Effect of chromatic aberration on atomic-resolved spherical aberration corrected STEM images

The effect of the chromatic aberration (_Cc)$(C_c)$ coefficient in a spherical aberration (_Cs)$(C_s)$- corrected electromagnetic lens on high-resolution high-angle annular dark field (HAADF) scanning transmission electron microscope (STEM) images is explored in detail. A new method for precise determination of the _Cc$C_c$ coefficient is demonstrated, requiring measurement of an atomic-resolution one-frame through-focal HAADF STEM image. This method is robust with respect to instrumental drift, sample thickness, all lens parameters except _Cc$C_c$, and experimental noise. It is also demonstrated that semi-quantitative structural analysis on the nanometer scale can be achieved by comparing experimental _Cs$C_s$- corrected HAADF STEM images with their corresponding simulated images when the effects of the _Cc$C_c$ coefficient and spatial incoherence are included.     

Energy-filtered transmission electron microscopy based on inner-shell ionization

We demonstrate that energy-filtered transmission electron microscopy (EFTEM) based on inner-shell ionization can contain atomic resolution information. We present a comparison between experimental data and simulation for the EFTEM image of the _N4,5${\mathrm{N}}_{4,5}$ edge (threshold energy 99 eV) of lanthanum in _LaB6${\mathrm{LaB}}_6$ in which direct interpretation of the location of the lanthanum columns is possible. Our first principles approach is based on calculating transition potentials for inelastic scattering. For our case study, the localization of the transition potentials is such that elastic contrast is only weakly preserved in the EFTEM image. This is not always the case, but we show how the approach based on calculating the elastic wave function and the transition potentials can provide insight about when direct interpretation may and may not be possible. In our test specimen, the direct interpretation fails for thicker specimens when the long tails of the transition potential from multiple adjacent sites leads to significant image features other than at the sites of the element of interest. We can thus anticipate instances where direct interpretation may be more reliable, such as looking for a single impurity in an otherwise well known sample.     

Stabilization of an inverted pendulum-cart system by fractional PI-state feedback

This paper deals with pole placement PI-state feedback controller design to control an integer order system. The fractional aspect of the control law is introduced by a dynamic state feedback as u(t)=_Kpx(t)+_KIIα(x(t))$u\left(t\right)=K_{p}x\left(t\right)+K_I{\mathfrak{I}}_{\alpha }\left(x\right(t\left)\right)$. The closed loop characteristic polynomial is thus fractional for which the roots are complex to calculate. The proposed method allows us to decompose this polynomial into a first order fractional polynomial and an integer order polynomial of order n−1$n-1$ (n being the order of the integer system). This new stabilization control algorithm is applied for an inverted pendulum-cart test-bed, and the effectiveness and robustness of the proposed control are examined by experiments.     

Image simulation of high resolution energy filtered TEM images

Inelastic image simulation software is presented, implementing the double channeling approximation which takes into account the combination of multiple elastic and single inelastic scattering in a crystal. The approach is described with a density matrix formalism. Two applications in high resolution energy filtered (EFTEM) transmission electron microscopy (TEM) images are presented: thickness-defocus maps for _SrTiO3${\mathrm{SrTiO}}_3$ and exit plane intensities for an (_LaAlO3)3(_SrTiO3)3$({\mathrm{LaAlO}}_3{)}_3({\mathrm{SrTiO}}_3{)}_3$ multilayer system. Both systems show a severe breakdown in direct interpretability which becomes worse for higher acceleration voltages, thicker samples and lower excitation edge energies. Since this effect already occurs in the exit plane intensity, it is a fundamental limit and image simulations in EFTEM are indispensable just as they are indispensable for elastic high resolution TEM images.     

Spin–charge separation and electron pairing instabilities in Hubbard nanoclusters

Electron charge and spin pairing instabilities in various cluster geometries for attractive and repulsive electrons are studied exactly under variation of interaction strength, electron doping and temperature. The exact diagonalization, level crossing degeneracies, spin–charge separation and separate condensation of paired electron charge and opposite spins yield intriguing insights into the origin of magnetism, ferroelectricity and superconductivity seen in inhomogeneous bulk nanomaterials and various phenomena in cold fermionic atoms in optical lattices. Phase diagrams resemble a number of inhomogeneous, coherent and incoherent nanoscale phases found recently in high-_Tc$T_c$ cuprates, manganites and multiferroic nanomaterials probed by scanning tunneling microscopy. Separate condensation of electron charge and spin degrees at various crossover temperatures offers a new route for superconductivity, different from the BCS scenario. The calculated phase diagrams resemble a number of inhomogeneous paired phases, superconductivity, ferromagnetism and ferroelectricity found in Nb and Co nanoparticles. The phase separation and electron pairing, monitored by electron doping and magnetic field surprisingly resemble incoherent electron pairing in the family of doped high-_Tc$T_c$ cuprates, ruthenocuprates, iron pnictides and spontaneous ferroelectricity in multiferroic materials.     

Exchange of angular momentum in EMCD experiments

In energy loss magnetic chiral dichroism (EMCD) experiments a chiral electronic transition is induced that obeys the dipole selection rule for the magnetic quantum number Δm=±1$\mathrm{\Delta }m=\pm 1$ or Δ_Lz=±?$\mathrm{\Delta }{L}_z=\pm ?$. The incident plane electron wave is inelastically scattered and is detected in the diffraction plane, i.e. again in a plane wave state. Naïve reasoning suggests that the angular momentum _Lz$L_z$ of the probe electron has not changed in the interaction since plane waves have 〈_Lz〉=0$〈L_z〉=0$. This leads to the seeming contradiction that angular momentum is not conserved in the interaction. A closer inspection shows that the density matrix of the probe has indeed 〈_Lz〉=±?$〈L_z〉=\pm ?$ after a chiral interaction. However, 〈_Lz〉$〈L_z〉$ is not conserved when the probe electron propagates further to the exit surface of the specimen because the rigid lattice breaks rotational symmetry. Thus, the angular momentum of the photo electron that is created in a chiral electronic transition stems from both the probing electron and the crystal lattice.     

Suppression of asymmetric flow behavior downstream of two side-by-side circular cylinders with a splitter plate in shallow water

The flow downstream of a pair of circular cylinder in a side-by-side arrangement normal to the free stream is known to exhibit intermittently bistable structure for the range of G/D = 1.2–2.2 where G is the center-to-center distance between the cylinders and D is the diameter of the cylinder. Eventually, the wake downstream of one of the two cylinders can be wider or narrower than the one downstream of the other cylinder depending on the direction of gap-flow deflection. In the present study, such an asymmetric flow behavior downstream of two side-by-side cylinders, which were vertically located in shallow water, was passively controlled with a splitter plate with a length of L   (1?L/D?5$1?L/D?5$). The center of splitter plate was just coincided with the mid-height of the gap between centers of the cylinders. The investigations were carried out in a water channel using dye visualization and particle image velocimetry, PIV for qualitative and quantitative measurements, respectively. The diameter of the cylinder, D was 40 mm while the depth of water was 20 mm so that the shallow flow condition was provided through the experiments. The Reynolds number, Re based on D was 5000 and the cylinder’s center to center spacing to the cylinder diameter ratio (G/D  ) was equal to 1.25. The results demonstrated that the deflection of the wake and thereby the bistability of the wake was considerably prevented with the presence of the splitter plate for L/D?3$L/D?3$ which resulted in two well symmetric, stable wakes having approximately the same order of magnitudes of vortex shedding frequencies around the cylinders.     

Finite-time H∞ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals

This paper is concerned with the problem of finite-time _H∞$H_{\infty }$ control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov–Krasovskii functional is constructed. Based on the derived condition, the reliable _H∞$H_{\infty }$ control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones.     

H∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays

The problem of _H∞$H_{\infty }$ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays is investigated in this paper. The transition probabilities under consideration are time-varying, i.e., Markovian chain is nonhomogeneous. By using the Lyapunov functional approach and reciprocally convex technique, a less conservative delay-dependent bounded real lemma is developed in terms of linear matrix inequalities. Moreover, a sufficient condition for the existence of the desired filter which guarantees the stochastic admissibility and the _H∞$H_{\infty }$ performance index of the resulting filtering error system is presented. Numerical examples are employed to show the usefulness of the proposed results.     

Novel intelligent real-time position tracking system using FPGA and fuzzy logic

The main aim of this paper is to test if FPGAs are able to achieve better position tracking performance than software-based soft real-time platforms. For comparison purposes, the same controller design was implemented in these architectures. A Multi-state Fuzzy Logic controller (FLC) was implemented both in a Xilinx^®${\mathrm{Xilinx}}^{\circledR }$ Virtex-II FPGA (XC2v1000) and in a soft real-time platform NI CompactRIO^®-9002${\mathrm{CompactRIO}}^{\circledR }\mathrm{-}9002$. The same sampling time was used. The comparative tests were conducted using a servo-pneumatic actuation system. Steady-state errors lower than 4 μm were reached for an arbitrary vertical positioning of a 6.2 kg mass when the controller was embedded into the FPGA platform. Performance gains up to 16 times in the steady-state error, up to 27 times in the overshoot and up to 19.5 times in the settling time were achieved by using the FPGA-based controller over the software-based FLC controller.     

Real space maps of magnetic moments on the atomic scale: Theory and feasibility

The recently discovered EMCD technique (energy loss magnetic chiral dichroism) can detect atom specific magnetic moments with nanometer resolution, exploiting the spin selectivity of electronic transitions in energy loss spectroscopy. Yet, direct imaging of magnetic moments on the atomic scale is not possible. In this paper we present an extension of EMCD that can overcome this limit. As a model system we chose bcc Fe. We present image simulations of the _L3${\mathrm{L}}_3$ white line signal, based on the kinetic equation for the density matrix of the 200 kV probe electron. With actual progress in instrumentation (high brightness sources, aberration corrected lenses) this technique should allow direct imaging of spin moments on the atomic scale.     

H∞ mode-dependent fault detection filter design for stochastic Markovian jump systems with time-varying delays and parameter uncertainties

This paper deals with the problem of robust _H∞$H_{\infty }$ fault detection for a class of stochastic Markovian jump systems (SMJSs) The aim is to design a linear mode-dependent fault detection filter such that the fault detection system is not only stochastically asymptotically stable in the large, but also satisfies a prescribed _H∞-norm$H_{\infty }\mathrm{-}\mathrm{norm}$ level for all admissible uncertainties. By using Lyapunov stability theory and generalized Itô formula, some novel mode-dependent and delay-dependent sufficient conditions in terms of linear matrix inequality (LMI) are proposed to insure the existence of the desired fault detection filter. A simulation example and an industrial nonisothermal continuous stirred tank reactor (CSTR) system are employed to show the effectiveness of the proposed method.     

Finite-time boundedness filtering for discrete-time Markovian jump system subject to partly unknown transition probabilities

This paper investigates the problem of finite-time boundedness filtering for discrete-time Markovian jump system subject partly unknown transition probabilities. By using the multiple Lyapunov function approach, a novel sufficient condition for finite-time bounded of _H∞$H_{\infty }$ filtering is derived and the system trajectory stays within a prescribed bound during a specified time interval. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method.     

A three-point electrical potential difference method for in situ monitoring of propagating mixed-mode cracks at high temperature

In this paper an electrical potential difference method for the real-time assessment of both the length and the direction of Mode II cracks is presented. Three measuring electrodes are placed in selected positions over the gauge area of a specially designed shear specimen and their readings are associated with the actual position of the crack tip using Finite Element Analysis (FEA). This information can be processed in real-time to provide continuous monitoring of the crack as it propagates either in pure Mode II (in-plane shear) or mixed Mode I (tension) and Mode II if the inclination of the crack exceeds 20°. In fatigue testing it is possible to produce dα/dN-Δ_KII$d\alpha /\mathit{dN}-\mathrm{\Delta }{K}_{\text{II}}$ (in pure-shear) and dα/dN-Δ_KI$d\alpha /\mathit{dN}-\mathrm{\Delta }{K}_{\text{I}}$ (in mixed-mode) plots on-line as the test is in execution. The method has been calibrated with optical measurements using a long-distance observation microscope on the nickel-based superalloy CMSX4 at high temperature. The main finding was that the central two sensing electrodes were sensitive to the length of the crack and insensitive to the crack angle, whereas the readings from the third electrode were sensitive to the crack angle and thus the exact position of the crack tip could be traced in real-time. Special techniques were implemented to rule-out thermoelectric effects and thermal stresses on the specimen.