Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions

The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.

Analysis and control for a new reconfigurable parallel mechanism

This article proposes a new reconfigurable parallel mechanism using a spatial overconstrained platform. This proposed mechanism can be used as a machine tool. The mobility is analyzed by Screw Theory. The inverse kinematic model is established by applying the closed-loop equation. Next, the dynamic model of the presented mechanism is established by Lagrange formulation. To control the presented mechanism, some controllers have been used. Based on this dynamic model, the fuzzy-proportion integration differentiation (PID) controller is designed to track the trajectory of the end effector. For each limb, a sliding mode controller is applied to track the position and velocity of the slider. Finally, some simulations using ADAMS and MATLAB are proposed to verify the effectiveness and stability of these controllers.

Kinematic analysis of a novel 2-PrRS-PR(P)S metamorphic parallel mechanism

Lower mobility parallel mechanisms have been developed in different structures and widely applied in industry, but still have disadvantages in various tasks and functional requirements. A 2-PrRS-PR(P)S metamorphic parallel mechanism with two working configurations and a transiting configuration is presented. First, the architecture and the way of metamorphosis about the mechanism are described in detail. The mobility of the metamorphic parallel mechanism is obtained with screw theory. Furthermore, the parasitic motions in different configurations are derived based on the geometry constraint conditions. Both the inverse kinematic problem and forward kinematic problem of the mechanism are investigated by the closed-loop equation and validated via numerical examples. Then, the velocity and acceleration in two working configurations are obtained by the derivation of the inverse kinematic problem. Finally, the reachable orientation workspaces are discussed using the three-dimensional search method in different configurations. A comparison with the 3-PRS PM without metamorphic mechanism in workspace is presented and an example of the metamorphic parallel mechanism in robotic supporting leg is presented. The above analyses provide theoretical foundations for application of this mechanism.

A New Analysis Way of Three-Phase Switched Capacitor Converter

The paper presents the theoretical analysis way of the switched capacitor converter (SCC). The main goal of this research is to suggest the analysis way of three-phase SCC. A common SCC operates by two phases; charging phase and discharging phase. Therefore, state-space averaging model or slow and fast switching limit (S-FSL) model has been suitable. Although the four-terminal equivalent model can cover all situation including three-phases cases, this model does not include the parameter of frequency and capacitance. Therefore, the four-terminal model has a weakness. In this situation, we selected the Fibonacci sequence SCC operated by three-phase as the target circuit, which topology has been proved to have higher efficiency, small size in the previous research. In the paper, we suggest the new analysis way of the three-phase SCC by combination of the four-terminal equivalent model and RC circuit model from each loop equation of the equivalent circuits of the SCC. By using the suggested way, it is possible to analyze the three-phase SCC, deriving the effect of the load, operation frequency and duty ratio variation. In order to verify the feasibility and the cogency of the suggested analysis way, comparative analysis is implemented by SPICE simulations. The error in the load regulation between the suggested way and the simulation result is negligible. Through this result, we establish the foundation of the analysis of the three-phase SCC.

Algebraic geometry and matrix models

This article discusses the connection between the matrix models and algebraic geometry. In particular, it considers three specific applications of matrix models to algebraic geometry, namely: the Kontsevich matrix model that describes intersection indices on moduli spaces of curves with marked points; the Hermitian matrix model free energy at the leading expansion order as the prepotential of the Seiberg-Witten-Whitham-Krichever hierarchy; and the other orders of free energy and resolvent expansions as symplectic invariants and possibly amplitudes of open/closed strings. The article first describes the moduli space of algebraic curves and its parameterization via the Jenkins-Strebel differentials before analysing the relation between the so-called formal matrix models (solutions of the loop equation) and algebraic hierarchies of Dijkgraaf-Witten-Whitham-Krichever type. It also presents the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations, along with higher expansion terms and symplectic invariants.

Loop equation in Lattice gauge theories and bootstrap methods

In principle the loop equation provides a complete formulation of a gauge theory purely in terms ofWilson loops. In the case of lattice gauge theories the loop equation is a well defined equation for a discrete set of quantities and can be easily solved at strong coupling either numerically or by series expansion. At weak coupling, however, we argue that the equations are not well defined unless a certain set of positivity constraints is imposed. Using semi-definite programming we show numerically that, for a pure Yang Mills theory in two, three and four dimensions, these constraints lead to good results for the mean value of the energy at weak coupling. Further, the positivity constraints imply the existence of a positive definite matrix whose entries are expectation values of Wilson loops. This matrix allows us to define a certain entropy associated with theWilson loops. We compute this entropy numerically and describe some of its properties. Finally we discuss some preliminary ideas for extending the results to supersymmetric N = 4 SYM.

An explanation for the phase lag in supersonic jet impingement

For the first time, a physical mechanism is identified to explain the phase lag term in Powell’s impinging feedback loop equation (Powell, J. Acoust. Soc. Am., vol. 83 (2), 1988, pp. 515–533). Ultra-high-speed schlieren reveals a previously unseen periodic transient shock in the wall jet region of underexpanded impinging flows. The motion of this shock appears to be responsible for the production of the acoustic waves corresponding to the impingement tone. It is suggested that the delay between the inception of the shock and the formation of the acoustic wave explains the phase lag in the aeroacoustic feedback process. This suggestion is quantitatively supported through an assessment of Powell’s feedback equation, using high-resolution particle image velocimetry and acoustic measurements.