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High-accuracy computer approximation of fractional derivatives and integrals by applying Grünwald–Letnikov formula generally requires a large number of input values. If required amount cannot be supplied, accuracy of approximation drops drastically. In this paper, we solve a difficult problem in this scope, i.e., when input data consists only of a small number of discrete values. Furthermore, some of the values may be unusable for computational purposes. Our problem solution includes an appropriate method of input data preprocessing, an interpolation algorithm with extrapolation abilities, a central point function discretization schema, recurrent computational method of coefficients and application of Horner's schema for the core of the Grünwald–Letnikov method: coefficients and function's values multiplication. Numerical method presented in the paper enables to compute fractional derivatives and integrals of complicated functions with much higher accuracy than it is possible when application of the default approach to Grünwald–Letnikov method computer implementation is applied. This new method usually takes only 10% of function's values required by the default approach for the same computations and is much less restrictive for their quality. The general novelty of the method is an efficient configuration of existing numerical methods and enhancement of their abilities by applying modern programming language — Python and arbitrary precision arithmetic for computations. [ABSTRACT FROM AUTHOR]

In this paper, we continue the work on implicit–explicit (IMEX) time discretizations for the incompressible Oseen's equations that we started in Burman et al. [Implicit–explicit time discretization for Oseen's equation at high Reynolds number with application to fractional step methods, SIAM J. Numer. Anal.61 (2023) 2859–2886]. The pressure velocity coupling and the viscous terms are treated implicitly, while the convection term is treated explicitly using extrapolation. Herein, we focus on the IMEX Crank–Nicolson method for time discretization. For the discretization in space we consider finite element methods with stabilization on the gradient jumps. The stabilizing terms ensure inf–sup stability for equal order interpolation and robustness at high Reynolds number. Under suitable Courant conditions, we prove the stability of the IMEX Crank–Nicolson scheme in this regime. The stabilization allows us to prove error estimates of order O (h k + 1 2 + τ 2). Here h is the mesh parameter, k the polynomial order and τ the time step. Finally, we discuss some fractional step methods that are implied by the IMEX scheme. Numerical examples are reported comparing the different methods when applied to the Navier–Stokes' equations. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel vertexing algorithm for determining the point of primary interaction, based on the linear extrapolation of tracks in the vicinity of the beamline. The algorithm considers tracks as infinitely elongated ellipsoids, thereby reducing the track vertexing problem to a vertex-to-points proximity problem. We have implemented the concept in C++ with the aid of our previously reported NXV4 package three for vectors and matrices, which gives very good CPU performance. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce a class of mixed-norm Herz spaces, Ė q → α → , p → (ℝ n) , which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on Ė q → α → , p → (ℝ n). Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on Ė q → α → , p → (ℝ n). As applications, the authors develop various real-variable theory of Hardy spaces associated with Ė q → α → , p → (ℝ n) by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of Ė q → α → , p → (ℝ n) and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem. [ABSTRACT FROM AUTHOR]

Real-time hybrid simulation (RTHS) is recently applied to study the vibration of the vehicle–bridge coupling system, where bridges and the vehicle are the numerical and experimental substructures respectively. Inevitable time delay of the boundary loading imposed to the experimental substructure will greatly affect the accuracy and stability of RTHS. To minimize the time delay effects, this paper proposes a recursive prediction optimal (RPO) compensator based on optimal control and recursive least squares. The numerical simulation of the RTHS of the vehicle–bridge coupling system is conducted using MATLAB/Simulink. The performance of the RPO method is compared with three traditional time delay compensation methods (i.e. the polynomial extrapolation (NI), the inverse compensation (IC) and the derivative feedforward (DF)) through both open-loop and RTHS simulations. The RPO method shows the best compensation performance in the frequency range up to 20 Hz. [ABSTRACT FROM AUTHOR]

We review the elastic and diffractive scatterings of protons (called also the “forward physics”) with emphasis on the LHC data, especially those deviating from the expectations based on extrapolations from earlier measurements at the ISR and Fermilab and thus triggering searches for new ideas, models and theories. We list these new data and provide a brief introduction of available theoretical approaches, mainly those based on analyticity, crossing symmetry and unitarity, particularly the Regge pole model realizing these concepts. Fits to the data are presented and tensions between theoretical predictions and the data that may indicate the way to further progress are in the focus of our paper. [ABSTRACT FROM AUTHOR]

This paper clarifies the terminologies used to describe the size effect on fatigue behavior of welded joints. It summarizes the existing research on size effect in the perspective of newly defined terminologies. It identifies knowledge gaps in designing tubular joints using the hot spot stress method, i.e. thin-walled tubular joints with wall thickness less than 4 mm and thick-walled tubular joints with wall thickness larger than 50 mm, or diameter to thickness ratio less than 24. It is the thin-walled tubular joints that are addressed in this paper. It is found that thin-walled tube-plate T-joints do not follow the conventional trend: the thinner the section is, the higher the fatigue life. It is also found that simple extrapolation of existing fatigue design curves may result in unsafe design of thin-walled tube–tube T-joints. The effect of chord stiffness on fatigue behavior of thin-walled tubular T-joints is also discussed. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) emerged as one of the most serious health issues of the modern era. Till date, it challenges the scientists working in the fields related to its prevention, least spread and eradication. It affects not only the person suffering from it but also the communities and their economies. Mathematical modeling is one of the ways to explore the possibilities of prediction (and control) strategies for contagious deceases. In this paper, we have tried to extend the scope of a currently available prediction model for a continuous time span. For this purpose, an analytical investigation of the system of nonlinear differential equations, governing the HIV infection of CD4T-cells, is carried out. A new emerging analytical technique Optimal Variational Iteration Method (OVIM) has been used to obtain an analytical and convergent solution. Analytical solutions are continuous solutions that can be used to predict the phenomena without the involvement of interpolation or extrapolation errors. On the other hand, their use in the derived equations, depending upon solution itself, is far easier than the numerical solutions. We have presented the error analysis and the prediction curves graphically. Moreover, a comparison with traditional Variational Iteration is also provided. It is concluded that the traditional method fails to converge for the updated models which involve the delayed differential equations. [ABSTRACT FROM AUTHOR]

This paper considers a set of shock physics experiments that investigate how materials respond to the extremes of deformation, pressure, and temperature when exposed to shock waves. Due to the complexity and the cost of these tests, the available experimental data set is often very sparse. A support vector machine (SVM) technique for regression is used for data estimation of velocity measurements from the underlying experiments. Because of good generalization performance, the SVM method successfully interpolates the experimental data. The analysis of the resulting velocity surface provides more information on the physical phenomena of the experiment. Additionally, the estimated data can be used to identify outlier data sets, as well as to increase the understanding of the other data from the experiment. [ABSTRACT FROM AUTHOR]

In this paper, a recent curved non-slip wall boundary treatment for isothermal Lattice Boltzmann equation (LBE) [Z. Guo, C. Zheng and B. Shi, Phys. Fluids14(6) (2002)] is extended to handle the thermal curved wall boundary for a double-population thermal lattice Boltzmann equation (TLBE). The unknown distribution population at a wall node which is necessary to fulfill streaming step is decomposed into its equilibrium and non-equilibrium parts. The equilibrium part is evaluated according to Dirichlet and Neumann boundary constraints, and the non-equilibrium part is obtained using a first-order extrapolation from fluid lattices. To validate the thermal boundary condition treatment, we carry out numerical simulations of Couette flow between two circular cylinders, the natural convection in a square cavity, and the natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder. The results agree very well with analytical solution or available data in the literature. Our numerical results also demonstrate that the TLBE together with the present boundary scheme is of second-order accuracy. [ABSTRACT FROM AUTHOR]

In this paper we study a subgrid model based on extrapolation of a modeling residual, in the case of a linear convection-diffusion-reaction problem Lu=f in two dimensions. The solution u to the exact problem satisfies an equation L[sub h]u=[f][sup h]+F[sub h](u), where L[sub h] is the operator used in the computation on the finest computational scale h, [f][sup h] is the approximation of f on the scale h, and F[sub h](u) is a modeling residual, which needs to be modeled. The subgrid modeling problem is to compute approximations of F[sub h](u) without using finer scales than h. In this study we model F[sub h](u) by extrapolation from coarser scales than h, where F[sub h](u) is directly computed with the finest scale h as reference. We show in experiments that a solution with subgrid model on a scale h in most cases corresponds to a solution without subgrid model on a mesh of size less than h/4. [ABSTRACT FROM AUTHOR]

To solve the problems with spraying over the inner wall of air-intake pipe, this paper introduces an algorithm of measurement path planning based on the spraying robot system and the laser displacement sensor technology. Scanning measurement path planning is the premise and basis of model construction and spray. Traditional methods, such as arc length extrapolation and polynomial are applicable only for the measurement of a plane curve with finite maximum curvature. Drawing references from existing method, this paper focuses on the pre-scanning measurement method for different types of cross-section curves. Algorithm simulation and model reconstruction show that this study solves the problem of collision avoidance for scanning measurement of the inner wall of air-intake pipe. [ABSTRACT FROM AUTHOR]

We construct and analyze a second-order parameter uniform numerical method for parabolic singularly perturbed space-delay problems with interior turning point. The considered problem's solution possesses an interior layer in addition to twin boundary layers due to the presence of delay. Some theoretical estimates on derivatives of the analytical solution, which are useful for conducting the error analysis, are given. The proposed technique employs an upwind scheme on a fitted Bakhvalov–Shishkin mesh in the spatial variable and implicit-Euler scheme on a uniform mesh in the time variable. This discretization of the problem is shown to be uniformly convergent of O (Δ τ + − 1) , where Δ τ is the step size in the temporal direction and K denotes the number of mesh-intervals in the spatial direction. Further, to improve the accuracy, we make use of Richardson extrapolation and establish parameter-uniform convergence of O ((Δ τ) 2 + − 2) for the resulting scheme. Numerical experiments are performed over two test problems for validation of the theoretical predictions. [ABSTRACT FROM AUTHOR]

In this paper, we solve the Ginzburg-Landau equations for a circular geometry containing a half-circular pillar. We consider the surface of the sample in a complete normal state (|ψ|surface = 0), this choice, leading to take the extrapolation de Gennes length equal to zero (b = 0). Our results point out that the critical fields, magnetization and vorticity, depend on the chosen boundary condition. [ABSTRACT FROM AUTHOR]

Fuzzy regression has been applied to marketing, management, and sales forecasting for many years. In this paper, two types of forecasting methods within the framework of fuzzy regression analysis are discussed. The first type is a conventional forecasting method, which intends to find the value of a dependent variable when the given values of independent variables are beyond the range covered by historical data. The second type considers forecasting in which the necessary values of independent variables are desired when the given value of a dependent variable does not fall within the range of historical data. While the first type can be applied in planning, the second one is useful for control and management. Numerical examples are provided for illustration. [ABSTRACT FROM AUTHOR]

The following effects in the nearly forward ("soft") region of the LHC are proposed to be investigated: • At small |t| the fine structure of the cone (Pomeron) should be scrutinized: (a) a break of the cone near t ≈ -0.1 GeV2, due to the two-pion threshold, and required by t-channel unitarity, and (b) possible small-period oscillations between t = 0 and the dip region. • In measuring the elastic pp scattering and total pp cross-section at the LHC, the experimentalists are urged to treat the total cross-section σt, the ratio ρ of real to imaginary part of the forward scattering amplitude, the forward slope B and the luminosity ${\mathcal L}$ as free parameters, and to publish model-independent results on dN/dt. • Of extreme interest are the details of the expected diffraction minimum in the differential cross-section. Its position, expected in the interval 0.4 < -t < 1 GeV2 at the level of about 10-2mb · GeV-2–10-1mb · GeV-2, cannot be predicted unambiguously, and its depth, i.e. the ratio of dσ/dt at the minimum to that at the subsequent maximum (about -t = 5 GeV2, which is about 5) is of great importance. • The expected slow-down with increasing |t| of the shrinkage of the second cone (beyond the dip-bump), together with the transition from an exponential to a power decrease in -t, will be indicative of the transition from "soft" to "hard" physics. Explicit models are proposed to help in quantifying this transition. • In a number of papers a limiting behavior, or saturation of the black disk limit (BDL), was predicted. This controversial phenomenon shows that the BDL may not be the ultimate limit, instead a transition from shadow to antishadow scattering may by typical of the LHC energy scale. [ABSTRACT FROM AUTHOR]

This paper presents large deflection, post-buckling analysis of plane and spatial elastic frames from a dynamic point of view. A co-rotational formulation combined with small deflection beam theory with the inclusion of the effect of axial force is adopted. A constant arc length method combined with the modified Newton-Raphson iteration method and the extrapolation technique to improve the convergence behaviour are employed to trace the non-linear equilibrium path up to the limit point. The change in the sign of the incremental work done is used to determine the occurrence of a limit point. As the limit state being examined is passed, the previous converged solution is adopted to start the non-linear dynamic analysis based on the average acceleration of the Newmark algorithm with a slow rate of load increment and in order to trace the postbuckling load-deflection path. As a result, the snap through problem is overcome without decreasing the external load. Numerical examples are presented to demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]

The odd–even staggering of neighboring nuclear masses is very useful in calculating local mass relations and nucleon-pair correlations. During the past decades, there has been an increasing interest in the odd–even features of the mass relations and related quantities exhibited in masses of neighboring nuclei. In this work, after choosing a nucleus, we made an analysis of its neighboring nuclei on the upper left corner and the lower right corner, respectively. We empirically obtained a new residual interaction formula of even-A (A is the mass number) nuclei, and it is a revision based on the existing empirical local formula of the proton–neutron interactions between the last proton and the last neutron (δ V 1 p − 1 n). We then calculated the even-A nuclear masses. The differences between our calculated values and the AME2012 database show that the root-mean-squared deviations (RMSD) are small (for even-A nuclei: A ≥ 42, RMSD ≈ 161 keV; A ≥ 100, RMSD ≈ 125 keV), while for heavy nuclei, some of our calculated values can reach an accuracy of a few tens of keV. With our residual interaction formula including one parameter, we have successfully predicted some unknown masses. Some of our predicted values are compared well with the experimental values (AME2016). In addition, the accuracy and simplicity of our predicted masses for medium and heavy nuclei are comparable to those of the AME2012 (AME2016) extrapolations. [ABSTRACT FROM AUTHOR]

In industrial applications it is quite common to use stochastic-volatility models driven by semi-martingale Markov volatility processes. However, in order to fit exactly market volatilities, these models are usually extended by adding a local-volatility term. Here, we consider the case of singular Volterra processes, and we extend them by adding a local-volatility term to their Markov lift by preserving the stylized results implied by these models on plain-vanilla options. In particular, we focus on the rough-Heston model, and we analyze the small-time asymptotics of its implied local-volatility function in order to provide a proper extrapolation scheme to be used in calibration. [ABSTRACT FROM AUTHOR]

In order to establish an accurate peak over threshold (POT) model for reasonable load extrapolation, a new threshold selection method based on multiple criteria decision making (MCDM) technology is proposed. The fitting test criterion is taken into consideration in the method. For each candidate threshold, the fitting values of several fitting test criteria are integrated into a comprehensive evaluation value through entropy method and MCDM technology. The threshold corresponding to the minimum comprehensive evaluation value is assumed as the optimal threshold. A random simulation study is carried out to evaluate the performance of the method and to compare them with other literature methods. Genuine load data are applied the proposed method. Both the results shown that the proposed method could be seen as an additional method that complements existing threshold selection methods. [ABSTRACT FROM AUTHOR]

The traditional Dead Reckoning algorithm predicts the future motion state based on a determined polynomial predictor, and the forecasting performance would vary with different types of motion entities. This paper proposes an enhanced dead reckoning algorithm based on hybrid extrapolation models, which can be used to reduce the communication in a distributed interactive simulation. The proposed algorithm perform extrapolation using a number of candidate predictors. Its idea is based on the assumption that a complex trajectory can be decomposed into several simple trajectories. The experimental evaluations show that the enhanced Dead Reckoning algorithm provides better performance in correction data reduction and accurate estimation. [ABSTRACT FROM AUTHOR]

Sensitivity analysis is a powerful tool for analyzing multi-parameter models. For example, the Fisher information matrix (FIM) and the Cramér–Rao bound (CRB) involve derivatives of a forward model with respect to parameters. However, these derivatives are difficult to estimate in ocean acoustic models. This work presents a frequency-agnostic methodology for accurately estimating numerical derivatives using physics-based parameter preconditioning and Richardson extrapolation. The methodology is validated on a case study of transmission loss in the 50–400 Hz band from a range-independent normal mode model for parameters of the sediment. Results demonstrate the utility of this methodology for obtaining Cramér–Rao bound (CRB) related to both model sensitivities and parameter uncertainties, which reveal parameter correlation in the model. This methodology is a general tool that can inform model selection and experimental design for inverse problems in different applications. [ABSTRACT FROM AUTHOR]

Quantitative technology forecasting uses quantitative methods to understand and project technological changes. It is a broad field encompassing many different techniques and has been applied to a vast range of technologies. A widely used approach in this field is trend extrapolation. Based on the literature available to us, there has been little or no attempt made to systematically review the empirical evidence on quantitative trend extrapolation techniques. This study attempts to close this gap by conducting a systematic review of the technology forecasting literature addressing the application of quantitative trend extrapolation techniques. We identified 25 studies relevant to the objective of this research and classified the techniques used in the studies into different categories, among which the growth curves and time series methods were shown to remain popular over the past decade while the newer methods, such as machine learning-based hybrid models, have emerged in recent years. As more effort and evidence are needed to determine if hybrid models are superior to traditional methods, we expect a growing trend in the development and application of hybrid models to technology forecasting. [ABSTRACT FROM AUTHOR]

Data uncertainty in real-life problems is a current challenge in many areas, including Operations Research (OR) and Constraint Programming (CP). This is especially true given the continual and accelerating increase in the amount of data associated with real-life problems, to which Large Scale Combinatorial Optimization (LSCO) techniques may be applied. Although data uncertainty has been studied extensively in the literature, many approaches do not take into account the partial or complete lack of information about uncertainty in real-life settings. To meet this challenge, in this paper we present a strategy for extrapolating data from limited uncertain information to ensure a certain level of robustness in the solutions obtained. Our approach is motivated and evaluated with real-world applications of harvesting and supplying timber from forests to mills and the well known knapsack problem with uncertainty. [ABSTRACT FROM AUTHOR]

The contractor renormalization (CORE) group method is applied to the even-leg spin tori to reveal their ground-state energies and the lowest excitation gaps. The spin tori are referred to the spin ladders that are closed along the rung direction. We designed an improved iterative CORE algorithm and applied it to the even-leg tori. The improvement is made by introducing an extrapolation based on a sequence of hierarchical data that is obtained by varying the size of the elementary block. Quite good results are obtained and compared with the ones by other methods. [ABSTRACT FROM AUTHOR]

A variational method that gives 4th-order accuracy by only using linear basis functions within the computational domain is proposed for the mode solving of anisotropic planar stratified waveguides with diagonal permitivity tensor. A non-uniform mesh is used to get rid of the necessity of incorporating interface corrections and higher-order basis functions, while Richardson-like extrapolation is used to obtain 4th-order accuracy. The scheme was derived for both TE and TM mode analysis and completed with infinite elements as transparent boundary conditions. The use of a simple extrapolation technique to further refine the results by using two consecutive calculated results is also demonstrated. [ABSTRACT FROM AUTHOR]

Comparisons are made of the Chicago Board of Options Exchange (CBOE) skew index with those derived from parametric skews of bilateral gamma models and from the differentiation of option implied characteristic exponents. Discrepancies can be due to strike discretization in evaluating prices of powered returns. The remedy suggested employs a finer and wider set of strikes obtaining additional option prices by interpolation and extrapolation of implied volatilities. Procedures of replicating powered return claims are applied to the fourth power and the derivation of kurtosis term structures. Regressions of log skewness and log excess kurtosis on log maturity confirm the positivity of decay in these higher moments. The decay rates are below those required by processes of independent and identically distributed increments. [ABSTRACT FROM AUTHOR]

Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems. In order to discretize the solution domain, Micken's type discretization on a uniform mesh is applied and then followed by the fitted operator approach. The convergence of the method is established and observed to be first-order convergent, but it is accelerated by Richardson extrapolation. To validate the applicability of the proposed method, some numerical examples are considered and observed that the numerical results confirm the agreement of the method with the theoretical results effectively. Furthermore, the method is convergent regardless of perturbation parameter and produces more accurate solution than the standard methods for solving singularly perturbed parabolic problems. [ABSTRACT FROM AUTHOR]

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM- α J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview. It is well established that no problem can ever be solved exactly in physics and chemistry: some may have one within the fundamental Born-Oppenheimer approximation, but even so, such a solution is most often computationally unaffordable. Because extrapolation is pragmatic and cost-effective, it may assume an important role when guided by an asymptotic theory that warrants realism while helping to avoid unsecure jumps into the unknown. Extrapolation is here illustrated in two major themes of quantum chemistry, electronic structure and reaction dynamics, with refinements alongside extensions to further branches of chemical physics being expected to come into view. [ABSTRACT FROM AUTHOR]

In the n -period Cox, Ross, and Rubinstein (CRR) model, we achieve smooth convergence of European vanilla options to their Black–Scholes limits simply by altering the probability at one node, in fact, at the preterminal node between the closest neighbors of the strike in the terminal layer. For barrier options, we do even better, obtaining order 1 / n convergence by altering the probability just at the node nearest the barrier, but only the first time it is hit. First-order smooth convergence for vanilla options was already achieved in Tian's flexible model but here we show how second order smooth convergence can be achieved by changing one probability, leading to convergence of order 1 / n 2 with Richardson extrapolation. We illustrate our results with examples and provide numerical evidence of our results. [ABSTRACT FROM AUTHOR]

In Phys. Rev. Lett. 115, 143001 (2015), H. Mera et al. developed a new simple but precise hypergeometric resummation technique. In this work, we suggest to obtain half of the parameters of the hypergeometric function from the strong-coupling expansion of the physical quantity. Since these parameters are taking now their exact values they can improve the precision of the technique for the whole range of the coupling values. The second order approximant 2 F 1 of the algorithm is applied to resum the perturbation series of the ground state energy of the 𝒫 𝒯 -symmetric (i ϕ 3) 0 + 1 field theory. It gives accurate results compared to exact calculations from the literature specially for very large coupling values. The 𝒫 𝒯 -symmetry breaking of the Yang–Lee model has been investigated where third, fourth and fifth orders were able to get very accurate results when compared to other resummation methods involving 1 5 0 orders. The critical exponent ν of the O (4) -symmetric model in three dimensions has been precisely obtained using only first order of perturbation series as input. The algorithm can be extended easily to accommodate any order of perturbation series in using the generalized hypergeometric function k + 1 F k as it shares the same analytic properties with 2 F 1 . [ABSTRACT FROM AUTHOR]

In this review paper, the finite difference methods (FDMs) for the fractional differential equations are displayed. The considered equations mainly include the fractional kinetic equations of diffusion or dispersion with time, space and time-space derivatives. In some way, these numerical methods have similar form as the case for classical equations, some of which can be seen as the generalizations of the FDMs for the typical differential equations. And the classical tools, such as the von Neumann analysis method, the energy method and the Fourier method are extended to numerical methods for fractional differential equations accordingly. At the same time, the techniques for improving the accuracy and reducing the computation and storage are also introduced. [ABSTRACT FROM AUTHOR]

We investigate the Casimir pressure between two dissimilar plates separated by a layer of magnetic fluid. Numerical computations of the Casimir pressure are performed for Au and SiO2 plates with an intervening layer of water and water-based ferrofluid obtained on addition to water a 5% volume fraction of magnetite nanoparticles with 10 nm diameter. It is shown that an addition of nanoparticles leads to a widening of separation region, where the Casimir interaction is repulsive. This result does not depend on whether the plasma or the Drude model is used for extrapolation of the optical data of Au to low frequencies. The effect of enhanced repulsion due to the presence of ferrofluid may be useful for preventing stiction of closely spaced elements in various microdevices. [ABSTRACT FROM AUTHOR]

We have developed polynomial-time algorithms to generate terms of the cogrowth series for groups ℤ ≀ ℤ , the lamplighter group, (ℤ ≀ ℤ) ≀ ℤ and the Brin–Navas group B. We have also given an improved algorithm for the coefficients of Thompson's group F , giving 32 terms of the cogrowth series. We develop numerical techniques to extract the asymptotics of these various cogrowth series. We present improved rigorous lower bounds on the growth-rate of the cogrowth series for Thompson's group F using the method from [S. Haagerup, U. Haagerup and M. Ramirez-Solano, A computational approach to the Thompson group F, Int. J. Alg. Comp.25 (2015) 381–432] applied to our extended series. We also generalise their method by showing that it applies to loops on any locally finite graph. Unfortunately, lower bounds less than 16 do not help in determining amenability. Again for Thompson's group F we prove that, if the group is amenable, there cannot be a sub-dominant stretched exponential term in the asymptotics. Yet the numerical data provides compelling evidence for the presence of such a term. This observation suggests a potential path to a proof of non-amenability: If the universality class of the cogrowth sequence can be determined rigorously, it will likely prove non-amenability. We estimate the asymptotics of the cogrowth coefficients of F to be c n ∼ c ⋅ μ n ⋅ κ n σ log δ n ⋅ n g , where μ ≈ 1 5 , κ ≈ 1 / e , σ ≈ 1 / 2 , δ ≈ 1 / 2 , and g ≈ − 1. The growth constant μ must be 16 for amenability. These two approaches, plus a third based on extrapolating lower bounds, support the conjecture [M. Elder, A. Rechnitzer and E. J. Janse van Rensburg, Random sampling of trivial words in finitely presented groups, Expr. Math.24 (2015) 391–409, S. Haagerup, U. Haagerup and M. Ramirez-Solano, A computational approach to the Thompson group F, Int. J. Alg. Comp.25 (2015) 381–432] that the group is not amenable. [ABSTRACT FROM AUTHOR]

We present a lattice calculation of the nucleon isovector axial and induced pseudoscalar form factors on the CLS ensembles using N f = 2 dynamical flavors of nonperturbatively 𝒪 (a) -improved Wilson fermions and an 𝒪 (a) -improved axial current together with the pseudoscalar density. Excited-state effects in the extraction of the form factors are treated using a variety of methods, with a detailed discussion of their respective merits. The chiral and continuum extrapolation of the results is performed both using formulae inspired by Heavy Baryon Chiral Perturbation Theory (HBChPT) and a global approach to the form factors based on a chiral effective field theory (EFT) including axial vector mesons. Our results indicate that careful treatment of excited-state effects is important in order to obtain reliable results for the axial form factors of the nucleon, and that the main remaining error stems from the systematic uncertainties of the chiral extrapolation. As final results, we quote g A = 1. 2 7 8 ± 0. 0 6 8 − 0. 0 8 7 + 0. 0 0 0 , 〈 r A 2 〉 = 0. 3 6 0 ± 0. 0 3 6 − 0. 088 + 0. 080 fm 2 , and g P = 7. 7 ± 1. 8 − 2. 0 + 0. 8 for the axial charge, axial charge radius and induced pseudoscalar charge, respectively, where the first error is statistical and the second is systematic. [ABSTRACT FROM AUTHOR]

The properties of massive protoneutron stars (PNSs) are of great significance for the study of supernova and the evolution of neutron stars or black holes. The mass of the massive neutron star PSR J1614-2230 is fitted by selecting the nuclear coupling constants and adjusting the hyperon coupling constants in the framework of the relativistic mean field (RMF) theory. The model is then extrapolated to calculate the properties of massive PNS with the trapped neutrinos. The effects of different trapped neutrinos on the composition and structure of massive PNSs are discussed for entropy per baryon . Results show that the presence of trapped neutrinos increase the energy density. Moreover, the significant neutrinos trapped, such as electron leptons number , reduces the pressure of massive PNSs in the density region 0.2-0.5fm, that is to say, the equation-of-state (EOS) is softened in this region. The maximum masses and corresponding radii of massive PNSs are calculated to be 2.110, 2.106, 2.095, 2.082 and 12.19, 11.88, 11.75 and 11.81 km for the electron leptons number . We calculate the distribution of the internal temperature, and get the effects of the trapped neutrinos on the internal temperature of massive PNSs for the first time. For the different electron leptons number , the central temperatures of the massive PNS, when the mass is taken to be the same as that of the observed neutron star PSR J1614-2230, are , , , MeV, respectively. [ABSTRACT FROM AUTHOR]

A robust extrapolation model requiring few input parameters to predict the kinetic constants characterizing the curing behavior of NR vulcanized in presence of sulfur and two accelerants (TBSS and DPG) at different concentrations is discussed. The numerical model based on the reproduction of rheometer curves by means of the well-known Han's kinetic model, which describes with kinetic base the most important NR vulcanization phases, namely curing initiation, formation of matured crosslinked polymer and reversion. The derived mathematical model is a closed form exponential function depending on only three kinetic constants. The procedure proposed is a two-step one. In the first step, kinetic constants of NR in the presence of single activators (i.e. either only with S and TBBS or S and DPG) are estimated by means of an interactive trial and error optimization software (GURU) that proceeds in approximating more and more strictly normalized experimental rheometer curves with Han's function. Four different concentrations of S and TBSS (or S and DPG) are assumed as calibration points. In the second step, from the results obtained previously, kinetic constants for NR with any S-TBBS-DPG concentration of technical relevance are deduced by means of standard mathematical extrapolation. The procedure is benchmarked on 16 different S-TBBS-DPG concentrations at two temperatures (150C and 180C), for which both experimental data are available and kinetic constants are previously derived with GURU. Quite good agreement is found, meaning that the approach may be useful for practical purposes, because expensive and cumbersome experimental investigations can be avoided. [ABSTRACT FROM AUTHOR]

The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological and interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as , considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods. [ABSTRACT FROM AUTHOR]