performance of kilns in further works.

Investigation and Optimization of Wave Suppression Baffles in Automobile Integrated Water Tanks

The risk of liquid agitation in pump-driven tanks within integrated tanks has significantly escalated due to the growing demands for tank integration in new-energy vehicles. In order to solve the problem of liquid sloshing in integrated tanks, this paper presents the design of a baffle structure aimed at reducing waves in integrated water tanks. The numerical simulation method of combining the level-set function with the volume of fluid (CLSVOF) has been employed, significantly enhancing the accuracy of numerical calculations related to a two-phase flow field inside an integrated tank. A comparison was made by analyzing different factors, notably baffle length (L), baffle depth (H), and baffle angle (θ), to investigate their influences in suppressing liquid agitation within the integrated water tank. Numerical computations were conducted utilizing design points acquired by the Latin hypercube sampling technique. The Kriging approximation modelling method was employed to hold down computing time. The Pareto solution was obtained by means of the non-dominated sorting genetic algorithm II, while the optimal solution set was evaluated and ranked using the multi-criteria decision-making algorithm (MCDM). The results show that increasing the baffle depth within a certain range can effectively suppress the wave height in the tank. When the baffle depth is increased to a certain value, the effect on wave-height suppression in the water tank is limited. When the baffle length and angle of the baffle exceed a certain value, it will also have the effect of suppressing the wave height in the tank. After comparing various factors of the baffle, it was ultimately found that the wave suppression effect is maximal when the length of the baffle is 13 millimeters, the depth of the baffle is 49 millimeters, and the angle of the baffle is -20 degrees. The main contribution of this study is the proposed wave-suppressing baffle structure, which provides new insights for the future structural design of integrated water tanks.

Ultraviolet Radiation Fields in Star-forming Disk Galaxies: Numerical Simulations with TIGRESS-NCR

With numerical simulations that employ adaptive ray-tracing (ART) for radiative transfer at the same time as evolving gas magnetohydrodynamics, thermodynamics, and photochemistry, it is possible to obtain a high-resolution view of ultraviolet (UV) fields and their effects in realistic models of the multiphase interstellar medium. Here, we analyze results from TIGRESS-NCR simulations, which follow both far-UV (FUV) wavelengths, important for photoelectric heating and polycyclic aromatic hydrocarbon excitation, and the Lyman continuum (LyC), which photoionizes hydrogen. Considering two models, representing solar neighborhood and inner-galaxy conditions, we characterize the spatial distribution and time variation of UV radiation fields, and quantify their correlations with gas. We compare four approximate models for the FUV to simulated values to evaluate alternatives when full ART is infeasible. By convolving FUV radiation with density, we produce mock maps of dust emission. We introduce a method to calibrate mid-IR observations, for example from JWST, to obtain high-resolution gas surface density maps. We then consider the LyC radiation field, finding most of the gas exposed to this radiation to be in ionization–recombination equilibrium and to have a low neutral fraction. Additionally, we characterize the ionization parameter as a function of the environment. Using a simplified model of the LyC radiation field, we produce synthetic maps of emission measure (EM). We show that the simplified model can be used to extract an estimate of the neutral fraction of the photoionized gas and mean free path of ionizing radiation from observed EM maps in galaxies.

Modeling and Performance Evaluation of a Cellular Network with OMA and NOMA Users with Batch Arrivals by Means of an M[X]/M/S/0 Model

Nowadays, efficient spectrum usage is one of the most important design principles to take into account in wireless communications due to the exponential growth of mobile devices. In that sense, solutions such as Non-Orthogonal Multiple Access (NOMA) and cognitive radio (CR) have been proposed. In essence, NOMA allows some interference level by using non-orthogonal resource allocation with a tolerable increase in receiver complexity employing successive interference cancellation (SIC). In this work, a novel mathematical model of teletraffic for users performing accessment, simultaneously, by means of Orthogonal Multiple Access (OMA) and NOMA, is developed using a Markovian process that considers bursts of arrivals to model the access schemes. This novel procedure implies a closed-form solution of the proposed system compared to other works where these parameters are estimated assuming the moment generating function obtained with approximation models. The model is validated with a discrete event simulator, considering different scenarios and simulation conditions. The simulation results are in agreement with the mathematical solution proposed.

Enhancement of sodium ion conductivity in phosphate-based glass-ceramics by chemical substitution approach

A NASICON-type sodium-ion conducting material was synthesized via the glass-ceramic route by investigating the zinc doped Na2O–Al2O3–TiO2–P2O5 system. The glasses and glass-ceramics corresponding to the formula Na2+xAl1-xZnxTi(PO4)3 (x = 0, 0.2, 0.4, 0.6, 0.8, 1), labeled as (NAZTP-Gx) and (NAZTP-GCx) respectively, were characterized using different techniques. Differential Scanning Calorimetry (DSC) measurements were carried out to identify the characteristic temperatures, the glass transition (Tg) and the crystallization temperature (Tc). X-ray Diffraction (XRD) analysis of the glass-ceramics confirmed the formation of a solid solution Na2+xAl1-xZnxTi(PO4)3 NASICON phase, Theoretical calculations employing the Perdew–Burke–Ernzerhoff generalized gradients approximation (PBE-GGA) model supported the potential substitution of aluminum by zinc in the octahedral site in the NASICON-phase. Further structural insights were obtained through Infrared (IR) and Raman spectroscopies. Scanning electron microscopy (SEM) analysis revealed a distinct flower-like shape of the formed crystallites in the glass-ceramic NAZTP-GC0.2. Electrical characterization using electrochemical impedance spectroscopy (EIS) demonstrated that the NAZTP-GC0.2 sample exhibited the highest ionic conductivity at 300 °C, reaching 4.1 × 10−5 (Ω−1 cm−1) with an activation energy of 0.25 eV. The DC polarization was performed on the NAZTP-GC0.2 glass-ceramic, revealing that the ions are the main charge carriers in the sample. This comprehensive analysis provides valuable insights into the partial zinc doping of NASICON glass-ceramics, offering potential for improved performance as solid electrolytes in various applications.

Online adaptive critic designs with tensor product B-splines and incremental model techniques

As an effective optimal control scheme in the field of reinforcement learning, adaptive dynamic programming (ADP) has attracted extensive attention in recent decades. Neural networks (NNs) are commonly employed in ADP algorithms to realize nonlinear function approximation. However, the learning process with NN approximation typically requires a substantial amount of training data and places a heavy computational burden. To improve learning efficiency and alleviate computational load, this paper develops a novel model-free ADP approach based on multivariate splines and incremental control techniques, aimed at achieving online learning of nonlinear control. By utilizing input and output data, an incremental linear approximation model is identified online without any prior knowledge of system dynamics. To improve nonlinear approximation capabilities and lessen computational demands, tensor product B-splines, instead of NNs, are integrated into the critic module to approximate the value function, and the recursive least squares temporal difference (RLS-TD) algorithm is employed to update the weights of spline bases. Convergence analysis of the proposed control scheme is conducted based on the dual-timescale stochastic approximation theory. To illustrate the effectiveness and feasibility of the proposed control scheme, numerical simulations are performed in solving the online nonlinear control problem within the context of the inverted pendulum system.

The Role of Two Models of Thermal Radiation and Variable Properties on Thermal Explosion Critical and Transition Conditions of the Optically Thin Droplets

ABSTRACT Determining the criticality and disappearance of optically thin droplets (gas phase) by thermal explosions is crucial for maintaining thermal stability in various industrial and nonindustrial applications. The governing nonlinear ordinary differential equations of this problem make use of two distinct approximation models for thermal radiation loss, which were completed by Cogley et al. and Sohrab et al. Two methods of solving the problem – the Semenov method and the inflection point method – are used to identify the circumstances of criticality and disappearance of criticality (transition conditions). The governing equations utilize the use of the temperature-dependent Arrhenius frequency factor of the reaction and the thermal conductivity of the gas. The analytical solution of the equations yields the transitional values of the distinctive parameters at various initial conditions. Numerical methods are used to determine the equation’s exact solution. At specific initial conditions, the impact of θo, θa, γSh,F, and αSh,F on the temperature-time histories of ignition (supercritical region), non-ignition (subcritical region), and the critical boundary between them is derived. Notable effects on the ignition, non-ignition, and critical temperatures and times include the changing frequency of the reaction, the gas thermal conductivity, and two approximation models of radiation heat loss. The two radiation heat loss approximation models of the analytical and numerical findings are compared.

Normalizing Basis Functions: Approximate Stationary Models for Large Spatial Data

ABSTRACTIn geostatistics, traditional spatial models often rely on the Gaussian process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes, necessitating the use of approximate methods. A powerful class of methods approximate the GP as a sum of basis functions with random coefficients. Although this technique offers computational efficiency, it does not inherently guarantee a stationary covariance. To mitigate this issue, the basis functions can be ‘normalized’ to maintain a constant marginal variance, avoiding unwanted artefacts and edge effects. This allows for the fitting of nearly stationary models to large, potentially non‐stationary datasets, providing a rigorous base to extend to more complex problems. Unfortunately, the process of normalizing these basis functions is computationally demanding. To address this, we introduce two fast and accurate algorithms to the normalization step, allowing for efficient prediction on fine grids. The practical value of these algorithms is showcased in the context of a spatial analysis on a large dataset, where significant computational speedups are achieved. While implementation and testing are done specifically within the LatticeKrig framework, these algorithms can be adapted to other basis function methods operating on regular grids.

Development and evaluation of an online professional development course to support delivery of tiered school-based rehabilitation services

Purpose The Facilitating Integration of Rehabilitation Services Through Training (FIRST) Course provides online professional development on tiered service delivery models for rehabilitation professionals working in education settings. Created by content and e-learning experts, this study describes our use of the Analysis, Design, Development, Implementation, Evaluation (ADDIE) instructional design model and the Successive Approximation Model (SAM) to develop, implement, and evaluate the FIRST Course, and reports the findings of an initial program evaluation. Method Rehabilitation professionals who completed the FIRST Course were invited to complete a cross-sectional survey to evaluate its utility. Results Between May 1, 2020, and August 11, 2023, 314 occupational therapists, 54 physiotherapists, and 170 speech-language pathologists completed the online course and survey. Respondents perceived the FIRST Course content to be relevant to their practice and to meet their learning needs regarding tiered services in education settings. Most respondents viewed the course positively and would recommend it to colleagues. More experienced respondents suggested a need for training on tiered service delivery models beyond an introductory level. Conclusions The ADDIE and SAM instructional design models were successfully applied to develop, implement, and evaluate online professional development for school-based rehabilitation professionals who wish to learn about tiered service delivery models.

Dual-Arm Space Robot On-Orbit Operation of Auxiliary Docking Prescribed Performance Impedance Control

The impedance control of a dual-arm space robot in orbit auxiliary docking operation is studied. First, for the closed-chain hybrid system formed by the dual-arm space robot after capture operation, the dynamic equation of position uncontrolled and attitude controlled is established. The second-order linear impedance model and second-order approximate environment model are established for the problem of simultaneous output force/pose control of the end of the manipulator. Then, aiming at the transient performance control requirements of the dual-arm space robot auxiliary docking operation in orbit, a sliding mode controller with equivalent replacement of tracking errors is designed by introducing Prescribed Performance Control (PPC) theory. Next, Radial Basis Function Neural Networks (RBFNN) are used to accurately compensate for the modeling uncertainties of the system. Finally, the stability of the system is verified by Lyapunov stability determination. The simulation results show that the attitude control accuracy is better than 0.5°, the position control accuracy is better than 10−3 m, and the output force control accuracy is better than 0.5 N when it reaches 30 N. It also indicated that the proposed control algorithm can limit the transient performance of the controlled system within the preset range and achieve high-precision force/pose control, which ensures a more stable on-orbit auxiliary docking operation of the dual-arm space robot.

First-Principles Calculations on Relative Energetic Stability, Mechanical, and Thermal Properties of B2-AlRE (RE = Sc, Y, La-Lu) Phases

The relative energetic stability, mechanical properties, and thermodynamic behavior of B2-AlRE (RE = Sc, Y, La-Lu) second phases in Al alloys have been investigated through the integration of first-principles calculations with the quasi-harmonic approximation (QHA) model. The results demonstrate a linear increase in the calculated equilibrium lattice constant a0 with the ascending atomic number of RE, while the enthalpy of formation ΔHf exhibits more fluctuating variations. The lattice mismatch δ between B2-AlRE and Al matrix is closely correlated with the transferred electron et occurring between Al and RE atoms. Furthermore, the mechanical properties of the B2-AlRE phases are determined. It is observed that the calculated elastic constants Cij, bulk modulus BH, shear modulus GH, and Young’s modulus EH initially decrease with increasing atomic number from Sc to Ce and then increase up to Lu. The calculated Cauchy pressure C12-C44, Pugh’s ratio B/G, and Poisson’s ratio ν for all AlRE particles exhibit a pronounced directional covalent characteristic as well as uniform deformation and ductility. With the rise in temperature, the calculated vibrational entropy (Svib) and heat capacity (CV) of AlRE compounds exhibit a consistent increasing trend, while the Gibbs free energy (F) shows a linear decrease across all temperature ranges. The expansion coefficient (αT) sharply increases within the temperature range of 0~300 K, followed by a slight change, except for Al, AlHo, AlCe, and AlLu, which show a linear increase after 300 K. As the atomic number increases, both Svib and CV increase from Sc to La before stabilizing; however, F initially decreases from Sc to Y before increasing up to La with subsequent stability. All thermodynamic parameters demonstrate similar trends at lower and higher temperatures. This study provides valuable insights for evaluating high-performance aluminum alloys.

Reactive scattering of H2 on Cu(111) at 925K: Effective Hartree potential vs sudden approximation.

We present new quantum dynamical results for the reactive scattering of hydrogen molecules from a Cu(111) surface at a surface temperature of 925K. Reaction, scattering, and diffraction probabilities are compared for results obtained using both an effective Hartree potential (EfHP) and a sudden approximation approach, implemented through the static corrugation model (SCM), to include surface temperature effects. Toward this goal, we show how the SRP48 DFT-functional and an embedded atom potential perform when used to calculate copper lattice constants and thermal expansion coefficients based on lattice dynamics calculations within the quasi-harmonic approximation. The so-calculated phonons are then used in the EfHP approach to replace the normal modes of a fictitious copper cluster used in earlier work. We find that both the EfHP and SCM approaches correctly predict the reaction probability curve broadening effect when the surface temperature is increased. Similarly, results for rovibrationally elastic scattering appear to be improved, predominantly for the SCM model. The behavior of the EfHP results appears to remain much closer to that of a Born-Oppenheimer static surface approach, which excludes any surface temperature effects. Finally, for the diffraction, we show very clear attenuation effects for the SCM approach, significantly decreasing specular diffraction probabilities at 925K surface temperature. These results demonstrate that state-of-the-art theoretical models are able to reproduce strictly quantum mechanical scattering effects with a sudden approximation model and open up interesting opportunities for further comparisons to experimental diffraction results.

Algebraic calming for the 2D Kuramoto-Sivashinsky equations

Abstract We propose an approximate model for the 2D Kuramoto–Sivashinsky equations (KSE) of flame fronts and crystal growth. We prove that this new ‘calmed’ version of the KSE is globally well-posed, and moreover, its solutions converge to solutions of the KSE on the time interval of existence and uniqueness of the KSE at an algebraic rate. In addition, we provide simulations of the calmed KSE, illuminating its dynamics. These simulations also indicate that our analytical predictions of the convergence rates are sharp. We also discuss analogies with the 3D Navier–Stokes equations of fluid dynamics.

DFT Analysis of Transition Metal (TM) Substitutions on Cu‐Based Chalcogenides: Structural, Electronic, and Thermophysical Properties for Interface Thermal Performance and Energy

ABSTRACTThe current investigation employs first‐principles DFT (density functional theory) calculations to examine the influence of transition metal replacements on the structural, thermodynamic, and thermoelectric properties of Cu‐based chalcogenides TMCu3Se4 (TM = Nb/Ta/V). The PBE‐generalized gradient approximation (GGA) model is utilized to compute the fundamental properties of Cu‐based chalcogenides under study. A thorough examination of the energy band structures indicates that these chalcogenides are semiconductor compounds with indirect energy bandgaps. We can infer from the calculated energy band structures that the bandgap values are 1.67, 1.77, and 1.05 eV for NbCu3Se4, TaCu3Se4, and VCu3Se4, respectively. The values for NbCu3Se4, TaCu3Se4, and VCu3Se4 are 0.661, 0.998, and 0.996, respectively. These values make them highly appropriate for usage in thermoelectric (TE) devices. The thermoelectric characteristics of pyrochlore oxides TMCu3Se4 (TM = Nb/Ta/V) suggest that these materials have promising potential for energy‐related applications. The analyzed thermodynamic properties demonstrate that the Cu0based chalcogenide materials TMCu3Se4 (TM = Nb/Ta/V) exhibit a notable level of thermal stability.

Spatiotemporal Modeling of Mitochondrial Network Architecture

In many cell types, mitochondria undergo extensive fusion and fission to form dynamic, responsive network structures that contribute to a number of homeostatic, metabolic, and signaling functions. The relationship between the dynamic interactions of individual mitochondrial units and the cell-scale network architecture remains an open area of study. In this work, we use coarse-grained simulations and approximate analytic models to establish how the network morphology is governed by local mechanical and kinetic parameters. The transition between fragmented structures and extensive networks is controlled by local fusion-to-fission ratios, network density, and geometric constraints. Similar fusion rate constants are found to account for the very different structures formed by mammalian networks (poised at the percolation transition) and well-connected budding yeast networks. Over a broad parameter range, the simulated network structures can be described by effective mean-field association constants that exhibit a nonlinear dependence on the microscopic nonequilibrium fusion, fission, and transport rates. Intermediate fusion rate constants are shown to result in the highest rates of network remodeling, with mammalian mitochondrial networks situated in a regime of high turnover. This spatially resolved modeling and simulation framework helps elucidate the emergence of cellular scale network structures, and allows for the quantitative extraction of microscopic kinetic parameters from past and future experimental data. Published by the American Physical Society 2024

Distance preserving machine learning for uncertainty aware accelerator capacitance predictions

Abstract Accurate uncertainty estimations are essential for producing reliable machine learning models, especially in safety-critical applications such as accelerator systems. Gaussian process models are generally regarded as the gold standard for this task; however, they can struggle with large, high-dimensional datasets. Combining deep neural networks with Gaussian process approximation techniques has shown promising results, but dimensionality reduction through standard deep neural network layers is not guaranteed to maintain the distance information necessary for Gaussian process models. We build on previous work by comparing the use of the singular value decomposition against a spectral-normalized dense layer as a feature extractor for a deep neural Gaussian process approximation model and apply it to a capacitance prediction problem for the High Voltage Converter Modulators in the Oak Ridge Spallation Neutron Source. Our model shows improved distance preservation and predicts in-distribution capacitance values with less than 1% error.

Influence of flexoelectricity on coupled electromechanical response of 2D MXene/graphene-based hybrid piezocomposites.

This study investigates the influence of flexoelectricity on the coupled electromechanical behavior of MXene/graphene-based hybrid piezocomposite (MGHPC) plates. We developed an analytical model based on Navier's solution and Kirchhoff's plate theory, as well as an approximate model based on the Ritz method for validation purposes. A three-phase micromechanical modeling is developed for determining the effective properties of MGHPC composed of 2D MXene and graphene nano-reinforcements embedded in an epoxy matrix. These micromechanical models were implemented to predict the static and dynamic electromechanical response of MGHPC plates subject to various edge support and loading conditions. Both the analytical and approximate solutions provided unequivocal evidence of the profound impact of the flexoelectric effect on the bending and modal analysis of MGHPC nanoplates. The flexoelectric effect enhanced the stiffness of the nanoplate, irrespective of the support condition. This implies that MGHPC plates can be tailored for precise resonance frequencies and static deflection within nanoelectromechanical systems. This can be achieved by manipulating parameters such as boundary conditions and geometric attributes, including plate thickness/aspect ratio and graphene/MXene nano-reinforcements volume fractions.

Self‐Assembling Design Method of Stator Slots for AC Rotating Machines

To maximize the performance of rotating machines, it is essential to establish a design method with minimal arbitrariness. This paper proposes a self‐assembling method to design stator slots for alternating current (AC) rotating machines. First, we develop a line‐current approximation model of the stator winding using pulse‐width modulation technique and realize an ideal spatial magnetic flux density distribution. Subsequently, we design the realistic stator with an acceptable current density of the winding by forming unique slot shapes in a self‐assembling manner under two synthetic conditions using the developed line‐current approximation model as the starting model. The designed stator realizes a rotating magnetic field similar to the conventional design results. Additionally, we perform an analysis of motor rotation characteristics by combining the self‐assembled stator with a surface‐mounted permanent magnet rotor to determine the possibility of a higher output compared to that when using a conventional stator. The self‐assembled motor without relying on empirical rules shows a possibility of further improving the torque characteristics, thereby contributing to designing the AC rotating machines. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.