Non-zero State Research Articles

Synthesizing scheduled robust model predictive control with target tracking

Systems with large operating regions and non-zero state target tracking have limited the industrial application of robust model predictive control (RMPC) with synthetic action. To overcome the problem, this paper presents a novel formulation of synthesizing scheduled RMPC for linear time varying (LTV) systems. Off-line, we compute the matrix that transforms target output into steady state first. Then a set of stabilizing state feedback laws which are corresponding to a set of estimated regions of stability covering the desired operating region are provided. On-line, these control laws are implemented as a single scheduled state feedback model predictive control (MPC) which switches between the set of local controllers and achieve the desired target at last. Finally, the algorithm is illustrated with an example.

Tubular image states: General formulation and properties for metallic and nonmetallic nanotubes

In this work we study the existence of image potential states around nanotubes by considering the interaction between a stationary charged particle and a polarizable cylinder of infinite length. For metallic nanotubes and wires we obtain the eigenstates and eigenenergies corresponding to nonzero angular momentum states, localized at a relatively long distance from the surface of the tube. We study the scaling properties of the system in order to define general conditions for which image states can be supported. We also analyze the case of nonmetallic carbon nanotubes, for which we do not obtain bound states.

On the Observability of Continuous-Time Switched Linear Systems Under Partially Unknown Inputs

This technical note addresses the problem of observability of continuous-time Switched Linear Systems (SLS) subject to unknown disturbances, unknown switching signals and unconstrained nonzero dwell time. For this class of hybrid systems, a geometric characterization of the observability properties is presented. In particular, attention is focused on the estimation of the SLS state from the continuous measurements. Using the well known concept of (A, B)-invariant subspaces, three main problems are addressed and solved, namely the observability for every nonzero state trajectory, the observability for almost every control input, and the observability for almost every state trajectory. It is also shown that the approach herein presented subsumes some of the classical results on observability of SLS previously reported in the literature, and allows expressing them in a common framework.

On the Effect of Switching, Predation and Harvesting on Systems Consisting of One Predator and Two Prey Species Which Live in Different Habitats

The present work deals with two prey species living in two habitats and a predator specie which attacks the most abundant prey specie. The harvesting of both prey species is taken into account in the analysis. Non-zero equilibrium states have been examined with regard to their stability and the conditions for stability have been obtained. Using as a bifurcation parameter the conversion rate of prey to predator, conditions for a bifurcation to occur are obtained. A Hopf bifurcation theorem has been derived. In the investigations we used six forms of predation and harvesting rates to analyze the theory, however, we display graphical results foronly one particular case.

A new dodecanuclear manganese single-molecule magnet from the arrangement of manganese triangles

Bridging-azido ligands are used to create a new dodecanuclear manganese cluster [Mn12O4(salox)12(N3)4(MeOH)6(H2O)2]·5MeOH·2H2O (1·5MeOH·2H2O) from the arrangement of manganese triangles, [Mn3O]. Single-crystal x-ray analysis shows that 1·5MeOH·2H2O contains a [MnIII12(μ3-O)4(μ2-N3)4]24+ core, constructed from four [MnIII3O]7+ building units, which is a new structural type in the family of Mn12 complexes. Variable temperature magnetic susceptibility and magnetization measurements of the complex 1·5MeOH·2H2O were carried out. The magnetic data indicate that complex 1·5MeOH·2H2O exhibits antiferromagnetic with a non-zero ground state spin value of S = 4. The frequency dependence of out-of-phase component in alternating current magnetic susceptibility and magnetic hysteresis loop measurements indicate that complex 1·5MeOH·2H2O is a new single-molecule magnet with a significant magnetoanisotropy of Ueff = 70 K.

Microwave readout scheme for a Josephson phase qubit

We present experimental results on a microwave scheme for reading out a Josephson phase qubit. A capacitively shunted superconducting quantum interference device (SQUID) is used as a nonlinear resonator which is inductively coupled to the qubit. The flux state of the qubit is detected by measuring the amplitude and phase of a microwave pulse reflected from the SQUID resonator. By this low-dissipative method, the qubit state measurement time is reduced to 25 μs, which is much faster than the conventional readout performed by switching the SQUID to its nonzero dc voltage state. The readout scheme presented here allows for reading out multiple qubits using a single microwave line by employing frequency-division multiplexing.

A novel method combining cellular neural networks and the coupled nonlinear oscillators’ paradigm involving a related bifurcation analysis for robust image contrast enhancement in dynamically changing difficult visual environments

It is well known that a machine vision-based analysis of a dynamic scene, for example in the context of advanced driver assistance systems (ADAS), does require real-time processing capabilities. Therefore, the system used must be capable of performing both robust and ultrafast analyses. Machine vision in ADAS must fulfil the above requirements when dealing with a dynamically changing visual context (i.e. driving in darkness or in a foggy environment, etc). Among the various challenges related to the analysis of a dynamic scene, this paper focuses on contrast enhancement, which is a well-known basic operation to improve the visual quality of an image (dynamic or static) suffering from poor illumination. The key objective is to develop a systematic and fundamental concept for image contrast enhancement that should be robust despite a dynamic environment and that should fulfil the real-time constraints by ensuring an ultrafast analysis. It is demonstrated that the new approach developed in this paper is capable of fulfilling the expected requirements. The proposed approach combines the good features of the ‘coupled oscillators’-based signal processing paradigm with the good features of the ‘cellular neural network (CNN)’-based one. The first paradigm in this combination is the ‘master system’ and consists of a set of coupled nonlinear ordinary differential equations (ODEs) that are (a) the so-called ‘van der Pol oscillator’ and (b) the so-called ‘Duffing oscillator’. It is then implemented or realized on top of a ‘slave system’ platform consisting of a CNN-processors platform. An offline bifurcation analysis is used to find out, a priori, the windows of parameter settings in which the coupled oscillator system exhibits the best and most appropriate behaviours of interest for an optimal resulting image processing quality. In the frame of the extensive bifurcation analysis carried out, analytical formulae have been derived, which are capable of determining the various states of the system (e.g. quenching state, non-zero equilibrium state, oscillatory states, etc). Both equilibrium and oscillatory states of the system have been depicted. It could be shown that each of these states has a significant impact on the quality of the resulting image contrast enhancement. A benchmark has been considered, whereby a comparison is performed between the results’ quality obtained by traditional CNN-based processing, on the one hand, with those obtained by ‘coupled nonlinear oscillators’-based processing, on the other hand. Thus, the superiority of the latter approach in terms of ensuring a constantly high enhancement quality despite luminosity-related spatio-temporal scene dynamics has been demonstrated both analytically/conceptually and through various experiments. A key drawback of the latter approach is, however, the potentially huge and challenging computing effort necessary for solving the coupled nonlinear and highly stiff ODEs when one attempts to solve them numerically on ‘von Neumann’-type computing platforms; this is evidently difficult to realize in real time for frame rates necessary in ADAS. On the other side, a major drawback of the traditional CNN-based image processing is the practical inability to adjust/recalculate templates in real time in the face of a dynamic scene, that is, in the presence of input images experiencing visibility- and/or lighting-related spatio-temporal dynamics. Nevertheless, CNN has the great advantage of ensuring ultrafast processing due to its inherent parallel processing and ‘analogue computing’ nature. Thus, the two approaches appear to complement each other very well. Therefore, the novel hybrid approach does integrate both schemes in an efficient way, that is ‘coupled nonlinear oscillators’-based image processing is the main processing scheme that is realized on top of a CNN-processors framework. The hybrid approach does evidently overcome the mentioned key practical problems faced by both the original approaches.

A delay model for viral infection in toxin producing phytoplankton and zooplankton system

An eco-epidemiological delay model is proposed and analysed for virally infected, toxin producing phytoplankton (TPP) and zooplankton system. It is shown that time delay can destabilize the otherwise stable non-zero equilibrium state. The coexistence of all species is possible through periodic solutions due to Hopf bifurcation. In the absence of infection the delay model may have a complex dynamical behavior which can be controlled by infection. Numerical simulation suggests that the proposed model displays a wide range of dynamical behaviors. Different parameters are identified that are responsible for chaos.

Hydrothermal syntheses, crystal structures and physicochemical properties of 2-D and 3-D inorganic coordination cobalt(ii)-sulfite polymers

The hydrothermal reaction of [Co(III)(NH(3))(6)]Cl(3) with Na(2)SO(3) yields, depending on the concentration of Na(2)SO(3), compounds {Na[Co(II)(2)(SO(3))(2)(mu(3)-OH)(H(2)O)]}(infinity) (1) and {Na(4)[Co(II)(2)(SO(3))(4)]}(infinity) (2). When (NH(4))(2)SO(3) x H(2)O was substituted for Na(2)SO(3), the trinuclear mixed valence cobalt(II/III) complex (NH(4))(4){Co(II)[Co(III)(SO(3))(3)(NH(3))(3)](2)} x 2H(2)O (3 x 2H(2)O) was isolated. The cobalt-sulfites 1-3 x 2H(2)O were structurally characterized. In 1, the 1-D chains along the a-axis of the subunit [Co(II)(2)Co(II)(3)(OH)(2)(SO(3))(2)] are cross-linked with Co(II)(1) atoms via Co-O(sulfite) and Co-O(hydroxide) bonds in 2-D sheets, that are further stacked through interlayer hydrogen bonds. In 2, the [Co(II)(2)(SO(3))(2)](infinity) chains along the b-axis are cross-linked with tetrahedral cobalts via Co(II)-O(sulfite) bonds in 2-D sheets parallel to the ab-plane and the sheets are further bound to sodium atoms via Na(+)-O(sulfite) bonds to form a 3-D structure. The 3-D inorganic coordination polymer, 2, crystallizes in the non-centrosymmetric space group P2(1)2(1)2(1). In addition, in compound 2 octahedral and tetrahedral cobalt atoms coexist, which is rather unusual for cobalt clusters. Compound 3 x 2H(2)O is a 0-D mixed-valence {[(NH(3))(3)Co(III)(mu-SO(3))(3)]Co(II)[(mu-SO(3))(3)Co(III)(NH(3))(3)]}(4-) trinuclear cluster and can be considered as an octahedral {Co(II)O(6)} complex ligated to two tridentate [(NH(3))(3)Co(III)(SO(3))(3)](3-) ligands. The trinuclear clusters are stacked through an extended network of hydrogen bonding into a 3-D structure. Variable temperature magnetic susceptibility studies for 1-3 x 2H(2)O revealed that 1 and 2 are 2-D magnetic systems with strong antiferromagnetic interaction between the Co(II) atoms leading to an S = 0 ground state for 1, while in compound 2 there is an almost zero interaction between the cobalt(II) atoms leading to a non-zero ground state. The trinuclear compound 3 x 2H(2)O has two diamagnetic Co(III) atoms and a high-spin Co(II) atom with D = 84(1) cm(-1), E = 6(1) cm(-1) and g = 2.56(1). The IR, the solid-state UV-vis spectra and the thermogravimetric analyses of compounds 1-3 x 2H(2)O are also reported.

UNUSUAL QUANTUM HALL EFFECTS, INDEX THEOREM AND SUPERSYMMETRY IN GRAPHENE

We exploit an index theorem and a high degree of symmetry to understand unusual quantum Hall effects of the n = 0 Landau level in graphene. The high symmetry such as the pseudospin symmetry of Fermi points in a graphene sheet cannot couple to an external magnetic field. In the absence of the magnetic field, the index theorem provides a relation between the zero-energy state of the graphene sheet and the topological deformation of the compact lattice. Under the topological deformation, the zero-energy state emerges naturally without the Zeeman splitting at the Fermi points in the graphene sheet. This results in the fact that the pseudospin is an exact symmetry. In the case of nonzero energy, the up-spin and down-spin states have the exact high symmetry of spin, forming the pseudospin singlet pairing. We describe the peculiar and unconventional quantum Hall effects of the n = 0 Landau level in graphene on the basis of the index theorem and the high degree of symmetry.

Suzuki reaction catalysed by a PC sp3P pincer Pd(II) complex: Evidence for a mechanism involving molecular species

{ Cis-1,3-bis[(di- tert-butylphosphino)methyl]cyclohexyl}palladium(II)trifluoroacetate ( 1) acts as a precatalyst for the Suzuki reaction of aryl halides with phenylboronic acid in the absence or presence of mercury to give the product in modest to reasonably good yields. The reaction was monitored by 31P- and 1H NMR spectroscopy in a stepwise fashion, concluding that complex 1 reacts with activated boronic acids in the first reaction step to yield the corresponding phenyl complex 2. Complex 2 thereafter generates the Suzuki cross-coupling product upon addition of aryl halide. This shows that (PCP)Pd complexes, in addition to the previously demonstrated Pd(0)/Pd(II) mechanism, can mediate cross-coupling reactions using molecular species in a non-zero oxidation state.

Structural effects on the spin-state transition in epitaxially strainedLaCoO3films

Using density-functional theory within the $\text{LSDA}+U$ method, we investigate the effect of strain on the spin state and magnetic ordering in perovskite lanthanum cobaltite, ${\text{LaCoO}}_{3}$. We show that, while strain-induced changes in lattice parameters are insufficient to stabilize a nonzero spin state, additional heteroepitaxial symmetry constraints---in particular the suppression of octahedral rotations---stabilize a ferromagnetic intermediate-spin state. By comparing with experimental data for the bulk material, we calculate an upper bound on the Hubbard $U$ value, and describe the role that the on-site Coulomb interaction plays in determining the spin-state configuration.

Tetra- and Binuclear Complexes of Hydroxy-Rich Ligands: Supramolecular Structures, Stabilization of Unusual Water Clusters, and Magnetic Properties

Three tetranuclear complexes [Cu4(H2L1)4]·10H2O (1), [Ni4(H2O)3(H2L1)3(OH)]NO3·6H2O (2) and [Zn4(H2L1)4]·2MeOH·2H2O (3) and two binuclear complexes [Cu2(H3L1)2(NO3)2] (4) and [Cu2(H3L2)2Cl2](ClO4)2·2H2O (5) have been synthesized from two potentially pentadentate hydroxyl-rich ligands H4L1 and H3L2 (H4L1 = tris(hydroxymethyl)(2-hydroxybenzylamino)methane, and H3L2 = tris(hydroxymethyl)(2-pyridylamino) methane). X-ray analyses reveal that complexes 1, 2, and 3 have cubane core structures. For 1, ten lattice water molecules are linked by twelve hydrogen bonds, forming an extremely unusual adamantanoid (H2O)10 cluster, which is linked to two tetranuclear moieties by octadruple hydrogen bonds. For 2, four water dimers are bridged by two nitrates, giving a [(H2O)8(NO3)2]2- cluster. 4 has a bis(μ2-phenoxo)-bridged dicopper(II) structure with the binuclear species linked by multiple hydrogen bonds, affording a ladder-like structure. 5 has a bis(μ2-Cl)-bridged dicopper(II) structure with the binuclear moieties linked by π−π interactions and hydrogen bonds, affording a 2D network. In these complexes, the hydroxyl-rich ligands coordinate in dianionic, monoanionic or neutral forms, with one of the alkoxyl groups of each ligand left noncoordinated and open for intermolecular interactions, resulting in the stabilization of various water clusters and the formation of various supramolecular assemblies. Magnetic measurements reveal that, for 1 and 2, antiferromagnetic and ferromagnetic couplings coexist, thus resulting in interesting nonzero spin ground state. The ferromagnetic behavior of 1 can be ascribed to the nearly perpendicular arrangement of dx2−y2 magnetic orbitals of Cu(II) centers with the dihedral angle of 84.06(3)° between the Cu(II) equatorial planes. 4 shows a strong antiferromagnetic interaction. On the other hand, 5 shows a ferromagnetic interaction between copper(II) centers. Magneto-structural correlations have been discussed.

Challenges in lin-log modelling of glycolysis in Lactococcus lactis

The performance of the lin-log method for modelling the glycolytic pathway in Lactococcus lactis using in vivo time-series data is investigated. The network structure of this pathway has been studied in previous reports and the authors concentrate here on the challenge of fitting the lin-log model parameters to experimental data. To calibrate the estimation methods, the performance of the lin-log method on a simpler model of a small gene regulatory system was first investigated, which has become a benchmark in the field. Two families of optimisation algorithms were employed. One computes the objective function by solving a system of ordinary differential equations (ODEs), whereas the other discretises the ODEs and incorporates them as nonlinear equality constraints in the optimisation problem. Gradient-based, simplex-based and stochastic search algorithms were used to solve the former, whereas only a gradient-based algorithm was used to solve the latter. Although the estimation methods succeeded in determining the parameter values for the small gene network model, they did not yield a satisfactory lin-log model for the glycolytic pathway. The main reasons are apparently that several system variables approach low, and ultimately zero concentrations, which are intrinsically problematic for lin-log models, and that this pathway does not offer a natural non-zero reference state. [Includes supplementary material.].

State Preparation and Dynamics of Ultracold Atoms in Higher Lattice Orbitals

We report on the realization of a multiorbital system with ultracold atoms in the excited bands of a 3D optical lattice by selectively controlling the band population along a given lattice direction. The lifetime of the atoms in the excited band is found to be considerably longer (10-100 times) than the characteristic time scale for intersite tunneling, thus opening the path for orbital selective many-body physics with ultracold atoms. Upon exciting the atoms from an initial lowest band Mott-insulating state to higher lying bands, we observe the dynamical emergence of coherence in 1D (and 2D), compatible with Bose-Einstein condensation to a nonzero momentum state.

Deterministic Models of an Active Magnetic Bearing System

In this paper the development of mathematical model of voltage-input and current-input active magnetic bearing (AMB) system in deterministic form is presented. The AMB system, which is open-loop unstable and highly coupled due to nonlinearities inherited in the system such as gyroscopic effect and mass imbalance, requires a dynamic controller that can stabilize the system. In order to synthesize the controller, the nonlinear AMB model is transformed into its deterministic form by using the known upper and lower bounds of the parameters and the state variables of the system. The voltage-input AMB model shows that the system contains mismatched uncertainty and non-zero system states value which suggests that synthesizing nonlinear dynamic controller for this model is almost unfeasible. Overcoming these problems, the current input AMB model, however, is in the structure that is more suitable for the design of a stabilizing controller. A result from a computer simulation work shows that the states of the system behave nonlinearly without feedback control; however, this final system model with its numerical values can be used for the design of a class of a dynamic controller for system stabilization.

Laser ablation of a platinum target in water. III. Laser-induced reactions

This is the third paper in our series studying the laser-target-liquid interactions occurring in laser ablation in liquids (LAL). Here, laser ablation of a platinum target in pure water at 355nm wavelength is studied as a function of laser energy. We describe three distinct reaction regimes between the ablated target species and water at different laser focusing conditions. At low laser fluence (<10J∕cm2), material removal is caused by laser heating of the platinum surface and the primary products are small clusters with a large percentage of platinum atoms in a nonzero oxidation state. At intermediate fluences (10–70J∕cm2), platinum nanoparticles are the primary products. Our previous studies demonstrated that in this fluence regime ablation occurs through both thermal vaporization and explosive ejection of molten droplets. In both cases reactivity is small due to the low reactivity of platinum with water. At high fluences (>70J∕cm2), we find large, faceted particles that are attributed to the drying of PtOx gels formed by reactive plasma etching of the target. Taken together these results demonstrate that significant tunability in the target-liquid interaction is possible during nanomaterial synthesis by LAL.

QCD at zero baryon density and the Polyakov loop paradox

We compare the grand canonical partition function at fixed chemical potential mu with the canonical partition function at fixed baryon number B, formally and by numerical simulations at mu=0 and B=0 with four flavours of staggered quarks. We verify that the free energy densities are equal in the thermodynamic limit, and show that they can be well described by the hadron resonance gas at T < T_c and by the free fermion gas at T>T_c. Small differences between the two ensembles, for thermodynamic observables characterising the deconfinement phase transition, vanish with increasing lattice size. These differences are solely caused by contributions of non-zero baryon density sectors, which are exponentially suppressed with increasing volume. The Polyakov loop shows a different behaviour: for all temperatures and volumes, its expectation value is exactly zero in the canonical formulation, whereas it is always non-zero in the commonly used grand-canonical formulation. We clarify this paradoxical difference, and show that the non-vanishing Polyakov loop expectation value is due to contributions of non-zero triality states, which are not physical, because they give zero contribution to the partition function.

Classical analysis of phase-locking transients and Rabi-type oscillations in microwave-driven Josephson junctions

We present a classical analysis of the transient response of Josephson junctions perturbed by microwaves and thermal fluctuations. The results include a specific low frequency modulation in phase and amplitude behavior of a junction in its zero-voltage state. This transient modulation frequency is linked directly to an observed variation in the probability for the system to switch to its non-zero voltage state. Complementing previous work on linking classical analysis to the experimental observations of Rabi-oscillations, this expanded perturbation method also provides closed form analytical results for attenuation of the modulations and the Rabi-type oscillation frequency. Results of perturbation analysis are compared directly (and quantitatively) to numerical simulations of the classical model as well as published experimental data, suggesting that transients to phase-locking are closely related to the observed oscillations.

A bistable reaction–diffusion system in a stretching flow

We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection–reaction–diffusion partial differential equations (PDE), for pulse-like and for plateau-like solutions, based on a non-perturbative approach. This reduction allows us to study the dynamics in two cases: first, close to a saddle–node bifurcation at which a pair of nontrivial steady states are born as the dimensionless reaction rate (Damköhler number) is increased, and, second, for large Damköhler number, far away from the bifurcation. The main aim is to investigate the initial-value problem and to determine when an initial condition subject to chaotic stirring will decay to zero and when it will give rise to a nonzero final state. Comparisons with full PDE simulations show that the reduced pulse model accurately predicts the threshold amplitude for a pulse initial condition to give rise to a nontrivial final steady state, and that the reduced plateau model gives an accurate picture of the dynamics of the system at large Damköhler number.