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Showing papers on "Electric potential published in 2017"


Journal ArticleDOI
TL;DR: It is shown that Coulombic ordering reduces when the pores can only accommodate a single layer of ions, and equally-charged ion pairs are formed due to the induction of an electric potential of opposite sign in the carbon pore walls.
Abstract: Ionic liquids are composed of equal quantities of positive and negative ions. In the bulk, electrical neutrality occurs in these liquids due to Coulombic ordering, in which ion shells of alternating charge form around a central ion. Their structure under confinement is far less well understood. This hinders the widespread application of ionic liquids in technological applications. Here we use scattering experiments to resolve the structure of a widely used ionic liquid (EMI–TFSI) when it is confined inside nanoporous carbons. We show that Coulombic ordering reduces when the pores can accommodate only a single layer of ions. Instead, equally charged ion pairs are formed due to the induction of an electric potential of opposite sign in the carbon pore walls. This non-Coulombic ordering is further enhanced in the presence of an applied external electric potential. This finding opens the door for the design of better materials for electrochemical applications.

210 citations


Journal ArticleDOI
TL;DR: In this paper, a finite element formulation accounting for multiphysics response of multilayered magneto-electro-elastic (MEE) plates in the thermal environment has been presented.

87 citations


Journal ArticleDOI
TL;DR: In this article, the static response of magneto-electro-elastic (MEE) plate subjected to hygrothermal loads is investigated using the finite element (FE) method.

74 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed a comprehensive analytical description of these coupled ferroelectric and ionic states by combining the Ginzburg-Landau-Devonshire description of the film with Langmuir adsorption model for the electrochemical reaction at the film surface, and explored the thermodynamic and kinetic characteristics of the ferroionic states as a function of temperature, film thickness, and external electric potential.
Abstract: The electric coupling between surface ions and bulk ferroelectricity gives rise to a continuum of mixed states in ferroelectric thin films, exquisitely sensitive to temperature and external factors, such as applied voltage and oxygen pressure. Here we develop the comprehensive analytical description of these coupled ferroelectric and ionic (ferroionic) states by combining the Ginzburg-Landau-Devonshire description of the ferroelectric properties of the film with Langmuir adsorption model for the electrochemical reaction at the film surface. We explore the thermodynamic and kinetic characteristics of the ferroionic states as a function of temperature, film thickness, and external electric potential. These studies provide a new insight into mesoscopic properties of ferroelectric thin films, whose surface is exposed to chemical environment as screening charges supplier.

71 citations


Journal ArticleDOI
TL;DR: How various theoretical models predict structural properties of the electric double layer such as the differential capacitance and compare some of these predictions with computer simulations are discussed.

63 citations


Journal ArticleDOI
TL;DR: In this paper, a device modeling of HTM free perovskite solar cells having the structure of FTO/ZnO/CH3NH3PbI3/carbon is performed.

56 citations


Journal ArticleDOI
TL;DR: In this article, a theoretical framework was established to investigate the circuit voltage, electric power of nanoscale mechanical energy harvesting, in which the mechanical vibration energy was converted into electrical energy by piezoelectric and flexoelectoric effects, and analytical solutions for the maximum electric potential, circuit voltage and electric power generated in bent BaTiO3 (BT), ZnO nanowires (NWs) and Pb(Mg1/3Nb2/3)O3(NFs) were derived.
Abstract: Due to the electromechanical coupling effect, mechanical energy can be converted into electrical energy in certain materials. A theoretical framework is established to investigate the circuit voltage, electric power of nanoscale mechanical energy harvesting, in which the mechanical vibration energy was converted into electrical energy by piezoelectric and flexoelectric effects. Analytical solutions for the maximum electric potential, circuit voltage and electric power generated in bent BaTiO3 (BT), ZnO nanowires (NWs) and Pb(Mg1/3Nb2/3)O3 (PMN) nanofilms (NFs) were derived. Static and dynamic analyses are conducted to obtain the fundamental information of these mechanical energy harvestings. Different from the previous studies, the flexoelectric-mechanism are included in the fundamental mechanical frameworks. The maximum electric potential generated in the BT, ZnO NWs and PMN NF is found to be enhanced by flexoelectricity in the static case, meanwhile the circuit voltage and electric power are dramatic enhanced by flexoelectricity when the geometric dimensions shrinks to dozens of nanometers. The mechanical limitation condition is employed to calculate the practical maximum electric potential, circuit voltage and electric power. This work tries to provide a comprehensive understanding of the mechanical energy harvesting capability of these nanoscale structures and provide valuable information for designing flexoelectricity-based nanogenerator devices.

48 citations


Journal ArticleDOI
TL;DR: In this paper, a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures is proposed, where the effect of the microstructural heterogeneity is taken into account by means of periodic perturbation functions, which derive from the solution of nonhomogeneous recursive cell problems defined over the unit periodic cell.

46 citations


Journal ArticleDOI
TL;DR: In this paper, a new RRAM simulation tool based on a 3D kinetic Monte Carlo algorithm has been implemented, which takes into account the temperature and electric potential 3D distributions within the device dielectric at each simulation time step.
Abstract: A new RRAM simulation tool based on a 3D kinetic Monte Carlo algorithm has been implemented. The redox reactions and migration of cations are developed taking into consideration the temperature and electric potential 3D distributions within the device dielectric at each simulation time step. The filamentary conduction has been described by obtaining the percolation paths formed by metallic atoms. Ni/HfO2/Si-n+ unipolar devices have been fabricated and measured. The different experimental characteristics of the devices under study have been reproduced with accuracy by means of simulations. The main physical variables can be extracted at any simulation time to clarify the physics behind resistive switching; in particular, the final conductive filament shape can be studied in detail.

44 citations


Journal ArticleDOI
TL;DR: In this paper, the bending analysis of a sandwich microbeam with a piezoelectric micro face-sheet is presented, where the microbeam is subjected to transverse loads and two-dimensional electric potential, and the numerical results indicate that maximum displacement and electric potential are approximately insensitive to applied voltage.
Abstract: The governing equations of bending analysis of a sandwich microbeam are derived in this article. The sandwich microbeam includes an elastic micro-core and two piezoelectric micro face-sheets. The microbeam is subjected to transverse loads and two-dimensional electric potential. Higher-order sinusoidal shear deformation beam theory is used for description of displacement field. To account for size dependency in governing equations of bending, strain gradient theory is used to mention higher-order stress and strains. An analytical approach for simply supported sandwich microbeam with short-circuited electric potential is proposed. The numerical results indicate that various types of parameters such as foundation, material and loads parameters have significant effect on the bending results. Comparison of valid references is performed to validate our numerical results. The numerical results indicate that maximum displacement and electric potential are approximately insensitive to applied voltage unlike to bea...

41 citations


Journal ArticleDOI
TL;DR: In this article, the skip-m current pattern is defined as a pair-wise injection strategy in which the number of non-current injecting electrodes enclosed between two injection electrodes is m.

Journal ArticleDOI
Abstract: This paper presents a nano-orifice based microfluidic device using a direct current dielectrophoresis (DC-DEP) method to continuously separate different types of micro and nanoparticles of similar sizes by their different electric conductivities in pressure-driven flow. The DC-DEP force is generated by applying a low electric potential difference via a small nano-size orifice on one side wall of the channel and a micron size orifice on the opposite wall. The particles will experience the DEP forces when passing through the vicinity of the small orifice where the strongest non-uniform electric field exists. Experiments were conducted by adjusting the electric conductivity of the suspending medium so that one kind of particles will experience positive DEP force while another experiences negative DEP. In this way, the separation of 140 nm polystyrene (PS) and 150 nm magnetic nanoparticles and the separation of 470 nm magnetic-coated PS and 490 nm PS nanoparticles were demonstrated, and the separation of 5.2 μm magnetic-coated PS and 7 μm PS particles and the separation of 14 μm sliver-coated hollow glass beads and 15 μm PS particles were also conducted. In comparison with the reported DC-DEP methods which are commonly used to separate microparticles by size and the alternative current DEP (AC-DEP) techniques which can separate different types of microparticles by applying high frequency alternating current with inserted microelectrodes, this method uses a pair of asymmetrical orifices on the opposite sides of channel walls to induce strong non-uniformity of electrical field and is capable of separating different kinds of nanoparticles. Furthermore, this method involves relatively low electric potential applied locally and hence the Joule heating effect and the electrochemical reaction at the electrodes are minimized.

Journal ArticleDOI
TL;DR: In this article, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler-Bernoulli beam theory.
Abstract: In this paper, free vibration, wave propagation, and bending analyses of a sandwich microbeam integrated with piezoelectric face-sheets resting on Pasternak foundation under electric potential are presented based on the strain gradient theory and Euler–Bernoulli beam theory. The material properties of core are assumed variable along the thickness direction and piezoelectric face-sheets are assumed homogeneous piezoelectric materials. A two-dimensional electric potential distribution along the axial and transverse direction is applied on the face-sheets of microbeam. Hamilton principal is used to derive governing differential equations of motion. Three behaviors of sandwich microbeam including free vibration, wave propagation, and bending analyses are studied in this paper. Some numerical results are presented to capture the effect of important parameters of the problem such as in-homogeneous index, applied voltage, parameters of foundation, and material length scales. The numerical results indicat...

Journal ArticleDOI
TL;DR: The 2-D Fourier transform and Wiener filter techniques are employed in the algorithm for shift-invariant system thus the relationship between potential and charge density can be processed in spatial frequency domain, which tremendously simplifies the conventional procedure.
Abstract: Charge accumulation on a solid dielectric surface is one of the critical concerns for the design and optimization of the insulation system in a high-voltage power equipment, since it will lead to the overstress of electrical insulation. Therefore, it is important to obtain the charge density distribution on a solid dielectric surface with high accuracy. The acquisition of surface charge for insulators requires multipoint potential measurements to establish the inverse calculation for the determination of an unknown charge distribution. Up to now, extensive studies have been conducted on this subject; nevertheless, the methods are either too complicated and time consuming, or only applicable for specific arrangements, or with poor accuracy. In this paper, the problem is divided into two categories, i.e., shift-variant system and shift-invariant system, and the basic principle of an improved inversion algorithm is interpreted to solve the problem. The 2-D Fourier transform and Wiener filter techniques are employed in the algorithm for shift-invariant system thus the relationship between potential and charge density can be processed in spatial frequency domain, which tremendously simplifies the conventional procedure. The accuracy and resolution of the algorithm are discussed in detail with the aid of numerical examples. In the end, experiments are conducted and the effectiveness of the algorithm is verified.

Journal ArticleDOI
TL;DR: In this article, a quantum-mechanical threshold voltage model for ultrathin double gate-all-around DGAA MOSFETs has been developed by solving three-dimensional (3D) Poisson's and 2-D Schrodinger's equations in the channel region.
Abstract: In this paper, a quantum-mechanical threshold voltage model for ultrathin double gate-all-around DGAA MOSFETs has been developed by solving three-dimensional (3-D) Poisson's and 2-D Schrodinger's equations in the channel region. The parabolic potential approximation is considered for Poisson's equation solution, whereas a hollow cylindrical potential well in the channel region is assumed to solve Schrodinger's equation. Simple equations for the wave function and energy quantization in the channel of DGAA MOSFET have been formulated. Discretized energy levels have been used for channel charge calculation in subthreshold regime of device operation. The calculated channel charge is compared with a threshold charge to formulate the threshold voltage model. The effects of the device parameters such as the channel thickness, oxide thickness, doping, etc. on threshold voltage and DIBL have been extensively studied. The proposed model results have been verified by comparing with the numerical simulation results obtained from the 3-D device simulator Visual TCAD of Cogenda Int.

Journal ArticleDOI
TL;DR: In this paper, a numerical method is developed for the computation of the electrostatic potential in a sum of Maxwellian plasmas, and the results are used to build synthetic mutual impedance spectra and quantify the effect of a warm electron population on mutual impedance experiments, in order to illustrate how the method could be applied for recent and future planetary space missions.
Abstract: Mutual impedance experiments have been developed to constrain the plasma bulk properties, such as density and temperature, of ionospheric and later space plasmas, through the electric coupling between an emitter and a receiver electric antennas. So far, the analytical modeling of such instruments has enabled to treat ionospheric plasmas, where charged particles are usually well characterized by Maxwellian electron distributions. With the growth of planetary exploration, mutual impedance experiments are or will be used to constrain space plasma bulk properties. Space plasmas are usually out of local thermodynamic equilibrium; therefore, new methods to calibrate and analyze mutual impedance experiments are now required in such non-Maxwellian plasmas. To this purpose, this work aims at modeling the electric potential generated in a two-electron temperature plasma by a pulsating point charge. A numerical method is developed for the computation of the electrostatic potential in a sum of Maxwellian plasmas. After validating the method, the results are used to build synthetic mutual impedance spectra and quantify the effect of a warm electron population on mutual impedance experiments, in order to illustrate how the method could be applied for recent and future planetary space missions, such as Rosetta, BepiColombo, and JUICE. In particular, we show how it enables to separate the densities and temperatures of two different electron populations using in situ measurements from the RPC-MIP mutual impedance experiment on board Rosetta.

Journal ArticleDOI
TL;DR: In this paper, the authors provided a theoretical model to analyze the thermoelectric conversion efficiency of a cracked material with finite height and width based on the nonlinearly coupled transport equations of electricity and heat.

Journal ArticleDOI
TL;DR: In this paper, the free vibration of magnetoelectroelastic (MEE) nanoplates resting on elastic foundations was investigated using nonlocal, refined plate, and surface effects.
Abstract: The theories of nonlocal, refined plate, and surface effects are used in this study to investigate the free vibration of magnetoelectroelastic (MEE) nanoplates resting on elastic foundations. For this purpose, the MEE nanoplate is subjected not only to external magnetic and electric potentials but also to thermal and shear in-plane loads. The refined plate theory is used and the Maxwell equations and magnetoelectric boundary conditions employed to determine the variations in the electric and magnetic potentials along the direction of the nanoplate thickness. This is followed by deriving the governing equations based on the Hamilton’s principle, which are then solved via the generalized differential quadrature method. In a later stage of the study, the effects of electric and magnetic potentials, nonlocal parameter, thermal and shear in-plane loading, Winkler and shear moduli, different boundary conditions, and aspect ratio are explored in a parametric study on the surface effects of vibration characteristics of MEE nanoplates. It is found that the effect of surface parameters enhanced with increases in nonlocal parameter, electric potential, in-plane shear load, and temperature change. However, this effect is observed to decrease when the magnetic potential, dimensionless Winkler and shear moduli, and nanoplate thickness are augmented.

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical currentvoltage model for a negative capacitance field effect transistor (NCFET) with a ferroelectric material (i.e., BaTiO3) is proposed.
Abstract: In this letter, a semi-analytical current–voltage model for a negative capacitance field-effect transistor (NCFET) with a ferroelectric material ( i.e. , BaTiO3) is proposed. Surface potential ( $\psi _{\mathrm {S}})$ in the channel region is determined first by solving the Landau–Khalatnikov (LK) equation numerically with Poisson’s equation. Then, the drain–current is achieved based on the current continuity equation using $\psi _{\mathrm {S}}$ determined earlier. In addition, by introducing a fitting potential for a given drain–voltage, threshold voltage shift can be captured, resulting in accurate surface potential and drain–current at different gate voltages. We have verified our model using the technology computer-aided design (TCAD)-MATLAB simulation, and our model exhibits an excellent agreement to the simulation results. In addition, the impacts of the ferroelectric thickness and channel doping concentration on the device performance and hysteresis window of NCFET are thoroughly explored.

Journal ArticleDOI
TL;DR: This work provides a physical basis by which the flow rate and the voltage can be chosen for any nanosuspension to precisely operate in the microdripping mode at a predetermined dropsize and droplet frequency.
Abstract: Electrosprays operate in several modes depending on the flow rate and electric potential. This allows the deposition of droplets containing nanoparticles into discrete nanodot arrays to fabricate various electronic devices. In this study, seven different suspensions with varying properties were investigated. In the dripping mode, the normalized dropsize decreases linearly with electric capillary number, Ca e , (ratio of electric to surface tension forces) up to Ca e ≈ 1.0. The effect of viscous forces is found to be negligible in the dripping mode since the capillary number is small. For flow rates with low Reynolds number, the mode changes to microdripping mode, and then to a planar oscillating microdripping mode as Ca e increases. The normalized dropsize remains nearly constant at 0.07 for Ca e > 3.3. The microdripping mode which is important for depositing discrete array of nanodots is found to occur in the range, 2 ≤ Ca e ≤ 2.5. The droplet frequency increases steadily from dripping to microdripping mode, but stays roughly constant in the oscillating microdripping mode. This work provides a physical basis by which the flow rate and the voltage can be chosen for any nanosuspension to precisely operate in the microdripping mode at a predetermined dropsize and droplet frequency.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the electromechanical coupling response of piezoelectric nanobeams with different electrical boundary conditions including the effect of flex-olectricity.
Abstract: The flexoelectric effect is coupling of polarization and strain gradient, which exists in a wide variety of materials and may lead to strong size-dependent properties at the nanoscale. Based on an extension to classical beam model, this paper investigates the electromechanical coupling response of piezoelectric nanobeams with different electrical boundary conditions including the effect of flexoelectricity. The electric Gibbs free energy and the variational principle are used to derive the governing equations with three types of electrical boundary conditions. Closed-form solutions are obtained for static bending of cantilever beams. The results show that the normalized effective stiffness increases with decreasing beam thickness in the open circuit electrical boundary conditions with or without surface electrodes. The induced electric potential due to the flexoelectric effect is obtained under the open circuit conditions, which may be important for sensing or energy harvesting applications. An intrinsic thickness depending on the material properties is identified for the maximum induced electric potential. The present results also show that the flexoelectricity has a more significant effect on the electroelastic responses than the piezoelectricity at the nano scales. Our analysis in the present study can be useful for understanding of the electromechanical coupling in nanobeams with flexoelectricity.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the nonlinear conduction of polymeric insulation, which may solve the surface charge accumulation, avoiding the distortion of electric field and the flashover phenomenon.
Abstract: The nonlinear conduction of polymeric insulation may solve the surface charge accumulation, avoiding the distortion of electric field and the flashover phenomenon. As the silicon carbide (SiC) powder is usually used to improve the nonlinear conduction of polymer composites, the epoxy/SiC nanocomposites are prepared and the dc conductivity, permittivity and isothermal surface potential decay characteristics are investigated. The experimental results show that the conduction of high filler loading is field dependent and is attributed to a new conduction mechanism. The permittivity is closely related to the interaction zone around nanoparticles. The isothermal surface potential decay characteristics are greatly affected by the charging polarity, charging level and filler loading. The investigation indicates that the nonlinear conduction plays an important role in the surface potential decay.

Journal ArticleDOI
TL;DR: In this paper, the Kirchhoff and Mindlin models for the wave propagation analysis of piezoelectric nanoplates were developed based on the nonlocal theory and the effects of small scale parameter and thermo-electro-mechanical loads were incorporated in the nanoplate models.
Abstract: Based on the nonlocal theory, this paper develops the Kirchhoff nanoplate and Mindlin nanoplate models for the wave propagation analysis of piezoelectric nanoplates. The effects of small scale parameter and thermo-electro-mechanical loads are incorporated in the nanoplate models. The Hamilton’s principle is employed to derive the governing equations of the nanoplate, which are solved analytically to obtain the dispersion relation for piezoelectric nanoplates. The results show that the nonlocal parameter, temperature change, mechanical load and external electric potential have significant influence on the wave propagation characteristics of the piezoelectric nanoplates. The cut-off wave number is observed to exist for piezoelectric nanoplates subjected to positive electric potential, axial tensile force and temperature rise.

Journal ArticleDOI
TL;DR: It is suggested that the model presented in this work can be integrated as a module into a more comprehensive model of oxygenic photosynthesis.

Journal ArticleDOI
TL;DR: In this article, an asymptotic approximation to the solution of the stationary Poisson-Nernst-Planck (PNP) equations in a d-dimensional ball (d = 1, 2, 3 ) in the limit of large total charge is presented.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated analytically the unsteady viscous flow driven by the combined effects of peristalsis and electro-osmosis through a microchannel.
Abstract: Electrokinetic transport of fluids through microchannels by micro-pumping and micro- peristaltic pumping has stimulated considerable interest in biomedical engineering and other areas of medical technology Deeper elucidation of the fluid dynamics of such transport requires the continuous need for more elegant mathematical models and numerical simulations, in parallel with laboratory investigations In this article we therefore investigate analytically the unsteady viscous flow driven by the combined effects of peristalsis and electro-osmosis through microchannel An integral number of waves propagating in the microchannel are considered as a model for transportation of fluid bolus along the channel length Debye-Huckel linearization is employed to evaluate the potential function Low Reynolds number and large wavelength approximations are employed Closed-form solutions are derived for the non-dimensional boundary value problem The computations demonstrate that magnitude of electric potential function is increased with a decrease in the thickness of the electrical double layer (EDL) Stronger electric field also decelerates the flow and decreases local wall shear stress Hydrodynamic pressure is increased with EDL thickness whereas it is suppressed with electric field Streamline visualization reveals that the quantity of trapped bolus is decreased with increase in EDL thickness and also with higher external electric field

Journal ArticleDOI
TL;DR: In this article, the authors present consistent QED and scalar QED calculations of particle creation effects in external electromagnetic field that correspond to three most important exactly solvable cases of t-electric potential steps: Sauter-like electric field, T-constant electric field and exponentially growing and decaying electric fields.
Abstract: In this paper, we present in detail consistent QED (and scalar QED) calculations of particle creation effects in external electromagnetic field that correspond to three most important exactly solvable cases of t-electric potential steps: Sauter-like electric field, T-constant electric field, and exponentially growing and decaying electric fields. In all these cases, we succeeded to obtain new results, such as calculations in the modified configurations of the above-mentioned steps and detailed considerations of new limiting cases in already studied steps. As was recently discovered by us, the information derived from considerations of exactly solvable cases allows one to make some general conclusions about quantum effects in fields for which no closed form solutions of the Dirac (or Klein–Gordon) equation are known. In the present paper, we briefly represent such conclusions about universal behavior of vacuum mean values in slowly varying strong electric fields.

Journal ArticleDOI
TL;DR: The Hellmann-generalized Morse potential as discussed by the authors is a superposition of the Hellmann potential and generalized generalized Morse or Deng-Fan potential, which consists of three different potentials which include Yukawa potential, Coulomb potential and Deng-fan potential.
Abstract: The approximate analytical solutions of the radial Schrӧdinger equation have been obtained with a newly proposed potential called Hellmann-generalized Morse potential. The potential is a superposition of Hellmann potential and generalized Morse or Deng-Fan potential. The Hellmann-generalized Morse potential actually comprises of three different potentials which includes Yukawa potential, Coulomb potential and Deng-Fan potential. The aim of combining these potentials is to have a wide application. The energy eigenvalue and the corresponding wave function are calculated in a closed and compact form using the parametric Nikiforov-Uvarov method. The energy equation for some potentials such as Deng-Fan, Rosen Morse, Morse, Hellmann, Yukawa and Coulomb potentials have also been obtained by varying some potential parameters. Some numerical results have been computed. We have plotted the behavior of the energy eigenvalues with different potential parameters and also reported on the numerical result. Finally, we computed the variance and information energy for the Hellmann-generalized Morse potential.

Journal ArticleDOI
TL;DR: In this paper, the two-dimensional problems of an elliptic hole or a rigid inclusion embedded in a thermoelectric material subjected to uniform electric current density and energy flux at infinity are studied based on the complex variable method of Muskhelishvili and conformal mapping technique.

Book
14 May 2017
TL;DR: In this paper, a FORTRAN code (Program SCAT 4) is described which was written in order to analyze elastic scattering of various particles against complex nuclei by means of the diffuse surface optical model of the nucleus.
Abstract: : A FORTRAN code (Program SCAT 4) is described which was written in order to analyze elastic scattering of various particles against complex nuclei by means of the diffuse surface optical model of the nucleus. Program SCAT 4 calculates in the center-of-mass system the differential elastic scattering cross sections the polarization and the total reaction cross section for particles of spin 0 or 1/2 having any mass, charge and (non-relativistic) energy scattered by spinless nuclei of any mass and charge for various sets of diffuse surface optical model parameters. The incident and target particles are assumed to interact through a two-body potential consisting of a complex nuclear potential which includes spin-orbit interaction and whose shape can be specified by input parameters. When the incident particle is charged, the two body potential contains, in addition, the coulomb potential between an incident point charge and an extended, constant charge density target. The calculations include numerical integrations of the radial Schroedinger equations for the effective partial waves. (Author)