Numerical Robust Stability Estimation in Milling Process

The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment, In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.

ON THE STABILITY ESTIMATION OF ANALYTIC CONTINUATION FOR POTENTIAL FIELD

This paper discusses the stability of solutions to a class of Cauchy problems for Laplace equations under two kinds of nonclassical circumstances. By means of conformal mapping and Tikhonov, Luan Wengui and Yamamoto's methods for solving ill-posed problems respectively, the stability estimations of weighted Holder type and logarithmic type, have been obtained accordingly.

On the Stability of the Solution to a Gonorrhea Diserete Mathematical Model

In this paper, the author studies the stability of the solution to a three-dimension-al gonorrhea discrete mathematical model by Liapunoy method. The parameter es-timator of the slability domain is obtained and the rationality of the model is ex-plained in a theoretic way.

Asymptotic Evaluations of the Stability Index for a Markov Control Process with the Expected Total Discounted Reward Criterion

In this work, for a control consumption-investment process with the discounted reward optimization criteria, a numerical estimate of the stability index is made. Using explicit formulas for the optimal stationary policies and for the value functions, the stability index is explicitly calculated and through statistical techniques its asymptotic behavior is investigated (using numerical experiments) when the discount coefficient approaches 1. The results obtained define the conditions under which an approximate optimal stationary policy can be used to control the original process.

Physiological,Biochemical and Molecular Responses of Barley Seedlings to Aluminum Stress

Barley(Hordeum vulgare L.)is one of the most Aluminum(Al)sensitive cereal species.In this study,the physiological,biochemical,and molecular response of barley seedlings to Al treatment was examined to gain insight into Al response and tolerance mechanisms.The results showed that superoxide dismutase(SOD),peroxidase(POD)and catalase(CAT)activity were inhibited to different degrees following Al exposure.The MDA content also significantly increased with increasing Al concentrations.SRAP results indicated significant differences between Al treatments and controls in terms of SRAP profile,and the genomic template stability(GTS)decreased with increasing Al concentration and duration.These integrative results help to elucidate the underlying mechanisms that the barley response to Al toxicity.

High-Order Local Discontinuous Galerkin Algorithm with Time Second-Order Schemes for the Two-Dimensional Nonlinear Fractional Diffusion Equation

In this article,some high-order local discontinuous Galerkin(LDG)schemes based on some second-order θ approximation formulas in time are presented to solve a two-dimen-sional nonlinear fractional diffusion equation.The unconditional stability of the LDG scheme is proved,and an a priori error estimate with O(h^(k+1)+At^(2))is derived,where k≥0 denotes the index of the basis function.Extensive numerical results with Q^(k)(k=0,1,2,3)elements are provided to confirm our theoretical results,which also show that the second-order convergence rate in time is not impacted by the changed parameter θ.

Numerical Analysis of Upwind Difference Schemes for Two-Dimensional First-Order Hyperbolic Equations with Variable Coefficients

In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.

NVERSE CONDUCTIVITY PROBLEM WITH INTERNAL DATA

This paper concerns the reconstruction of a scalar coefficient of a second-order elliptic equation in divergence form posed on a bounded domain from internal data.This problem finds applications in multi-wave imaging,greedy methods to approximate parameter-dependent elliptic problems,and image treatment with partial differential equations.We first show that the inverse problem for smooth coefficients can be rewritten as a linear transport equation.Assuming that the coefficient is known near the boundary,we study the well-posedness of associated transport equation as well as its numerical resolution using discontinuous Galerkin method.We propose a regularized transport equation that allow us to derive rigorous convergence rates of the numerical method in terms of the order of the polynomial approximation as well as the regularization parameter.We finally provide numerical examples for the inversion assuming a lower regularity of the coefficient,and using synthetic data.

Optimal Three Cylinder Inequality at the Boundary for Solutions to Parabolic Equations and Unique Continuation Properties

Let Γ be a portion of a C^(1,α) boundary of an n-dimensional domain D. Letu be a solution to a second order parabolic equation in D x (-T, T) and assume that u = 0 on Γ x(-T, T), 0 ∈ Γ. We prove that u satisfies a three cylinder inequality near Γ x (—T, T). As aconsequence of the previous result we prove that if u(x,t) = O (|x|~k ) for every t ∈ (-T,T) andevery k ∈ N, then u is identically equal to zero.