The fractional reaction–subdiffusion equation is one of the most famous subdiffusion equations. These equations are widely used in recent years to simulate many physical phenomena. In this paper, we ...consider a new version of such equations, namely the variable order linear and nonlinear reaction–subdiffusion equation. A numerical study is introduced using the weighted average methods for the variable order linear and nonlinear reaction–subdiffusion equations. A stability analysis of the proposed method is given by a recently proposed procedure similar to the standard John von Neumann stability analysis. The paper is ended with the results of numerical examples that support the theoretical analysis.
This paper is concerned with the parameter estimation problem for Cox-Ingersoll-Ross model based on discrete observation. First, a new discretized process is built based on the Euler-Maruyama scheme. ...Then, the parameter estimators are obtained by employing the maximum likelihood method and the explicit expressions of the error of estimation are given. Subsequently, the consistency property of all parameter estimators are proved by applying the law of large numbers for martingales, Holder's inequality, B-D-G inequality and Cauchy-Schwarz inequality. Finally, a numerical simulation example for estimators and the absolute error between estimators and true values is presented to demonstrate the effectiveness of the estimation approach used in this paper.
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BFBNIB, DOBA, GIS, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
In this study, the voltage stability margin for direct current (DC) networks in the presence of constant power loads is analyzed using a proposed convex mathematical reformulation. This convex model ...is developed by employing a second-order cone programming (SOCP) optimization that transforms the non-linear non-convex original formulation by reformulating the power balance constraint. The main advantage of the SOCP model is that the optimal global solution of a problem can be obtained by transforming hyperbolic constraints into norm constraints. Two test systems are considered to validate the proposed SOCP model. Both systems have been reported in specialized literature with 6 and 69 nodes. Three comparative methods are considered: (a) the Newton-Raphson approximation based on the determinants of the Jacobian matrices, (b) semidefinite programming models, and (c) the exact non-linear formulation. All the numerical simulations are conducted using the MATLAB and GAMS software. The effectiveness of the proposed SOCP model in addressing the voltage stability problem in DC grids is verified by comparing the objective function values and processing time.
In this article, the Fredericton approach to deformation analysis is presented. It is possible to use several deformation models to determine the differences between the geodetic observations or ...between the coordinates of points in geodetic network in more epochs. The most appropriate deformation model has been chosen based on statistical testing and available information about dynamics at the area of interest. First, a theoretical background of the approach is described. Then it is applied to the generated observations in two epochs. In the present example, the results of the Fredericton approach differ only slightly from the results obtained with the Delft, Karlsruhe in Hannover approaches.
A study on geometry design of spiral bevel gears based on conjugate curves is put forward in this paper. According to the theory of conjugate curves, generation principle and mathematical model of ...spiral bevel gears are developed for a given spiral bevel curve. The meshing equation in the given contact position for conjugate curves is derived. Tubular meshing surfaces contacting along the orientation of designated contact angle are proposed to build up the circular-arc tooth profiles, which inherit all properties of conjugate curves. Numerical example is illustrated for this research including the computerized simulation of three dimensional models and analysis of meshing characteristics. Theoretical and numerical results demonstrate the feasibility and correctness of conjugate curves theory. Compared with general spiral bevel gears, this novel gear is different in the viewpoints of meshing and generation principles. And it is expected to have more excellent transmission performance which will be further studied in future.
This paper gives a new theoretical analysis of the space-time continuous Galerkin (STCG) method for the wave equation. We prove the existence and uniqueness of the numerical solutions and get optimal ...orders of convergence to numerical solutions regarding space that do not need any compatibility conditions on the space and time mesh size. Finally, we employ a numerical example to validate the effectiveness and feasibility of the STCG method.
The instantaneous tangential rigidity (corresponding to the applied horizontal load) of a triguy support with unequal ropes is determined. The differences between the ropes can be due to the ...different location, both horizontal and vertical, of their anchoring foundations and to the different types of ropes used. The horizontal rigidity of such a support has no general axis of symmetry. Therefore a formula for this rigidity in any direction and a formula for extreme rigidity angles are given in this paper. A notion of the guy’s eigenvalue, standing for the initial tension force above which the guy participates effectively in the support’s rigidity, is introduced. A numerical example is provided.
In this work, two-grid characteristic finite volume schemes for the nonlinear parabolic problem are considered. In our algorithms, the diffusion term is discretized by the finite volume method, while ...the temporal differentiation and advection terms are treated by the characteristic scheme. Under some conditions about the coefficients and exact solution, optimal error estimates for the numerical solution are obtained. Furthermore, the two- grid characteristic finite volume methods involve solving a nonlinear equation on coarse mesh with mesh size H, a large linear problem for the Oseen two-grid characteristic finite volume method on a fine mesh with mesh size h = O（H2） or a large linear problem for the Newton two-grid characteristic finite volume method on a fine mesh with mesh size h = 0（I log hll/2H3）. These methods we studied provide the same convergence rate as that of the characteristic finite volume method, which involves solving one large nonlinear problem on a fine mesh with mesh size h. Some numerical results are presented to demonstrate the efficiency of the proposed methods.
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Dostopno za:
BFBNIB, DOBA, IZUM, KILJ, NMLJ, NUK, ODKLJ, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
The exact solution to the problem of elasticity for a plate with a cylindrical inclusion is found taking into account its specific weight. A method that is based on aWeber-type integral transform and ...does not use the Papkovich–Neuber solution is proposed to solve the problem numerically using new approaches to evaluating integrals that include strongly oscillating functions
Revealing stealthy attacks in control systems Teixeira, A.; Shames, I.; Sandberg, H. ...
2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton),
2012-Oct., 2012
Conference Proceeding
Odprti dostop
In this paper the problem of revealing stealthy data-injection attacks on control systems is addressed. In particular we consider the scenario where the attacker performs zero-dynamics attacks on the ...system. First, we characterize and analyze the stealthiness properties of these attacks for linear time-invariant systems. Then we tackle the problem of detecting such attacks by modifying the system's structure. Our results provide necessary and sufficient conditions that the modifications should satisfy in order to detect the zero-dynamics attacks. The results and proposed detection methods are illustrated through numerical examples.
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