Order Approximation Research Articles

Efficient and Accurate Separable Models for Discretized Material Optimization: A Continuous Perspective Based on Topological Derivatives

Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models constructed from convex separable first order approximations have a long and successful tradition in the design optimization community and have led to powerful optimization tools like the prominently used method of moving asymptotes (MMA). In this paper, we introduce several new separable approximations to a model problem and examine them in terms of accuracy and fast evaluation. The models can, in general, be nonconvex and are based on the Sherman–Morrison–Woodbury matrix identity on the one hand, and on the mathematical concept of topological derivatives on the other hand. We show a surprising relation between two models originating from these two—at a first sight—very different concepts. Numerical experiments show a high level of accuracy for two of our proposed models while also their evaluation can be performed efficiently once enough data has been precomputed in an offline stage. Additionally it is demonstrated that suboptimal decisions can be avoided using our most accurate models.

Exact and leading order radiative effects in semi-inclusive deep inelastic scattering

Radiative effects in semi-inclusive hadron leptoproduction of unpolarized particles are calculated within the leading order approximation. The contributions of the infrared-free sum of the effects of real and virtual photon emission as well as the contribution of the exclusive radiative tail are considered. It is demonstrated how the obtained formulas in the leading log approximation can be obtained using the standard approach of the leading log approximation as well as from the exact expressions for the radiative correction of the lowest order. The method of the electron structure function is used to calculate the higher order corrections. The results are analytically compared to the results obtained by other groups. Numeric illustrations are given in the kinematics of the modern experiments at Jefferson Laboratory. Published by the American Physical Society 2024

Free convective heat flow from cold and heated conical shape bodies in Newtonian liquids

Investigation on the simulation effects of free convection flow from a cold and heated cone with a downward pointing tip in various stagnant fluids is presented in this study. Examining the steady-state isotherm patterns around the cone to determine heat transfer characteristics. Results are presented for friction factor and Nusselt number distributions Over the surface of the cone for distinct dimensionless quantities like Pr and Gr to deliver an extensive class of dimensionless numbers. The commercial program ANSYS CFX 16.0 was used to solve the regulating equations which governs the motion vis., momentum mass and energy were computed. The temperature as well as flow fields are coupled using the Boussinesq approximation in order to simplify the governing equations and capture natural convection. Heat transmission has a rather minimal influence on the local Nusselt number for low Grashof and Prandtl values, according to the findings. It gains strength as the Grashof and Prandtl numbers grow, because of the extreme curvature of the isotherms, the maximum value of the local Nusselt number may be found around the corner of the vertical cone in both cones. The current simulations closely match the numerical values provided in the printed matter.

Multicontinuum homogenization. General theory and applications

In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic variables at each macroscale point are defined and the resulting multicontinuum equations are formulated. In this paper, we propose a general formulation and associated ingredients that allow performing multicontinuum homogenization. Our derivation consists of several main parts. In the first part, we propose a general expansion, where the solution is expressed via the product of multiple macro variables and associated cell problems. The second part consists of formulating the cell problems. The cell problems are formulated as saddle point problems with constraints for each continua. Defining the continua via test functions, we set the constraints as an integral representation. Finally, substituting the expansion to the original system, we obtain multicontinuum systems. We present an application to the mixed formulation of elliptic equations. This is a challenging system as the system does not have symmetry. We discuss the local problems and various macroscale representations for the solution and its gradient. Using various order approximations, one can obtain different systems of equations. We discuss the applicability of multicontinuum homogenization and relate this to high contrast in the cell problem. Numerical results are presented.

An energy-efficient GMRES–multigrid solver for space-time finite element computation of dynamic poroelasticity

We present and analyze computationally Geometric MultiGrid (GMG) preconditioning techniques for Generalized Minimal RESidual (GMRES) iterations to space-time finite element methods (STFEMs) for a coupled hyperbolic–parabolic system modeling, for instance, flow in deformable porous media. By using a discontinuous temporal test basis, a time marching scheme is obtained. Higher order approximations that offer the potential to inherit most of the rich structure of solutions to the continuous problem on computationally feasible grids increase the block partitioning dimension of the algebraic systems, comprised of generalized saddle point blocks. Our V-cycle GMG preconditioner uses a local Vanka-type smoother. Its action is defined in an exact mathematical way. Due to nonlocal coupling mechanisms of 348 unknowns, the smoother is applied on patches of elements. This ensures damping of higher order error frequencies. By numerical experiments of increasing complexity, the efficiency of the solver for STFEMs of different polynomial order is illustrated and confirmed. Its parallel scalability is analyzed. Beyond this study of classical performance engineering, the solver’s energy efficiency is investigated as an additional and emerging dimension in the design and tuning of algorithms on the hardware.

Specialization, market access and real income

This paper estimates the impact of external demand shocks on real income. We utilize a first order approximation to a wide class of small open economy models that feature sector-level gravity in trade flows, which allows us to measure foreign shocks and characterize their welfare impact in terms of reduced-form elasticities. We use machine learning techniques to group 4-digit manufacturing sectors into a smaller number of clusters, and show that the cluster-level elasticities of income with respect to foreign shocks can be estimated using high-dimensional statistical techniques. Foreign demand shocks in complex intermediate and capital goods have large positive impacts on real income, whereas impacts in other sectors are negligible. We show that the estimates imply that countries that specialize in these sectors enjoy greater gains from increased openness, and that (small) export subsidies to these sectors are welfare-improving. Finally, a calibrated multi-sector production and trade model with input–output linkages and external economies of scale can match the empirical estimates.

Fixed-point algorithms for solving the critical value and upper tail quantile of Kuiper's statistics

Kuiper's statistic is a good measure for the difference of ideal distribution and empirical distribution in the goodness-of-fit test. However, it is a challenging problem to solve the critical value and upper tail quantile, or simply Kuiper pair, of Kuiper's statistics due to the difficulties of solving the nonlinear equation and reasonable approximation of infinite series. In this work, the contributions lie in three perspectives: firstly, the second order approximation for the infinite series of the cumulative distribution of the critical value is used to achieve higher precision; secondly, the principles and fixed-point algorithms for solving the Kuiper pair are presented with details; finally, finally, a mistake about the critical value cnα for (α,n)=(0.01,30) in Kuiper's distribution table has been labeled and corrected where n is the sample capacity and α is the upper tail quantile. The algorithms are verified and validated by comparing with the table provided by Kuiper. The methods and algorithms proposed are enlightening and worth of introducing to the college students, computer programmers, engineers, experimental psychologists and so on.

A computational strategy for estimation of mean using optimal imputation in presence of missing observation.

In this study, we suggest an optimal imputation strategy for the elevated estimation of the population mean of the primary variable utilizing the known auxiliary parameters for the missing observations. Under this strategy, we suggest a new modified Searls type estimator, and we study its sampling properties, mainly bias and mean squared error (MSE), for an approximation of order one. The introduced estimator is compared theoretically with the estimators of population mean in competition under the imputation method. The efficiency conditions for the introduced estimator to be more efficient than the estimators in the competition are derived. To be sure about the efficiencies, these efficiency conditions are verified through the three natural populations. We have also conducted a simulation study and generated an artificial population with the same parameters as a natural population. The estimator with minimum MSE and the highest Percentage Relative Efficiency (PRE) is recommended for practical use in different areas of applications.

Deriving the Kramers’ dispersion formula from the canonical transformations of Heisenberg’s equation of motion

We obtain the canonical transformations for the time-dependent Hamiltonian from Heisenberg’s equation of motion, based on which we derive the Kramers’ dispersion formula via the perturbation theory of matrix mechanics to the second order approximation.

Comparison of neural network architectures for feature extraction from binary black hole merger waveforms

We evaluate several neural-network architectures, both convolutional and recurrent, for gravitational-wave time-series feature extraction by performing point parameter estimation on noisy waveforms from binary-black-hole mergers. We build datasets of 100 000 elements for each of four different waveform models (or approximants) in order to test how approximant choice affects feature extraction. Our choices include SEOBNRv4P and IMRPhenomPv3, which contain only the dominant quadrupole emission mode, alongside IMRPhenomPv3HM and NRHybSur3dq8, which also account for high-order modes. Each dataset element is injected into detector noise corresponding to the third observing run of the LIGO-Virgo-KAGRA (LVK) collaboration. We identify the temporal convolutional network architecture as the overall best performer in terms of training and validation losses and absence of overfitting to data. Comparison of results between datasets shows that the choice of waveform approximant for the creation of a dataset conditions the feature extraction ability of a trained network. Hence, care should be taken when building a dataset for the training of neural networks, as certain approximants may result in better network convergence of evaluation metrics. However, this performance does not necessarily translate to data which is more faithful to numerical relativity simulations. We also apply this network on actual signals from LVK runs, finding that its feature-extracting performance can be effective on real data.

H2O-rich rutile as an indicator for modern-style cold subduction

The trace-element and isotope geochemistry of rutile are robust tools to determine metamorphic temperatures, age, and host-/source lithologies. The use of rutile as single grain indicator for pressure, temperature, time and composition (P–T–t–X) of the host rock, which is vital in the use of detrital rutile to trace plate-tectonic regimes throughout Earth’s history, requires the identification of a pressure dependent trace element in rutile. We investigate the pressure dependence of hydrogen in rutile using polarized in-situ Fourier Transform Infrared (FTIR) spectroscopy. H2O contents in rutile vary between < 10–2500 μg/g H2O with higher contents in samples with higher peak metamorphic pressures, making H2O-in-rutile a viable pressure indicator. The highest H2O contents at ~ 450–2000 μg/g are observed in mafic low temperature eclogite-facies rutile related to modern-style cold subduction conditions. Hydrogen zoning in FTIR maps indicates that H+ is retained at temperatures below 600–700 °C. Ratios of H2O/Zr, using H2O as pressure indicator and Zr as temperature proxy, are a proxy for thermal gradients of metamorphic rutile (i.e. P/T). Low temperature eclogite samples are also characterized by high Fe contents and therefore Fe/Zr-ratios might be used as a first order approximation for H2O/Zr-ratios to identify mafic low temperature eclogite facies rutile. Based on common discrimination diagrams, Nb, W, and Sn can be used to distinguish different host/source rock lithologies of rutile. Combining both H2O/Zr-ratios and Nb, W, and Sn contents can thus identify modern-style cold subduction signatures in rutile. The developed systematics can consequently be used to trace cold-subduction features in the (pre-Proterozoic) detrital record.

A novel isogeometric model for dynamic buckling analysis of doubly curved two-directional functionally graded porous shallow microshells in thermal environments via variable length-scale parameters

In this study, the thermo-mechanical dynamic buckling analysis of two-directional functionally graded porous (2D-FGP) shallow microshells resting on elastic foundations with arbitrary boundary conditions is performed using the isogeometric approach. The isogeometric approach takes advantage of non-uniform rational B-spline basic functions to exactly represent the structure geometry models and the attainment of higher order approximation conditions. The characteristics of the material vary in both the thickness and axial x orientation. Especially, a new point in this material length-scale parameter of microshell is analyzed as a function of spatial coordinates and as a function of the material gradient parameters. Using Hamilton’s principle, the modified couple stress theory, and Kirchhoff-Love’s shell theory, the governing equations of a 2D-FGP microshell lying on a Pasternak medium are obtained. A computer program that employs an isogeometric analysis method to analyze the static and dynamic buckling of a 2D-FGP doubly curved shallow microshell with various boundary conditions. The numerical results for thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with various planforms, such as rectangular and circular, are presented. Several special cases are used to demonstrate the accuracy and efficacy of the developed model by comparing the numerical results obtained by the proposed formulations with other published data. In addition, the effects of certain parameters, such as the length scale parameters, the power-law indexes, the thickness-to-sides ratio, and the radius ratio, on the dynamic thermo-mechanical buckling response of the 2D-FGP shallow microshells with double curvature are explored in depth.

A Canonical Transformation for the Anderson Lattice Hamiltonian with f–f Electron Coupling

In this work, a new canonical transformation for the Anderson lattice Hamiltonian with f–f electron coupling was developed, which was further used to identify a new Kondo lattice Hamiltonian. Different from the single impurity Kondo effect, the resulted new Kondo lattice Hamiltonian only includes the spin-flip scattering processes between conduction electrons and f-electrons, while the normal process of non-spin-flip scattering is absent in this Hamiltonian, under the second order approximation. The new Kondo lattice Hamiltonian may be used to study some anomalous physical properties in some Kondo lattice intermetallic compounds.

Design based synthetic imputation methods for domain mean

In real life, situations may arise when the available data are insufficient to provide accurate estimates for the domain, the small area estimation (SAE) technique has been used to get accurate estimates for the variable under study. The problem of missing data is a serious problem that has an impact on sample surveys, but small area estimates are especially prone to it. This paper is a basic effort that suggests design based synthetic imputation methods for the domain mean estimation using simple random sampling in order to address the issue of missing data under SAE. The expression of the mean square error for the proposed imputation methods are obtained up to first order approximation. The efficiency conditions are determined and a thorough simulation study is carried out using artificially generated data sets. An application is included with real data that further supports this study.

Regularized Nyström Subsampling in Covariate Shift Domain Adaptation Problems

The unsupervised domain adaptation problem with covariate shift assumption is considered. Within the framework of the Reproducing Kernel Hilbert Space concept, an algorithm is constructed that is a combination of the Nyström subsampling and the iterated Tikhonov regularization. This approach allows significantly reduce the amount of computing resources involved and at the same time achieves the minimal (by order) approximation accuracy under the big data settings.

A Multiagent Meta-Based Task Offloading Strategy for Mobile-Edge Computing

Task offloading in mobile edge computing (MEC) improves the efficacy of mobile devices in terms of computing performance, data storage, and energy consumption by offloading computational tasks to edge servers. Efficient task offloading can leverage MEC technology to reduce task processing latency and energy consumption. By integrating the reasoning ability and machine intelligence of the cognitive computing architecture, such as SOAR and ACT-R, reinforcement learning (RL) algorithms have been applied to resolve the task offloading in MEC. To solve the problem that conventional Deep RL (DRL) algorithms cannot adapt to dynamic environments, this paper proposed a task offloading scheduling strategy which combined multi-agent reinforcement learning and meta-learning. In order to make the two actions of charging time and offloading strategy fully considered at the same time, we implemented a learning network of two agent on a mobile device. To efficiently train the policy network, we proposed a first order approximation method based on clipped surrogate objective. Finally, the experiments are designed with variety of the number of subtasks, transmission rate, and edge server performance, and the results show that the MRL-based strategy has the overwhelming overall performance and can be quickly applied in various environments with good stability and generalization.

Half-metallic ferromagnetic features of V-doped Cu2O alloys: TB-mBJ and DFT + U insights

The goal of this study is based on the determination of the half-metallic ferromagnetic features of V-doped Cu2O alloys (Cu2(1-x)V2xO (x = 0, 0.25, 0.50, 0.75 and 1)) using both GGA + U and TB-mBJ-GGA approximations (GGA: the generalized gradient approximation) within the accurate full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) method implemented in the WIEN2k package. The structural properties are computed by using the GGA approximation in order to find the equilibrium structural parameters of each alloy, such as: lattice parameter, bulk modulus and its first-pressure derivative. The electronic properties calculated by TB-mBJ-GGA and GGA + U approximations show the complete half-metallicity of Cu1.50V0.50O, CuVO, Cu0.50V1.50O and V2O alloys, in fact, all the half-metallic gaps (EHM) of the compete half-metals are given in this study. The magnetic properties of the studied alloys show that the majority of the total magnetic moment (MTot) comes from the V atom with small contributions from Cu atom and the interstitial zone. The N0α and N0β exchange-splitting constants are given in order to analyze the contributions to conduction and valence bands during the exchange and splitting process. Furthermore, the hybridization between the 2p-O and 3d-V states (p-d hybridization) is the cause for the appearance of feeble magnetic moments on the non-magnetic Cu and O sites and the reduction of the atomic magnetic moment of the V atom.

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\vert$$\\end{document}5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

Original and modified non-perturbative renormalization group equations of the BMW scheme at the arbitrary order of truncation

We consider the non-perturbative renormalization group (RG) equations, obtained as approximations of the exact Wetterich RG flow equation within the Blaizot–Mendez–Wschebor (BMW) truncation scheme. For the first time, we derive explicit RG flow equations for the scalar model at the arbitrary order of truncation. Moreover, we consider original, as well as modified, approximations, used to obtain a set of closed equations. We compare these equations at the s = 2 order of truncation with those recently derived in J. Phys. A: Math. Theor. 53, 415002 (2020) within a new truncation scheme and find a striking similarity. Namely, the first-order equations of the latter scheme, those of the original BMW scheme, and those of the modified BMW scheme (at s = 2) differ only in one term. We solved these equations by a recently proposed and tested method of semi-analytic approximations. Thus, the critical exponents η, ν, and ω were evaluated, recovering also the known results of the original BMW scheme. In addition, we estimated the subleading correction-to-scaling exponent ω2 for the three equations considered. To the best of our knowledge, this exponent has not yet been extracted from the Wetterich equation beyond the local potential (the zeroth order) approximation. Our current estimate for the 3D Ising model is ω2 = 2.02 (40), where the error bars include the expected truncation error in the BMW scheme.

Selection of reference model for adaptive PMSM drive based on MRAC approach

The selection of a reference model (RM) for a Model-Reference Adaptive Control is one of the most important aspects of the synthesis process of the adaptive control system. In this paper, the four different implementations of RM are developed and investigated in an adaptive PMSM drive with variable moment of inertia. Adaptation mechanisms are based on the Widrow-Hoff rule (W-H) and the Adaptation Procedure for Optimization Algorithms (APOA). Inadequate order or inaccurate approximation of RM for the W-H rule may provide poor behavior and oscillations. The results prove that APOA is robust against an improper selection of RM and provides high-performance PMSM drive operation.