Numerical Stability

In this article, we first consider some penalized finite element methods for the stationary Navier-stokes equations, based on the finite element space pair (X h , M h ) which satisfies the discrete inf-sup condition for the P 2 -P 0 element or does not satisfy the discrete inf-sup condition for the P 1 -P 0 element. Then, we consider two-level penalty finite element methods which involve solving one small Navier-Stokes problem on a coarse mesh with mesh size H, a large Stokes problem on a fine mesh with mesh size h = O( i/2-1 H 2 ) for the P i -P 0 element with i = 1, 2, where 0 < < 1 is a penalty parameter. The methods we study provide an approximate solution (u h , p h ) with the convergence rate of same order as the penalty finite element solution (u h , p h ), which involves solving one large Navier-Stokes problem on a fine mesh with mesh size h. Hence, our method can save a large amount of computational time.

Consider a system composed of n sensors operating in synchronous rounds. In each round an input vector of sensor readings x is produced, where the i-th entry of x is a binary value produced by the i-th sensor. The sequence of input vectors is assumed to be smooth: exactly one entry of the vector changes from one round to the next one. The system implements a faulttolerant averaging consensus function f . This function returns, in each round, a representative output value v of the sensor readings x. Assuming that at most t entries of the vector can be erroneous, f is required to return a value that appears at least t + 1 times in x. The instability of the system is the number of output changes over a random sequence of input vectors. Our first result is to design optimal instability consensus systems with and without memory. Intuitively, in the memoryless case, we show that an optimal system is D 0 , that outputs 1 unless it is forced by the fault-tolerance requirement to output 0 (on vectors with t or less 1's). For the case of systems with memory, we show that an optimal system is D 1 , that initially outputs the most common value in the input vector, and then stays with its output unless forced by the fault-tolerance requirement to change (i.e., a single bit of memory suffices). Our second result is to quantify the gain factor due to memory by computing c n (t), the number of decision changes performed by D 0 per each decision change performed by D 1 . If t = n 2 the system is always forced to decide the simple majority and, in that case, memory becomes useless. We show that the same type of phenomenon occurs when n 2t is constant. Nevertheless, as soon as n 2t ∼ √ n, memory plays an important stabilizing role because the ratio c n (t) grows like Θ( √ n). We also show that this is an upper bound: c n (t) = O( √ n). Our results are average case versions of previous works where the sequence of input vectors was assumed to be, in addition to smooth, geodesic: the i-th entry of the input vector was allowed to change at most once over the sequence. It thus eliminates some anomalies that ocurred in the worst case, geodesic instability setting.

This notebook explores the application of Discrete Exterior Calculus (DEC) to model thermodynamic-like dynamics on a simplicial complex shaped as a tetrahedron. The working hypotheses are: 1. Field Placement Consistency Electric-like fields ( E ) can be represented as 1forms on edges, and magnetic-like fields ( B ) as 2-forms on faces. Constitutive mappings (Hodge stars) should connect these spaces in a way that preserves dimensional consistency. The familiar "laws" of thermodynamics can be approximated in this discrete setting: Zeroth Law: Stationary distributions of coupled Markov processes converge to equivalence. First Law: Energy evolves consistently under Faraday-and Ampère-like updates, with damping acting as dissipation. Second Law: Entropy production rate (EPR) is non-negative and sensitive to counterfactual transitions. Third Law: Reducing transition rates to/from the "null" node simulates a lowtemperature regime, with stationary probability concentrating at the null. A consistent discrete energy functional can be written in terms of squared norms of the constitutive fields ( D , H ), and its rate of change balances with input and dissipation power. The simulation produced the following key observations: Zeroth Law: The stationary distributions of the two coupled graphs were equal within numerical tolerance, confirming the expected equilibrium consistency. First Law: Energy evolved smoothly over 50 timesteps, with a slight decay due to the imposed damping term. Average frequency decreased gradually from ~9.95 Hz, consistent with dissipative dynamics.

We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regimes is made. The linear stability of fixed points is studied, yielding exact analytical expressions for parameter values at which a perioddoubling bifurcation occurs. The dynamics is apparently ergodic at certain energies in all three models, in contrast to the regularity of the circular and elliptic billiard dynamics in the field-free case. This finding is confirmed using a sensitive test involving Lyapunov weighted dynamics. In the last part of the paper a time dependence is introduced in the billiard boundary, where it is shown that for the circular billiard the average velocity saturates for zero gravitational force but in the presence of gravitational it increases with a very slow growth rate, which may be explained using Arnold diffusion. For the oval billiard, where chaos is present in the static case, the particle has an unlimited velocity growth with an exponent of approximately 1/6.

To measure the arterial input function (AIF), an essential component of tracer kinetic analysis, in a population of patients using an optimized dynamic contrast-enhanced (DCE) imaging sequence and to estimate inter- and intrapatient variability. From these data, a representative AIF that may be used for realistic simulation studies can be extracted. Thirty-nine female patients were imaged on multiple visits before and during a course of neoadjuvant chemotherapy for breast cancer. A total of 97 T -weighted DCE studies were analyzed including bookend estimates of T and model-fitting to each individual AIF. Area under the curve and cardiac output were estimated from each first pass peak, and these data were used to assess inter- and intrapatient variability of the AIF. Interpatient variability exceeded intrapatient variability of the AIF. There was no change in cardiac output as a function of MR visit (mean value 5.6 ± 1.1 L/min) but baseline blood T increased significantly following t...

The aim of this paper is to present some results on the control synthesis of time-delay linear systems. Our objective is to find linear controllers able to increase the first stability window imposing that the delay-free system is stable. Our method treats time-delay systems control design with numeric routines based on Linear Matrix Inequalities (LMI) arisen from classical linear time invariant system theory coupled together with a unidimensional search. The proposed algorithm is simple, efficient and easy to be numerically implemented. Some examples illustrating state and output feedback design are solved and discussed in order to shed the light on the most relevant characteristic of the theoretical results. The paper ends with some discussion on further theoretical extensions of the proposed methodology.

Let $G$ be a graph. A Hamilton path in $G$ is a path containing every vertex of $G$. The graph $G$ is traceable if it contains a Hamilton path, while $G$ is $k$-traceable if every induced subgraph of $G$ of order $k$ is traceable. In this paper, we study hamiltonicity of $k$-traceable graphs. For $k \geq 2$ an integer, we define $H(k)$ to be the largest integer such that there exists a $k$-traceable graph of order $H(k)$ that is nonhamiltonian. For $k \le 10$, we determine the exact value of $H(k)$. For $k \ge 11$, we show that $k+2 \le H(k) \le \frac{1}{2}(3k-5)$.

In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication.

image Figure 1: Given a segmented image as input we produce a stereo pair (or a motion parallax animation) by hallucinating plausible 3D geometry for the scene. First, segments are depth-sorted using simple depth and occlusion cues. Next, the geometry and texture of each object is completed using symmetry and convexity priors. Finally, we infer a depth placement for each object. We urge the reader to view the companion video before reading the paper, and to examine our anaglyphs in full size using red/cyan glasses. All of the results in this paper are available in the supplementary material. We introduce a novel method for enabling stereoscopic viewing of a scene from a single pre-segmented image. Rather than attempting full 3D reconstruction or accurate depth map recovery, we hallucinate a rough approxi-mation of the scene’s 3D model using a number of simple depth and occlusion cues and shape priors. We begin by depth-sorting the segments, each of which is assumed to represent a se...

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the influence of the minus sign problem on convergence. Also here in the absence of a minus sign problem we encounter convergence problems for strong interactions.

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with results from exact and stochastic diagonalizations. We find good agreement for the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on the superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by fluctuations or systematic errors of the method. Although we notice that the Quantum-Monte-Carlo method has convergence problems for large interactions, coinciding with a minus sign problem, we confirm the results of the diagonalization techniques for small and moderate interaction strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive case, to study the i...

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.

The paper inhere describes an approach and method for studying and investigating the causes and mechanism for development of an emergency in a power transformer that results in a large fire in an administrative building with lots of casualties and material losses.

The paper considers a method for converting a divergent Dirichlet series into a convergent Dirichlet series by directly converting the coefficients of the original series 1→ δn(s) for the Riemann Zeta function. In the first part of the paper, we study the properties of the coefficients δ∗ n of a finite Dirichlet series for approximating the Riemann Zeta function on the interval ∆H . In general, the coefficients δ∗ n of a finite Dirichlet series are complex numbers. The dependence of the coefficients δ∗ n of a finite Dirichlet series on the ordinal number of the coefficient n is established, which can be set by a sigmoid, and for each N there is a single sigmoid δ̂n and a single interval ∆H for which the condition is satisfied ∣∣∣ N ∑

Se estudia la in uencia de la topología de redes eléctricas y alimentadores en el condicionamiento de las matrices asociadas a su modelado matemático. Se observa que el número de condición de estas matrices tiene una gran dependencia de la estructura de la red y que es afectado por el grado de enmallamiento de la red. Se incluyen resultados de simulaciones computacionales de distintos casos que permiten establecer una relación de consecuencia. Palabras clave: Matrices de redes, condicionamiento numérico, estabilidad numérica.

Se estudia la in uencia de la topología de redes eléctricas y alimentadores en el condicionamiento de las matrices asociadas a su modelado matemático. Se observa que el número de condición de estas matrices tiene una gran dependencia de la estructura de la red y que es afectado por el grado de enmallamiento de la red. Se incluyen resultados de simulaciones computacionales de distintos casos que permiten establecer una relación de consecuencia. Palabras clave: Matrices de redes, condicionamiento numérico, estabilidad numérica.

The aim of the following work is to individualise and to deepen some numerical methods finalized to represent the spraying process of a liquid fuel in a combustion chamber. First objective is to reach an optimisation of the representation the mixing process which happens between fuel droplets and oxidiser gas to obtain a better combustion reaction. Since a functional representation of diffusion and convective terms in turbulent regime needs high order derivative, it's demonstrated that a spectral-like approach with Compact Schemes is able to simulate the atomisation mechanism. In this context, we have evaluated the opportunity to be able to reformulate the procedure of EPD's reconstruction by another very efficient functional expression to integrate NS.

We extend the authors’ prior theory of the RT-equations from the setting of affine connections, to the general setting of connections defined on vector bundles over arbitrary manifolds, including YangMills connections over Lorentzian manifolds in Physics. By this, our theory of the RT-equations extends optimal regularity and Uhlenbeck compactness from the case of vector bundles over Riemannian manifolds with compact Lie group, to vector bundles over arbitrary manifolds, allowing for both compact and non-compact Lie groups. Our results here apply to L connections, p &gt; n.

We consider the Bresse system with temperature and we show that there exist exponential stability if and only if the wave propagation is equal. We show that, in general, the system is not exponentially stable but that there exists polynomial stability with rates that depend on the wave propagations and the regularity of the initial data. Moreover, we introduce a necessary condition to dissipative semigroup decay polynomially. This result allows us to show some optimality to the polynomial rate of decay.

Recursive Kirchhoff extrapolation has attractive merits that make it an ideal candidate for implementation in pre-stack depth migrations. However, the artifacts resulting from data and operator aperture truncations may cause instability and inaccuracy. Tapering is widely recognized as an effective tool to deal with truncation problems. In wavefield extrapolation, the conventional method is to apply a taper to the data edges and then extrapolate the tapered data with a tapered extrapolator. However, as we show in this paper, this method may result in a loss of accuracy, especially for the first-step of wavefield extrapolation where the input surface data are usually zero-padded to the extent of the migration aperture. We introduce an adaptive tapering scheme that varies with output locations and handles both truncations dynamically. Synthetic examples show that the extrapolation with adaptive tapering achieves a better accuracy than conventional separate application of data tapering and operator tapering.

Recursive Kirchhoff extrapolation has attractive merits that make it an ideal candidate for implementation in pre-stack depth migrations. However, the artifacts resulting from data and operator aperture truncations may cause instability and inaccuracy. Tapering is widely recognized as an effective tool to deal with truncation problems. In wavefield extrapolation, the conventional method is to apply a taper to the data

In this paper we prove a Lévy-Ottaviani type of property for the Bernoulli process defined on an interval. Namely, we show that under certain conditions on functions (ai) n i=1 and for independent Bernoulli random variables (εi) n i=1 , P(sup t∈[0,1] n i=1 ai(t)εi c) is dominated by CP( n i=1 ai(1)εi 1), where c and C are explicit numerical constants independent of n. The result is a partial answer to the conjecture of W. Szatzschneider that the domination holds with c = 1 and C = 2.

The uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered. The existence of both weak and strong solutions to the system is proven by the Galerkin method. The exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the Riemannian manifold. This equivalent energy function shows particularly that the system is essentially a dissipative system. This result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in [A. Guesmia, A new approach of stabilization of nondissipative distributed systems, SIAM J. Control Optim. 42 (2003) 24-52] where the system is claimed to be nondissipative.

Measured and analytical data are unlikely to be equal due to measured noise, model inadequacies, structural damage, etc. It is necessary to update the physical parameters of analytical models for proper simulation and design studies. Starting from simulated measured modal data such as natural frequencies and their corresponding mode shapes, a new computationally efficient and symmetry preserving method and associated theories are presented in this paper to update the physical parameters of damping and stiffness matrices simultaneously for analytical modeling. A conjecture which is proposed in [Y.X. Yuan, H. Dai, A generalized inverse eigenvalue problem in structural dynamic model updating, J. Comput. Appl. Math. 226 (2009) 42-49] is solved. Two numerical examples are presented to show the efficiency and reliability of the proposed method. It is more important that, some numerical stability analysis on the model updating problem is given combining with numerical experiments.

In this paper, using the fixed point theorem, we investigate the boundedness and asymptotic stability of the zero solution of the discrete Volterra equation Necessary conditions for the existence of a periodic solution of the above equation are also obtained.

In this paper, we will first study the existence and uniqueness of the solution for a one dimensional Inverse Heat Conduction Problem (IHCP) via an auxiliary problem. Then a stable numerical method consists of the zeroth-, first-and second-order Tikhonov regularization method to the matrix form of Duhamel's principle for solving this IHCP by using noisy data is presented. The inverse problem has a unique solution, but this solution is unstable hence the problem is ill-posed. This instability is overcome using the Tikhonov regularization method with the gcv criterion for the choice of the regularization parameter. The stability and accuracy of the scheme presented is evaluated by comparison with the Singular Value Decomposition (SVD) method.

SUMMARYIn this paper, we address the solution of three‐dimensional heterogeneous Helmholtz problems discretized with second‐order finite difference methods with application to acoustic waveform inversion in geophysics. In this setting, the numerical simulation of wave propagation phenomena requires the approximate solution of possibly very large indefinite linear systems of equations. For that purpose, we propose and analyse an iterative two‐grid method acting on the Helmholtz operator where the coarse grid problem is solved inaccurately. A cycle of a multigrid method applied to a complex shifted Laplacian operator is used as a preconditioner for the approximate solution of this coarse problem. A single cycle of the new method is then used as a variable preconditioner of a flexible Krylov subspace method. We analyse the properties of the resulting preconditioned operator by Fourier analysis. Numerical results demonstrate the effectiveness of the algorithm on three‐dimensional applic...

Secondary bifurcations of hexagonal patterns are analyzed in a model of a single-mirror arrangement with an alkali metal vapor as the nonlinear medium. A stability analysis of the hexagonal structures is performed numerically. Different instabilities are predicted in dependency on the wave number of the hexagons. Some of the instabilities take place at a finite wave number and result in the formation of structures with 12 spatial modes. These structures are compared with those observed experimentally.

Four types of partitioned time-marching schemes, namely the iterative staggered serial (ISS) scheme, the conventional serial staggered serial (CSS) scheme, the generalized serial staggered scheme (GSS), and the serial staggered scheme with fluid loads predictions (FPSS), are presented for accuracy comparisons of nonlinear fluid-structure interactions (FSI). A 2-DOF aeroelastic model for an airfoil is used as an example to illustrate the effects of different control parameters of the schemes. Some modifications are made to the schemes to improve the FSI simulation accuracy. The numerical results show that the GSS and FPSS are accurate and robust if the default parameters are adopted. Moreover, the accuracy of FPSS can be further improved by simply tuning the control parameters.

Four types of partitioned time-marching schemes, namely the iterative staggered serial (ISS) scheme, the conventional serial staggered serial (CSS) scheme, the generalized serial staggered scheme (GSS), and the serial staggered scheme with fluid loads predictions (FPSS), are presented for accuracy comparisons of nonlinear fluid-structure interactions (FSI). A 2-DOF aeroelastic model for an airfoil is used as an example to illustrate the effects of different control parameters of the schemes. Some modifications are made to the schemes to improve the FSI simulation accuracy. The numerical results show that the GSS and FPSS are accurate and robust if the default parameters are adopted. Moreover, the accuracy of FPSS can be further improved by simply tuning the control parameters.

A system of ordinary differential equations (ODEs) is produced by the semidiscretize method of discretizing the advection diffusion equation (ADE). Runge-Kutta methods of the second and fourth orders are used to solve the system of ODEs. We compute the ADE numerically for initial and boundary conditions, for which the exact solution is known. In the semi-discretization approach, we estimate the error for both the second and fourth-order Runge-Kutta schemes. The semi-discretization method's outcome is contrasted with the ADE's numerical solution derived from the complete discretization explicit centered difference scheme.

Floating-point arithmetics may lead to numerical errors when numbers involved in an algorithm vary strongly in their orders of magnitude. In the paper we study numerical stability of Zernike invariants computed via complex-valued integral images according to a constant-time technique from [2], suitable for object detection procedures. We indicate numerically fragile places in these computations and identify their cause, namely-binomial expansions. To reduce numerical errors we propose piecewise integral images and derive a numerically safer formula for Zernike moments. Apart from algorithmic details, we provide two object detection experiments. They confirm that the proposed approach improves accuracy of detectors based on Zernike invariants.

We study the question of asymptotic stability, as time tends to infinity, of solutions of dissipative anisotropic Kirchhoff systems, involving the p(x)-Laplacian operator, governed by time-dependent nonlinear damping forces and strongly nonlinear power-like variable potential energies. This problem had been considered earlier for potential energies which arise from restoring forces, whereas here we allow also the effect of amplifying forces. Global asymptotic stability can then no longer be expected, and should be replaced by local stability. The results are further extended to the more delicate problem involving higher order damping terms.

We develop a wavelet transform on the sphere, based on the spherical HEALPix coordinate system (Hierarchical Equal Area iso-Latitude Pixelization). HEALPix is heavily used for astronomical data processing applications; it is intrinsically multiscale and locally euclidean, hence appealing for building multiscale system. Furthermore, the equal-area pixelization enables us to employ average-interpolating refinement, giving wavelets of local support. HEALPix wavelets have numerous applications in geopotential modeling. A statistical analysis demonstrates wavelet compressibility of the geopotential field and shows that geopotential wavelet coefficients have many of the statistical properties that were previously observed with wavelet coefficients of natural images. The HEALPix wavelet expansion allows to evaluate a gravimetric quantity over a local region far more rapidly than the classic approach based on spherical harmonics. Our software tools are specifically tailored to demonstrate these advantages.

We develop a wavelet transform on the sphere, based on the spherical HEALPix coordinate system (Hierarchical Equal Area iso-Latitude Pixelization). HEALPix is heavily used for astronomical data processing applications; it is intrinsically multiscale and locally euclidean, hence appealing for building multiscale system. Furthermore, the equal-area pixelization enables us to employ average-interpolating refinement, giving wavelets of local support. HEALPix wavelets have numerous applications in geopotential modeling. A statistical analysis demonstrates wavelet compressibility of the geopotential field and shows that geopotential wavelet coefficients have many of the statistical properties that were previously observed with wavelet coefficients of natural images. The HEALPix wavelet expansion allows to evaluate a gravimetric quantity over a local region far more rapidly than the classic approach based on spherical harmonics. Our software tools are specifically tailored to demonstrate these advantages.

We show that, under some assumptions, the linear recurrence (or difference equation) of order one in a Banach space is nonstable in the Hyers-Ulam sense. Our results are also connected with the notion of shadowing in dynamical systems and computer sciences.

In most decisional models based on pairwise comparison between alternatives, the reciprocity of the individual preference representations expresses a natural assumption of rationality. In those models self-dual aggregation operators play a central role, in so far as they preserve the reciprocity of the preference representations in the aggregation mechanism from individual to collective preferences. In this paper we propose a simple method by which one can associate a self-dual aggregation operator to any aggregation operator on the unit interval. The resulting aggregation operator is said to be the self-dual core of the original one, and inherits most of its properties. Our method constitutes thus a new characterization of self-duality, with some technical advantages relatively to the traditional symmetric sums method due to Silvert. In our framework, moreover, every aggregation operator can be written as a sum of a self-dual core and an anti-self-dual remainder which, in some cases, seems to give some indication on the dispersion of the variables. In order to illustrate the method proposed, we apply it to two important classes of continuous aggregation operators with the properties of idempotency, symmetry, and stability for translations: the OWA operators and the exponential quasiarithmetic means.

We present an algorithm which is numerically stable and optimal in time and space complexity for constructing the convex hull for a set of points on a plane. In contrast to existing numerically stable algorithms which return only an approximate hull, our algorithm constructs a polygon that is truly convex. The algorithm is simple and easy to implement. We assume a floating point arithmetic as a computation model.

The off-lattice Boltzmann (OLB) method consists of numerical schemes which are used to solve the discrete Boltzmann equation. Unlike the commonly used lattice Boltzmann method, the spatial and time steps are uncoupled in the OLB method. In the currently proposed schemes, which can be broadly classified into Runge-Kutta-based and characteristics-based, the size of the time-step is limited due to numerical stability constraints. In this work, we systematically compare the numerical stability of the proposed schemes in terms of the maximum stable time-step. In line with the overall LB method, we investigate the available schemes where the advection approximation is explicit, and the collision approximation is either explicit or implicit. The comparison is done by implementing these schemes on benchmark incompressible flow problems such as Taylor vortex flow, Poiseuille flow and, lid-driven cavity flow. It is found that the characteristics-based OLB schemes are numerically more stable than the Runge-Kutta-based schemes. Additionally, we have observed that, with respect to time-step size, the scheme proposed by Bardow et al. [? ] is the most numerically stable and computationally efficient scheme compared to similar schemes, for the flow problems tested here.

The massive Thirring (MT) model and its dual the sine-Gordon model are known to be integrable. Some versions of their multi-field extensions have appeared in the literature (see e.g. [1]). On the other hand, the noncommutative (NC) version of the MT model has been proposed recently . Here we discuss some properties of the affine Kac-Moody algebraic formulation of a noncommutative version of the so-called generalized massive Thirring model.

For numerical simulations of cavitating flows, many physical models are currently used. One approach is the void fraction transport equation-based model including source terms for vaporization and condensation processes. Various source terms have been proposed by different researchers. However, they have been tested only in different flow configurations, which make direct comparisons between the results difficult. A comparative study, based on the expression of the source terms as a function of the pressure, is presented in the present paper. This analytical approach demonstrates a large resemblance between the models, and it also clarifies the influence of the model parameters on the vaporization and condensation terms and, therefore, on the cavity shape and behavior. Some of the models were also tested using a 2D CFD code in configurations of cavitation on two-dimensional foil sections. Void fraction distributions and frequency of the cavity oscillations were compared to existing ...

We analyse and compare three algorithms for "downdating" the Cholesky factorization of a positive definite matrix. Although the algorithms are closely related, their numerical properties differ. Two algorithms are stable in a certain "mixed" sense, while the other is unstable. In addition to comparing the numerical properties of the algorithms, we compare their computational complexity and their suitability for implementation on parallel or vector computers. Only the Abstract is given here. The full paper appeared as . For an application of downdating, see .

This paper contains a numerical stability analysis of factorization algorithms for computing the Cholesky decomposition of symmetric positive definite matrices of displacement rank 2. The algorithms in the class can be expressed as sequences of elementary downdating steps. The stability of the factorization algorithms follows directly from the numerical properties of algorithms for realizing elementary downdating operations. It is shown that the Bareiss algorithm for factorizing a symmetric positive definite Toeplitz matrix is in the class and hence the Bareiss algorithm is stable. Some numerical experiments that compare behavior of the Bareiss algorithm and the Levinson algorithm are presented. These experiments indicate that in general (when the reflection coefficients are not all positive) the Levinson algorithm can give much larger residuals than the Bareiss algorithm.

Householder reflections applied from the left are generally used to zero a contiguous sequence of entries in a column of a matrix A. Our purpose in this paper is to introduce new rm Householder and TOW hyperbolic Householder reflections which are also applied from the left, but now zero a contiguous sequence of entries in a row of A. We then show how these row Householder reflections can be used to design efficient sliding-data-window recursive least-squares (RLS) covariance algo-

We present theory and algorithms for the equality constrained indefinite least squares problem, which requires minimization of an indefinite quadratic form subject to a linear equality constraint. A generalized hyperbolic QR factorization is introduced and used in the derivation of perturbation bounds and to construct a numerical method. An alternative method is obtained by employing a generalized QR factorization in combination with a Cholesky factorization. Rounding error analysis is given to show that both methods have satisfactory numerical stability properties and numerical experiments are given for illustration. This work builds on recent work on the unconstrained indefinite least squares problem by Chandrasekaran, Gu, and Sayed and by the present authors.

In this paper, an iterative numerical method that solves nonlinear fuzzy Hammerstein-Volterra integral equations with constant delay is developed. By using the error estimates, a practical stopping criterion of the algorithm is obtained. The convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples. The study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology.

In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.

A thermodynamically consistent damage model is proposed for the simulation of progressive delamination in composite materials under variable-mode ratio. The model is formulated in the context of Damage Mechanics. A novel constitutive equation is developed to model the initiation and propagation of delamination. A delamination initiation criterion is proposed to assure that the formulation can account for changes in the loading mode in a thermodynamically consistent way. The formulation accounts for crack closure effects to avoid interfacial penetration of two adjacent layers after complete decohesion. The model is implemented in a finite element formulation, and the numerical predictions are compared with experimental results obtained in both composite test specimens and structural components.