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This work examines asteroid’s motion with orbital eccentricity e in the range (0.1, 0.2) across the two-body mean motion resonance (MMR) with Jupiter due to the Yarkovsky effect. We calculated time delays dtr caused by the resonance on the mobility of an asteroid with the Yarkovsky drift speed. Our results considered only asteroids that successfully cross over the resonance without close encounters with planets. We found a functional relation that accurately describes dependence between the average time lead/lag dtr, the strength of the resonance (SR), and the semimajor axis drift speed da/dt with asteroids' orbital eccentricities in the range (0.1, 0.2). We analysed average values of dtr using this functional relation comparing with obtained values of dtr from the numerical integrations, which were performed in an ORBIT9 integrator with a very large number of test asteroids. We checked the validity of our previous functional relation, derived for asteroids’ orbital eccentricities in the range (0, 0.1) (Figure 1), on the present results for eccentricities in the range (0.1, 0.2) (Figure 2). Also, we tried to find a unique functional relation for the whole interested interval of asteroids' orbital eccentricities (0, 0.2) and discussed it.

We establish a way to handle main collective fluctuations in correlated quantum systems based on a fluctuating local field concept. This technique goes beyond standard mean-field approaches, such as Hartree-Fock and dynamical mean-field theories (DMFT), as it includes a fluctuating classical field that acts on the leading order parameter of the system. Effective model parameters of this theory are determined from the variational principle, which allows one to resolve the Fierz ambiguity in decoupling of the local interaction term. In the saddle-point approximation for the fluctuating field our method reproduces the mean-field result. The exact numerical integration over this field allows one to consider nonlinear fluctuations of the global order parameter of the system while local correlations can be accounted for by solving the DMFT impurity problem. We apply our method to the magnetic susceptibility of finite Hubbard systems at half-filling and demonstrate that the introduced technique leads to a superior improvement of results with respect to parental mean-field approaches, without significant numerical complications. We show that the fluctuating local field method can be used in a very broad range of temperatures substantially below the Néel temperature of DMFT, which remains a major challenge for all existing theoretical approaches. © 2020 American Physical Society. The authors are very grateful to Maria Bandelmann for help with graphics. The work of E.A.S. is supported by the Russian Science Foundation, Grant No. 18-12-00185. A.I.L. acknowledges support by the Cluster of Excellence “Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG), Project No. ID390715994.

The pricing of financial options is usually based on statistical sampling of the evolution of the underlying under a chosen model, using a suitable numerical scheme. It is widely accepted that using low-discrepancy sequences instead of pseudorandom numbers in most cases increases the accuracy. It is important to understand and quantify the reasons for this effect. In this work, we use Global Sensitivity Analysis in order to study one widely used model for pricing of options, namely the Heston model. The Heston model is an important member of the family of the stochastic volatility models, which have been found to better describe the observed behaviour of option prices in the financial markets. By using a suitable numerical scheme, like those of Euler, Milstein, Kahl-Jäckel, Andersen, one has the flexibility needed to compute European, Asian or exotic options. In any case the problem of evaluating an option price can be considered as a numerical integration problem. For the purposes of modelling and complexity reduction, one should make the distinction between the model nominal dimension and its effective dimension. Another notion of “average dimension” has been found to be more practical from the computational point of view. The definitions and methods of evaluation of effective dimensions are based on computing Sobol’ sensitivity indices. A classification of functions based on their effective dimensions is also known. In the context of quantitative finance, Global Sensitivity Analysis (GSA) can be used to assess the efficiency of a particular numerical scheme. In this work we apply GSA based on Sobol sensitivity indices in order to assess the interactions of the various dimensions in using the above mentioned schemes. We observe that the GSA offers useful insight on how to maximize the advantages of using QMC in these schemes.

Earlier works on the smooth and discontinuous (SD) oscillator concentrated mainly on the time domain analysis using analytical, semi-analytical and numerical integration methods. In this paper, the frequency domain analysis of the SD oscillator subjected to harmonic excitation which is as important and giving further insight into the dynamics is carried out. Multi-Harmonic Balance Method (MHBM) in combination with arc length continuation is used to obtain the periodic solutions and their branches in the frequency domain for different values of the smoothing parameter α and exciting frequency ω. Stability of the periodic motions and bifurcation behavior are analyzed using the Floquet theory. For the discontinuous case, the oscillator is treated as a Filippov system and an event driven numerical integration method is used to obtain the response. For α > 1 , the dynamics of the SD oscillator is similar to that of the hardening Duffing oscillator, for α = 1 , it is like that of the Ueda oscillator and for 0 α 1 it is like that of the Duffing oscillator with double well potential. The SD oscillator exhibits period 1 solutions, higher order periodic solutions, chaotic solutions through symmetry breaking bifurcations, period doubling and boundary crises in different parameter ranges. Chaos is observed over a larger frequency range interspersed by narrow windows of higher order periodic solutions.

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others. © 2013 Alex Elías-Zúñiga et al.

A flexible diaphragm coupling, connecting two rotating shafts, is investigated for its dynamic characteristics, when subjected to parallel offset misalignment. The diaphragm coupling is a constant velocity coupling which becomes asymmetric once misaligned. Asymmetry creates directional difference or spatial variation of stiffness, as shown by a quasi-static finite element (FE) analysis using ABAQUS software. As the shafts rotate, this spatial variation in stiffness makes the diaphragm coupling–rotor system model to become time-varying. The time-varying direct and cross–coupled stiffness terms of the coupling are synthesized from the FE model and used in the governing equations of motion of the coupling–rotor system. This leads to a parametrically excited system due to the time-periodic stiffness coefficients of the coupling. Using Simulink, numerical integration has been performed to find the response of the system for both mass unbalance and inclination unbalance excitations that arise due to the tilt of the principal axes of the diaphragm due to parallel misalignment. The responses obtained clearly indicate the effect of parametric excitation at one-fourth, one-third, and one-half of the principal parametric resonance. To verify this model, an experimental setup has been developed for the coupling–rotor system model with misalignment. The experimental results clearly show the asymmetry between the two lateral direction responses, as predicted by the model.

International audience; this work, the multiple absorption coefficient zonal method (MACZM) is being implemented and validated numerically. The method is demonstrated to be highly suitable for the analysis of radiative heat transfer in multidimensional inhomogeneous non-grey media. A uniform rectangular fine grid is considered and small CPU time is achieved. This makes the method of great interest for transient applications. The validity of the method is demonstrated in two steps. First, cases with simple geometry are considered and results are compared to results generated by direct numerical integration. Results are also generated by MODRAY, which is a source project based on an original method called the flux-planes approximation, and are shown to be equally accurate. Second, the case of a steel reheating furnace is considered. In a previous work, the furnace heat balance and temperature profiles were simulated using a finite difference computation approach and radiative exchange factors generated by MODRAY. Experiments were performed and results generated by the model were found to be in good agreement with experimental data. The radiative exchange factors are now recalculated with MACZM. They are shown to be very close to those generated by MODRAY. The comparison of the two methods clearly shows that MACZM is much faster for the calculation of the volume-volume radiative exchange factors on a uniform rectangular grid.

A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order rational elliptic form solutions to obtain approximate solutions of two nonlinear oscillators. At the end of the paper, we compare the numerical integration values of the angular frequencies with approximate solution results, based on the proposed rational elliptic balance method. © 2010 Elsevier Ltd. All rights reserved.

In this work, we derive approximate semi-analytical solutions of the steady, creeping, weakly compressible plane and axisymmetric Poiseuille flows of a Herschel-Bulkley fluid. Since the flow is weakly compressible, the radial velocity component is assumed to be zero and the derivatives of the axial velocity with respect to the axial direction are assumed to be much smaller than those with respect to the radial direction. The axial velocity is then given by an expression similar to that holding for the incompressible flow, the only difference being that the pressure-gradient is a function of the axial coordinate and satisfies a non-linear equation involving the density of the fluid. In the present work, a linear as well as an exponential equation of state, relating the density of the fluid to the pressure, are considered. The pressure distribution along the flow direction is calculated by means of numerical integration and the two-dimensional axial velocity can then be constructed. The effects of compressibility, the equation of state, the Bingham number and the power-law exponent on the solutions are investigated. © 2008 Elsevier B.V. All rights reserved. 158 1-3 162 169 Cited By :13

We discuss a constitutive model for stochastically distributed fiber reinforced tissues, where the active behavior of the fibers depends on the relative orientation of the electric field. Unlike other popular approaches, based on numerical integration over the unit sphere, or on the use of second order structure tensors, for the passive behavior we adopt a second order approximation of the strain energy density of the distribution. The purely mechanical quantities result to be dependent on two (second and fourth order, respectively) averaged structure tensors. In line with the approximation used for the passive behavior, we model the active behavior accounting for the statistical fiber distribution. We extend the Helmholtz free energy density by introducing a directional active potential, dependent on a stochastic permittivity tensor associated to a particular direction, and approximate the total active potential through a second order Taylor expansion of the permittivity tensor. The approximation allows us to derive explicitly the active stress and the active constitutive tensors, which result to be dependent on the same two averaged structure tensors that characterize the passive response. Active anisotropy follows from the distribution of the fibers and inherits its stochastic parameters. Examples of passive and active behaviors predicted by the model in terms of response to biaxial testing are presented, and comparisons with passive experimental data are provided.

A tradeoff analysis is performed on a test case representative of the cooling system of 1 MN thrust class oxygen/hydrogen liquid rocket engine. The aim of the analysis is to find the channel aspect ratio that maximizes the heat extracted from the hot gas, for a given coolant pressure drop and hot-gas side wall temperature. The analysis requires many cooling channel flow calculations that are performed by means of a simplified model, referred to as quasi-two-dimensional, and a three-dimensional conjugate heat transfer model based on numerical integration of the Navier–Stokes and Fourier’s equations. Both models are able to describe, with different level of details, the whole cooling device composed by the coolant and the solid domain, which is exposed to the hot gas. The fast quasi-two-dimensional approach is used to select channel geometries showing the same pressure loss. Discussion is made on results obtained with the more accurate three-dimensional model. Results identify, for the selected test case, a...

We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion. © 2013 Alex Elías- Zúñiga and Oscar Martínez-Romero.

We consider time-averaging methods based on the Magnus series expansion jointly with exponential integrators for the numerical integration of general linear non-homogeneous differential equations. The schemes can be considered as averaged methods which transform, for one time step, a non-autonomous problem into an autonomous one whose flows agree up to a given order of accuracy at the end of the time step. The problem is reformulated as a particular case of a matrix Riccati differential equation and the Möbius transformation is considered, leading to a homogeneous linear problem. The methods proposed can be used both for initial value problems (IVPs) as well as for two-point boundary value problems (BVPs). In addition, they allow to use different approximations for different parts of the equation, e.g. the homogeneous and non-homogeneous parts, or to use adaptive time steps. The particular case of separated boundary conditions using the imbedding formulation is also considered. This formulation allows us to transform a stiff and badly conditioned BVP into a set of well conditioned IVPs which can be integrated using some of the previous methods. The performance of the methods is illustrated on some numerical examples. © 2012 IMACS. Published by Elsevier B.V. All rights reserved., We would like to thank the referees for their suggestions and comments that helped us to improve the presentation of the work as well as to clarify the main results. The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of S.B. has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (co-financed by the ERDF of the European Union) and the work of E.P. has also been partially supported by Ministerio de Ciencia e Innvacion of Spain, by the project MTM2009-08587.

The Centaurs are a transitional population of minor bodies of the solar system and the evolutionary link between the trans-Neptunian objects and the short period comets. The surface properties of these objects are very peculiar, because currently available data suggest that their visual surface colors divide the population into two distinctive groups, those with reddish slopes of the visual reflection spectra and those with neutral spectra. Moreover, some of them are known to posses comas produced by cometary activity. Aims. We aim to investigate possible links between the orbital dynamical history and the surface physical properties of the bodies of this population. Methods. By means of numerical integrations of the equations of motion we calculated the orbital evolution of three groups of Centaurs: the Red group, the Gray group, and the Active group. We looked for statistical differences in the timescales spent by the objects of each group at heliocentric distances below certain values that are associated with locations where certain particular physical processes occur at the surfaces. Results. We find remarkable differences when we compare the fraction of objects that penetrate below typical heliocentric distances for each group. Conclusions. Our results suggest that the observed bimodality in the distribution of surface colors of the Centaurs is caused by the different thermal reprocessing on the surface of bodies of the Red group on one side and the Active and Gray groups on the other. Centaurs of the Gray group likely had cometary activity, therefore their color distribution is similar to that of comet nuclei. © 2012 ESO. Fil:Melita, M.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

The dynamics of a face are often implemented as a system of connected particles with various forces acting upon them. Animation of such a system requires the approximation of velocity and position of each particle through numerical integration. There are many numerical integrators that are commonly used in the literature. We conducted experiments to determine the suitability of numerical integration methods in approximating the particular dynamics of mass-spring-damper systems. Among Euler, semi-implicit Euler, Runge-Kutta and Leapfrog, we found that simulation with Leapfrog numerical integration characterizes a mass-spring-damper system best in terms of the energy loss of the overall system. This research is part of project "Expression Recognition based on Facial Anatomy", grant number 109E061, supported by The Support Programme for Scientific and Technological Research Projects (1001) of The Scientific and Technological Research Council of Turkey (TUBITAK) Publisher's Version

The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the numerical integration of this problem using the imbedding formulation. An algorithm to implement this explicit method in an efficient way with respect to the computational cost of the scheme is presented. This method can also be used for nonlinear boundary value problems if the quasilinearization technique is considered. Some numerical examples illustrate the performance of this method. © 2010 Elsevier Ltd., The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032 and the Ministerio de Ciencia e Innovacion (Spain) under projects MTM2007-61572 and MTM2009-08587 (co-financed by the ERDF of the European Union).

A computationally effective framework is presented that addresses the contribution of subgrid-scale vertical velocity variations in predictions of cloud droplet number concentration (CDNC) in large-scale models. Central to the framework is the concept of a "characteristic updraft velocity" w*, which yields CDNC value representative of integration over a probability density function (PDF) of updraft (i.e., positive vertical) velocity. Analytical formulations for w* are developed for computation of average CDNC over a Gaussian PDF using the Twomey droplet parameterization. The analytical relationship also agrees with numerical integrations using a state-of-the-art droplet activation parameterization. For situations where the variabilities of vertical velocity and liquid water content can be decoupled, the concept of w* is extended to the calculation of cloud properties and process rates that complements existing treatments for subgrid variability of liquid water content. It is shown that using the average updraft velocity w* (instead of w*) for calculations of Nd, re, and A (a common practice in atmospheric models) can overestimate PDF-averaged Nd by 10%, underestimate re by 10%-15%, and significantly underpredict autoconversion rate between a factor of 2-10. The simple expressions of w* presented here can account for an important source of parameterization "tuning" in a physically based manner. Copyright 2010 by the American Geophysical Union.

[EN] We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since the system can be split into the kinetic and remaining part, and each part can be solved efficiently using fast Fourier transforms. Splitting the system into the quantum harmonic-oscillator problem and the remaining part allows us to get higher accuracies in many cases, but it requires us to change between Hermite basis functions and the coordinate space, and this is not efficient for time-dependent frequencies or strong nonlinearities. We show how to build methods that combine the advantages of using Fourier methods while solving the time-dependent harmonic oscillator exactly (or with a high accuracy by using a Magnus integrator and an appropriate decomposition). © 2011 American Physical Society., We would like to acknowledge the referees for their careful reading and suggestions. The authors acknowledge the support of the Generalitat Valenciana through the project GV/2009/032. The work of S. B. has also been partially supported by Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03 (cofinanced by the ERDF of the European Union).

This contribution presents the kinetostatic analysis of a spatial compliant mechanism actuated by three Shape Memory Alloy (SMA) wire actuators. This mechanism exploits both shape memory and superelastic effects of SMA actuators. The moving platform of the mechanism is mounted on a pillar made of superelastic SMA and its mobility is obtained from the large deflection of the pillar by the selective actuation of any one or two wires in differential manner. The deflection expressions obtained are basically force-displacement kinematic relationships, derived after incorporating follower forces and variable moments developed by the actuators. Two sets of geometric parameters, related to deflected and undeflected conditions, have been utilized to solve the coupled relationship between the force developed by the SMA actuation and the force required for the elastica deflection. The deflection expressions are solved using Romberg integration method and the numerical results obtained have been validated by comparing them with those obtained from FEM simulation. The results show that, for the design of compliant mechanisms exhibiting large displacements the force-displacement relationships in linear form, as applicable to small deflections, are no longer valid.

This paper deals with the formulation of a nine-noded piezolaminated degenerated shell finite element for modeling and analysis of multilayer composite general shell structures with bonded/embedded distributed piezoelectric sensors and actuators. The distributed PZT sensors and actuators used in the composite smart structures are relatively thin and could have arbitrary variation of curvatures and thicknesses. They cannot be modeled with shell elements based on curvilinear shell theories which would need the specification of constant shell curvatures and thicknesses. Modeling them with piezo finite elements available in popular commercial codes like ABAQUS, ANSYS, MARC, etc, would need relatively greater computational effort as they are based on solid element formulation. In view of these, the present proposed degenerated piezoelectric shell element would be a better choice giving good computational accuracy and efficiency. The main advantage of a degenerate shell element is that it is not based on any shell theories and is applicable over a wide range of curvatures and thicknesses. This element is developed by using the degenerate solid approach based on Reissner-Mindlin assumptions which allow the shear deformation and rotary inertia effect to be considered and the 3D field is reduced to a 2D field in terms of mid-surface nodal variables. Uniformly reduced integration is carried out to overcome membrane locking and shear locking and the numerical integration is carried out in all three directions to obtain accurate results. The present element has 45 elastic degrees of freedom and 10 electric degrees of freedom per piezoelectric layer in the element. The potential induced due to bending deformation is more accurately represented by assuming quadratic variation of the electric potential through the thickness of each piezoelectric layer. This is achieved by interpolating using nodal mid-plane electric potentials and one electric degree of freedom representing the potential difference between the top and bottom surfaces of the piezoelectric layer. Few case studies of composite general shells with piezoelectric sensors and actuators have been considered by modeling them with the above elements and the active vibration control performance has been studied using linear quadratic Gaussian (LQG) control. � 2008 IOP Publishing Ltd.

Summary form only given. Broad area semiconductor (BAS) laser are relevant high conversion light sources despite that the spatial and temporal quality of the emitted beam is relatively low due to the absence of a natural transverse mode selection mechanism [1]. To overcome this serious drawback different solutions have been incorporated in the design, such as external gratings, external injection spatially modulated injection or distributed feedback. In addition, in BAS lasers a modulation instability (or Bespalov-Talanov instability) can occur due to nonlinear focussing, leading to filamentation effects and deteriorating the spatial quality of the laser emission. In absence of cavity mirrors, planar semiconductor structures can act as light amplifiers undergoing however analogue disadvantages.In the present work, we study a simple and effective new mechanism to improve the spatial beam quality of a planar semiconductor amplifier configuration. We consider a two-dimensional modulation, which can feasibly be realized by a periodical grid of electrodes for the electrical pump of the semiconductor, as illustrated in Fig. 1.a. The main result obtained is that such a micro-modulation of the spatial pump profile on a spatial scale of the order of several wavelengths, can indeed lead to a substantial improvement of the spatial quality of the amplified beam on a large spatial scale, see Fig. 1.b. The quantitative analysis of the spatial filtering is performed by numerical integration of a paraxial propagation model derived from [2,3], and on analytical estimations. Previous studies of wave propagation in media with spatially modulated Gain/Loss (GL) profiles show that a periodic modulation of GL on a wavelength scale can lead to particular beam propagation effects, such as self-collimation, spatial (angular) filtering, or beam focalisation [4]. In those works a purely GL modulation has been considered; however, in semiconductor media due to the linewidth enhancement factor, hfactor, a periodical spatial pump distribution causes a combined Gain and refraction Index Modulation (GIM). Hence, the aim of the present paper, performed under realistic parameters and conditions, is to demonstrate how the angular spectrum of the radiation from a spatially modulated GIM BAS amplifier becomes narrower while propagating and being amplified. The study predicts that the normalized beam quality factor - M 2 factor- can reduce almost to unity indicating that the BAS amplifier output becomes perfectly Gaussian for even strongly random initial input beam profiles, for a single-pass propagation length on the order of millimeters, see Fig. 1.c. Beyond the present report, this new technique could be implemented to improve the spatial quality of emission of BAS lasers.