Modeling of Formation of Nanostructured Metal Surfaces by Electrodeposition through a Monolayer Colloidal Crystal Mask

AbstractElectrochemical deposition is a feasible and well-controlled method for the formation of various micro- and nanostructures. A rich variety of periodical nanostructures of functional materials with multi-shaped and tunable morphologies can be fabricated by the electrochemical deposition, in particular, using monolayer colloidal crystal (MCC) mask. A mathematical model of the mass-transfer processes and deposit surface evolution during the metal electrodeposition through MCC mask is presented. The mathematical model involves the equations for the potential and deposit surface evolution. The problem was solved numerically by the boundary element method, and the “Level Set” method. The numerical experiments were used to study the effect of parameters, which characterize the mask geometry and the process conditions, on the initial distribution of current density over the deposit surface and the variation of current density distribution in the course of the deposition

Effect of Current Efficiency on Electrochemical Micromachining by Moving Electrode

AbstractIn this work, the effect of current efficiency on the electrochemical micromachining by moving electrode is studied theoretically. The Laplace equation for the electric potential and the equation of workpiece surface evolution are used as the mathematical model of the process. A new scheme of solution of free boundary problem for steady-state electrochemical micromachining is proposed. According to the scheme, the initial approximation of the workpiece surface is prescribed. In the course of modeling, the workpiece surface moves in the normal direction at a rate proportional to the discrepancy of the steady-state condition. The effect of various dependences of current efficiency on the local current density is analyzed. As a result of simulation, the dependences of the shape and sizes of machined surface on the current efficiency and the machining parameters are obtained

Effective Functional Form of Regge Trajectories

We present theoretical arguments and strong phenomenological evidence that hadronic Regge trajectories are essentially nonlinear and can be well approximated, for phenomenological purposes, by a specific square-root form.Comment: 29 pages, LaTeX. Published versio

Modeling of the Induced Resonant Torquesduring the Motionof an Asymmetric Spacecraft in the Atmosphere

В настоящей работе исследуется неуправляемое движение асимметричного космического аппарата в атмосфере. Предположим, что космический корабль - это твердое тело с малыми массово-инерционными и малыми аэродинамическими асимметриями. Целью исследования является изучение математических моделей малых механических моментов, наведённых главным резонансом в нерезонансных областях движения. В предлагаемом исследовании решаются следующие задачи: получены выражения для наведённого механического момента, определены величины областей действия данного момента. Автор приходит к выводу, что применение метода усреднения позволяет исследовать механический момент, наведённый резонансом. Данный момент способствует значительной эволюции угловой скорости вращения космического аппарата в нерезонансных областях, прилегающих к резонансу. This paper investigates an uncontrolledmotion of an asymmetric spacecraft in the atmosphere. Suppose that the spacecraft is a rigid body with small mass-inertial and small aerodynamic asymmetries. The aim of the research is to study of mathematical models of the small mechanical torques caused by the principal resonance. The proposed study solves the following problems: revealing specific features of the mechanical torque, determining the magnitude of a domain of activity of the torque. The author conclude that the application of the averaging method allow us to research the mechanical torque induced by the resonance. This torque results in a significant angular speed evolution of rotation of a spacecraft in the non-resonance areas adjacent to the resonance

Modeling of the Secondary Resonance Effects in the Spherical Motion of a Rigid Body with Flywheels

Методы асимптотического анализа применяются для исследования эволюция движения асимметричного твёрдого тела с маховиками. Показывается, что влияние малых моментов, возникающих в результате смещения центра масс и малых управляющих моментов от маховиков, приводит к возникновению нелинейных резонансных эволюционных эффектов. Целью этой работы является изучение резонансных эффектов в сферическом движении асимметричного твёрдого тела с маховиками. Применение метода интегральных многообразий и метода усреднения позволило исследовать указанные резонансные эффекты. Усреднённые уравнения показали, что резонансные эффекты могут приводить либо к регулярной прецессии, либо к длительному резонансу. The evolution of the motion of an asymmetric rigid body with flywheels can be explored by the methods of asymptotic analysis. It is shown, that the effect of small moments resulting from the displacement of the centre of mass and of small control moments from the flywheels lead to the emergence of non-linear resonance evolutionary effects. The aim of this work is to investigate the resonance effects in the spherical motion of the asymmetrical rigid body with flywheels. To explore these resonance effects we applied the method of integral manifolds and the averaging method. The averaged equations have shown that resonance effects may result in either regular precession or prolonged resonance