I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG explanations: linearization* property; I (...) then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not provide (...) a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

A hydraulic actuator is a system that can provide a large power amplification in industries and factories. In this paper, mass lifter hydraulic actuator system to a desired displacement is designed using optimal control theory. MPC and LQR controllers are used to design and improve the performance of the hydraulic actuator. The hydraulic actuator system is linearized using Taylor series linearization method and designed using Matlab/Simulink tool. Comparison of the hydraulic actuator with MPC and LQR controllers using three desired output (...) displacement signals (step, sine wave and white noise) is done and simulation results have been analyzed successfully. For the desired step input signal, the hydraulic actuator system with MPC controller lower rise and settling times with small percentage overshoot as compared to the hydraulic actuator system with LQR controller and for the desired sine wave signal, the hydraulic actuator system with MPC controller almost track the desired sine wave input signal correctly as compared to the hydraulic actuator system with LQR controller. While for the desired white noise input signal, the hydraulic actuator system with MPC controller have tried to track the desired white noise input signal with small variation in amplitude as compared to the hydraulic actuator system with LQR controller. Finally the comparative simulation results prove the effectiveness of the proposed hydraulic actuator system with MPC controller. (shrink)