Towards a More General Type of Univariate Constrained Interpolation With Fractal Splines

Recently, in [Electronic Transaction on Numerical Analysis, 41 (2014), pp. 420-442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic splines and investigated their basic shape preserving properties. The main goal of the current article is to embark on univariate constrained fractal interpolation that is more general than what was considered so far. To this end, we propose some strategies for selecting the parameters of the rational fractal spline so that the interpolating curves lie strictly above or below a prescribed linear or a quadratic spline function. Approximation property of the proposed rational cubic fractal spine is broached by using the Peano kernel theorem as an interlude. The paper also provides an illustration of background theory, veined by examples.Comment: 7 pages, 6 figure

On the shape and orientation control of an orbiting shallow spherical shell structure

The dynamics of orbiting shallow flexible spherical shell structures under the influence of control actuators was studied. Control laws are developed to provide both attitude and shape control of the structure. The elastic modal frequencies for the fundamental and lower modes are closely grouped due to the effect of the shell curvature. The shell is gravity stabilized by a spring loaded dumbbell type damper attached at its apex. Control laws are developed based on the pole clustering techniques. Savings in fuel consumption can be realized by using the hybrid shell dumbbell system together with point actuators. It is indicated that instability may result by not including the orbital and first order gravity gradient effects in the plant prior to control law design

The dynamics and control of large flexible space structures, 2. Part A: Shape and orientation control using point actuators

The equations of planar motion for a flexible beam in orbit which includes the effects of gravity gradient torques and control torques from point actuators located along the beam was developed. Two classes of theorems are applied to the linearized form of these equations to establish necessary conditions for controlability for preselected actuator configurations. The feedback gains are selected: (1) based on the decoupling of the original coordinates and to obtain proper damping, and (2) by applying the linear regulator problem to the individual model coordinates separately. The linear control laws obtained using both techniques were evaluated by numerical integration of the nonlinear system equations. Numerical examples considering pitch and various number of modes with different combination of actuator numbers and locations are presented. The independent model control concept used earlier with a discretized model of the thin beam in orbit was reviewed for the case where the number of actuators is less than the number of modes. Results indicate that although the system is controllable it is not stable about the nominal (local vertical) orientation when the control is based on modal decoupling. An alternate control law not based on modal decoupling ensures stability of all the modes

Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators

Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply connected death islands in the parameter space of the coupling strength and the time delay parameter for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds in [Phys. Rev. Lett. 80, 5109 (1998); Physica 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay and the onset of both in-phase and anti-phase collective oscillations.Comment: 4 aps formatted RevTeX pages; 6 figures; to appear in Phys. Rev. Let

On the Validity and Applicability of Models of Negative Capacitance and Implications for MOS Applications

The observation of room temperature sub-60 mV/dec subthreshold slope (SS) in MOSFETs with ferroelectric (FE) layers in the gate stacks or in series with the gate has attracted much attention. Recently, we modeled this effect in the framework of a FE polarization switching model. However, there is a large amount of literature attributing this effect to a stabilization of quasi-static (QS) negative capacitance (NC) in the FE. The technological implications of a stabilized non-switching (NS) QSNC model vs a FE switching model are vastly different; the latter precluding applications to sub-60 mV/dec SS scaled CMOS due to speed limitations and power dissipated in switching. In this letter, we provide a thorough analysis assessing the foundations of models of QSNC, identifying which specific assumptions (ansatz) may be unlikely or unphysical, and analyzing their applicability. We show that it is not reasonable to expect QSNC for two separate capacitors connected in series (with a metal plate between dielectric (DE) and FE layers). We propose a model clarifying under which conditions a QS "apparent NC" for a FE layer in a FE-DE bi-layer stack may be observed, quantifying the requirements of strong interface polarization coupling in addition to capacitance matching. In this regime, our model suggests the FE layer does not behave as a NC layer, simply, the coupling leads to both the DE and FE behaving as high-k DE with similar permittivities. This may be useful for scaled EOT devices but does not lead to sub-60 mV/dec SS.Comment: Version published in Appl. Phys. Let

Double-heralded generation of two-photon-states by spontaneous four-wave-mixing in the presence of noise

We present an experimental method for creating and verifying photon-number states created by non-degenerate, third-order nonlinear-optical photon-pair sources. By using spatially multiplexed, thresholding single-photon detectors and inverting a conditional probability matrix, we determine the photon-number probabilities created through heralded spontaneous four-wave-mixing. The deleterious effects of noise photons on reliable heralding are investigated and shown to degrade the conditional preparation of two-photon number states more than they degrade conditional single-photon states. We derive the equivalence between the presence of unwanted noise in the herald channel and loss in the signal channel of heralded experiments. A procedure for characterizing the noise-photon contributions, and a means of estimating the herald noise-free photon-number distribution is demonstrated.Comment: 13 pages, 7 figures. Submitted to Optics Express on 1 February, 201

The dynamics and control of large flexible space structures, part 11

A mathematical model is developed to predict the dynamics of the proposed Spacecraft Control Laboratory Experiment during the stationkeeping phase. The Shuttle and reflector are assumed to be rigid, while the mass connecting the Shuttle to the reflector is assumed to be flexible with elastic deformations small as compared with its length. It is seen that in the presence of gravity-gradient torques, the system assumes a new equilibrium position primarily due to the offset in the mass attachment point to the reflector from the reflector's mass center. Control is assumed to be provided through the Shuttle's three torquers and throught six actuators located by painrs at two points on the mass and at the reflector mass center. Numerical results confirm the robustness of an LQR derived control strategy during stationkeeping with maximum control efforts significantly below saturation levels. The linear regulator theory is also used to derive control laws for the linearized model of the rigidized SCOLE configuration where the mast flexibility is not included. It is seen that this same type of control strategy can be applied for the rapid single axis slewing of the SCOLE through amplitudes as large as 20 degrees. These results provide a definite trade-off between the slightly larger slewing times with the considerable reduction in over-all control effort as compared with the results of the two point boundary value problem application of Pontryagin's Maximum Principle

Controllability of inherently damped large flexible space structures

Graph theoretic techniques are used to study controllability of linear systems which represent large flexible orbiting space systems with inherent damping. The controllability of the pair of matrices representing the system state and control influence matrices is assured when all states in the model are reachable in a digraph sense from at least one input and also when the term rank of a Boolean matrix whose non trivial components are based on the state and control influence matrices has a term rank of the order of the state vector. The damping matrix does not influence the required number of actuators but gives flexibility to the possibility locations of the actuators for which the system is controllable