Design Templates for Some Fractional Order Control Systems

Time domain characteristics of first and second order systems are well known. But the same simplicity and explicitness do not exist for low order fractional order systems (FOSs). Considering the step response, the templates are developed for designing the behavior of simple FOSs with a 2-term denominator polynomial (one is unity and the other involves fractional power). Although the explicit relations between design parameters and the performance parameters such as time constant, rise time, overshoot, settling time for fractional order control systems (FOCSs) do not exist and can't be obtainable as in the ordinary integer order control systems, the obtained templates in this paper can be used for designing low order FOCSs. Hence, the drawback of non-existence of similar explicit formulas for FOCSs is eliminated by using these templates

Comparison of Step Response Characteristics of Simple Fractional Order Systems and Second Order Systems

The step response characteristics of first and second order systems are well known. On the other hand, the step response of fractional order systems (FOSs) with 2-term fractional denominator is like those of first and second order systems. But there are important differences between the two types of characteristics. Considering the step response, the behavior of simple FOS with a denominator polynomial having unity term and the other involves fractional power is investigated in this paper comparatively with 1st and 2nd order systems. The results bring light for the design of fractional order control systems (FOCSs)

Dynamics in near-potential games

We consider discrete-time learning dynamics in finite strategic form games, and show that games that are close to a potential game inherit many of the dynamical properties of potential games. We first study the evolution of the sequence of pure strategy profiles under better/best response dynamics. We show that this sequence converges to a (pure) approximate equilibrium set whose size is a function of the “distance” to a given nearby potential game. We then focus on logit response dynamics, and provide a characterization of the limiting outcome in terms of the distance of the game to a given potential game and the corresponding potential function. Finally, we turn attention to fictitious play, and establish that in near-potential games the sequence of empirical frequencies of player actions converges to a neighborhood of (mixed) equilibria, where the size of the neighborhood increases according to the distance to the set of potential games

Interference of axially-shifted Laguerre–Gaussian beams and their interaction with atoms

Counter-propagating co-axial Laguerre–Gaussian (LG) beams are considered, not in the familiar scenario where the focal planes coincide at z = 0, but when they are separated by a finite axial distance d. The simplest case is where both beams are doughnut beams which have the same linear polarisation. The total fields of this system are shown to display novel amplitude and phase distributions and are shown to give rise to a ring or a finite ring lattice composed of double rings and single central ring. When the beams have slightly different frequencies the ring lattice pattern becomes a finite set of rotating Ferris wheels and the whole pattern also moves axially between the focal planes. We show that the fields of such an axially shifted pair of counter-propagating LG beams generate trapping potentials due to the dipole force which can trap two-level atoms in the components of the ring lattice. We also highlight a unique feature of this system which involves the creation of a new longitudinal optical atom trapping potential due to the scattering force which arises solely when $d\ne 0$. The results are illustrated using realistic parameters which also confirm the importance of the Gouy and curvature effects in determining the ring separation both radially and axially and gives rise to the possibility of atom tunnelling between components of the double rings

Determination of volatile compounds of the first rose oil and the first rose water by HS-SPME/GC/MS techniques

Background: Rose water and rose oil are used in the perfume, cosmetic, pharmaceutical and food industries. The determination of volatile compounds in rose oil and rose water obtained from oil-bearing rose is highly important in terms of availability in the industry and in human health.Materials and Methods: Twenty four and twenty six volatile compounds were determined in the first rose oil and in the first rose water. Thus, in this study, volatile compounds in the first rose oil and first rose water have been determined by HS-SPME/GC/MS (Headspace-Solid Phase Micro Extraction/Gas Chromatography Mass Spectrometry) techniques which were not published previously for determining volatile compounds in rose oil and rose water.Results: Twenty four and twenty six volatile compounds were found in the first rose oil and in the first rose water, respectively. It was further discovered that both first rose oil and first rose water are rich in oxygenated monoterpenes and sesquiterpenes, with a third group of volatile compounds known as aliphatic hydrocarbons being found only in first rose oil. Citronellol contents of the first rose oil and rose water were found to be 43.40% and 40.13% respectively, whereas geraniol contents were 11.81% and 15.97%, respectively.Conclusion: These findings suggest that HS-SPME/GC/MS is a suitable technique for the determination of volatile compounds of rose oil and rose water.Keywords: Oil-bearing rose, Rosa damascena, HS-SPME/GC/MS, volatile compounds

Microeconomic Origins of Macroeconomic Tail Risks

Using a multisector general equilibrium model, we show that the interplay of idiosyncratic microeconomic shocks and sectoral heterogeneity results in systematic departures in the likelihood of large economic downturns relative to what is implied by the normal distribution. Such departures can emerge even though GDP fluctuations are approximately normally distributed away from the tails, highlighting the different nature of large economic downturns from regular business-cycle fluctuations. We further demonstrate the special role of input-output linkages in generating tail comovements, whereby large recessions involve not only significant GDP contractions, but also large simultaneous declines across a wide range of industries