Isotropic Function Research Articles

Machine Learning of Analytical Electron Density in Large Molecules Through Message-Passing.

Machine learning milestones in computational chemistry are overshadowed by their unaccountability and the overwhelming zoo of tools for each specific task. A promising path to tackle these problems is using machine learning to reproduce physical magnitudes as a basis to derive many other properties. By using a model of the electron density consisting of an analytical expansion on a linear set of isotropic and anisotropic functions, we implemented in this work a message-passing neural network able to reproduce electron density in molecules with just a 2.5% absolute error in complex cases. We also adapted our methodology to describe electron density in large biomolecules (proteins) and to obtain atomic charges, interaction energies, and DFT energies. We show that electron density learning is a new promising avenue with a variety of forthcoming applications.

Isotropic quantitative differential phase contrast microscopy using radially asymmetric color-encoded pupil

Differential phase contrast (DPC) microscopy provides isotropic phase images by applying asymmetric illumination patterns on the sample. The movement of specimens during series image acquisition may lead to motion blur artifacts, which are difficult to prevent. Here, we propose a new method based on pupil engineering and color multiplexing to obtain an isotropic phase transfer function and to reduce the required frames simultaneously. Radially asymmetric color pupils are implemented in a DPC microscope using a programmable thin-film transistor as a digital pupil, which gives flexibility and dynamic control for projecting illumination patterns on samples. With our approach, an isotropic quantitative phase map can be obtained using only pairwise color images for phase reconstruction. A radially asymmetric color pupil is synthesized by encoding the red, green, and blue colors. To recover accurate phase values, a color-leakage correction algorithm is applied to calibrate each color channel. Compared to a half-circle illumination pupil, our method can significantly enhance the image acquisition speed. The phase recovery accuracy is more than 97%. To show the imaging performance of our proposed method, quantitative phase imaging of living 3T3 mouse fibroblast cells is performed. Our quantitative phase measurement method may find important applications in biomedical research.

The [formula omitted]-family of covariance functions: A Matérn analogue for modeling random fields on spheres

The Matérn family of isotropic covariance functions has been central to the theoretical development and application of statistical models for geospatial data. For global data defined over the whole sphere representing planet Earth, the natural distance between any two locations is the great circle distance. In this setting, the Matérn family of covariance functions has a restriction on the smoothness parameter, making it an unappealing choice to model smooth data. Finding a suitable analogue for modelling data on the sphere is still an open problem. This paper proposes a new family of isotropic covariance functions for random fields defined over the sphere. The proposed family has a parameter that indexes the mean square differentiability of the corresponding Gaussian field, and allows for any admissible range of fractal dimension. Our simulation study mimics the fixed domain asymptotic setting, which is the most natural regime for sampling on a closed and bounded set. As expected, our results support the analogous results (under the same asymptotic scheme) for planar processes that not all parameters can be estimated consistently. We apply the proposed model to a dataset of precipitable water content over a large portion of the Earth, and show that the model gives more precise predictions of the underlying process at unsampled locations than does the Matérn model using chordal distances.

Lipschitz continuity for isotropic matrix functions

We prove a sharp Lipschitz bound for isotropic matrix functions in terms of the Lipschitz constant for the underlying vector field.

Multivariate Haar systems in Besov function spaces

We determine all cases for which the -dimensional Haar wavelet system on the unit cube is a conditional or unconditional Schauder basis in the classical isotropic Besov function spaces , , , defined in terms of first-order -moduli of smoothness. We obtain similar results for the tensor-product Haar system , and characterize the parameter range for which the dual of is trivial for . Bibliography: 31 titles.

Modeling of thin sheet forming processes by combining solid-shell finite element with isotropic elastoviscoplastic model. Application to magnetic pulse forming processes

Sheet metal alloys are used in many industries to save material, reduce weight and improve the overall performance of products. For the last decades, many types of elements have been developed to resolve the locking problems encountered in the simulation of thin structures. Among these approaches, a family of assumed-strain solid-shell elements has proved to be very efficient and attractive in simulating thin 3D structures with various constitutive models. Furthermore, these elements are able to account for anisotropic behavior of thin structures since isotropic yield functions cannot capture the real physics of some forming processes. In this work, von Mises isotropic yield criterion with Johnson-cook hardening model are combined with a linear prismatic solid-shell element to simulate sheet metal forming processes. A new element assembly technique has been developed to permit the assembly of prismatic elements in a tetrahedral element-based software. This technique splits the prism into multiple tetrahedral elements in such a way that all the cross-terms are accounted for. Furthermore, a tetrahedral based partitioning code has been modified to account for the new prismatic element shape without changing the core structure of the code. More accurate results were obtained using low number of solid-shell elements compared to its counterpart tetrahedral element (MINI element). This reduction in the number of elements accelerated the simulation, especially in the coupled magnetic-structure simulation used for magnetic pulse forming process. The proposed element and criteria are implemented into FORGE (in-house code developed at CEMEF) for simulating magnetic pulse forming process.

A random field model of external metal-loss corrosion on buried pipelines

This paper proposes a random field model to characterize the corrosion depth on the external surface of buried steel oil and gas pipelines. The model addresses the intermingling of corroded and corrosion-free areas on the pipe surface, similar to the spatial intermittency of rainfall accumulation within a geographic area, by using a latent homogeneous Gaussian random field and a spatial position-dependent threshold associated with the latent Gaussian field. High-resolution corrosion measurement data obtained from corroded pipe segments removed from in-service pipelines are used to estimate parameters of the proposed model, including the probability of corrosion at a given point, marginal distribution of the nonzero corrosion depth and correlation structure of the latent Gaussian field. The results indicate that the nonzero corrosion depth follows a shifted lognormal distribution. The isotropic γ-exponential correlation function is adequate to characterize the correlation structure of the latent Gaussian field with the correlation length varying from 17 to 50 mm and γ from 0.69 to 0.82. A comparison of simulated and measured corrosion fields suggests that the proposed model is able to capture the characteristics of naturally-occurring corrosion field on the pipe surface. The proposed model provides a useful tool for developing fitness-for-service assessment methodologies for corroded pipelines.

근피로 유발에 따른 FES 적용이 노인의 하지 등속성 근기능 및 관절위치감각에 미치는 영향

근피로 유발에 따른 FES 적용이 노인의 하지 등속성 근기능 및 관절위치감각에 미치는 영향

An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

Based on the Cayley-Hamilton theorem and fixed-point method, we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional (3D) inner-product space, which avoids introducing the generating function and Taylor series expansion. The proof is also extended to any finite-dimensional inner-product space.

Spatial estimation methods for mapping corn silage and grain yield monitor data

Harvester-mounted yield monitor systems are increasingly used to document corn (Zea mays L.) yield. The three most commonly used spatial estimation methods to convert point data gathered with yield monitors to regular, grid-based, raster maps include nearest neighbor (NN), inverse distance weighting (IDW) and kriging. Seven spatial estimation methods (NN, IDW using 10, 20, 30 and all data points and kriging with exponential and Matern covariance functions) were evaluated to determine the method that most accurately captures intra-field spatial variability of corn silage and corn grain yield in New York. Yield monitor data from two dairy farms and two grain operations were cleaned using Yield Editor prior to spatial analyses. The dataset included 7–10 years of data per farm for a combined 7484 ha (245 fields) of silage and 6971 ha (253 fields) of grain. Data were split into training (80%) and cross-validation datasets (remaining 20% of the data). Normalized root mean squared error (NRMSE) was used to evaluate the accuracy of the spatial estimation methods. Kriging with the Matern covariance function resulted in the most accurate corn silage and grain yield raster maps both at the farm and field level. There were statistically significant differences in NRMSE between kriging with the Matern isotropic covariance function and all other models for both corn silage and grain, regardless of field size, year when data were obtained or farm that supplied the data. These results are beneficial to ensure accurate and precise spatial mapping of yield products toward optimized corn growth management.

THE ROLE OF VASODILATION FACTORS IN THE PATHOGENESIS OF CHRONIC HEART FAILURE OF ISCHEMIC ORIGIN IN ATRIAL FIBRILLATION

The purpose of the study is to study the possible role of vasodilation factors in the pathogenesis of chronic heart failure (CHF) in persistent atrial fibrillation (AF) in patients with stable coronary heart disease. Materials and methods. A survey of 86 patients with stable coronary heart disease complicated by CHF II-III FC according to the NYHA classification. There was 1 group - 22 patients with CHF with reduced LV EF ≤ 40.0% and AF; I (comparative group) - 20 patients with CHF with reduced LV EF without AF; 2-nd group - 24 patients with preserved LV EF ≥ 40.1% and AF and II (comparative group) - 20 patients with CHF with preserved LV EF without AF. The content of endothelial nitric oxide synthase (eNOS), nitrites (NO2-) and nitrates (NO3-) was determined. All patients underwent electrocardiographic examination (ECG) for the initial screening of arrhythmias and conduction, diagnosis of focal changes in the ventricular myocardium. Structural and hemodynamic characteristics of the heart muscle were determined by echocardiography.Results. In the examined patients of the 1st group with CHF of ischemic origin and reduced LV EF ≤ 40.0% and AF in comparison with the 2nd group of patients with CHF with preserved LV EF and AF, a significant increase in the values of ICO, ICD, IMML, the size of LA and a decrease in LV EF (p <0.01), indicating the development of LVH (remodeling) and a decrease in isotropic heart function. When comparing the levels of vasodilation factors in patients with CHF with low LV EF and AF and data from the CHF comparison group without AF, a significant decrease in eNOS by 96.8% (almost twice) and a significant decrease in serum nitrite and nitrate levels (p < 0.01), indicating the development of endothelial dysfunction. Conclusions. In patients with CHF of ischemic origin in the development of persistent forms of AF pathogenetic role is played by a significant decrease in vasodilating factors (content of eNOS, nitrites and nitrates). At decrease in EF of LV ≤ 40,0% there is a significant decrease in vasodilating factors, as a result of disturbance of endothelial function that testifies to need of correction of the revealed changes directed on slowing down of disease progression.

The dynamical structure of broken power-law and double power-law models for dark matter haloes

ABSTRACT Galaxy kinematics and gravitational lensing are two complementary ways to constrain the distribution of dark matter on galaxy scales. The typical dark matter density profiles adopted in dynamical studies cannot easily be adopted in lensing studies. Ideally, a mass model should be used that has the global characteristics of realistic dark matter distributions, and that allows for an analytical calculation of the magnifications and deflection angles. A simple model with these properties, the broken power-law (BPL) model, has very recently been introduced. We examine the dynamical structure of the family of BPL models. We derive simple closed expressions for basic dynamical properties, and study the distribution function under the assumption of velocity isotropy. We find that none of the BPL models with realistic parameters has an isotropic distribution function that is positive over the entire phase space, implying that the BPL models cannot be supported by an isotropic velocity distribution, or models with a more radially anisotropic orbital structure. This result limits the attractiveness of the BPL family as a tool for lensing studies to some degree. More generally, we find that not all members of the general family of double power-law or Zhao models, often used to model dark matter haloes, can be supported by an isotropic or radially anisotropic distribution function. In other words, the distribution function may become negative even for spherically symmetric models with a well-behaved density profile.

A THERMODYNAMIC CONSISTENT ELASTOPLASTIC FRACTIONAL TIME-DEPENDENT DAMAGE MODEL FOR ROCK-LIKE MATERIALS

This paper aims at presenting a thermodynamically consistent elastoplastic fractional time-dependent damage model for describing short- and long-term behaviors of rock-like materials. The model utilizes generalized potential theory with a yield criterion, a non-associated flow rule and an isotropic plastic hardening function for describing the evolution of plasticity. A time-dependent Lemaitre-type damage is introduced through fractional derivative considering the short- and long-term evolution of microstructure, which leads to progressive degradation of elastic modulus and failure strength of material. In this context, both instantaneous and delayed deformations shall be well described within the unique constitutive model. For practical application, an efficient and convergent semi-implicit return mapping (SRM) algorithm involving a plasticity-damage decoupling corrector is developed. The proposed model is finally adopted to predict the mechanical and deformation behavior of several types of rocks under different loading conditions in conventional or quasi-static (different loading strain rate) triaxial compression tests, creep tests and relaxation tests. Comparisons between model predictions and experimental data demonstrate that the proposed model has the capability to reproduce main features of short and long-term behaviors of rock-like materials.

Stress correlations in frictional granular media

This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.

Inverse Bremsstrahlung Absorption in an Unmagnetized Plasma With a Kappa Distribution Function

In thermonuclear fusion, one of the ways of laser energy absorption is called collisional absorption or inverse bremsstrahlung (IB) absorption. The present research is an attempt to calculate the IB absorption in homogeneous and unmagnetized plasma through the kinetic theory and the Fokker–Planck equation. The isotropic distribution function, $f_{0}$ , is considered as the Kappa distribution, and the IB absorption is calculated according to the laser electric field and the electric current in plasma. As the results show, the IB absorption value increases at short laser wavelengths, low spectral indices, $\kappa $ , and low electron temperatures. The theoretical study of IB absorption offered in this research allows optimizing the parameters of laser and plasma to obtain good energy efficiency in inertial confinement fusion experiments.

Models for the difference of continuous covariance functions

A linear combination, with negative weights, of two continuous covariance functions has been analyzed by a few authors just for special cases and only in the real domain. However, a covariance is a complex valued function: for this reason, the general problem concerning the difference of two covariance functions in the complex domain needs to be analyzed, while it does not yet seem to have been addressed in the literature; hence, exploring the conditions such that the difference of two covariance functions is again a covariance function can be considered a further property. Therefore, this paper yields a contribution to the theory of correlation, hence the results cannot be restricted to the particular field of application. Starting from the difference of two complex covariance functions defined in one dimensional Euclidean space, wide families of models for the difference of two complex covariance functions can be built in any dimensional space, utilizing some well known properties. In particular, the difference of two real covariance functions has been considered; moreover, the difference between some special isotropic covariance functions has also been analyzed. A detailed analysis of the parameters of the models involved has been proposed; this kind of analysis opens a gate for modeling, in any dimensional space, the correlation structure of a peculiar class of complex valued random fields, as well as the subset of real valued random fields. Some relevant hints about how to construct the subset of real covariance functions characterized by negative values have also been given.

On the Transversely Isotropic, Hyperelastic Response of Central Nervous System White Matter Using a Hybrid Approach

Abstract A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress–strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for microstructural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. It is noted that the model is not limited to small strains and can be applied to large deformations.

Efficient implementation of isotropic cubic response functions for two-photon absorption cross sections within the self-consistent field approximation.

Within the self-consistent field approximation, computationally tractable expressions for the isotropic second-order hyperpolarizability have been derived and implemented for the calculation of two-photon absorption cross sections. The novel tensor average formulation presented in this work allows for the evaluation of isotropic damped cubic response functions using only ∼3.3% (one-photon off-resonance regions) and ∼10% (one-photon resonance regions) of the number of auxiliary Fock matrices required when explicitly calculating all the needed individual tensor components. Numerical examples of the two-photon absorption cross section in the one-photon off-resonance and resonance regions are provided for alanine-tryptophan and 2,5-dibromo-1,4-bis(2-(4-diphenylaminophenyl)vinyl)-benzene. Furthermore, a benchmark set of 22 additional small- and medium-sized organic molecules is considered. In all these calculations, a quantitative assessment is made of the reduced and approximate forms of the cubic response function in the one-photon off-resonance regions and results demonstrate a relative error of less than ∼5% when using the reduced expression as compared to the full form of the isotropic cubic response function.

Multivariate isotropic random fields on spheres: Nonparametric Bayesian modeling and Lp fast approximations

We study multivariate Gaussian random fields defined over d-dimensional spheres. First, we provide a nonparametric Bayesian framework for modeling and inference on matrix-valued covariance functions. We determine the support (under the topology of uniform convergence) of the proposed random matrices, which cover the whole class of matrix-valued geodesically isotropic covariance functions on spheres. We provide a thorough inspection of the properties of the proposed model in terms of (a) first moments, (b) posterior distributions, and (c) Lipschitz continuities. We then provide an approximation method for multivariate fields on the sphere for which measures of Lp accuracy are established. Our findings are supported through simulation studies that show the rate of convergence when truncating a spectral expansion of a multivariate random field at a finite order. To illustrate the modeling framework developed in this paper, we consider a bivariate spatial data set of two 2019 NCEP/NCAR Flux Reanalyses.

Implementation of Particle Swarm Optimization Algorithm in Matlab Code for Hyperelastic Characterization

The purpose of this paper is to demonstrate the applicability of Particle Swarm Optimization algorithm to determine material parameters in incompressible isotropic elastic strain-energy functions using combined tension and torsion loading. Simulation of rubber behavior was conducted from the governing equations of the deformation of a cylinder composed of isotropic hyperelastic incompressible materials. Four different forms of strain-energy function were considered based respectively on polynomial, exponential and logarithmic terms to reproduce load force (N) and torque (M) trends using natural rubber experimental data. After highlighting the minimization of the objective function generated in the fitting process, the study revealed that a particle swarm optimization algorithm could be successfully used to identify the best material parameters and characterize the behavior of rubber-like hyperelastic materials.