Skyhook surface sliding mode control on semi-active vehicle suspension systems for ride comfort enhancement

A skyhook surface sliding mode control method was proposed and applied to the control on the semi-active vehicle suspension system for its ride comfort enhancement. A two degree of freedom dynamic model of a vehicle semi-active suspension system was given, which focused on the passenger’s ride comfort perform-ance. A simulation with the given initial conditions has been devised in MATLAB/SIMULINK. The simula-tion results were showing that there was an enhanced level of ride comfort for the vehicle semi-active sus-pension system with the skyhook surface sliding mode controller

Painlev\'e V and time dependent Jacobi polynomials

In this paper we study the simplest deformation on a sequence of orthogonal polynomials, namely, replacing the original (or reference) weight $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ according to the Toda equations, giving rise to the time dependent orthogonal polynomials, using Sogo's terminology. The resulting "time-dependent" Jacobi polynomials satisfy a linear second order ode. We will show that the coefficients of this ode are intimately related to a particular Painlev\'e V. In addition, we show that the coefficient of $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ These results are found from combining a pair of non-linear difference equations and a pair of Toda equations. This will in turn allow us to show that a certain Fredholm determinant related to a class of Toeplitz plus Hankel operators has a connection to a Painlev\'e equation

Hybrid power semiconductor

The voltage rating of a bipolar transistor may be greatly extended while at the same time reducing its switching time by operating it in conjunction with FETs in a hybrid circuit. One FET is used to drive the bipolar transistor while the other FET is connected in series with the transistor and an inductive load. Both FETs are turned on or off by a single drive signal of load power, the second FET upon ceasing conductions, rendering one power electrode of the bipolar transistor open. Means are provided to dissipate currents which flow after the bipolar transistor is rendered nonconducting

Valid and efficient formula for free energy difference from nonequilibrium work

Atomic force microscopes and optical tweezers afford direct probe into the inner working of single biomolecules by mechanically unfolding them.^1-15^ Critical to the success of this type of probe is to correctly extract the free energy differences between the various conformations of a protein/nucleic acid along its forced unfolding pathways. Current studies rely on the Jarzynski equality^16^ (JE) or its undergirding Crooks fluctuation theorem^17^ (CFT), even though questions remain on its validity^17-19^ and on its accuracy.^13,20-21^ The validity of JE relies on the assumption of microscopic reversibility.^17,18^ The dynamics of biomolecules, however, is Langevin stochastic in nature. The frictional force in the Langevin equation breaks the time reversal symmetry and renders the dynamics microscopically irreversible even though detailed balance holds true. The inaccuracy of JE has largely been attributed to the fact that one cannot sample a large enough number of unfolding paths in a given study, experimental or computational.^13,15^ Here I show that both of these questions can be answered with a new equation relating the nonequilibrium work to the equilibrium free energy difference. The validity of this new equation requires detailed balance but not microscopic reversibility. Taking into the new equation equal number of unfolding and refolding paths, the accuracy is enhanced ten folds in comparison to a JE study based on a similar but larger number of unfolding paths