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Analytical Expression (analytical + expression)
Kinds of Analytical Expression Selected AbstractsAnalytical Expressions for Quantitative Scanning Electrochemical Microscopy (SECM)CHEMPHYSCHEM, Issue 3 2010Christine Lefrou Dr. Abstract Scanning electrochemical microscopy (SECM), is a recent analytical technique in electrochemistry, which was developed in the 1990s and uses microelectrodes to probe various surfaces. Even with the well-known disc microelectrodes, the system geometry is not as simple as in regular electrochemistry. As a consequence even the simplest experiments, the so-called positive and negative feedback approach curves, cannot be described with exact analytical expressions. This review gathers all the analytical expressions available in the SECM literature in steady-state feedback experiments. Some of them are claimed as general expressions, other are presented as approximate. Their validity is discussed in the light of the current understanding and computer facilities. [source] A mathematical model for steady-state regolith production at constant erosion rateEARTH SURFACE PROCESSES AND LANDFORMS, Issue 5 2010M.I. Lebedeva Abstract It has been hypothesized that many soil profiles reach a steady-state thickness. In this work, such profiles were simulated using a one-dimensional model of reaction with advective and diffusive solute transport. A model ,rock' is considered, consisting of albite that weathers to kaolinite in the presence of chemically inert quartz. The model yields three different steady-state regimes of weathering. At the lowest erosion rates, a local-equilibrium regime is established where albite is completely depleted in the weathering zone. This regime is equivalent to the transport-limited regime described in the literature. With an increase in erosion rate, transition and kinetic regimes are established. In the transition regime, both albite and kaolinite are present in the weathering zone, but albite does not persist to the soil,air interface. In the weathering-limited regime, here called the kinetic regime, albite persists to the soil,air interface. The steady-state thickness of regolith decreases with increasing erosion rate in the local equilibrium and transition regimes, but in the kinetic regime, this thickness is independent of erosion rate. Analytical expressions derived from the model are used to show that regolith production rates decrease exponentially with regolith thickness. The steady-state regolith thickness increases with the Darcy velocity of the pore fluid, and in the local equilibrium regime may vary markedly with small variations in this velocity and erosion rate. In the weathering-limited regime, the temperature dependences for chemical weathering rates are related to the activation energy for the rate constant for mineral reaction and to the ,H of dissolution, while for local equilibrium regimes they are related to the ,H only. The model illustrates how geochemical and geomorphological observations are related for a simple compositional system. The insights provided will be useful in interpreting natural regolith profiles. Copyright © 2010 John Wiley & Sons, Ltd. [source] Study of Electrochemical Processes with Coupled Homogeneous Chemical Reaction in Differential Pulse Voltammetry at Spherical Electrodes and MicrohemispheresELECTROANALYSIS, Issue 16 2010Eduardo Laborda Abstract Homogeneous chemical reactions coupled to oxidation-reduction processes at electrode surfaces are very common in electrochemistry. In this paper we cope with the application of Differential Pulse Voltammetry at spherical electrodes and microhemispheres for the study of this kind of systems. Analytical expressions are deduced from which the influence of the different experimental variables is examined. Several diagnostic criteria for elucidation of the reaction mechanism from DPV peak parameters are given, as well as working curves for extraction of the kinetic rate constants of the chemical reaction. [source] Analytical approach for the toroidal relaxation of viscoelastic earthGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2006Hansheng Wang SUMMARY This paper is concerned with post-seismic toroidal deformation in a spherically symmetric, non-rotating, linear-viscoelastic, isotropic Maxwell earth model. Analytical expressions for characteristic relaxation times and relaxation strengths are found for viscoelastic toroidal deformation, associated with surface tangential stress, when there are two to five layers between the core,mantle boundary and Earth's surface. The multilayered models can include lithosphere, asthenosphere, upper and lower mantles and even low-viscosity ductile layer in the lithosphere. The analytical approach is self-consistent in that the Heaviside isostatic solution agrees with fluid limit. The analytical solution can be used for high-precision simulation of the toroidal relaxation in five-layer earths and the results can also be considered as a benchmark for numerical methods. Analytical solution gives only stable decaying modes,unstable mode, conjugate complex mode and modes of relevant poles with orders larger than 1, are all excluded, and the total number of modes is found to be just the number of viscoelastic layers between the core,mantle boundary and Earth's surface,however, any elastic layer between two viscoelastic layers is also counted. This confirms previous finding where numerical method (i.e. propagator matrix method) is used. We have studied the relaxation times of a lot of models and found the propagator matrix method to agree very well with those from analytical results. In addition, the asthenosphere and lithospheric ductile layer are found to have large effects on the amplitude of post-seismic deformation. This also confirms the findings of previous works. [source] Combined double- and triple-crystal X-ray diffractometry with account for real defect structures in all crystals of X-ray optical schemesPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 8 2007A. P. Shpak Abstract Analytical expressions for coherent and diffuse scattering intensities with account for imperfections in all the crystals of double- and triple-crystal diffractometers (DCD and TCD) have been derived from the generalized dynamical theory of X-ray scattering in real single crystals which contain microdefects of various types. The analysis of TCD and DCD profiles measured from Czochralski-grown silicon single crystal with oxygen precipitates and dislocation loops has been carried out. Characteristics of defect structures in sample and monochromator have been determined by using the combined DCD+TCD method. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] On the high-resolution mass analysis of the product ions in tandem time-of-flight (TOF/TOF) mass spectrometers using a time-dependent re-acceleration techniqueRAPID COMMUNICATIONS IN MASS SPECTROMETRY, Issue 1 2010Sergey Kurnosenko The time-dependent reacceleration of product ions produced as a result of dissociation of a single precursor ion in a tandem time-of-flight mass spectrometer is considered for the first time. Analytical expressions for the shapes of electric pulses bringing all the kinetic energies of the product ions to the same value are derived for two cases: forward acceleration mode and deceleration, followed by re-acceleration in the reversed direction (reversed mode). Secondary time-of-flight focusing resulting from the re-acceleration in the reversed mode is shown to be mass-dependent and, when averaged over a wide mass range, the focusing is tight enough to provide mass resolution exceeding 10,000. After time-dependent re-acceleration, additional compression of the ion packet width leading to better mass resolution can be obtained by decelerating the ions in a constant field. Copyright © 2009 John Wiley & Sons, Ltd. [source] Diffraction line profiles from polydisperse crystalline systemsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2001Paolo Scardi Diffraction patterns for polydisperse systems of crystalline grains of cubic materials were calculated considering some common grain shapes: sphere, cube, tetrahedron and octahedron. Analytical expressions for the Fourier transforms and corresponding column-length distributions were calculated for the various crystal shapes considering two representative examples of size-distribution functions: lognormal and Poisson. Results are illustrated by means of pattern simulations for a f.c.c. material. Line-broadening anisotropy owing to the different crystal shapes is discussed. The proposed approach is quite general and can be used for any given crystallite shape and different distribution functions; moreover, the Fourier transform formalism allows the introduction in the line-profile expression of other contributions to line broadening in a relatively easy and straightforward way. [source] Comparative Study of Flat and Round Collectors Using a Validated 1D Fluid Probe ModelCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-6 2006P. Peleman Abstract In the literature two different types of Gundestrup-like probe designs are proposed: design with flat and with round collectors. In this paper we study the influence of different collector shapes of Gundestrup-like probes on the accuracy of the measurement of the parallel and perpendicular flows. A one dimensional fluid probe model is used for deducing both Mach numbers of the unperturbed flow from the probe data. An analytical expression relates the plasma flow to the measured ion saturation currents collected at the upstream and downstream collecting surfaces of the probe. For flat collectors, the analytical model is validated by comparing it to a two dimensional quasi-neutral Particle In Cell (PIC) simulation code. An extension of the theoretical model then allows us to study round collectors. We performed an accuracy study which showed that systematic errors are introduced when round collectors are employed for determination of the perpendicular flow which is systematically overestimated. The error can reach more than 70% when the perpendicular flow increases and when the angle of the collecting surface with respect to the magnetic field (, , 0)is small. The correct analytical expression is applied to experimental data from Gundestrup probe measurements with round collectors on the CASTOR tokamak. The analysis shows that for these measurements the error introduced by using the expression for flat collectors remains negligible, supporting our former use of the model for flat collectors. A new advanced Gundestrup-like probe design and the motivation for the choice of flat collectors are presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Advances in the Study of Ion Transfer at Liquid Membranes with Two Polarized Interfaces by Square Wave VoltammetryELECTROANALYSIS, Issue 14 2010A. Molina Abstract A general analytical expression has been deduced for the I/E response of the square wave voltammetry corresponding to ion transfer processes in systems with two liquid/liquid polarized interfaces. This expression has been evaluated through the experimental study of a series of quaternary ammonium cations and metal chloro complex anions. We have found that systems with two liquid/liquid polarizable interfaces present the striking advantage that the difference between peak potentials of square wave voltammograms of cations and anions with similar standard ion transfer potential is much greater than in systems with a single polarizable one. [source] Core loss estimation in three-phase transformer using vector hysteresis model and classical loss model incorporated in 2D magnetodynamicsEUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 2 2003O. Deblecker This paper deals with the computation of the magnetic field and core loss in a three-phase three-limb transformer at no-load. The computational algorithm consists of the vector hysteresis model incorporated in 2D magneto-dynamics via the differential reluctivity tensor. The hysteretic nonlinearity is handled by a simple iteration scheme. The eddy-current losses in the laminated steel core are accounted for by considering an additional conductivity matrix in the FE equations. The magnetisation-dependant vector Preisach model with an analytical expression for the distribution function is adopted for describing the hysteretic constitutive law in the rolling and transverse directions of the laminations. The parameters and mean field term are fitted on the basis of a set of BH-symmetric (quasistatic) loops. Numerical results are presented that confirm the effectiveness of the proposed method for the no-load simulation of the transformer in the transient and the steady-states. [source] A mode II weight function for subsurface cracks in a two-dimensional half-spaceFATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 10 2002A. MAZZÙ ABSTRACT The general properties of a mode II Weight Function for a subsurface crack in a two-dimensional half-space are discussed. A general form for the WF is proposed, and its analytical expression is deduced from the asymptotic properties of the displacements field near the crack tips and from some reference cases obtained by finite elements models. Although the WF has general validity, the main interest is on its application to the study of rolling contact fatigue: its properties are explored for a crack depth range within which the most common failure phenomena in rolling contact are experimentally observed, and for a crack length range within the field of short cracks. The accuracy is estimated by comparison with several results obtained by FEM models, and its validity in the crack depth range explored is shown. [source] General Steady-State Shape Factor for a Partially Penetrating WellGROUND WATER, Issue 1 2010Vitaly A. Zlotnik We present the closed form of a general steady-state shape factor for a partially penetrating well in a uniform anisotropic aquifer. Our simple analytical expression for the shape factor has a uniform representation for full range of parameters and meets or exceeds the accuracy of previous results obtained through semiempirical methods (e.g., Bouwer and Rice [1976] equations). This general shape factor pertains to the flow of fluids (water or air) in subsurface formations when the upper formation boundary has constant potential and the lower boundary is impermeable. The results of our investigation are directly applicable to analyses of (1) slug tests with falling or rising head and (2) injection/extraction tests with constant head, essential techniques for the characterization of hydraulic conductivity of aquifers, streambeds, or lakebeds as well as the design of aquifer and soil remediation systems. [source] Analytical solutions for a three-invariant Cam clay model subjected to drained loading historiesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2006Dunja Peri Abstract Analytical solutions are derived for a three-invariant Cam clay model subjected to proportional and circular drained loading histories. The solutions are presented for a specific volume, and volumetric and generalized shear strains. In the case of a proportional loading only straight effective stress paths are considered while in the case of a circular loading the maximum possible change in Lode's angle is ,/3 due to plastic isotropy. Additionally, a concept of deviatoric stiffness is devised and an analytical expression for the generalized hardening modulus is derived. Qualitative and quantitative analyses are carried out in the form of direct comparisons between analytical solutions for drained and undrained loading histories thus offering an improved understanding of the three-invariant model. Copyright © 2006 John Wiley & Sons, Ltd. [source] Quantitative structural damage detection using high-frequency piezoelectric signatures via the reverberation matrix methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2007W. Yan Abstract High-frequency structural analysis so far has been a major issue in dynamic analysis, for which many conventional methods such as finite element method and transfer matrix method are unable to perform well. Since the electromechanical impedance technique for structural health monitoring (SHM) operates at very high frequencies, the reverberation matrix method (RMM), which was just developed a few years ago, is employed to study dynamics of the monitored structures, which are bonded with piezoelectric lead zirconate titanate (PZT) patches. A piecewisely homogeneous Euler,Bernoulli beam model is introduced to approximate the non-homogeneous beam and only one-dimensional axial vibration of PZT wafers is considered. The imperfect interfacial bonding between PZT patches and the host beam is investigated based on a shear lag model. Using a hybrid technique combining electromechanical impedance method and RMM, an analytical expression of impedance (or admittance) related to the response of the coupled model of PZT patch-bonding layer-host beam system is derived for SHM. The proposed method is examined by comparing with other theoretical methods as well as by means of a test on an intelligent system using a steel beam with two symmetrically installed PZT wafers. It could be further applied to predicting the dynamics of monitored Timoshenko beams, continuous beams, and framed structures as well. Copyright © 2006 John Wiley & Sons, Ltd. [source] Wavelet Galerkin method in multi-scale homogenization of heterogeneous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2006Shafigh Mehraeen Abstract The hierarchical properties of scaling functions and wavelets can be utilized as effective means for multi-scale homogenization of heterogeneous materials under Galerkin framework. It is shown in this work, however, when the scaling functions are used as the shape functions in the multi-scale wavelet Galerkin approximation, the linear dependency in the scaling functions renders improper zero energy modes in the discrete differential operator (stiffness matrix) if integration by parts is invoked in the Galerkin weak form. An effort is made to obtain the analytical expression of the improper zero energy modes in the wavelet Galerkin differential operator, and the improper nullity of the discrete differential operator is then removed by an eigenvalue shifting approach. A unique property of multi-scale wavelet Galerkin approximation is that the discrete differential operator at any scale can be effectively obtained. This property is particularly useful in problems where the multi-scale solution cannot be obtained simply by a wavelet projection of the finest scale solution without utilizing the multi-scale discrete differential operator, for example, the multi-scale analysis of an eigenvalue problem with oscillating coefficients. Copyright © 2005 John Wiley & Sons, Ltd. [source] Lyapunov spectrum determination from the FEM simulation of a chaotic advecting flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006Philippe CarrièreArticle first published online: 7 SEP 200 Abstract The problem of the determination of the Lyapunov spectrum in chaotic advection using approximated velocity fields resulting from a standard FEM method is investigated. A fourth order Runge,Kutta scheme for trajectory integration is combined with a third order Jacobian matrix method with QR -factorization. After checking the algorithm on the standard Lorenz and coupled quartic oscillator systems, the method is applied to a model 3-D steady flow for which an analytical expression is known. Both linear and quadratic approximated velocity fields succeed in predicting the Lyapunov exponents as well as describing the chaotic or regular regions inside the flow with satisfactory accuracy. A more realistic flow is then studied in order to delineate the possible limitations of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Hybrid adaptive predictive control for a dynamic pickup and delivery problem including traffic congestionINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2 2008Cristián E. Cortés Abstract This paper presents a hybrid adaptive predictive control approach to incorporate future information regarding unknown demand and expected traffic conditions, in the context of a dynamic pickup and delivery problem with fixed fleet size. As the routing problem is dynamic, several stochastic effects have to be considered within the analytical expression of the dispatcher assignment decision objective function. This paper is focused on two issues: one is the extra cost associated with potential rerouting arising from unknown requests in the future, and the other is the potential uncertainty in travel time coming from non-recurrent traffic congestion from unexpected incidents. These effects are incorporated explicitly in the objective function of the hybrid predictive controller. In fact, the proposed predictive control strategy is based on a multivariable model that includes both discrete/integer and continuous variables. The vehicle load and the sequence of stops correspond to the discrete/integer variable, adding the vehicle position as an indicator of the traffic congestion conditions. The strategy is analyzed under two scenarios. The first one considers a predictable congestion obtained using historical data (off-line method) requiring a predictive model of velocities distributed over zones. The second scenario that accepts unpredictable congestion events generates a more complex problem that is managed by using both fault detection and isolation and fuzzy fault-tolerant control approaches. Results validating these approaches are presented through a simulated numerical example. Copyright © 2007 John Wiley & Sons, Ltd. [source] Harmonic Balance, Melnikov method and nonlinear oscillators under resonant perturbationINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2008Michele Bonnin Abstract The subharmonic Melnikov's method is a classical tool for the analysis of subharmonic orbits in weakly perturbed nonlinear oscillators, but its application requires the availability of an analytical expression for the periodic trajectories of the unperturbed system. On the other hand, spectral techniques, like the Harmonic Balance, have been widely applied to the analysis and design of nonlinear oscillators. In this manuscript, we show that bifurcations of subharmonic orbits in perturbed systems can be easily detected computing the Melnikov's integral over the Harmonic Balance approximation of the unperturbed orbits. The proposed method significantly extends the applicability of the Melnikov's method since the orbits of any nonlinear oscillator can be easily detected by the Harmonic Balance technique, and the integrability of the unperturbed equations is not required anymore. As examples, several case studies are presented, the results obtained are confirmed by extensive numerical experiments. Copyright © 2007 John Wiley & Sons, Ltd. [source] Time-dependent heat transfer coefficient of a wallINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 9 2003Periklis E. Ergatis Abstract A time-dependent coefficient of heat transfer is proposed for the computation of thermal power required, so that a room temperature reaches a desired value within a given time. A mathematical formulation of the room heating transient phenomenon is constructed in a dimensionless form. Using an integral approximate solution an analytical expression for this coefficient is provided and it is verified by diagrams adopted by DIN 4701. Copyright © 2003 John Wiley & Sons, Ltd. [source] An analytical and experimental analysis of a very fast thermal transientINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 11 2001C. Aprea Abstract According to some international standards, some products, developed for use under heavy thermal conditions, have to be tested by subjecting them for a short time to a particular heating and cooling thermal stress to allow them an acceptable future operative life. It is possible to obtain these fast thermal gradients in confined environments, called climatic chambers where the air is heated by an electrical resistance and is cooled with a finned evaporator which is linked to a vapour compression system subjected to a particular control system of the refrigerating power. In particular, in this paper the air and object tested thermal transients are studied from an analytical and experimental point of view. The study of the mathematical model is realized assuming simplified hypotheses about the air, the object and the air cooled evaporator temperature. The most complex circumstances are related to a very fast temperature decrease because under this working condition the mathematical model is characterized by a nonlinear differential system. The nonlinear term is represented by the refrigerating power that varies in a definite range with the evaporator temperature according to a sinusoid trend. For this power a suitable analytical expression, derived by the control system performance and by the compressor characteristic, has been found. The analytical,experimental comparison during a cooling thermal stress of typical products subjected to international standard tests as the electronic boards, has been carried out showing acceptable results. The model presented is useful to foresee the climatic chamber performances in the presence of a specific refrigerating power trend; this is the start-point for the design of the vapour compression plant and its control system. Copyright © 2001 John Wiley & Sons, Ltd. [source] A CFL-like constraint for the fast marching method in inhomogeneous chemical kineticsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2008Ramón Escobedo Abstract Level sets and fast marching methods are a widely used technique for problems with moving interfaces. Chemical kinetics has been recently added to this family, for the description of reaction paths and chemical waves in homogeneous media, in which the velocity of the interface is described by a given field. A more general framework must consider variable velocities due to inhomogeneities induced by chemical changes. In this case, a constraint must be satisfied for the correct use of fast marching method. We deduce an analytical expression of this constraint when the Godunov scheme is used to solve the Eikonal equation, and we present numerical simulations of a case which must be enforced to obey the constraint. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Wigner function of the rotating Morse oscillatorINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2005Jerzy Stanek Abstract We present an analytical expression of the Wigner distribution function (WDF) for the bound eigenstates of the rotating Morse oscillator (RMO). The effect of rotational excitation on the WDF on the quantum phase space has been demonstrated. This effect has been visualized by a series of contour diagrams for given rovibrational quantum states. Rotations of the molecule have been proved to qualitatively and quantitatively change the Wigner function. As a result, the most probable distance between atoms in a rotating molecule changes, and depends on the parity of the vibrational quantum number. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Design of fault-tolerant control for MTTFINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 16 2008Hongbin Li Abstract Mean time to failure (MTTF) is an important reliability index of fault-tolerant control systems, which is chosen as a design objective in this paper. However, it is usually evaluated from stochastic reliability models, and no analytical expression is available to relate MTTF to controller parameters. To overcome this difficulty, a two-stage design scheme is proposed in this paper: A gradient-based search is firstly carried out on probabilistic H, performance characteristics for MTTF requirement; a sequential randomized algorithm with a weighted violation function is then developed for a controller design to satisfy the required H, performance, and its convergence is guaranteed with probability 1. Two iterative algorithms are carried out alternately to implement this scheme, and a controller can be designed for MTTF requirement. Copyright © 2008 John Wiley & Sons, Ltd. [source] Corrections for surface X-ray diffraction measurements using the Z -axis geometry: finite size effects in direct and reciprocal spaceJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2000O. Robach X-ray diffraction data have to be corrected by geometrical correction factors prior to any quantitative analysis. Here the case of grazing incidence X-ray diffraction measurements is considered, including the case of high exit angles. First, an approach taking into account the evolution of the diffracting area during an , scan is presented. From the calculation of the effective part of the sample surface that participates in the diffraction phenomena at each step of the scan, a more accurate correction factor than those commonly used is derived and the evolution of the line shape along a zero-width rod is explained. Secondly, the case of finite-width rods, under the point-like sample approximation, is considered: the influence of the partial integration, as a result of the detector in-plane acceptance, of a rod with an anisotropic in-plane shape, is studied and leads to an analytical expression for the corresponding correction factor. Finally, a full numerical simulation is presented, which provides an alternative method for correcting the experimental intensities and shows in which conditions the previous formulae are no longer valid. [source] The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspaceJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 1 2002Marise Gallant The synthesis of three-degree-of-freedom planar parallel manipulators is performed using a genetic algorithm. The architecture of a manipulator and its position and orientation with respect to a prescribed workspace are determined. The architectural parameters are optimized so that the manipulator's constant-orientation workspace is as close as possible to a prescribed workspace. The manipulator's workspace is discretized and its dexterity is computed as a global property of the manipulator. An analytical expression of the singularity loci (local null dexterity) can be obtained from the Jacobian matrix determinant, and its intersection with the manipulator's workspace may be verified and avoided. Results are shown for different conditions. First, the manipulators' workspaces are optimized for a prescribed workspace, without considering whether the singularity loci intersect it or not. Then the same type of optimization is performed, taking intersections with the singularity loci into account. In the following results, the optimization of the manipulator's dexterity is also included in an objective function, along with the workspace optimization and the avoidance of singularity loci. Results show that the end-effector's location has a significant effect on the manipulator's dexterity. © 2002 John Wiley & Sons, Inc. [source] Prediction of the location of stationary steady-state zone positions in counterflow isotachophoresis performed under constant voltage in a vortex-stabilized annular columnJOURNAL OF SEPARATION SCIENCE, JSS, Issue 18 2007Schurie L. M. Harrison Abstract A theoretical model is presented and an analytical expression derived to predict the locations of stationary steady-state zone positions in ITP as a function of current for a straight channel under a constant applied voltage. Stationary zones may form in the presence of a countercurrent flow whose average velocity falls between that of a pure leader zone and of a pure trailer zone. A comparison of model predictions with experimental data from an anionic system shows that the model is able to predict the location of protein zones with reasonable accuracy once the ITP stack has formed. This result implies that an ITP stack can be precisely directed by the operator to specific positions in a channel whence portions of the stack can be removed or redirected for further processing or analysis. [source] Light propagation in multi-step index optical fibresLASER & PHOTONICS REVIEWS, Issue 3 2008J. Zubia Abstract This paper reviews the theoretical analysis of light propagation we have carried out on multimode multi-step index (MSI) optical fibres. Starting from the Eikonal equation, we derive the analytical expressions that allow calculating the ray trajectories inside these fibres. We also analyse the effects of leaky rays on the transmission properties of MSI fibres. For this purpose, a single analytical expression for the evaluation of the ray power transmission coefficient is calculated. Afterwards, we investigate the effects of extrinsic and intrinsic coupling losses on the performance of MSI fibres, providing analytical expressions to calculate the coupling loss and, also, determining the most critical parameters. Finally, we carry out a comprehensive numerical analysis of the fibre bandwidth under different source configurations. [source] Analysis of the timing jitter of dispersion-managed solitons controlled by filtersLASER PHYSICS LETTERS, Issue 10 2004M. H. Sousa Abstract Using a variational approach, an exact analytical expression is derived for the variance of the timing jitter of a dispersion-managed soliton in the presence of lumped narrowband filters. The asymptotic timing jitter shows a linear dependence with distance, which is in contrast with the cubic dependence in the unfiltered case. We show that the suppression of the timing can be achieved by choosing conveniently the position and the strength of the optical filter. (© 2004 by ASTRO, Ltd. Published exclusively by WILEY-VCH Verlag GmbH & Co. KGaA) [source] Chain Length Distributions of Polyolefins Made in Stopped-Flow Reactors for Non-Instantaneous Site ActivationMACROMOLECULAR REACTION ENGINEERING, Issue 2 2008João B. P. Soares Abstract We developed an analytical solution to describe how the chain length distribution (CLD) of polymers made with coordination polymerization catalysts vary as a function of time for very short polymerizations considering non-instantaneous site activation. This solution is an extension of our previous analytical expression for instantaneous site activation. We validated the analytical solution with dynamic Monte Carlo simulation and obtained excellent agreement. Simulation results indicate that, unless the catalyst activation rate is much lower than the propagation rate, it will have only a minor effect on the initial shape of the CLD of polymers made in stopped-flow reactors (SFR). We also show how incorrect polymerization kinetic parameters may be estimated when assuming instantaneous site activation when this hypothesis is not applicable to the polymerization data under investigation. [source] RAFT Miniemulsion Polymerization Kinetics, 1 , Polymerization RateMACROMOLECULAR THEORY AND SIMULATIONS, Issue 2 2009Hidetaka Tobita Abstract The polymerization kinetics of a RAFT-mediated radical polymerization inside submicron particles (30,<,Dp,<,300 nm) is considered. When the time fraction of active radical period, ,A, is larger than ca. 1%, the polymerization rate increases with reducing particle size, as for the cases of conventional emulsion polymerization. The rate retardation by the addition of RAFT agent occurs with or without intermediate termination in zero-one systems. For the particles with Dp,<,100 nm, the statistical variation of monomer concentration among particles may not be neglected. It was found that this monomer-concentration-variation (MCV) effect may slow down the polymerization rate. An analytical expression describing the MCV effect is proposed, which is valid for both RAFT and conventional miniemulsion polymerizations. [source] | ||||||||||||||||||||||||||||||||||||||||||||||||||||