Order Estimation Research Articles

Domestic and international CO2 source-sink matching for decarbonizing India's electricity

India is the third largest CO2 emitter in the world and the ascending trend has not shown clear signs of leveling off. Electricity generation is the most important contributing sector. This paper examines the role of CO2 capture, utilization and storage (CCUS) in decarbonizing India's electricity. We build a source-sink matching optimization model and unlike previous research, include transport by ship to overseas CO2 storage sites. We initialize the model with open-source data on power sector emissions and sinks to work out the least-cost solutions for achieving various CO2 matching scenarios. CO2 can be captured in fossil-fuel-fired power plants in India, while the utilization and storage could be either within or beyond the country's border. We assess the potential chain of shipping CO2 to the Middle East for enhanced oil recovery and CO2 storage. The economics of such international CCUS chains may affect the role of CCUS in India's decarbonization scenarios. We provide first order estimates of costs and conditions to make such a proposition attractive. The model is available with an open-source license and is customizable to include additional sources, onshore and overseas sinks, and shipping terminals.

Space fractional kinetic model for different types of suspension profiles in turbulent flows with a neural network-based estimation of fractional orders

Estimation of particle concentration distribution profile is important to understand the inherent mixing process, changes of river morphology, and nature of transportation of particles. In this study, the effects of non-locality are investigated to analyze, distinguish and predict different types of profiles of the suspended concentration distribution in turbulent flows through open channels, pipes, and mixing boxes. The effects of non-locality are captured through fractional derivatives and integrals. Starting from the fractional Liouville equation and considering the power-law jumps of particles in the carrier fluid, the fractional kinetic equation is derived through mathematical analysis. The kinetic model is solved and an analytical model is proposed using the Laplace transformation. The proposed solution contains the two parameters (as α the order of fractional model and μ the shape parameter) Mittag-Leffler function and is a more general one that contains several previous models as special cases. The proposed model can predict four different types of suspension concentration distributions namely type-I, type-II, plume-like, and convex type profiles under different conditions. Further, the model is validated with existing experimental data of dilute and dense flow in open channels and pipes, flows in square pipes, slurry pipelines, and fluid mud gravity currents. Satisfactory results are obtained. A detailed non-linear multivariate regression analysis is carried out with a wide range of selected data and models are proposed to compute model parmeters. To increase the efficiency of the model, an artificial neural network (ANN) model is proposed to predict the model parameters. The ANN-based models show better results than the regression analysis. Validation results show that non-locality has significant effects on the structure of the concentration profiles. From the analysis of the model parameters, it is found that type-I profile occurs under the subdiffusion process where α⩽1 and μ=1 and other three types (type-II, plume-like and convex) of profiles are associated with the superdiffusion process when α>1 and μ>1.

Analytical Deflection Profiles and Pull-In Voltage Calculations of Prestressed Electrostatic Actuated MEMS Structures

This paper presents a zeroth and first order perturbative analysis of prestressed electrostatic actuated Microelectromechanical systems (MEMS). Perturbation theory is used to calculate the deflection profile of various MEMS structures, from which the pull-in voltage is estimated using the weighed residual method, where both a Galerkin expression and a Dirac delta function have been used as weight functions. A prestressed circular Capacitative Micromachined Ultrasonic Transducer (CMUT) is used as the main example in this paper. This device is modeled as a circular clamped plate subjected to an electrostatic pressure. The calculated pull-in voltage has been compared with experimental data of highly prestressed CMUTs, where a relative error between -36% and -8% is observed for a model that does not include stress. The model that includes the residual stress lowers the range of the relative error to values between -5% and 21%. To improve the accuracy of the pull-in voltage estimate Richardson extrapolation has been calculated from the zeroth and first order estimates. The pull-in voltage models are compared with a Finite Element Model (FEM), where an overestimation, in the high stress regime, of 10% is observed for the zeroth order model, less than 5% for the Galerkin method and 3% for the Richardson extrapolation. [2020-0358]

Superconvergence analysis of a mixed finite element approximation for the nonlinear fourth-order Rosenau-RLW equation

The focus of this paper is on a implicit Backward-Euler (BE) scheme with the mixed finite element method (FEM) for the two-dimentional general Rosenau-RLW equation. In which the bilinear element is used to approximate the exact solution v and the variable p=−Δv, and the zero-order nédéléc's finite element to the variable q→=ϕ∇v, respectively. An important point is that with the proposed scheme we are able to bound the numerical solution in H1-norm, so that we can efficiently solve the nonlinear term. Moreover, the stability, existence and uniqueness of approximate solution are demonstrated. Based on the combination of the interpolation and projection technique, the superconvergence estimates of order O(h2+τ) for v in H1-norm and the introducing variable q→ in L2-norm, and optimal error estimate of order O(h+τ) for introducing variable p in H1-norm is proved. Finally, numerical example is done to certify our theoretical results.

Superconvergence analysis for nonlinear Schrödinger equation with two-grid finite element method

In this paper, two-grid finite element method is applied to solve the nonlinear Schrödinger equation. On one hand, prior estimates of the numerical solution on the coarse grid and the introduced temporal equation are derived. Subsequently, taking advantage of the mathematical induction method and an identical equation of the inner product, result with order O(h2+τ) in L2-norm is deduced on the coarse grid and unconditional boundedness of the numerical solution is deduced as a result. Unconditional superclose result with order O(h2+τ) in H1-norm is arrived at based on the above results. On the other hand, on the fine grid, an Euler scheme is constructed based on the numerical solution of the coarse grid. To achieve unconditional superconvergent estimate of order O(H4+h2+τ) in H1-norm, we give fine estimate of the nonlinear term with H2=O(h). At last, numerical example is introduced to confirm the theoretical analysis. Here, H and h are the spatial parameters on the coarse grid and the fine grid, respectively, and τ is the time step.

Control of high-order processes: repeated-pole plus dead-time models' identification

This paper aims to present two approaches for repeated-pole plus dead-time (RPPDT) models identification procedures for highorder processes based. First approach is based on using two or three points over the process reaction curve −an open-loop test− whereas the second approach is based on the use of the process relay control oscillating signals −a closed-loop test. Equations are provided for both model parameters identification as well as order estimation. Comparison tests confirm that the RPPDT models provide a better representation of the high-order process dynamics than its simple, usually employed, first-order approximation. These models are suitable for process representation in dynamic simulations and control system design studies.

Sparse estimation of Linear Non-Gaussian Acyclic Model for Causal Discovery

We consider the problem of inferring the causal structure from observational data, especially when the structure is sparse. This type of problem is usually formulated as an inference of a Directed Acyclic Graph (DAG) model. The Linear Non-Gaussian Acyclic Model (LiNGAM) is one of the most successful DAG models, and various estimation methods have been developed. However, existing methods are not efficient for some reasons: (i) the sparse structure is not always incorporated in causal order estimation, and (ii) the information of higher-order moments of the data is not used in parameter estimation. To address these issues, we propose a new estimation method for a linear DAG model with non-Gaussian noises. The proposed method is based on a single statistical criterion that includes the log-likelihood of independent component analysis (ICA) and two penalty terms. The two penalties are related to the sparsity and the consistency condition, respectively. This criterion enables us to leverage the sparse structure and the information of higher-order moments throughout the estimation. For stable and efficient optimization, we propose some devices, such as a modified natural gradient. Numerical experiments show that the proposed method outperforms the existing methods.

Variations on Hammersley’s interacting particle process

The longest increasing subsequence problem for permutations has been studied extensively in the last fifty years. The interpretation of the longest increasing subsequence as the longest 21-avoiding subsequence in the context of permutation patterns leads to many interesting research directions. We introduce and study the statistical properties of Hammersleytype interacting particle processes related to these generalizations and explore the finer structures of their distributions. We also propose three different interacting particle systems in the plane analogous to the Hammersley process in one dimension and obtain estimates for the asymptotic orders of the mean and variance of the number of particles in the systems.

Kolmogorov widths of weighted Sobolev classes on a multi-dimensional domain with conditions on the derivatives of order [formula omitted] and zero

In this paper order estimates of the Kolmogorov widths for some weighted Sobolev classes in a weighted Lebesgue space are obtained. The weighted Sobolev classes are defined by a restriction on the weighted Lp1-norm of the highest order derivative and the weighted Lp0-norm of the function.

Second order estimates for a class of complex Hessian equations on Hermitian manifolds

In this paper, we derive an a priori second order estimate for solutions which are in Γk+1 cone to a class of complex Hessian equations with both sides of the equation depending on the gradient on compact Hermitian manifolds.

Development of an Inverse Plume Model for Mass Eruption Rate in Unsteady Conditions

Abstract Following volcanic eruptions, forecasters need accurate estimates of mass eruption rate (MER) to appropriately predict the downstream effects. Most analyses use simple correlations or models based on large eruptions at steady conditions, even though many volcanoes feature significant unsteadiness. To address this, a superposition model is developed based on a technique used for spray injection applications, which predicts plume height as a function of the time-varying exit velocity. This model can be inverted, providing estimates of MER using field observations of a plume. The model parameters are optimized using laboratory data for plumes with physically relevant exit profiles and Reynolds numbers, resulting in predictions that agree to within 10% of measured exit velocities. The model performance is examined using historic eruptions with well-documented unsteadiness, again providing MER estimates of the correct order of magnitude. This method can provide a rapid alternative for real-time forecasting of small, unsteady eruptions.

English

We introduce and study various discontinuous Galerkin (DG) finite element approximations for a parabolic variational inequality associated with a general obstacle problem in ℝd (d = 2, 3). For the fully-discrete DG scheme, we employ a piecewise linear finite element space for spatial discretization, whereas the time discretization is carried out with the implicit backward Euler method. We present a unified error analysis for all well known symmetric and non-symmetric DG fully discrete schemes, and derive error estimate of optimal order $${\cal O}(h + \Delta t)$$ in an energy norm. Moreover, the analysis is performed without any assumptions on the speed of propagation of the free boundary and only the realistic regularity $${u_t} \in {{\cal L}^2}(0,T;{{\cal L}^2}(\Omega ))$$ is assumed. Further, we present some numerical experiments to illustrate the performance of the proposed methods.

Adaptive Fractional-Order Sliding Mode Control for Admittance-Based Telerobotic System With Optimized Order and Force Estimation

This article proposes a variable structure control with neural network and optimized fractional-order selection policy for the sensorless telerobotic system with uncertain time delay, model uncertainty, fractional calculus numerical approximation bias, and external disturbance. Expanded from the integer-order calculus based on the definition of Caputo and the comparison principle, the Riemann–Liouville-based uniformly ultimately bounded stability is introduced to synthesize the sliding mode control with varying order, and the corresponding neural network based force estimation, which is optimized by the specified order based on the greed algorithm. Combined with the mixed-type error, the proposed hybrid integer-order and fractional-order analysis methodology is capable of guaranteeing the Riemann–Liouville-based uniformly ultimately bounded stability of tracking and synchronization errors under time delay. According to Euler difference, the proposed synthesis method can suppress the combined error in the boundedness of approximating double Euler difference errors. Numerical simulation and experiment of the telerobotic system under the control of the proposed method verify the stability analyses.

Corrigendum to “Second order estimates for complex Hessian equations with gradient terms on both sides” [J. Differ. Equ. 271 (2021) 128–151

Corrigendum to “Second order estimates for complex Hessian equations with gradient terms on both sides” [J. Differ. Equ. 271 (2021) 128–151

Probing non-standard [formula omitted] interaction at the LHC at [formula omitted] TeV

In the detailed probe of Higgs boson properties at the Large Hadron Collider (LHC), and in looking for new physics signatures in the electroweak symmetry breaking sector, the bottom quark Yukawa coupling has a crucial role. We investigate possible departure from the standard model value of bb¯h coupling, phenomenologically expressed in terms of a modification factor αb, in bb¯-associated production of the 125-GeV scalar at the high-luminosity LHC. In a next-to-leading order estimate, we make use of a gradient boosting algorithm to improve the statistical significance upon a cut-based analysis. It is found possible to probe down to αb=3 with more than 5σ significance, with L=3000 fb−1 and s = 13 TeV, while the achievable limit at 95% C.L. is ±1.95. Scale dependence of this limit is also reported.

Identifying an unknown source term in a time-space fractional parabolic equation

An inverse problem of identifying an unknown space-dependent source term in a time-space fractional parabolic equation is considered in this paper. Under reasonable boundedness assumptions about the source function, a Hölder-type stability estimate of optimal order is proved. To regularize the inverse source problem, a mollification regularization method is applied. Error estimates of the regularized solution are proved for both a priori and a posteriori rules for choosing the mollification parameter. A direct numerical method for solving the regularized problem is proposed and numerical examples are presented to illustrate its effectiveness.

Order estimates of the uniform approximations by Zygmund sums on the classes of convolutions of periodic functions

The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials of the form $$Z^{s}_{n-1}(f;t):=\frac{a_{0}}{2}+\sum_{k=1}^{n-1}\Big(1-\big(\frac{k}{n}\big)^{s}\Big) \big(a_{k}(f)\cos kt+b_{k}(f)\sin kt\big), s>0,$$ where $a_{k}(f)$ and $b_{k}(f)$ are the Fourier coefficients of $f$. We establish the exact-order estimates of uniform approximations by the Zygmund sums $Z^{s}_{n-1}$ of $2\pi$-periodic continuous functions from the classes $C^{\psi}_{\beta,p}$. These classes are defined by the convolutions of functions from the unit ball in the space $L_{p}$, $1\leq p<\infty$, with generating fixed kernels $$\Psi_{\beta}(t)\sim\sum_{k=1}^{\infty}\psi(k)\cos\left(kt+\frac{\beta\pi}{2}\right), \Psi_{\beta}\in L_{p'}, \beta\in \mathbb{R}, \frac1p+\frac{1}{p'}=1.$$ We additionally assume that the product $\psi(k)k^{s+1/p}$ is generally monotonically increasing with the rate of some power function, and, besides, for $1< p<\infty$ it holds that $\sum_{k=n}^{\infty}\psi^{p'}(k)k^{p'-2}<\infty$, and for $p=1$ the following condition $\sum_{k=n}^{\infty}\psi(k)<\infty$ is true. It is shown, that under these conditions Zygmund sums $Z^{s}_{n-1}$ and Fejér sums $\sigma_{n-1}=Z^{1}_{n-1}$ realize the order of the best uniform approximations by trigonometric polynomials of these classes, namely for $1<p<\infty$ $${E}_{n}(C^{\psi}_{\beta,p})_{C}\asymp{\cal E}\left(C^{\psi}_{\beta,p}; Z_{n-1}^{s}\right)_{C}\asymp\Big(\sum_{k=n}^{\infty}\psi^{p'}(k)k^{p'-2}\Big)^{1/p'}, \ \frac{1}{p}+\frac{1}{p'}=1,$$ and for $p=1$ $$ {E}_{n}(C^{\psi}_{\beta,1})_{C}\asymp{\cal E}\left(C^{\psi}_{\beta,1}; Z_{n-1}^{s}\right)_{C}\asymp {\left\{{\begin{array}{l l} \sum\limits_{k=n}^{\infty}\psi(k), & \cos \frac{\beta\pi}{2}\neq 0,\\ \psi(n)n, &\cos \frac{\beta\pi}{2}= 0, \end{array}} \right.} $$ where $${E}_{n}(C^{\psi}_{\beta,p})_{C}:=\sup_{f\in C^{\psi}_{\beta,p}}\inf\limits_{t_{n-1}\in\mathcal{T}_{2n-1}}\|f(\cdot)-t_{n-1}(\cdot)\|_{C}, $$ and $\mathcal{T}_{2n-1}$ is the subspace of trigonometric polynomials $t_{n-1}$ of order $n-1$ with real coefficients, $${\cal E}\left(C^{\psi}_{\beta,p}; Z_{n-1}^{s}\right)_{C}:=\mathop{\sup}\limits_{f\in C^{\psi}_{\beta,p}}\|f(\cdot)-Z^{s}_{n-1}(f;\cdot)\|_{C}.$$

Higher order Lupaş-Kantorovich operators and finite differences

It is well-known that Lupas operators are not exponential type operators, although they preserve linear functions. The differential operator is not applicable to estimate nice representation between Lupas operators and its Kantorovich variant. In the present paper we use finite difference method viz. backward differences to estimate the recurrence relation for moments of the Lupas operators. We introduce higher order Lupas-Kantorovich operators and estimate some direct results.

A SDFEM for Singularly Perturbed System of Convection-Diffusion Delay Differential Equations

In this article, we consider a system of convection-diffusion equations with delay terms. When a parameter multiplying the second order derivatives in the equations is small, boundary layers as well as interior layers appear in their solutions. A numerical method based on finite element and Shishkin mesh is presented. We derive an error estimate of order O(N −1 log2 N) in the energy norm with respect to the parameter using the streamline-diffusion finite element method. Numerical experiments are also presented to support our theoretical results.

Experimental support for genomic prediction of climate maladaptation using the machine learning approach Gradient Forests.

Gradient Forests (GF) is a machine learning algorithm that is gaining in popularity for studying the environmental drivers of genomic variation and for incorporating genomic information into climate change impact assessments. Here we (i) provide the first experimental evaluation of the ability of "genomic offsets" - a metric of climate maladaptation derived from Gradient Forests - to predict organismal responses to environmental change, and (ii) explore the use of GF for identifying candidate SNPs. We used high-throughput sequencing, genome scans, and several methods, including GF, to identify candidate loci associated with climate adaptation in balsam poplar (Populus balsamifera L.). Individuals collected throughout balsam poplar's range also were planted in two common garden experiments. We used GF to relate candidate loci to environmental gradients and predict the expected magnitude of the response (i.e., the genetic offset metric of maladaptation) of populations when transplanted from their "home" environment to the common gardens. We then compared the predicted genetic offsets from different sets of candidate and randomly selected SNPs to measurements of population performance in the common gardens. We found the expected inverse relationship between genetic offset and performance: populations with larger predicted genetic offsets performed worse in the common gardens than populations with smaller offsets. Also, genetic offset better predicted performance than did "naive" climate transfer distances. However, sets of randomly selected SNPs predicted performance slightly better than did candidate SNPs. Our study provides evidence that genetic offsets represent a first order estimate of the degree of expected maladaptation of populations exposed to rapid environmental change and suggests GF may have some promise as a method for identifying candidate SNPs.