Simple Approximate Model Research Articles

Inverted hysteresis as a diagnostic tool for perovskite solar cells: Insights from the drift-diffusion model

Despite current–voltage hysteresis in perovskite solar cells (PSCs) having been the subject of significant research over the past decade, inverted hysteresis (IH), although frequently observed, is still not properly understood. Several mechanisms, based on numerical simulations, have been proposed to explain it but a satisfactory description of the underlying cause remains elusive. To rectify this omission, we analyze a drift-diffusion model of a planar three-layer PSC, using asymptotic techniques, to show how inverted hysteresis comes about. The asymptotic analysis of the drift-diffusion model yields a simple approximate model that shows excellent agreement with numerical simulations of the full drift-diffusion model provides fundamental insights into the causes of IH and reconciles the alternative explanations found in the literature. This approximate model is analyzed further to isolate the material properties and external conditions that contribute to inverted hysteresis and constitutes a diagnostic tool in which the appearance of IH can be used to infer properties of the cell.

Simulation framework for microwave SQUID multiplexer optimization

So far, performance prediction and optimization of microwave SQUID multiplexers have largely been based on simple approximate analytical models and experimental results. This is caused by the complexity of the underlying physics and the intricacy of operation and readout parameters. As a simplified description can never account for all potential effects occurring in a real device, we have developed a software framework to simulate the characteristics and performance of a microwave SQUID multiplexer. Our simulation framework is a powerful tool to guide understanding and optimization of microwave SQUID multiplexers and other related devices. It includes common readout schemes such as open-loop or flux ramp-modulated readout as well as the nonlinear behavior of Josephson tunnel junctions. Moreover, it accounts for the non-zero response time of superconducting microwave resonators with high loaded quality factors as well as the most significant noise contributions such as amplifier noise, resonator noise, as well as SQUID noise. This ultimately leads to a prediction of device performance that is significantly better compared to simple analytical methods. Using the simulation framework, we discuss first steps toward full microwave SQUID multiplexer optimization and highlight some other applications for which our simulation framework can be used.

Diffusive exit rates through pores in membrane-enclosed structures

The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the channel. We propose a simple approximate model, validated with stochastic simulations, for estimating the effective release rate from cylinders, and other simple-shaped domains, as a function of channel parameters. The results demonstrate that, for very small pores, a low density of channels scattered over the boundary is sufficient to achieve substantial rates of particle release. Furthermore, we show that increasing the length of passive channels will both reduce release rates and lead to a less steep dependence on channel density. Our results are compared to previously-measured local calcium release rates from tubules of the endoplasmic reticulum, providing an estimate of the relevant channel density responsible for the observed calcium efflux.

Estimating the Potential Accuracy of Some Orbital Parameters from Angular Measurements: a 2D model

The problem of estimating some parameters of a cosmic body orbits from angular measurements is considered. Contrary to the existing opinion that angular measurements are unsuitable for obtaining accuracies that are of practical interest, it is shown that, if the orbit is such that the impact place is in the vicinity of the observer, then such parameters as the impact point and time can be determined with quite acceptable accuracy. A fairly simple means for evaluating the accuracy of the "motion-measurement" process by reducing it to an analysis in a plane is described. The analysis is based on several principles. A family of orbits unfavorable to the observer is singled out, and an analysis is performed on this family. These are orbits whose plane touches the observer's Earth parallel, with the touching point being the intersection point of the observer and cosmic body trajectories. The article substantiates a simple approximate plane model, in which the observer’s true motion is replaced without changing its velocity by motion in the orbit plane. Information about the impact point is contained in the observations when the height decreases, which makes it possible to consider the gravity acceleration of as a constant in the descending mode. The motion model is simplified compared with the Keplerian motion: a simple motion scheme is obtained in the polar coordinate system. As a result, it becomes unnecessary to solve the differential equation representing the change in acceleration. A measurement formula that takes into account the Earth curvature and the observer latitude is derived, and the parameters determining the analyzed scheme are added: the distance to the impact point, incidence angle and impact moment, and horizontal velocity. The model accuracy is analyzed using the Fisher matrix. As a result, an approximate problem on a plane with four parameters is obtained instead of a problem in 3D space with seven parameters. The difficulties with the accuracy of estimating the displacement and impact moment in the model remain, and they are analyzed. The accuracy is estimated using the concept of Fisher information and the multidimensional Rao-Kramer information inequality instead of analyzing the processing algorithm.

Half-life prediction of some neutron-rich exotic nuclei prior to peak A = 130

β-decay is amongst the key properties of nuclei required for the modeling of r-process nucleosynthesis. It also governs the flow of abundances among neighboring isotopic chains of high-mass elements. In the present work, a simple proton-neutron quasi particle random phase approximation (p–n-QRPA) model has been used for the calculation of β-decay half-lives of Rb, Sr, Y and Zr neutron-rich isotopes. For 97−103Rb, 98−107Sr, 101−109Y and 104−112Zr, where the experimental data were available, the half-life values are reproduced with reasonable accuracy. The same set of model parameters are later used to predict half-lives for few neutron-rich nuclei (104−112Rb, 108−113Sr, 110−114Y and 113−115Zr) where measured data is not available. The p–n-QRPA results (including only allowed transitions) are compared with previous calculations (allowed plus forbidden) and exhibit agreement within a factor of 2.0 when compared with the recent available experimental data.

Semi-supported Steel Plate Shear Wall with Oblique Sides

This paper presents a new configuration for semi-supported steel plate shear walls to increase their efficiency. For this purpose, the infill steel plate is proposed to be a trapezoidal shape instead of a rectangular one. To find the most efficient inclination angle of lateral sides, a numerical parametric study was conducted. Five different values of inclination angle including 60, 75, 90, 105, and 120 degrees were considered. Furthermore, two thicknesses of 1.75 and 2.00 mm were considered for the steel plate. The area of the steel plate was the same for all the models. The models were analyzed using finite element software ABAQUS. Both geometric and material nonlinearity have been considered. To validate the finite element modeling, the available experimental results were used. According to the results, comparing to the wall with rectangular plate, the inclination angle of 60° increases the ultimate lateral strength and stiffness of the 1.75 mm-thick walls by 46% and 66%, respectively. Furthermore, a simple approximate model is presented to calculate the load-deformation response of the proposed wall using SAP 2000 program. Despite the simplicity of the method, the results were in good agreement with the results of ABAQUS.

Multi-objective parametric design of PI/PID controllers via multi-level game-theoretic optimization for systems with time delay

In this research study, a new methodology of multi-objective optimal design is presented for control systems with time delay. Stackelberg method as an approach of game theory is implemented to develop the multi-objective optimization of proportional–integral (PI) and proportional–integral–derivative (PID) controllers. The surface area of control effort and tracking error are put in order of precedence together as the more important conflicting objective functions of the players in Stackelberg game design. Besides, the desirability of other effective criteria including frequency and time domains are measured as constraints in the procedure of the game-theoretic design. The main purpose of the proposed method is to optimally set and formulate controller parameters in the Stackelberg game-control system (SG-CS) design. Mapping the leader’s variables into the optimized values of the follower’s variables obtained via differential evolution (DE), the effectiveness of the proposed method is demonstrated in constructing a simple and explicit approximate model for rational reaction sets (RRSs). These obtained optimal models for the RRS allow the user to access the set of optimal controller parameters in the entire accessible strategic space of design variables in a formulated form. Utilizing the optimal synthesis for two case studies is validated the superiority of SG-CS design in establishing the explicit relationship between the controller’s parameters.

Optimization design of horizontal well fracture stage placement in shale gas reservoirs based on an efficient variable-fidelity surrogate model and intelligent algorithm

Hydraulic fracturing technique increases shale gas well productivity significantly. Horizontal well fracture optimization has been studied by many researchers worldwide in the past decade. However, most of these researches relied on computationally expensive numerical simulation models for objectives evaluation during the optimization process. This affects the optimization efficiency significantly. To address this issue, surrogate model methods which adapt a simple approximate model are employed to lessen the computational burden. In this study therefore, a novel intelligent variable-fidelity radial basis function (VFRBF) surrogate-assisted model for multi-objective fracture stage placement optimization, namely VFRBF-FSO, is proposed to reduce the computational burden of the numerical simulation-based production optimization. In the VFBRF-FSO method, low-fidelity (LF) and high-fidelity (HF) samples were adopted simultaneously to establish the variable-fidelity (VF) surrogate model. To the best of our knowledge, this is the first time that variable-fidelity model is used for shale gas horizontal well fracture stage placement optimization. The uniqueness of this proposed method is that a scaling factor and an augment matrix are used to integrate the LF and HF samples to increase the accuracy of the surrogate model. Moreover, two cases with different wells and well types were studied to illustrate the effectiveness and accuracy of the VFRBF-FSO method. The optimization results showed that the VFRBF-FSO method performed comparably with the HF model-based method in terms of convergence and diversity. However, the VFRBF-FSO reduced the simulation runs on the two cases with different wells and fracture types to about five times that of the HF model.

A novel self-adaptive multi-fidelity surrogate-assisted multi-objective evolutionary algorithm for simulation-based production optimization

Multi-objective production optimization (MOPO) which aims at finding an optimal well control scheme is regarded as a win-win strategy for improving economic and production gains. Generally, the MOPO processes involve computationally expensive numerical simulations and high-dimensional decision variables which limit their application to actual reservoir optimization problems. Surrogate-assisted multi-objective optimization method which uses a simple yet efficient approximation model shows huge potential in solving production optimization problems since it lessens the computational burden by decreasing the use of computationally expensive numerical simulations. In this paper, a novel self-adaptive multi-fidelity surrogate-assisted (SAMFS) multi-objective production optimization algorithm (SAMFS-MOPO) is proposed to reduce the computational burden and enhance the accuracy of the surrogate model. A similar method has been applied to well spacing optimization but the uniqueness of this method is that two fidelity samples are used to establish a multi-fidelity (MF) surrogate model, while i-updating and g-updating strategies are used to renew the MF surrogate model during the optimization process so as to improve its accuracy and reduce the computational burden. To the best of our knowledge, this is the first time a self-adaptive multi-fidelity surrogate model is used for production optimization. Furthermore, three classic multi-objective benchmark problems and two reservoirs with different complexities were applied to illustrate the effectiveness and accuracy of the proposed SAMFS-MOPO method. It was found that the SAMFS-MOPO method had superior performance in convergence, diversity, and efficiency than other conventional methods.

A rigorous universal model for the dynamic strength of materials across loading rates

The dynamic strength for a broad range of materials with different microstructures exhibits surprisingly similar behavior. Two distinct regimes are observed with a sharp transition between them. At low loading rates, the strength has a weak linear dependence on the log loading rate until a critical rate above which a dramatic increase is observed. We explain this behavior by considering material failure as a bond-breaking process driven by external loading and thermal fluctuation within a Langevin dynamics framework. The analysis leads to nondimensional measures for which the dynamic response collapses onto a universal curve, independent of material properties, describing both loading rate regimes and the transition between them. A simple approximate model is derived that provides an excellent fit to experimental data for a broad range of materials, including concrete, ceramics, and metals.

Natural frequencies and modal shapes of three-dimensional moonpool with recess in infinite-depth and finite-depth waters

In this study new extensions of the theoretical models developed by Molin (2001) and Molin et al. (2018) are proposed to solve the resonance problem for three-dimensional circular and rectangular moonpools with recesses. Eigenfunction expansions are adopted to describe the velocity potentials in all the subdomains. Then, the velocity potentials and normal velocities are matched at the common boundaries such that the eigenvalue problems are formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Both the models for infinite and finite water depths are derived for circular moonpools with recesses. Applications are also made for the three-dimensional rectangular moonpools with recesses. In addition, frozen-mode approximation is derived, which yields simple formulas for prediction of the natural frequencies for piston-mode resonances. The proposed models in this study are validated by comparing the obtained results with the experimental data and the results using other numerical models. Moreover, for the first sloshing mode in rectangular moonpool, simple approximation model is proposed based on the assumption that the half of the wavelength of a standing wave is the same as the moonpool length. The validity of the model is examined by comparing the solutions with the results by the diffraction–radiation code WAMIT.

The mechanical behavior of single crystal and polycrystalline pure magnesium

We present a simplified constitutive model, based on the dominant deformation mechanisms, to capture the mechanical behavior of magnesium. This approach takes into account (1) the accumulation and annihilation of 〈a〉 and 〈c+a〉 dislocations, (2) the volume fraction of extension twins, and (3) two material domains — the parent region and the twinned region. We first show that the model successfully captures the material responses of single crystal magnesium under different loading conditions. We then extend the model for application to a polycrystalline magnesium alloy. The results provide a simple and straightforward approximate model for magnesium and its alloys under various loading conditions.

Development of an approximate model for the prediction of bubble departure diameter in pool boiling of water

Several researchers have attempted to develop model to predict bubble departure diameter in pool boiling for last eighty years. But all these models predictions have a large difference with real life experimental values. In the present investigation, an attempt has been made to develop a physics based simple approximate model which in turn predicts the bubble departure diameter for nucleate boiling zone within the range of ±25%.

Theoretical Minimum Thermal Load in Buildings

Summary Building cooling and heating accounts for a large portion of total global energy use and requires commensurate amounts of resources, which contribute significantly to global warming. Traditionally, addressing this issue has meant improving the efficiency of equipment supplying the thermal energy, reducing envelope heat transfer, and reducing air infiltration. However, this approach is already reaching practical limits. In this perspective, we explore (1) how to reduce thermal load in buildings theoretically and (2) how to achieve that reduction and dramatically lower the energy required to support building loads practically. First, we discuss our framework developed for calculating the theoretical minimum thermal load (TMTL) in buildings. Our analysis shows that current thermal loads in buildings are more than an order of magnitude higher than the TMTL. We also introduce an approximate formula to calculate energy savings from zonal control of thermal load, which shows that the majority of zonal control benefits can be achieved with fewer than 10 zones. Then, we discuss pros and cons of various approaches and strategies to achieve the TMTL. We conclude our perspective with some longer-term R&D ideas, such as thermally adaptive clothing and thermal storage to help approach the TMTL, while providing the additional benefit of interacting with the renewable grid of the future.

A Simple and Straightforward Linear Approximation Model of Predicting the Glucose and HbA1C Values to Manage Type 2 Diabetes Based on GH-Method: Math-Physical Medicine (No. 472)

Based on research work over 6.5 years, the author summarized his work results into a set of simple and straightforward linear model to predict approximate, but accurate enough, sensor glucose and HbA1C values. It utilizes both of the linear elastic glucose theory (LEGT) from strength of engineering materials and the first-order interpolation perturbation theory (perturbation) from quantum mechanics to construct various PPG waveforms. To start, he measures his weight in early morning, next he estimates his fasting plasma glucose (FPG) at his wakeup moment, then approximates his breakfast post-prandial plasma glucose (PPG) at 0-minute time instant, and finally applies either LEGT model or perturbation model to construct his daily PPG waveform over a three-hours timeframe. Based on the estimated FPG value and three PPG values, he can then assess his daily average sensor glucose (eAG) and HbA1C (A1C) value on that particular day.

Predicting observed and hidden extreme events in complex nonlinear dynamical systems with partial observations and short training time series.

Extreme events appear in many complex nonlinear dynamical systems. Predicting extreme events has important scientific significance and large societal impacts. In this paper, a new mathematical framework of building suitable nonlinear approximate models is developed, which aims at predicting both the observed and hidden extreme events in complex nonlinear dynamical systems for short-, medium-, and long-range forecasting using only short and partially observed training time series. Different from many ad hoc data-driven regression models, these new nonlinear models take into account physically motivated processes and physics constraints. They also allow efficient and accurate algorithms for parameter estimation, data assimilation, and prediction. Cheap stochastic parameterizations, judicious linear feedback control, and suitable noise inflation strategies are incorporated into the new nonlinear modeling framework, which provide accurate predictions of both the observed and hidden extreme events as well as the strongly non-Gaussian statistics in various highly intermittent nonlinear dyad and triad models, including the Lorenz 63 model. Then, a stochastic mode reduction strategy is applied to a 21-dimensional nonlinear paradigm model for topographic mean flow interaction. The resulting five-dimensional physics-constrained nonlinear approximate model is able to accurately predict extreme events and the regime switching between zonally blocked and unblocked flow patterns. Finally, incorporating judicious linear stochastic processes into a simple nonlinear approximate model succeeds in learning certain complicated nonlinear effects of a six-dimensional low-order Charney-DeVore model with strong chaotic and regime switching behavior. The simple nonlinear approximate model then allows accurate online state estimation and the short- and medium-range forecasting of extreme events.

Experiments and models about the force between permanent magnets: asymptotic analysis of a difficult problem

We propose a simple experiment, which allows students to explore quantitatively the magnetic interaction between neodymium cylindrical magnets. The experiment employs a precision digital balance, two screws with known thread pitch and two transparent tubes to measure the repulsive force between two magnets as a function of their distance. Different measurements are performed, focusing on the behavior of the interaction force at short and long distances and the role of the magnets’ aspect ratio. We discuss the comparison between theoretical expectations resulting from conceptually simple approximate models and experimental results. The experiments employ inexpensive materials and address a relevant topic in the physics curriculum. Thus, they are appropriate for the undergraduate physics laboratory, for advanced high school students, and in the context of teacher education and in-service training to enhance students’ knowledge of magnetism.

Вероятностный анализ требований к угломерной системе обнаружения смещения эллиптической орбиты

The article addresses the requirements for a goniometric system intended to detect displacements of the space body orbit, which measures angles at discrete moments of time with a random error. Two statistical hypotheses about the zero and specified nonzero displacement values are considered. The likelihood ratio statistics is obtained, and the information distance for it is determined, which characterizes the discrimination confidence level, and which depends on the measurement device accuracy s and discreteness Dt, and also on the orbit parameters. By specifying the orbits and discrimination confidence level, the accuracy s and discreteness Dt are determined through information discrepancy. The information discrepancy is calculated on a family of orbits unfavorable for the observer, the plane of which touches the orbit of the moving observer, and the touching point is the intersection point of the corresponding trajectories. To refine the information distance, a simple flat approximate motion-measurement model is substantiated, in which the true motion of the observer (outside the space body orbit plane) is replaced, without changing its speed, by motion in the space body orbit plane over the earth's sphere circumference. The justification is corroborated by calculating the errors. The obtained simple model is used for estimating the potential possibility of detecting the specified displacement. Tables and graphs for practically determining the discreteness and accuracy of the system are given. The appendix contains all formulas necessary for carrying out similar calculations. Examples show that from angular measurements it is possible to obtain quite reliable detection for the range of orbit parameters that are of practical interest.

Room-temperature stability of excitons and transverse-electric polarized deep-ultraviolet luminescence in atomically thin GaN quantum wells

We apply first-principles calculations to study the effects of extreme quantum confinement on the electronic, excitonic, and radiative properties of atomically thin (1–4 atomic monolayers) GaN quantum wells embedded in AlN. We determine the quasiparticle bandgaps, exciton energies and wave functions, radiative lifetimes, and Mott critical densities as a function of well and barrier thickness. Our results show that quantum confinement in GaN monolayers increases the bandgap up to 5.44 eV and the exciton binding energy up to 215 meV, indicating the thermal stability of excitons at room temperature. Exciton radiative lifetimes range from 1 to 3 ns at room temperature, while the Mott critical density for exciton dissociation is approximately 1013 cm−2. The luminescence is transverse-electric polarized, which facilitates light extraction from c-plane heterostructures. We also introduce a simple approximate model for calculating the exciton radiative lifetime based on the free-carrier bimolecular radiative recombination coefficient and the exciton radius, which agrees well with our results obtained with the Bethe–Salpeter equation predictions. Our results demonstrate that atomically thin GaN quantum wells exhibit stable excitons at room temperature for potential applications in efficient light emitters in the deep ultraviolet as well as room-temperature excitonic devices.

Acoustic emission from finite two-dimensional cracks: Directivity functions and frequency spectra

In this paper, the acoustic emission accompanying the formation of brittle cracks of finite length is investigated theoretically using the approach based on the application of Huygens' principle for elastic solids. In the framework of this approach, the main input information required for calculations of acoustic emission spectra is the normal displacements of the crack edges as a function of frequency and wavenumber. Two simple approximate models defining this function are used in this paper for calculations of the acoustic emission spectra and directivity functions of a crack of finite length. The simplest model considers a crack that opens monotonously to its static value. The more refined model accounts for oscillations during crack opening and considers a crack of finite size as a resonator for symmetric modes of Rayleigh waves propagating along the crack edges and partly reflecting from the crack tips. Analytical solutions for generated acoustic emission spectra are obtained for both models and compared with each other. It is shown that resonant properties of a crack are responsible for the appearance of noticeable peaks in the frequency spectra of generated acoustic emission signals that can be used for evaluation of crack sizes. The obtained analytical results are illustrated by numerical calculations.