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This paper presents a fractional order modeling and analysis method for a DC-DC Boost converter in discontinuous conduction mode (DCM) by using circuit averaging method. First, an equivalent averaged circuit model for the fractional order Boost converter in DCM operation is proposed. Then at the second stage, the corresponding DC circuit model is obtained by averaged circuit model. Finally, the transfer function of the duty cycle to the output voltage and also the transfer function of the input voltage to the output voltage in DCM operation are derived from the corresponding small signal equivalent circuit model. Simulation results are presented to show the correctness of the proposed method. These simulation results indicate that the fractional order model has a specific significance for the performance of the DC-DC converter.

By using the positive linear functional, including the generalized averaging technique, some new Kamenev-type oscillation criteria are established for the second order matrix differential system (r(t)P(t)ψ(X(t))K(X0(t)))0+p(t)R(t)ψ(X(t))K(X0(t))+Q(t)F(X0(t))G(X(t)) = 0. The results improve and generalize those given in some previous papers. This paper is dedicated to the memory of Professor Aydın Tiryaki (June1956-May 2016)

By employing the generalized Riccati technique and the integral averaging technique, new Kamenev-type oscillation criteria are established for a class of second-order matrix differential systems. These criteria extend, improve, and unify a number of existing results and handle the cases which are not covered by known criteria. In particular, two interesting examples that illustrate the importance of our results are included.

An approach to modeling thermal noise effects in stochastic magnetization dynamics using a jump-noise process is presented. The damping term present in classical Landau-Lifshitz and Landau-Lifshitz-Gilbert equations is shown to result from the average of the jump-noise process in the presented stochastic Landau-Lifshitz equation approach. A numerical technique for solving the Landau-Lifshitz equation driven by a jump-noise process based on the Monte Carlo method is introduced and the results obtained from this method are shown. The drawback of using the Monte Carlo approach is discussed as well as the introduction of an averaging method to model stochastic magnetization dynamics on energy graphs. This averaging technique takes advantage of the difference in time-scale between the precessional motion and thermal effects in the stochastic Landau-Lifshitz model. By averaging over precessional trajectories, a stochastic magnetization dynamics equation on graphs is obtained. This averaging technique is demonstrated to be consistent with Monte Carlo results through numerical simulations. Application of the averaging technique to self-oscillations in magnetization dynamics due to the spin-transfer torque phenomenon is investigated and numerical results are presented. Finally, the power spectral density for magnetization dynamics on energy graphs is calculated. Numerical results for the power spectral density are studied and analyzed.

[EN] Significant research effort has been devoted to produce one-sided error estimates for Finite Element Analyses, in particular to provide upper bounds of the actual error. Typically, this has been achieved using residual-type estimates. One of the most popular and simpler (in terms of implementation) techniques used in commercial codes is the recovery-based error estimator. This technique produces accurate estimations of the exact error but is not designed to naturally produce upper bounds of the error in energy norm. Some attempts to remedy this situation provide bounds depending on unknown constants. Here, a new step towards obtaining error bounds from the recovery-based estimates is proposed. The idea is (1) to use a locally equilibrated recovery technique to obtain an accurate estimation of the exact error, (2) to add an explicit-type error bound of the lack of equilibrium of the recovered stresses in order to guarantee a bound of the actual error and (3) to efficiently and accurately evaluate the constants appearing in the bounding expressions, thus providing asymptotic bounds. The numerical tests with h-adaptive refinement process show that the bounding property holds even for coarse meshes, providing upper bounds in practical applications., The authors also thank the support of the Framework Programme 7 Initial Training Network Funding under grant number 289361 "Integrating Numerical Simulation and Geometric Design Technology".

We consider a continuous time stochastic individual based model for a population structured only by an inherited vector trait and with logistic interactions. We consider its limit in a context from adaptive dynamics: the population is large, the mutations are rare and we view the process in the timescale of mutations. Using averaging techniques due to Kurtz (1992), we give a new proof of the convergence of the individual based model to the trait substitution sequence of Metz et al. (1992) first worked out by Dieckman and Law (1996) and rigorously proved by Champagnat (2006): rigging the model such that "invasion implies substitution", we obtain in the limit a process that jumps from one population equilibrium to another when mutations occur and invade the population., Comment: 23 pages

The infrared spectrum of CO 2-(pH 2) 2 trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH 2-CO 2 (J. Chem. Phys.2010, 132, 214309) and pH 2-pH 2 potentials (J. Chem. Phys.2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH 2 rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys.2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH 2 density in the body-fixed frame is used, and shows that in the ground state the two pH 2 molecules are localized much more closely together than is the case for the two He atoms in the analogous CO 2-(He) 2 species. A clear tunneling splitting is evident for the torsional motion of the two pH 2 molecules on a ring about the CO 2 molecular axis, in contrast to the case of CO 2-(He) 2 where a more regular progression of vibrational levels reflects the much lower torsional barrier. © 2011 American Chemical Society.

Oscillation theorems for the damped elliptic differential equation of second order $\sum_{i, j=1}^{N}D_i[\,a_{ij}(x)D_jy\,]+\sum_{i=1}^{N}b_i(x)D_iy+c(x,y)=0$ ¶ are obtained. The results are extensions of averaging techniques due to Coles and Kamenev, and include earlier known results in literature.

Some oscillation theorems are established by the averaging technique for the second order nonlinear neutral delay differential equation $$ \begin{array}{l} (r(t) |x^{\prime}(t)|^{\gamma-1} x^{\prime}(t))^{\prime} + q_1(t) |y(t-\sigma_1)|^{\alpha-1} y(t-\sigma_1) \\ \hspace{5mm} + q_2(t) |y(t-\sigma_2)|^{\beta-1} y(t-\sigma_2) = 0, \quad t \geq t_0, \end{array} $$ where $x(t) = y(t) + p(t) y(t-\tau)$, $\tau$, $\sigma_1$ and $\sigma_2$ are nonnegative constants, $\alpha$, $\beta$ and $\gamma$ are positive constants, and $r$, $p$, $q_1$, $q_2 \in C([t_0, \infty), \mathbb{R})$. The results obtained here essentially improve some known results in the literature. In particular, two interesting examples that point out the applications of our results are also included.

The present work deals with the recovery of the in-boundary stress on smooth boundary parts in Boundary Element Method (BEM) in two dimensions. First, two Boundary Integral Representations (BIRs) of tangential derivative of boundary displacements, whose integral kernels multiplying either tangential derivative of displacements or displacements are smooth and bounded, are presented. Two procedures for an in-boundary stress recovery based on these BIRs are developed and analyzed. The first procedure, which directly uses the results obtained from a BEM analysis, displacements and tractions, requires the performing of integrations involved in these BIRs either over the real boundary of the solid or over a smooth approximation of the boundary part where the evaluation point is placed. The second procedure, which can be applied on a non-smooth (e.g. polygonal) approximation of the boundary, requires the use, in the first BIR introduced here, of an integral density which is previously smoothed by a local smoothing procedure. The third recovery procedure considered in this work is directly given by a local smoothing procedure of this kind. Results obtained by these three recovery procedures are compared in a series of numerical tests, the best results being obtained by the first procedure developed in this work. Ministerio de Educación Cultura PB98-1118

Current developments towards assessment of surface finish using the area averaging technique have gained attention in the field of automotive manufacturing. In particular, use of tiny non-contact sensors plays a vital role during in-situ and online monitoring and process control. In this work, an attempt has been made for using non-contact capacitive sensor for characterisation of different theoretical (periodic) profiles. The capacitive response model is developed to predict equivalent theoretical capacitive displacement profile and relate accurately to a measured surface finish of the profile. The proposed model is simulated to predict dimensional parameters of various theoretical profiles. Furthermore, the feasibility to relate the capacitive response to dimensional and non-dimensional parameters of the theoretical profile is studied. The developed model is validated with the different theoretical profiles. Further, the model is validated with experimentally processed theoretical profiles using measurement setup. The results show that the observed and predicted non-dimensional parameters are well agreed with model output and measured output results. Further, it can be applied in non-periodic profile measurement using a sensor. Copyright � 2013 Inderscience Enterprises Ltd.