Additional Integral Term Research Articles

The fourth gravity test and quintessence matter field

After the previous work on gravitational frequency shift, light deflection (arXiv:1003.5296) and perihelion advance (arXiv:0812.2332), we calculate carefully the fourth gravity test, i.e. radar echo delay in a central gravity field surrounded by static free quintessence matter, in this paper. Through the Lagrangian method, we find the influence of the quintessence matter on the time delay of null particle is presence by means of an additional integral term. When the quintessence field vanishes, it reduces to the usual Schwarzschild case naturally. Meanwhile, we also use the data of the Viking lander from the Mars and Cassini spacecraft to Saturn to constrain the quintessence field. For the Viking case, the field parameter $\alpha$ is under the order of $10^{-9}$. However, $\alpha$ is under $10^{-18}$ for the Cassini case.

Observation of ion-acoustic shock wave transition due to enhanced Landau damping

Ion-acoustic shock waves are observed experimentally introducing strong Landau damping by increasing the ion temperature in a double plasma device. An oscillatory ion-acoustic shock wave undergoes transition with enhanced Landau damping and forms a monotonic shock wave. Numerical results of the Korteweg–de Vries equation with an additional integral term to account for the strength of Landau damping are compared with the experimental findings. Enhancement of Landau damping is found to increase the dissipation of the wave, which manifests in quenching of the oscillatory structure behind the shock front.

Indirect Sliding Mode Control of Power Converters Via Double Integral Sliding Surface

The steady-state regulation error in power converters that use the conventional hysteresis-modulation-based sliding mode controller can be suppressed through the incorporation of an additional integral term of the state variables into the controller. However, it is found that with the indirect type of sliding mode controller (derived based on the equivalent control approach), the same approach of integral sliding mode control is ineffective in alleviating the converter's steady-state error. Moreover, the error increases as the converter's switching frequency decreases. This paper presents an in-depth study of the phenomenon and offers a solution to the problem. Specifically, it is proposed that an additional double-integral term of the controlled variables to be adopted for constructing the sliding surface of indirect sliding mode controllers. Simulation and experimental results are provided for verification.

Numerical Analysis and Simulation Analysis for Space‐Time Data

AbstractSpatio temporal dynamics of the positive column of a dc neon glow discharge is studied and investigated experimentally and theoretically. Spatio temporal analysis by means of biorthogonal decomposition method (BOD) gives insights into the mechanism of irregularity and can be employed for characterization of spatio‐ temporal complexity. In the weak nonlinear region, the wave dynamics is approximated by an amplitude equation of the Ginzburg‐Landau equation (CGLE) with complex coefficients and an additional integral term based on a fluid model. In the present work we deal with irregular spatio‐temporal data. A comparison between the numerical analysis of the experimental data and simulation results are studied. A good agreement between the dynamical behaviour for experimental space‐time data and theoretical simulation space‐time results was obtained. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Wave instability induced by nonlocal spatial coupling in a model of the light-sensitive Belousov-Zhabotinsky reaction

We study spatiotemporal patterns resulting from instabilities induced by nonlocal spatial coupling in the Oregonator model of the light-sensitive Belousov-Zhabotinsky reaction. In this system, nonlocal coupling can be externally imposed by means of an optical feedback loop which links the intensity of locally applied illumination with the activity in a certain vicinity of a particular point weighted by a given coupling function. This effect is included in the three-variable Oregonator model by an additional integral term in the photochemically induced bromide flow. A linear stability analysis of this modified Oregonator model predicts that wave and Turing instabilities of the homogeneous steady state can be induced for experimentally realistic parameter values. In particular, we find that a long-range inhibition in the optical feedback leads to a Turing instability, while a long-range activation induces wave patterns. Using a weakly nonlinear analysis, we derive amplitude equations for the wave instability which are valid close to the instability threshold. Therein, we find that the wave instability occurs supercritically or subcritically and that traveling waves are preferred over standing waves. The results of the theoretical analysis are in good agreement with numerical simulations of the model near the wave instability threshold. For larger distances from threshold, a secondary breathing instability is found for traveling waves.

Assessing implicit models for nonpolar mean solvation forces: The importance of dispersion and volume terms

Continuum solvation models provide appealing alternatives to explicit solvent methods because of their ability to reproduce solvation effects while alleviating the need for expensive sampling. Our previous work has demonstrated that Poisson-Boltzmann methods are capable of faithfully reproducing polar explicit solvent forces for dilute protein systems; however, the popular solvent-accessible surface area model was shown to be incapable of accurately describing nonpolar solvation forces at atomic-length scales. Therefore, alternate continuum methods are needed to reproduce nonpolar interactions at the atomic scale. In the present work, we address this issue by supplementing the solvent-accessible surface area model with additional volume and dispersion integral terms suggested by scaled particle models and Weeks-Chandler-Andersen theory, respectively. This more complete nonpolar implicit solvent model shows very good agreement with explicit solvent results and suggests that, although often overlooked, the inclusion of appropriate dispersion and volume terms are essential for an accurate implicit solvent description of atomic-scale nonpolar forces.

Transport phenomena in heterogeneous media based on volume averaging theory

Models are developed to describe transport phenomena in a porous medium that take into account the scales and other characteristics of the medium morphology. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using an advanced averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. The description of the structural morphology determines the importance of these terms and the range of application of the closure schemes. A natural way to transfer from transport equations in a porous media with integral terms to differential equations with coefficients that could be experimentally evaluated and determined is described.Some numerical results that illustrate what occurs when the porosity approaches unity or the porosity approaches zero show that solutions smoothly converge to the transport characteristics of a plane channel. A simple heat sink is modeled as a two-temperature process allowing solution of the conjugate problem to be accomplished and is optimized using design of experiment (DOE) methods. As a final example, acoustic energy absorption in a porous media is addressed.

Multiple reciprocity boundary element analysis of two-dimensional anisotropic thermoelasticity involving an internal arbitrary non-uniform volume heat source

In the direct boundary element method (BEM) formulation of anisotropic thermoelasticity, thermal loads manifest themselves as additional volume integral terms in the boundary integral equation (BIE). Conventionally, this requires internal cell discretisation throughout the whole domain. In this paper, the multiple reciprocity method in BEM analysis is employed to treat the general 2D thermoelasticity problem when the thermal loading is due to an internal non-uniform volume heat source. By successively performing the “volume-to-surface” integral transformation, the general formulation of the associated BIE for the problem is derived. The successful implementation of such a scheme is illustrated by three numerical examples.

Integral Operators on Sparse Grids

In this paper we are concerned with the construction and use of wavelet approximation spaces for the fast evaluation of integral expressions. The spaces are based on biorthogonal anisotropic tensor product wavelets. We introduce sparse grid (hyperbolic cross) approximation spaces which are adapted not only to the smoothness of the kernel but also to the norm in which the error is measured. Furthermore, we introduce compression schemes for the corresponding discretizations. Numerical examples for the Laplace equation with Dirichlet boundary conditions and an additional integral term with a smooth kernel demonstrate the validity of our theoretical results.

NONLINEAR H∞ CONTROL WITH PID STRUCTURE FOR ROBOT MANIPULATORS

In this paper the nonlinear H∞ control for robot manipulators introduced in (Feng, W., Postlethwaite, I., 1994) is extended. An additional integral term is included to cope with persistent disturbances, such as constant weights at the end-efecctor. The extended controller is interpreted like a computed torque control with and external PID, whose gain matrices vary with the position and velocity of the robot joints. A particular case of the cost variable weighting matrix is studied in which the resulting external nonlinear PID does not depend on the attenuation level γ of the H∞ formulation. Finally, experimental results are presented for the RM-10 industrial robot.

Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

In the direct formulation of the boundary element method, body-force and thermal loads manifest themselves as additional volume integral terms in the boundary integral equation. The exact transformation of the volume integral associated with body-force loading into surface ones for two-dimensional elastostatics in general anisotropy, has only very recently been achieved. This paper extends the work to treat two-dimensional thermoelastic problems which, unlike in isotropic elasticity, pose additional complications in the formulation. The success of the exact volume-to-surface integral transformation and its implementation is illustrated with three examples. The present study restores the application of BEM to two-dimensional anisotropic elastostatics as a truly boundary solution technique even when thermal effects are involved.

Amplitude equation at ionization instability and the onset of turbulence in a neon glow discharge

We investigate the bifurcations of ionization waves from the homogeneous stationary state of the positive column in a neon glow discharge. In the weak nonlinear region the wave dynamics is approximated by an amplitude equation of the Ginzburg-Landau type with complex coefficients and an additional integral term. This nonlocal term describes the influence of the external circuit on the ionization waves. Conditions are derived for the band of Eckhaus stable wave solutions. The dependence of the complex coefficients on the plasma parameters is discussed and used to classify the solution manifold of the amplitude equation. Raising the gas pressure from $130 \mathrm{Pa}$ up to $720 \mathrm{Pa},$ the intermittency, bichaos, and amplitude turbulence regions are visited successively. Some of these theoretical results are supported by numerical calculations for selected parameter values.

Improved formulations for higher order absorbingboundary conditions

New formulations for higher order ABCs are introduced. Third and fourth order ABCs are reduced to first and second order derivatives with each one having one additional integral term. Considerable reductions in computer storage and computational time are achieved.

TREATMENT OF BODY-FORCE VOLUME INTEGRALS IN BEM BY EXACT TRANSFORMATION FOR 2-D ANISOTROPIC ELASTICITY

In the Boundary Element Method (BEM) based on the direct formulation, body-force effects manifest themselves as an additional volume integral term in the Boundary Integral Equation (BIE). The numerical solution of the integral equation with this term destroys the notion of the BEM as atruly boundary solution method. This paper discusses the treatment of this volume integral for two-dimensional anisotropic elasticity with body-forces present. The analytical basis for transforming this integral exactly into boundary ones is presented for geometrically convex regions. This restores the application of the BEM to such problems as a truly boundary solution technique. Numerical examples are presented to demonstrate the veracity of the transformation and implementation. © 1997 by John Wiley & Sons, Ltd.

A Two-Temperature Model for Turbulent Flow and Heat Transfer in a Porous Layer

A new model of turbulent flow and of two-temperature heat transfer in a highly porous medium is evaluated numerically for a layer of regular packed particles. The layer can have heat exchange from the defining surfaces. The commonly used models of variable morphology functions for porosity and specific surface were used to obtain comparisons with other works in a relatively high Reynolds number range. A few outstanding features of the closure models for additional integral terms in equations of flow and heat transfer are advanced. Closures were developed for capillary and globular medium morphology models. It is shown that the approach taken to close the integral resistance terms in the momentum equation for a regular structure can be obtained in a way that allows the second order terms for laminar and turbulent regimes to naturally occur. These terms are taken to be close to the Darcy term or Forchheimer terms for different flow velocities. The two-temperature model was compared with a one-temperature model using thermal diffusivity coefficients and effective coefficients from various authors. Calculated pressure drop along a layer showed very good agreement with experiment for a porous structure of spherical beads. A simplified model with constant coefficients was compared with analytical solutions.

Adaptive model-following controller for robotic manipulators

A nonlinear state-space model representing the robot dynamics and containing a disturbance term due to gravitational loading is presented. An adaptive model-following control problem satisfying the matching conditions is formulated using a suitable linear time-invariant reference model. The control input is designed to have two components: a non-adaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further added and then the overall asymptotic hyperstability is established. Simulation experiments on the first three joints of a PUMA 560 robot manipulator have indicated the potential of our design approach.

A design approach to adaptive model-following control of robotic manipulators

In this paper, the robot dynamics are represented by a nonlinear state-space model containing a disturbance term due to gravitational loading. Using a suitable linear time-invariant reference model, an adaptive model-following control problem is formulated which satisfies the matching conditions. The control input is designed to have two components: a nonadaptive linear component to do the task of model-following and a nonlinear unit-vector component based on hyperstability theory to do the adaptive task. An additional integral feedback term is further superimposed and then the overall asymptotic hyperstability is established. The simulation results on the first three joints of PUMA 560 robot manipulator indicate the potential of our design approach.

Breakdown of global coupling in oscillatory chemical reactions

The effects of global coupling through the gas phase in oscillatory surface chemical reactions are investigated using a model which represents the complex Ginzburg–Landau equation with an additional integral term. Depending on the parameters of the model, global coupling is found to have either a synchronizing or desynchronizing effect. Respectively, the breakdown of global coupling requires the presence of strong supercritical inhomogeneities or spontaneously occurs in a uniform system.

Nonlinear Transformations on the Wiener Space

We study shift transformations on a general abstract Wiener space $(E, H, \mu)$, which have the form: $E \ni \omega \mapsto \mathscr{J}^\phi\omega \equiv \omega - \int^T_0 \phi_t(\omega)Z(dt) \in E,$ where $\phi_t(\omega)$ is a scalar function on $\lbrack 0, T\rbrack \times E$ and $Z$ is an orthogonal $H$-valued measure. Under suitable conditions for the kernel $\phi$, we construct explicitly a probability measure $\mu^\phi$ on $E$, which is equivalent to the standard Wiener measure $\mu$ and has the property: $\mu^\phi\{\mathscr{F}^\phi \in A\} = \mu(A), A \in \mathscr{B}_E$. The main result presents an analog of the well-known Cameron-Martin-Girsanov theorem for the case where the shift is allowed to anticipate. This leads to an additional integral term in the Girsanov exponent. Also, the Wiener-Ito integral in this exponent is now replaced by an extended stochastic integral.

Sliding mode using discontinuous control algorithms of integral type

This paper deals with the robust stabilization of continuous-time dynamical systems in the presence of parametric and external time-varying disturbances. Modified Variable Structure control algorithms with additional integral terms are considered here and analysed. A comparison with a typical ‘static’ VS algorithm is made. Static VS algorithms can reject completely the disturbance only if the amplitude of the switching term, in the control input, is larger than the amplitude of the disturbance itself. This paper shows how it is possible, by adding an integral term in the VS control algorithm, to reach and remain in the sliding mode if the amplitude of the switching term is smaller than the amplitude of the disturbance. Some simulations supporting the theoretical results are reported and discussed.