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Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the displacement of two incompressible phases in a Darcy–Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a combined finite volume–nonconforming finite element scheme together with a phase-by-phase upstream according to the total velocity. [ABSTRACT FROM AUTHOR]

In Jung and Roh (2017), we investigated some properties of approximate solutions of the second-order inhomogeneous linear differential equations. In this paper as an application of above paper we will study the stability of the time independent Schrödinger equation with a potential box of finite walls. [ABSTRACT FROM AUTHOR]

This paper presents an effective method to automatically construct trivariate tensor-product spline models of complicated geometry and arbitrary topology. Our method takes as input a solid model defined by its triangulated boundary surface. Using cuboid decomposition, an initial polycube approximating the input boundary mesh is built. This polycube serves as the parametric domain of the tensor-product spline representation required for isogeometric analysis. The polycube’s nodes and arcs decompose the input model’s boundary into quadrilateral patches, and these patches form hexahedral domains. Using aligned global parameterization, the nodes are re-positioned and the arcs are re-routed across the surface in a way to achieve low overall patch distortion, and alignment to principal curvature directions and sharp features. The optimization process is based on one of the main contributions of this paper: a novel way to design cross fields with topological (i.e., imposed singularities) and geometrical (i.e., imposed directions) constraints by solving only sparse linear systems. Based on the optimized polycube and parameterization, compatible B-spline boundary surfaces are reconstructed. Finally, the interior volumetric parameterization is computed using Coon’s interpolation. In the context of parametric studies based on geometrical parameters, this method can be used to compute the morphing required for reduced order modeling. For different parametric instances with the same topology but different geometries, this method allows to have the same representation: i.e., meshes (or parameterizations) with the same topology. The efficiency and the robustness of the proposed approach are illustrated by several examples. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study the approximation ratio of the solutions achieved after an ϵ -approximate one-round walk in non-atomic congestion games. Prior to this work, the solution concept of one-round walks had been studied for atomic congestion games with linear latency functions only (Christodoulou et al. [1] , Bilò et al. [2]). We give an explicit formula to determine the approximation ratio for non-atomic congestion games having general latency functions. In particular, we focus on polynomial latency functions, and, we prove that the approximation ratio is exactly ((1 + ϵ) (p + 1)) p + 1 for every polynomial of degree p. Then, we show that, by resorting to static (resp. dynamic) resource taxation, the approximation ratio can be lowered to (1 + ϵ) p + 1 (p + 1) p (resp. (1 + ϵ) p + 1 (p + 1) !). [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the Approximate Agreement problem in the Mobile Byzantine Fault model. Our contribution is three-fold. First, we refine the problem specification to adapt it to the Mobile Byzantine Fault environment. Then, we propose the first mapping from the existing variants of Mobile Byzantine models to the Mixed-mode Fault model. This mapping further help us to prove the correctness of MSR (Mean-Subsequence-Reduce) algorithms class in our context and it is of independent interest. We also prove lower bounds for solving Approximate Agreement under all existing Mobile Byzantine fault models. [ABSTRACT FROM AUTHOR]

Abstract This article deals with a backward diffusion problem for an inhomogeneous backward diffusion equation with fractional Laplacian in R : u t (x , t) + − Δ α u (x , t) = f (x , t) , (x , t) ∈ R × [ 0 , T ] , u (x , T) = g (x) , x ∈ R , lim x → ± ∞ u (x , t) = 0. This problem is an ill-posed problem due to the instability in solution. The goal of this paper is not only to provide a simple but effective regularization scheme to obtain the Hölder convergence rate, but also to give an approximation of solution of the equation with fractional diffusion to the one of the equation with Laplacian in both L 2 (R) and L p (R) setting. This result holds, in particular, when f (x , t) is spatially compactly supported, in which the difficulties due to the fractional Laplacian have been successfully overcome thanks to an additional condition on Fourier transform of f. We further study the convergence of solution of inhomogeneous problem to that of the homogeneous problem. Finally, numerical simulations, with finite difference schemes, based on Discrete Fourier Transform (DFT) algorithm are also presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper develops an analytical method to measure the performance of a multi-product unreliable production line with finite buffers between workstations. The performance measure used in this paper is Total Cycle Time. The proposed method is an approximation that generalizes the processing times to ease the variation of product types in a multi-product system. A decomposition method is then employed to approximate the production rate of a multi-product production line. The decomposition method considers generally distributed processing times as well as random failure and repair. A GI/G/1/N queuing model is also applied to obtain parameters such as blocking and starvation probabilities that are needed for the approximation procedure. Several numerical experiments under different scenarios are performed and results are validated by simulation models in order to assess the accuracy and strength of the proposed method. Consequent analysis and discussion of the results are also presented. [ABSTRACT FROM AUTHOR]

Motivated by a recent paper by the RBC–UKQCD Collaboration, which observes large violations of the naïve factorization hypothesis in K → π π decays, we study in this paper the accuracy of the Vacuum Insertion Approximation (VIA) for the matrix elements of the complete basis of four-fermion Δ F = 2 operators. We perform a comparison between the matrix elements in QCD, evaluated on the lattice, and the VIA predictions. We also investigate the dependence on the external meson masses by computing matrix elements for K , D s , B s and static mesons. In commonly used renormalization schemes, we find large violations of the VIA in particular for one of the two relevant Wick contractions in the kaon sector. These deviations, however, decrease significantly as the meson mass increases and the VIA predictions turn out to be rather well verified for B -meson matrix elements and, even better, in the infinite mass limit. [ABSTRACT FROM AUTHOR]

We are promoting the use of variational principles as some generalizing idea that allows us to create consistent approximations of mathematical models. In this paper, we formulate a computing technology to solve direct and inverse problems of atmospheric dynamics and chemistry. For the implementation, we use functional decomposition methods, splitting techniques, and integrating factors designed as the solutions of some adjoint problems. One of the main purposes of the paper is to relate the theory of approximation with the concept of Eulerian integrating factors that plays the fundamental role in the theory of differential equations. We demonstrate the utility and versatility of the concept applying it to solve the systems of differential equations of convection–diffusion (with dominant convection) and stiff systems of kinetic equations. To identify the prospects of our approach, we briefly introduce how to use integrating factors in the case of unstructured grids. [Copyright &y& Elsevier]

In this paper, we define analysis-suitable++ (AS++) T-splines which include analysis-suitable (AS) T-splines as a special case and maintain all the good mathematical properties as AS T-splines. We prove that AS++ T-splines are always linear independent regardless of the knot values and show that the classical construction of the dual basis for tensor-product B-splines and AS T-splines can be generalized to AS++ T-spline spaces. We also discuss how all of these issues pave the way to a mathematical theory for AS++ T-splines. [ABSTRACT FROM AUTHOR]

Confined concrete has superior anti-penetration performance over unconfined concrete. A finite dynamic spherical cavity-expansion approximation model with radially elastic confinement is proposed to analyze the confinement on concrete targets and predict the depth of penetration (DOP), taking steel-tube-confined concrete (STCC) targets normally penetrated by rigid projectiles as an example. Firstly, the validity of a nonlinear failure criterion to describe strength feature of concrete in the comminuted region is demonstrated by triaxial compressible tested data and the reference range of dimensionless parameter m in the modified Griffith criterion is recommended. Secondly, the relationship between the stresses in concrete and cavity-expansion velocity is developed. Furthermore, the confinement effects on response modes of confined concrete, radial stress at cavity wall and stresses distribution in concrete are analyzed. Lastly, an engineering model is also established to predict the DOP of STCC targets normally penetrated by rigid projectiles. The results show that the radial stress at cavity wall is not a constant during the cavity-expansion process in finite concrete with radially elastic confinement, which is different from the steady spherical cavity-expansion of infinite material in which the radial stress at cavity wall is a constant with constant cavity-expansion velocity. The possible response phases of confined concrete targets normally penetrated by rigid projectiles include “elastic-cracked-comminuted”, “cracked-comminuted” and “full-comminuted”, depending on the relationship among cavity-expansion velocity, radial confining stiffness and radius ratio of cavity to target. The DOP data from the engineering model established in this paper agree well with those of experiments in the published references. [ABSTRACT FROM AUTHOR]

Recently a WENO scheme, with smoothness indicators constructed based on L 1 measure is introduced by Ha et al. (2013) and the improved version of this scheme is presented by Kim et al. (2016), referred to as WENO-NS and WENO-P schemes respectively. These schemes perform better than the existing many fifth-order WENO schemes for the problems which contain discontinuities and attain fifth-order accuracy at the critical points where the first derivative vanishes but not at the points where the second derivatives are zero. This paper deals with modification of the above said methods to obtain a new fifth-order weighted essentially non-oscillatory (WENO) scheme. A new global-smoothness indicator is proposed which shows an improved behavior over the solutions of WENO-NS and WENO-P schemes and the proposed scheme attains an optimal order of approximation, even at the critical points where the first and second derivatives vanish but not the third derivative. Examples are taken in the numeric section to check the robustness and accuracy of the proposed scheme for one and two-dimensional system of Euler equations. [ABSTRACT FROM AUTHOR]

It is well understood that during the pharmaceutical aqueous film coating process the amount of liquid water that interacts with the porous tablet core can affect the quality of the final product. Therefore, understanding and simulating the mechanisms of water droplet spreading, absorption and evaporation is crucial for controlling the process and optimising the shelf-life of the tablets. The purpose of the work presented in this paper is to define and describe the spreading, absorption and evaporation phenomena after droplet impingement on a tablet. We divided the droplet behaviour into three phases of different dynamics and duration: the kinematic, capillary and evaporation phases. To model the kinematic phase, we combined and modified 1-D spreading models from the literature which solve the kinetic energy balance equation for the first milliseconds of spreading. For the capillary phase, we simplified and solved the continuity and Navier-Stokes equations using the lubrication approximation theory. Finally, for the evaporation phase, we adopted a modelling approach for the second drying stage of slurry droplets inside a spray dryer. During this stage, one can no longer describe the droplet as a liquid system containing solids, having to regard it as a wet particle with a dry crust and a wet core. In our work, we represented in a novel way the crust as the dry surface of the tablet and the wet core as the wetted area inside the porous matrix. We implemented the mathematical model presented in this work in gPROMS, employing the Modelbuilder platform. Our numerical results (droplet height and spreading, wetting, evaporation front profiles) are in good agreement with recent experimental data that we found in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the hedging problem based on the CVaR in incomplete markets. As the superhedging is quite expensive in terms of initial capital, we construct a self-financing strategy that minimizes the CVaR of hedging risk under a budget constraint on the initial capital. In incomplete markets, no explicit solution can be provided. To approximate the problem, we apply the Neyman–Pearson lemma approach with a specific equivalent martingale measure. Afterwards, we explicit the solution for call options hedging under the exponential-Lévy class of price models. This approach leads to an efficient and easy to implement method using the fast Fourier transform. We illustrate numerical results for the Merton model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate the Minimum Eccentricity Shortest Path (MESP) problem in unweighted graphs. It asks for a given graph to find a shortest path with minimum eccentricity. Let n and m denote the number of vertices and the number of edges of a given graph. We demonstrate that: • a minimum eccentricity shortest path plays a crucial role in obtaining the best to date approximation algorithm for a minimum distortion embedding of a graph into the line; • the MESP problem is NP-hard for planar bipartite graphs with maximum degree 3 and W[2]-hard for general graphs; • a shortest path of minimum eccentricity k can be computed in O ( n 2 k + 2 m ) time; • a 2-approximation, a 3-approximation, and an 8-approximation for the MESP problem can be computed in O ( n 3 ) time, in O ( n m ) time, and in O ( m ) time, respectively; • in a graph with a shortest path of eccentricity k , a k -dominating set can be found in n O ( k ) time. [ABSTRACT FROM AUTHOR]

Taylor series approximation like q ( t + τ ) ≈ q + τ ∂ q ∂ t are often used to derive, extend or interpret typical heat conduction models. Researchers may take it for granted that the single-phase-lagging (SPL) model can be considered as an extension of the Cattaneo–Vernotte (CV) model because there is such approximation relationship between them. We point out in this paper that this Taylor series approximation itself has some defects based on analyses in mathematics, physics and some examples first. Then, we show essential differences in both mathematics and physics between the CV and SPL models. It is found that their mathematical characteristics and accordance with the laws of thermodynamics are significantly different, which indicates that using this approximation to connect the two models may be defective in some cases. What’s more, higher order approximation can’t solve these problems and defects. [ABSTRACT FROM AUTHOR]

Costas loop is a classical phase-locked loop (PLL) based circuit for carrier recovery and signal demodulation. The PLL is an automatic control system that adjusts the phase of a local signal to match the phase of the input reference signal. This tutorial is devoted to the dynamic analysis of the Costas loop. In particular the acquisition process is analyzed. Acquisition is most conveniently described by a number of frequency and time parameters such as lock-in range, lock-in time, pull-in range, pull-in time, and hold-in range. While for the classical PLL equations all these parameters have been derived (many of them are approximations, some even crude approximations), this has not yet been carried out for the Costas loop. It is the aim of this analysis to close this gap. The paper starts with an overview on mathematical and physical models (exact and simplified) of the different variants of the Costas loop. Then equations for the above mentioned key parameters are derived. Finally, the lock-in range of the Costas loop for the case where a lead-lag filter is used for the loop filter is analyzed. [ABSTRACT FROM AUTHOR]

We analyze the classical problem of the interaction between two charged surfaces separated by a solution containing neutralizing counter-ions. The focus is on obtaining a description where the solvent is treated explicitly rather than through a dielectric approximation as is conventionally done. We summarize the results of three papers where we have used a Stockmayer fluid model in Monte Carlo simulations. It is shown that the attractive ion–ion correlation mechanism is also operating when the solvent is described explicitly. There appears an oscillatory component to the force, but when this is accounted for, there is a semi-quantitative agreement between the continuum model and the model with explicit solvent. The properties of the continuum model can be reached in a molecular system by making the solvent molecules much smaller than the ions. It is demonstrated that having an explicit solvent model makes the analysis of force mechanisms more delicate due to the interplay between several different microscopic contributions to the force. Finally, it is argued that the agreement between the forces calculated using the continuum and the explicit solvent models, respectively, has as its basis the circumstance that the force between the surfaces is mainly caused by long-range ion–ion interactions, for which the dielectric approximation is most adequate. This argument applies equally well to an aqueous system as to the Stockmayer fluid. [ABSTRACT FROM AUTHOR]

A precise theoretical description of W- and Z-boson production in the resonance region is essential for the correct interpretation of high-precision measurements of the W-boson mass and the effective weak mixing angle. Currently, the largest unknown fixed-order contribution is given by the mixed QCD-electroweak corrections of O ( α s α ) . We argue, using the framework of the pole expansion for the NNLO QCD-electroweak corrections established in a previous paper, that the numerically dominant corrections arise from the combination of large QCD corrections to the production with the large electroweak corrections to the decay of the W / Z boson. We calculate these so-called factorizable corrections of “initial–final” type and estimate the impact on the W-boson mass extraction. We compare our results to simpler approximate combinations of electroweak and QCD corrections in terms of naive products of NLO QCD and electroweak correction factors and using leading-logarithmic approximations for QED final-state radiation as provided by the structure-function approach or QED parton-shower programs. We also compute corrections of “final–final” type, which are given by finite counterterms to the leptonic vector-boson decays and are found to be numerically negligible. [ABSTRACT FROM AUTHOR]

In this paper we propose a new iterative finite difference (IFD) scheme based on the Newton–Raphson–Kantorovich approximation method in function space to solve the classical one-dimensional Bratu’s problem. This new numerical method produces accurate solutions with low computational cost. The effectiveness and accuracy of the IFD method are confirmed through several numerical examples and compared to some existing numerical solvers. [ABSTRACT FROM AUTHOR]

In this paper, efficient numerical schemes are proposed for solving the fractional water wave models that describe the propagation of surface water wave. By using the weighted and shifted Grünwald–Letnikov (WSGL) formula to approximate the nonlocal fractional operators, we design a series of second order accurate difference schemes for the considered models. The existence, stability and convergence of numerical solutions of the proposed numerical schemes are established rigorously. The analysis shows that the proposed numerical schemes are unconditionally stable with second order accuracy for both temporal and spatial discretizations. Several numerical results are provided to verify the efficiency and accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

The goal of this paper is to obtain a numerical approximation of the effective Hamiltonian for a system of PDEs deriving from a second order discrete model for traffic flow. We will propose an explicit and an implicit discretization for this effective Hamiltonian and we will provide the corresponding error estimates of Crandall–Lions type. Finally, we will also present some numerical simulations. [ABSTRACT FROM AUTHOR]

Given an edge-weighted graph G = ( V , E ) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R . A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we consider the full Steiner tree problem when G is a unit disk graph. We present a 20-approximation algorithm for the full Steiner tree problem in G . As for λ -precise unit disk graphs we present a ( 10 + 1 λ ) -approximation algorithm, where λ is the length of the shortest edge in G . [ABSTRACT FROM AUTHOR]

The central problem in case based reasoning (CBR) is to infer a solution for a new problem-instance by using a collection of existing problem–solution cases. The basic heuristic guiding CBR is the hypothesis that similar problems have similar solutions. Recently, some attempts at formalizing CBR in a theoretical framework have been made, including work by Hüllermeier who established a link between CBR and the probably approximately correct (PAC) theoretical model of learning in his ‘case-based inference’ (CBI) formulation. In this paper we develop further such probabilistic modelling, framing CBI it as a multi-category classification problem. We use a recently-developed notion of geometric margin of classification to obtain generalization error bounds. [ABSTRACT FROM AUTHOR]

Proximity searching is the problem of retrieving, from a given database, those objects closest to a query. To avoid exhaustive searching, data structures called indexes are built on the database prior to serving queries. The curse of dimensionality is a well-known problem for indexes: in spaces with sufficiently concentrated distance histograms, no index outperforms an exhaustive scan of the database. In recent years, a number of indexes for approximate proximity searching have been proposed. These are able to cope with the curse of dimensionality in exchange for returning an answer that might be slightly different from the correct one. In this paper we show that many of those recent indexes can be understood as variants of a simple general model based on K-nearest reference signatures. A set of references is chosen from the database, and the signature of each object consists of the K references nearest to the object. At query time, the signature of the query is computed and the search examines only the objects whose signature is close enough to that of the query. Many known and novel indexes are obtained by considering different ways to determine how much detail the signature records (e.g., just the set of nearest references, or also their proximity order to the object, or also their distances to the object, and so on), how the similarity between signatures is defined, and how the parameters are tuned. In addition, we introduce a space-efficient representation for those families of indexes, making it possible to search very large databases in main memory. Small indexes are cache friendly, inducing faster queries. We perform exhaustive experiments comparing several known and new indexes that derive from our framework, evaluating their time performance, memory usage, and quality of approximation. The best indexes outperform the state of the art, offering an attractive balance between all these aspects, and turn out to be excellent choices in many scenarios. Our framework gives high flexibility to design new indexes. [ABSTRACT FROM AUTHOR]

In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Generalized Multiscale Finite Element Method (GMsFEM) for the Brinkman model in two dimensions. In the fine grid, we use mixed finite element method with the velocity and pressure being continuous piecewise quadratic and piecewise constant finite element spaces, respectively. Using the GMsFEM framework we construct suitable coarse-scale spaces for the velocity and pressure that yield a robust mixed GMsFEM. We develop a novel approach to construct a coarse approximation for the velocity snapshot space and a robust small offline space for the velocity space. The stability of the mixed GMsFEM and a priori error estimates are derived. A variety of two-dimensional numerical examples are presented to illustrate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In probabilistic model analysis and optimization, expected values of a model output f ( x ) in face of continuous random inputs x are estimated through n -dimensional integrals, where n = d i m ( x ) . Cubature formulae are approximations of these integrals by a weighted sum of function evaluations at carefully chosen points. When each function evaluation corresponds to a heavy computational simulation, and particularly in optimization problems, one needs very efficient formulae with few integration points, even though only having modest accuracy. In this paper, we evaluate the performance of several cubature formulae with few points, including Smolyak type formulae, also known as sparse grid integration, and recently proposed thinned cubatures, constructed using orthogonal arrays. Tests are made for a wide family of smooth and non-oscillatory functions f ( x ) , possibly with significant anisotropy, and covering both normal and uniform input probability distributions. Two practical case studies are also presented, one of analysis of a large scale mass transfer model with uncertain parameters and a second one of optimal production planning under uncertain market conditions. Results clearly indicate that cubatures with large negative weights, including Smolyak type formulae, are not reliable, contrary to positive thinned cubatures that produce very reasonable estimates up to dimension 24. These thinned cubatures may also surpass quasi-Monte Carlo methods also up to dimension 24. [ABSTRACT FROM AUTHOR]

In this paper, we consider the two-agent scheduling problem with rejection on a single machine. In the problem we have two agents A and B with job families J A and J B , respectively. A job in J A or J B is either accepted and processed on the machine, or rejected with a certain rejection penalty having to be paid. The objective is to minimize the sum of the given objective function f A of the accepted jobs and total rejection penalty of the rejected jobs of the first agent A , given that the second agent B only accepts schedules such that the sum of the given objective function f B of the accepted jobs and total rejection penalty of the rejected jobs of the agent B does not exceed a fixed value Q ( Q is a positive integer), where f A and f B are non-decreasing functions on the completion times of their respective jobs. We show that, for all pairs ( f A , f B ) ∈ C max A , C max B , L max A , L max B , ∑ C j A , C max B , ∑ C j A , L max B , ∑ C j A , ∑ w j B U j B , the problems are NP-hard. When ( f A , f B ) = C max A , L max B , we provide a pseudo-polynomial-time algorithm. Moreover, when ( f A , f B ) = C max A , L max B and all B -jobs are accepted, we give a 2-approximation algorithm and an fully polynomial-time approximation scheme. Finally, for ( f A , f B ) ∈ ∑ C j A , L max B , ∑ C j A , ∑ w j B U j B K , we present pseudo-polynomial-time algorithms, respectively. [ABSTRACT FROM AUTHOR]

This paper applies a new modification of the Homotopy Perturbation Method that is called Rational Homotopy Perturbation Method (RHPM) to obtain an analytic approximation of stiff systems of ordinary differential equations. The procedure of the method will be explained briefly and some examples are presented to illustrate the method. The results of RHPM, are compared with those of traditional Homotopy Perturbation Method. The results show the accuracy and fast convergence of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper the numerical simulation of aeroelastic interactions of flexibly supported two-degrees of freedom (2-DOF) airfoil in two-dimensional (2D) incompressible viscous turbulent flow subjected to a gust (sudden change of flow conditions) is considered. The flow is modeled by Reynolds averaged Navier-Stokes equations (RANS), and by k - ω turbulence model. The considered flow problem is discretized in space using the fully stabilized finite element (FE) method implemented in the developed in-house program, which allows to solve interaction problems. In order to treat the time dependent inlet boundary condition the standard stabilization procedure was modified. Further, the under relaxation procedure was introduced in order to overcome the artificial instability of the coupling algorithm. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code. [ABSTRACT FROM AUTHOR]

This paper proposes a new approximation method for conic sections by quartic Bézier curves with G 1 end-point continuity. We give an upper bound on the Hausdorff distance between the conic section and the quartic Bézier approximation curve, and also show that the approximation order is eight. Moreover, using the subdivision scheme at the shoulder point of the conic section, the resulting approximation curve has G 2 (curvature)-continuity with the conic section at the endpoints. Finally, we prove that our approximation has a smaller error bound than previous quartic Bézier approximations, and also present some numerical examples to demonstrate the validity and effectiveness of our method. [ABSTRACT FROM AUTHOR]

In the present paper we consider a 1D Poisson model characterized by the presence of an interface, where a transmission condition arises due to jumps of the coefficients. We aim at studying finite element methods with meshes not fitting such an interface. It is well known that when the mesh does not fit the material discontinuities the resulting scheme provides in general lower order accurate solutions. We focus on so-called embedded approaches, frequently adopted to treat fluid–structure interaction problems, with the aim of recovering higher order of approximation also in presence of non fitting meshes; we implement several methods inspired by: the Immersed Boundary method, the Fictitious Domain method, and the Extended Finite Element method. In particular, we present four formulations in a comprehensive and unified format, proposing several numerical tests and discussing their performance. Moreover, we point out issues that may be encountered in the generalization to higher dimensions and we comment on possible solutions. [ABSTRACT FROM AUTHOR]

In this paper, a new nonmonotone trust region algorithm with simple quadratic models is proposed. Unlike traditional nonmonotone trust region method, our trust region subproblem is very simple by using a new scale approximation of the minimizing function's Hessian. The global convergence of the proposed algorithm is established under some reasonable conditions. Numerical tests on a set of large scale standard test problems are presented and show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a method for the accurate calculation of output quantities resulting from a parameter-dependent, single-phase flow model. In particular, given a small-dimensional set of inputs (as compared to the fine model), we treat the problem using a combined local–global model reduction technique. The local model reduction is achieved through the use of the Generalized Multiscale Finite Element Method (GMsFEM) where a set of independently calculated basis functions are used in order to construct a suitable coarse approximation space. The multiscale basis function computations are localized to specified coarse subdomains, and follow an offline–online procedure in which a set of eigenvalue problems are used to capture the underlying behavior of the system. Because the offline stage accounts for a one-time preprocessing step, the online coarse space may be cheaply constructed for a given input state. We then apply balanced truncation (BT) to the online coarse system in order to obtain a global reduced-order approximation of the output state. BT recasts the model equation into a systems framework where the input–output mapping may be approximated through the spectral construction of a reduced-order model, and requires the solution of a set of Lyapunov equations. As the Lyapunov equations represent an expensive computation, the efficiency of the proposed method depends on the size of the online coarse space. The combined approach is shown to be flexible with respect to the online space and reduced dimensions, and may be readily modified in order to ensure that the resulting output errors are comparable. [Copyright &y& Elsevier]

Magnetic materials are considered as crucial components for a wide range of products and devices. Usually, complexity of such materials is defined by their permeability classification and coupling extent to non-magnetic properties. Hence, development of models that could accurately simulate the complex nature of these materials becomes crucial to the multi-dimensional field-media interactions and computations. In the past few decades, artificial neural networks (ANNs) have been utilized in many applications to perform miscellaneous tasks such as identification, approximation, optimization, classification and forecasting. The purpose of this review article is to give an account of the utilization of ANNs in modeling as well as field computation involving complex magnetic materials. Mostly used ANN types in magnetics, advantages of this usage, detailed implementation methodologies as well as numerical examples are given in the paper. [ABSTRACT FROM AUTHOR]

This paper presents an efficient mathematical model for studying the slip-buckling behaviour of longitudinally delaminated elastic Reissner’s two-layer composite columns. The present mathematical model is used to evaluate exact critical buckling loads of these columns for the first time. The results prove that the presence of longitudinal delamination can significantly reduce the critical buckling load. The comparison of the results show that if sections outside of full delamination are undelaminated, the results are identical to the ones in the literature. On the other hand, the significant discrepancy may exist when those sections are partially longitudinally delaminated. Moreover, the critical buckling load for shear-stiff column with almost freely sliding longitudinal delamination along the whole column length can be up to approximately 4 times smaller compared to the buckling load of the same but undelaminated column. [ABSTRACT FROM AUTHOR]

This paper develops a stable model predictive tracking controller (SMPTC) for coordinated control of a large-scale power plant. First, a Takagi–Sugeno (TS) fuzzy model is established to approximate the behavior of the boiler–turbine coordinated control system (CCS) using fuzzy clustering and subspace identification (SID). Then, an SMPTC is designed based on the fuzzy model to track the power and pressure set-points while guaranteeing the input-to-state stability and the input constraints of the system. An output-based objective function is adopted for the proposed SMPTC so that the controller could be directly applicable for the data-driven model. Moreover, the effect of modeling mismatches and unknown plant variations has been overcome by the use of a disturbance term and steady-state target calculator (SSTC). Simulation results for a 600 MW power plant show that an off-set free tracking performance can be achieved over a wide range load variation. [ABSTRACT FROM AUTHOR]

This paper introduces a mathematical model which approximates the topographic shape of punctiform sink marks to a Gaussian-bell-like function. Such a model enables the description of sink mark shapes with few parameters, and the calculation of features which can be used to describe the visibility of the sink marks. The topography of test series of sink marks on black high-gloss plastic parts was measured with a chromatic coding confocal microscope. The obtained data was fitted to the model which enables calculation of a sink mark's amplitude and volume. These two parameters are proposed to feature a sink mark's intensity. The results were compared to deflectometric measurements of the sink marks. Despite the fact that the two measurement methods are based on different principles, the results show high correlation. Especially, the behavior of sink mark volumes agreed well with the behavior of sink mark intensity which was measured using deflectometry. Therefore, the model also represents a viable option for the calibration of deflectometric applications. Additionally, the model can be used in future to simulate sink mark properties such as visual perceptibility. [ABSTRACT FROM AUTHOR]

Surrogate models - simple functional approximations of complex models - can facilitate engineering analysis of complicated systems by greatly reducing computational expense. The construction of a surrogate model requires evaluation of the original model to gather the data necessary for building the surrogate. Sequential sampling procedures are proposed for determining and minimizing the required number of samples for efficient global surrogate construction. In this paper, two new adaptive sampling algorithms - one purely adaptive and one combining adaptive and space-filling characteristics - are proposed and compared to a purely space-filling approach. Our analysis suggests a mixed adaptive sampling approach for constructing surrogates for systems where the behavior of the underlying model is unknown. Results of the case study, optimization of carbon dioxide capture process with aqueous amines, revealed that the mixed adaptive sampling algorithm may reduce the required sample size by up to 40% compared to a purely space-filling design. [ABSTRACT FROM AUTHOR]

This paper investigates the relation between the uncertain mechanical properties of wood and its extensibility at the ultrastructural scale. A statistical approximation to the output of a multi-scale constitutive model is adopted to predict the extensibility of wood in the presence of parametric uncertainty. By means of this procedure, a very large number of computationally intensive fully-coupled multi-scale simulations are avoided. Following this approach, four different micromechanical parameters are chosen to assess their influence on the extensibility of the material under tensile loading conditions. These are the degree of cellulose crystallinity, the ultimate strain and Young's modulus of the hemicellulose-lignin matrix, and the thickness of the amorphous cellulose layer which covers the periodic crystalline portions of cellulose. We believe that a better understanding of the mechanisms of deformation and extensibility in wood and in natural materials can pave the way for the development of new strategies to design more advanced materials in engineering structures. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the pricing of vulnerable options when the underlying asset follows a stochastic volatility model. We use multiscale asymptotic analysis to derive an analytic approximation formula for the price of the vulnerable options and study the stochastic volatility effect on the option price. A numerical experiment result is presented to demonstrate our findings graphically. [Copyright &y& Elsevier]

Abstract: In this paper, two heat conductor models with fading memory are obtained by different approximations of Tzou’s dual-phase-lag theory. For the first model, we obtain a close coincidence between the restrictions of the second law and the asymptotic stability. Otherwise, for the second model the thermodynamic restrictions appear more restrictive compared with the conditions following from the asymptotic stability. [Copyright &y& Elsevier]

Abstract: Releasing sky lanterns is a popular way of celebrating festivals and ceremonies in the Asian countries. This paper presents a computer-aided approach to help novice users to design flyable sky lantern with desired shape. Given a closed up-right 3D model with a user-specified cutting on the bottom, our system optimizes the shape by regularizing the boundary, smoothing the geometry and improving the volume-to-area ratio to make it feasible for flying. The optimized shape is then approximated by a set of developable patches. Next, through a physical analysis step that tests the flying condition and determines the optimal size, the approximated shape is flattened into 2D patches, which can be printed out and glued together to form the airbag. Finally, the user can attach the airbag to a bamboo frame and assemble the fuel cell. We successfully apply our prototype system to design and construct real sky lanterns. [Copyright &y& Elsevier]