Empirical Parameters Research Articles

Laminar drag reduction in surfactant-contaminated superhydrophobic channels

Although superhydrophobic surfaces (SHSs) show promise for drag reduction applications, their performance can be compromised by traces of surfactant, which generate Marangoni stresses that increase drag. This question is addressed for soluble surfactant in a three-dimensional laminar channel flow, with periodic SHSs made of long finite-length longitudinal grooves located on both walls. We assume that bulk diffusion is sufficiently strong for cross-channel concentration gradients to be small. Exploiting long-wave theory and accounting for the difference between the rapid transverse and slower longitudinal Marangoni flows, we derive a one-dimensional model for surfactant transport from the full three-dimensional transport equations. Our one-dimensional model allows us to predict the drag reduction and surfactant distribution across the parameter space. The system exhibits multiple regimes, involving competition between Marangoni effects, bulk and interfacial diffusion, bulk and interfacial advection, shear dispersion and surfactant exchange between the bulk and the interface. We map out asymptotic regions in the high-dimensional parameter space, and derive explicit closed-form approximations of the drag reduction, without any fitting or empirical parameters. The physics underpinning the drag reduction effect and the negative effect of surfactant is discussed through analysis of the velocity field and surfactant concentrations, which show both uniform and non-uniform stress distributions. Our theoretical predictions of the drag reduction compare well with results from the literature solving numerically the full three-dimensional transport problem. Our atlas of maps provides a comprehensive analytical guide for designing surfactant-contaminated channels with SHSs, to maximise the drag reduction in applications.

Development of NOTCH, an all-electron, beyond-NDDO semiempirical method: Application to diatomic molecules.

In this work, we develop a new semiempirical method, dubbed NOTCH (Natural Orbital Tied Constructed Hamiltonian). Compared to existing semiempirical methods, NOTCH is less empirical in its functional form as well as parameterization. Specifically, in NOTCH, (1) the core electrons are treated explicitly; (2) the nuclear-nuclear repulsion term is calculated analytically, without any empirical parameterization; (3) the contraction coefficients of the atomic orbital (AO) basis depend on the coordinates of the neighboring atoms, which allows the size of AOs to depend on the molecular environment, despite the fact that a minimal basis set is used; (4) the one-center integrals of free atoms are derived from scalar relativistic multireference equation-of-motion coupled cluster calculations instead of empirical fitting, drastically reducing the number of necessary empirical parameters; (5) the (AA|AB) and (AB|AB)-type two-center integrals are explicitly included, going beyond the neglect of differential diatomic overlap approximation; and (6) the integrals depend on the atomic charges, effectively mimicking the "breathing" of AOs when the atomic charge varies. For this preliminary report, the model has been parameterized for the elements H-Ne, giving only 8 empirical global parameters. Preliminary results on the ionization potentials, electron affinities, and excitation energies of atoms and diatomic molecules, as well as the equilibrium geometries, vibrational frequencies dipole moments, and bond dissociation energies of diatomic molecules, show that the accuracy of NOTCH rivals or exceeds those of popular semiempirical methods (including PM3, PM7, OM2, OM3, GFN-xTB, and GFN2-xTB) as well as the cost-effective abinitio method Hartree-Fock-3c.

Square-wave optoelectronic oscillators: Effects of noise in bit generators

Optoelectronic oscillators delivering optical square waves may potentially serve as sources of optical or microwave bits. Noise analysis and prediction of eye diagrams and various figures of merit can involve intensive numerical simulation specific to a given problem at hand. Here we present an analytically tractable model of the effects of amplitude noise and timing jitter on the use of such a square-wave generator as an optical binary bit train. The approach depends on a small number of empirical parameters characterizing the temporal correlations of noise in the system. We compute in closed form the time-averaged signal, autocorrelation function, power spectral density, eye diagram, quality factor, bit-error rate, and Allan variance. While the model exploits simplification as the cost of tractability, the availability of such a model is expected to be of interest more broadly in digital communications to provide a simple tool for analysis and characterization.

Comparative analysis of molecular interactions in quaternary fluid system performed by classical and ab initio molecular dynamics

Molecular interactions in the quaternary fluid system acetic acid–n-propanol–n-propyl acetate–water were analyzed by classical and ab initio molecular dynamics methods. It was shown that ab initio molecular dynamics simulation can reproduce the molecular mobility tendency and structural features of a multicomponent system without empirical parameters.

A Reinforcement Learning Based Slope Limiter for Second‐Order Finite Volume Schemes

AbstractHyperbolic equations admit discontinuities in the solution and thus adequate and physically sound numerical schemes are necessary for their discretization. Second‐order finite volume schemes are a popular choice for the discretization of hyperbolic problems due to their simplicity. Despite the numerous advantages of higher‐order schemes in smooth regions, they fail at strong discontinuities. Crucial for the accurate and stable simulation of flow problems with discontinuities is the adequate and reliable limiting of the reconstructed slopes. Numerous limiters have been developed to handle this task. However, they are too dissipative in smooth regions or require empirical parameters which are globally defined and test case specific. Therefore, this paper aims to develop a new slope limiter based on deep learning and reinforcement learning techniques. For this, the proposed limiter is based on several admissibility constraints: positivity of the solution and a relaxed discrete maximum principle. This approach enables a slope limiter which is independent of a manually specified global parameter while providing an optimal slope with respect to the defined admissibility constraints. The new limiter is applied to several well‐known shock tube problems, which illustrates its broad applicability and the potential of reinforcement learning in numerics.

Implementation of trait-based ozone plant sensitivity in the Yale Interactive terrestrial Biosphere model v1.0 to assess global vegetation damage

Abstract. A major limitation in modeling global ozone (O3) vegetation damage has long been the reliance on empirical O3 sensitivity parameters derived from a limited number of species and applied at the level of plant functional types (PFTs), which ignore the large interspecific variations within the same PFT. Here, we present a major advance in large-scale assessments of O3 plant injury by linking the trait leaf mass per area (LMA) and plant O3 sensitivity in a broad and global perspective. Application of the new approach and a global LMA map in a dynamic global vegetation model reasonably represents the observed interspecific responses to O3 with a unified sensitivity parameter for all plant species. Simulations suggest a contemporary global mean reduction of 4.8 % in gross primary productivity by O3, with a range of 1.1 %–12.6 % for varied PFTs. Hotspots with damage >10 % are found in agricultural areas in the eastern US, western Europe, eastern China, and India, accompanied by moderate to high levels of surface O3. Furthermore, we simulate the distribution of plant sensitivity to O3, which is highly linked with the inherent leaf trait trade-off strategies of plants, revealing high risks for fast-growing species with low LMA, such as crops, grasses, and deciduous trees.

A novel dynamic dry friction model for applications in mechanical dynamical systems

This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.

Reconfigurable Laser-Stimulated Lock-In Thermography for Surface Micro-Crack Detection.

Surface crack detection and sizing is essential for the manufacturing and maintenance of engines, run parts, and other metal elements of aircrafts. Among various non-destructive detection methods, the fully non-contact and non-intrusive technique based on laser-stimulated lock-in thermography (LLT) has recently attracted a lot of attention from the aerospace industry. We propose and demonstrate a system of reconfigurable LLT for three-dimensional surface crack detection in metal alloys. For large area inspection, the multi-spot LLT can speed up the inspection time by a factor of the number of spots. The minimum resolved size of micro-holes is ~50 µm in diameter limited by the magnification of the camera lens. We also study the crack length ranging from 0.8 to 3.4 mm by varying the modulation frequency of LLT. An empirical parameter related to the thermal diffusion length is found to show the linear dependence with the crack length. With the proper calibration, this parameter can be used to predict the sizing of the surface fatigue cracks. Reconfigurable LLT allows us to quickly locate the crack position and accurately measure its dimensions. This method is also applicable to the non-destructive detection of surface or sub-surface defect in other materials used in various industries.

Remote substituent effects on catalytic activity of metal-organic frameworks: a linker orbital energy model

The Hammett equation is commonly used to theoretically depict the remote electronic effects of substituents on catalytic activities of metal nodes of metal-organic frameworks (MOFs). However, the application of the theory to MOF catalysts usually encounters problems because it relies heavily on empirical parameters with unknown transferability. To develop an alternative prediction theory, the linker orbital energy model has been proposed by density functional theory calculations. The model provides a simple method to approximately depict the remote electronic substituent effects on catalytic activities of metal nodes of MOFs, and its general applicability to MOFs is supported by extensively revisiting the structure-activity relationships reported in the literatures. The model can be used to design catalytic activity of metal nodes of MOFs by engineering the electronic properties of linkers and substituents.

Quantum version of the integral equation theory-based dielectric scheme for strongly coupled electron liquids.

A novel dielectric scheme is proposed for strongly coupled electron liquids, which handles quantum mechanical effects beyond the random phase approximation level and treats electronic correlations within the integral equation theory of classical liquids. The self-consistent scheme features a complicated dynamic local field correction functional and its formulation is guided by abinitio path integral Monte Carlo simulations. Remarkably, our scheme is capable of providing unprecedently accurate results for the static structure factor with the exception of the Wigner crystallization vicinity, despite the absence of adjustable or empirical parameters.

Gloss-Bridge: A Method to Reduce the Visual Perception Gap between Real-World Glossiness and PBR Reflectance Properties in Virtual Reality

With the rapid development of virtual reality (VR) technology, digital materials have become more realistic and controllable, offering new opportunities for material perception research. However, material parameters for physically based rendering (PBR), which are widely used in industry, are often derived from design experience and lack interpretability. This study aims to investigate the visual perception difference of material glossiness between real and virtual environments. A compensation method is proposed to bridge the glossiness perception gap between the real-world and PBR. Two psychophysical experiments are conducted. Experiment 1 measures the psychological perception of materials with different glossiness in the real world and VR using a two-alternative forced-choice (2AFC) design. Experiment 2 establishes a connection between multiple parameters in PBR and the psychologically perceived glossiness obtained in Experiment 1 through a material matching adjustment experiment. Finally, a material glossiness mapping method for VR real-time rendering, Gloss-Bridge, is introduced. This method maps the physical quantity (measured by gloss meter) to various PBR parameters. By using physical parameters instead of empirical parameters, it eliminates tedious hyper-parameter adjustments. This achievement provides a design basis for the production of VR materials based on subjective perception and physical parameters.

Performance test and effect evaluation of guar gum-stabilized loess as a sustainable slope protection material

During the rainy season, many slopes are eroded by precipitation on the China Loess Plateau (CLP). Hence, Guar gum (GG) is used to stabilize the topsoil of loess slopes to control rainwater erosion. To test the engineering performance of GG-stabilized loess and its feasibility in slope protection practice, the mechanical and hydraulic properties of specimens with different GG contents were measured in the laboratory. The results show that GG can effectively improve loess mechanical behavior during shear and disintegration and endow loess with good impermeability and water retention ability. With increasing GG content, the cohesion initially increased and subsequently decreased, the disintegration rate and permeability coefficient decreased, and the height of soil–water characteristic curve increased. When the GG content was 1.0%, the comprehensive engineering performance of the treated specimens was optimized. The cohesion, residual water content, and Van Genuchten (VG) model empirical fitting parameter increased by 125.7%, 148.9%, and 34.5%, while the disintegration rate, permeability coefficient, and VG model scale parameter decreased by 84.3%, 84.1%, and 80%, respectively. According to the scanning electron microscopy images, the stabilization mechanism of GG on loess relied on the hydrogel adhesion of soil particles and pore filling. Finally, field model test was used to verify that the GG-stabilized loess had excellent vegetation growth status and erosion control effect. After 120d of natural rainfall, the vegetation coverage increased by 67.6%, and the cumulative erosion decreased by 47.5%. Thus, utilizing GG-stabilized loess as a slope protection material shows great potential and is expected to promote the green construction of engineering and the sustainable development of soil and water conservation in the CLP.

Model selection in atomistic simulation.

There are many atomistic simulation methods with very different costs, accuracies, transferabilities, and numbers of empirical parameters. I show how statistical model selection can compare these methods fairly, even when they are very different. These comparisons are also useful for developing new methods that balance cost and accuracy. As an example, I build a semiempirical model for hydrogen clusters.

Reconstructing physical parameters from template gravitational wave spectra at LISA: first order phase transitions

A gravitational wave background from a first order phase transition in the early universe may be observable at millihertz gravitational wave (GW) detectors such as the Laser Interferometer Space Antenna (LISA). In this paper we introduce and test a method for investigating LISA's sensitivity to gravitational waves from a first order phase transition using parametrised templates as an approximation to a more complete physical model. The motivation for developing the method is to provide a less computationally intensive way to perform Markov Chain Monte Carlo (MCMC) inference on the thermodynamic parameters of a first order phase transition, or on generally computationally intensive models. Starting from a map between the physical parameters and the parameters of an empirical template, we first construct a prior on the empirical parameters that contains the necessary information about the physical parameters; we then use the inverse mapping to reconstruct approximate posteriors on the physical parameters from a fast MCMC on the empirical template. We test the method on a double broken power law approximation to spectra in the sound shell model. The reconstruction method substantially reduces the proposal evaluation time, and despite requiring some precomputing of the mapping, this method is still cost-effective overall. In two test cases, with signal-to-noise ∼ 40, the method recovers the physical parameters and the spectrum of the injected gravitational wave power spectrum to 95% confidence. In previous Fisher matrix analysis we found the phase boundary speed v w was expected to be the best constrained of the thermodynamic parameters. In this work, for an injected phase transition GW power spectrum with v w = 0.55, with a direct sample on the thermodynamic parameters we recover 0.630+0.17 -0.059 and for our reconstructed sample 0.646+0.098 -0.075.

Geometrically Exact Beam-based Aeroelastic Modeling and Solution Of Composite Rotor Blades in Forward Flight

In this paper, the geometrically exact beam model and aeroelastic solution methods for composite rotor blades in forward flight by the latest variational asymptotic beam sectional analysis (VABS) have been employed. The geometrically exact beam equations of motion in the mixed variational form and the latest VABS are used to deal with one-dimensional blade analysis and the structural property of blade cross section, respectively. The methods can be used for the aeroelastic solution of composite rotor blades with arbitrary cross-sectional shape and material distribution, large deflections and significant nonclassical effects such as cross-sectional warping, transverse shear deformation, and elastic couplings caused by anisotropic material properties. The Peters–He finite state dynamic inflow model and the Peters finite state airloads theory are used to calculate the induced velocity and blade airloads, respectively. An auto-pilot trim scheme is used for calculating the blade pitch controls to meet the trim requirements. The convergence issue encountered when solving the geometrically exact, mixed variational aeroelastic equations in time domain has been successfully addressed. The values of the empirical parameters in the auto-pilot trim scheme for the presented aeroelastic model have been properly selected. The accuracy of the presented aeroelastic modeling and solution methods has been verified against the SA349/2 flight-test data. The influence of transverse shear deformation on the aeroelastic response of composite rotor blades was also investigated, indicating that this effect has a nonnegligible influence on the aeroelastic response of the five different kinds of elastically coupled hingeless composite rotors investigated in this paper.

Эмпирический закон кинетики изменения силы трения скольжения при самопроизвольных изменениях состояния фрикционного контакта

The analysis, model revisited and the generalization of the existing empirical mathematical model of the force variation law depending upon time in case of spontaneous changes in the state of the friction contact of solids, is completed. Using the adhesion-deformation theory of friction, a phenomeno-logical model of friction force dependence on time and sliding dis-tance, is constructed, taking into account spontaneous changes in the state of frictional contact. The developed model makes it possible to interpret the transition empirical parameters and characteristics from a molecular-mechanical point of view.

Machine learning and visualization assisted solid solution strengthening phase prediction of high entropy alloys

Solid solution strengthening (SSS) influences the mechanical properties and microstructure of multi-principal high entropy alloys (HEAs). Thus, given the vast compositional space of HEAs, accurately predicting the microstructure of HEAs is regarded as a challenge. Data-driven machine learning (ML) is seen as a powerful tool for predicting the subtle relationship between the composition and structure of HEAs, but the difficulty in interpreting ML models hinders improvement in the performance of phase prediction models. In this work, ML is applied to the modeling of phase prediction, and a complete workflow of ML-based alloy structure prediction is proposed. In this paper, we train an artificial neural network (ANN) model from 12 ML models in a feature pool of 30 material descriptors, which achieves an F1 score of 0.94 on independent test sets. Shapley Additive exPlanations theory is applied to explain how models make classification predictions for phase structures. Finally, the effect of empirical parameters on the phase structure of HEAs was verified by visualization from the ML perspective.

A non-self-consistent tight-binding electronic structure potential in a polarized double-ζ basis set for all spd-block elements up to Z = 86.

Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations; (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix; (c) new P-dependent terms emulating non-local exchange are included; and (d) only element-specific empirical parameters (about 50 per element) need to be determined. The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3-4 orders of magnitude. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn-Sham potential. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods.

GIS-based slope-adjusted curve number methods for runoff estimation

Accurate estimation of surface runoff and determination of susceptible lands to runoff generation in ungauged watersheds were the problems for hydrologic engineering which could be predicted through a simple model such as Soil Conservation Service Curve Number (SCS-CN). Due to the slope effects on this method, slope adjustment for curve number was developed to improve its precision. So, the main objectives of this study were to apply GIS-based slope SCS-CN approaches for surface runoff estimation and compare the accuracy of three slope-adjusted models including: (a) model with three empirical parameters, (b) model with two parameters slope function, and (c) model with one parameter in the region located in the central part of Iran. For this purpose, soil texture, hydrologic soil group, land use, slope, and daily rainfall volume maps were utilized. In order to provide the curve number map of the study area, land use and hydrologic soil group layers built in Arc-GIS were intersected and the curve number was determined. Then, three slope adjustment equations were used to modify curve numbers of AMC-II by employing slope map. Finally, recorded runoff data of the hydrometric station were applied to assess the performance of the models through four statistical indicators of the root mean square error (RMSE), the Nash-Sutcliffe efficiency (E), the coefficient of determination [Formula: see text], and percent bias (PB). Land use map analysis showed that rangeland was the dominant land use, whereas the soil texture map specified the greatest and smallest area belonging to loam and sandy loam textures, respectively. Although the runoff results showed the overestimation of large rainfall values and underestimation for rainfall with less than 40mm volume in both models, the values of E (0.78), RMSE (2), PB (16), and [Formula: see text] (0.88) revealed that eq. (a) with three empirical parameters was the most accurate equation. The maximum percent of runoff generated by rainfall for eqs. (a), (b), and (c) were 68.43, 67.28, and 51.57% which showed that bareland located in south part with the slope of more than 5% was susceptible to runoff generation and should be paid attention to watershed management.

Flow-induced vibration modeling of bluff bodies with data assimilation

Vortex-induced vibration (VIV) and galloping are two typical flow-induced vibration (FIV) problems of bluff bodies, which often cause fatigue damage or destruction of structures. Therefore, the accurate and effective FIV prediction has become a requirement of the industry in order to prevent structural damage and guide design. Although the semi-empirical model (such as the wake oscillator model) is an efficient FIV prediction tool, the precision ability of existing models is constrained due to empirical parameters and unideal mathematical equations. Generally, the numerical simulation and wind tunnel experiments are relatively accurate methods, but for complex fluid–structure interaction problems, their cost is too high. As a result, a data-driven FIV prediction model is proposed to accomplish effective and high-precision prediction in this study. The Ensemble Kalman filter (ENKF) data assimilation (DA) technique is used to combine the experimental data with a semi-empirical model. First, the sensitivity of empirical parameters is analyzed, and the most sensitive ones are selected as the target parameters for data assimilation. The mean deviation of ensemble (MDE) is proposed to represent the sensitivity of parameters. Then DA-based model is used to predict the galloping and VIV of a rectangular cylinder. The results indicate that the accuracy of the DA-based model is up to 10 times greater than that of the initial semi-empirical model. With the data-driven technology, the typical ‘quasi-steady’ theory of galloping has been improved for low Scruton number values. For the wake oscillator model, assimilating the parameters of the acceleration and velocity coupled terms can improve the prediction accuracy of VIV. Also, this modeling procedure can be regarded as a new parameter identification method from forced and free vibration.