Design constraints for third-order PLL nodes in master-slave clock distribution networks

Clock signal distribution in telecommunication commercial systems usually adopts a master-slave architecture, with a precise time basis generator as a master and phase-locked loops (PLLs) as slaves. In the majority of the networks, second-order PLLs are adopted due to their simplicity and stability. Nevertheless, in some applications better transient responses are necessary and, consequently, greater order PLLs need to be used, in spite of the possibility of bifurcations and chaotic attractors. Here a master-slave network with third-order PLLs is analyzed and conditions for the stability of the synchronous state are derived, providing design constraints for the node parameters, in order to guarantee stability and reachability of the synchronous state for the whole network. Numerical simulations are carried out in order to confirm the analytical results. (C) 2009 Elsevier B.V. All rights reserved.

Using bifurcations in the determination of lock-in ranges for third-order phase-locked loops

Transmission and switching in digital telecommunication networks require distribution of precise time signals among the nodes. Commercial systems usually adopt a master-slave (MS) clock distribution strategy building slave nodes with phase-locked loop (PLL) circuits. PLLs are responsible for synchronizing their local oscillations with signals from master nodes, providing reliable clocks in all nodes. The dynamics of a PLL is described by an ordinary nonlinear differential equation, with order one plus the order of its internal linear low-pass filter. Second-order loops are commonly used because their synchronous state is asymptotically stable and the lock-in range and design parameters are expressed by a linear equivalent system [Gardner FM. Phaselock techniques. New York: John Wiley & Sons: 1979]. In spite of being simple and robust, second-order PLLs frequently present double-frequency terms in PD output and it is very difficult to adapt a first-order filter in order to cut off these components [Piqueira JRC, Monteiro LHA. Considering second-harmonic terms in the operation of the phase detector for second order phase-locked loop. IEEE Trans Circuits Syst [2003;50(6):805-9; Piqueira JRC, Monteiro LHA. All-pole phase-locked loops: calculating lock-in range by using Evan`s root-locus. Int J Control 2006;79(7):822-9]. Consequently, higher-order filters are used, resulting in nonlinear loops with order greater than 2. Such systems, due to high order and nonlinear terms, depending on parameters combinations, can present some undesirable behaviors, resulting from bifurcations, as error oscillation and chaos, decreasing synchronization ranges. In this work, we consider a second-order Sallen-Key loop filter [van Valkenburg ME. Analog filter design. New York: Holt, Rinehart & Winston; 1982] implying a third order PLL The resulting lock-in range of the third-order PLL is determined by two bifurcation conditions: a saddle-node and a Hopf. (C) 2008 Elsevier B.V. All rights reserved.

Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion.

WRITING ELECTRONIC FERROMAGNETIC STATES IN A HIGH-TEMPERATURE PARAMAGNETIC NUCLEAR SPIN SYSTEM

In this paper, we use Nuclear Magnetic Resonance (NMR) to write electronic states of a ferromagnetic system into high-temperature paramagnetic nuclear spins. Through the control of phase and duration of radio frequency pulses, we set the NMR density matrix populations, and apply the technique of quantum state tomography to experimentally obtain the matrix elements of the system, from which we calculate the temperature dependence of magnetization for different magnetic fields. The effects of the variation of temperature and magnetic field over the populations can be mapped in the angles of spin rotations, carried out by the RF pulses. The experimental results are compared to the Brillouin functions of ferromagnetic ordered systems in the mean field approximation for two cases: the mean field is given by (i) B = B(0) + lambda M and (ii) B = B(0) + lambda M + lambda`M(3), where B(0) is the external magnetic field, and lambda, lambda` are mean field parameters. The first case exhibits second order transition, whereas the second case has first order transition with temperature hysteresis. The NMR simulations are in good agreement with the magnetic predictions.

Pseudolikelihood equations for Potts MRF model parameter estimation on higher order neighborhood systems

This letter presents pseudolikelihood equations for the estimation of the Potts Markov random field model parameter on higher order neighborhood systems. The derived equation for second-order systems is a significantly reduced version of a recent result found in the literature (from 67 to 22 terms). Also, with the proposed method, a completely original equation for Potts model parameter estimation in third-order systems was obtained. These equations allow the modeling of less restrictive contextual systems for a large number of applications in a computationally feasible way. Experiments with both simulated and real remote sensing images provided good results.

The low-lying electronic states of BeAs: a first principles characterization

The electronic structure and spectroscopic properties of a manifold of states of a new molecular species, BeAs, have been investigated theoretically at the complete active space self-consistent field/multireference single and double excitations configuration interaction (CASSCF/MRSDCI) approach, using the aug-cc-pV5Z-PP basis set for arsenic, which includes a relativistic effective core potential, and the cc-pV5Z set for beryllium. Potential energy curves of five quartet and eight doublet (I > + S) states correlating with the five lowest-lying dissociation limit are constructed. The effect of spin-orbit coupling is also included in the description of the ground state, and of the doublet states correlating with the second dissociation channel. Dipole moment functions and vibrationally averaged dipole moments are also evaluated. The similarities and differences between BeAs, BeP, and BeN are analyzed. Spin-orbit effects are small for the ground state close to the equilibrium distance, but avoided crossings between Omega = 1/2 states, and between Omega = 3/2 states changes significantly the I > + S curves for the lowest-lying doublets.

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit Coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given, The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 angstrom and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.

New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are inluded as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.

Fully Connected PLL Networks: How Filter Determines the Number of Nodes

Synchronization plays an important role in telecommunication systems, integrated circuits, and automation systems. Formerly, the masterslave synchronization strategy was used in the great majority of cases due to its reliability and simplicity. Recently, with the wireless networks development, and with the increase of the operation frequency of integrated circuits, the decentralized clock distribution strategies are gaining importance. Consequently, fully connected clock distribution systems with nodes composed of phase-locked loops (PLLs) appear as a convenient engineering solution. In this work, the stability of the synchronous state of these networks is studied in two relevant situations: when the node filters are first-order lag-lead low-pass or when the node filters are second-order low-pass. For first-order filters, the synchronous state of the network shows to be stable for any number of nodes. For second-order filter, there is a superior limit for the number of nodes, depending on the PLL parameters. Copyright (C) 2009 Atila Madureira Bueno et al.

Electrochemical Reduction Using Glassy Carbon Electrode in Aqueous Medium of a Potential Anti-Chagas Drug: NFOH

Nitrofurazone (NF) presents activity against Chagas' disease, yet it has a high toxicity. Its analog, hydroxymethylnitrofurazone (NFOH), is more potent against Trypanosoma cruzi and much less toxic than the parent drug, NF. The electrochemical reduction of NFOH in an aqueous medium using a glassy carbon electrode (GCE) is presented. By cyclic voltammetry in anacidic medium, one irreversible reduction peak related to hydroxylamine derivative formation was registered, being linearly pH dependent. However, from pH > 7, a reversible reduction peak at a more positive potential appears and corresponds to the formation of a nitro radical anion. The radical-anion kinetic stability was evaluated by Ip(a)/Ip(c) the current ratio of the R-NO(2)/R-NO(2)-redox couple. The nitro radical anion decays with a second-order rate constant (k(2)) of 6.07, 2.06, and 1.44(X 10(3)) L mol(-1) s(-1) corresponding to pH 8.29, 9.29, and 10.2, respectively, with a corresponding half-time life (t(1/2)) of 0.33, 0.97, and 1.4 s for each pH value. By polishing the GCE surface with diamond powder and comparing with the GCE surface polished with alumina, it is shown that the presence of alumina affects the lifetime of the nitro radical anion. (C) 2009 The Electrochemical Society. [DOI: 10.1149/1.3130082] All rights reserved.

SOLITON SOLUTIONS TO SYSTEMS OF COUPLED SCHRODINGER EQUATIONS OF HAMILTONIAN TYPE

We study the existence of positive solutions of Hamiltonian-type systems of second-order elliptic PDE in the whole space. The systems depend on a small parameter and involve a potential having a global well structure. We use dual variational methods, a mountain-pass type approach and Fourier analysis to prove positive solutions exist for sufficiently small values of the parameter.

High-temperature X-ray powder diffraction study of the tetragonal-cubic phase transition in nanocrystalline, compositionally homogeneous ZrO2-CeO2 solid solutions

Crystal structure of compositionally homogeneous, nanocrystalline ZrO2-CeO2 solutions was investigated by X-ray powder diffraction as a function of temperature for compositions between 50 and 65 mol % CeO2 center dot ZrO2-50 and 60 mol % CeO2 solid solutions, which exhibit the t'-form of the tetragonal phase at room temperature, transform into the cubic phase in two steps: t'-to-t '' followed by t ''-to-cubic. But the ZrO2-65 mol % CeO2, which exhibits the t ''-form, transforms directly to the cubic phase. The results suggest that t'-to-t '' transition is of first order, but t ''-to-cubic seems to be of second order. (C) 2008 International Centre for Diffraction Data.

Phase transitions and spatially ordered counterion association in ionic-lipid membranes: A statistical model

We propose a statistical model to account for the gel-fluid anomalous phase transitions in charged bilayer- or lamellae-forming ionic lipids. The model Hamiltonian comprises effective attractive interactions to describe neutral-lipid membranes as well as the effect of electrostatic repulsions of the discrete ionic charges on the lipid headgroups. The latter can be counterion dissociated (charged) or counterion associated (neutral), while the lipid acyl chains may be in gel (low-temperature or high-lateral-pressure) or fluid (high-temperature or low-lateral-pressure) states. The system is modeled as a lattice gas with two distinct particle types-each one associated, respectively, with the polar-headgroup and the acyl-chain states-which can be mapped onto an Ashkin-Teller model with the inclusion of cubic terms. The model displays a rich thermodynamic behavior in terms of the chemical potential of counterions (related to added salt concentration) and lateral pressure. In particular, we show the existence of semidissociated thermodynamic phases related to the onset of charge order in the system. This type of order stems from spatially ordered counterion association to the lipid headgroups, in which charged and neutral lipids alternate in a checkerboard-like order. Within the mean-field approximation, we predict that the acyl-chain order-disorder transition is discontinuous, with the first-order line ending at a critical point, as in the neutral case. Moreover, the charge order gives rise to continuous transitions, with the associated second-order lines joining the aforementioned first-order line at critical end points. We explore the thermodynamic behavior of some physical quantities, like the specific heat at constant lateral pressure and the degree of ionization, associated with the fraction of charged lipid headgroups.

Extra phase noise from thermal fluctuations in nonlinear optical crystals

We show theoretically and experimentally that scattered light by thermal phonons inside a second-order nonlinear crystal is the source of additional phase noise observed in optical parametric oscillators. This additional phase noise reduces the quantum correlations and has hitherto hindered the direct production of multipartite entanglement in a single nonlinear optical system. We cooled the nonlinear crystal and observed a reduction in the extra noise. Our treatment of this noise can be successfully applied to different systems in the literature.

Metal-insulator transition in Nd(1-x) Eu(x) NiO(3) probed by specific heat and anelastic measurements

Oxides RNiO(3) (R - rare-earth, R not equal La) exhibit a metal-insulator (MI) transition at a temperature T(MI) and an antiferromagnetic (AF) transition at T(N). Specific heat (C(P)) and anelastic spectroscopy measurements were performed in samples of Nd(1-x)Eu(x)NiO(3), 0 <= x <= 0.35. For x - 0, a peak in C(P) is observed upon cooling and warming at essentially the same temperature T(MI) - T(N) similar to 195 K, although the cooling peak is much smaller. For x >= 0.25, differences between the cooling and warming curves are negligible, and two well defined peaks are clearly observed: one at lower temperatures that define T(N), and the other one at T(MI). An external magnetic field of 9 T had no significant effect on these results. The elastic compliance (s) and the reciprocal of the mechanical quality factor (Q(-1)) of NdNiO(3), measured upon warming, showed a very sharp peak at essentially the same temperature obtained from C(P), and no peak is observed upon cooling. The elastic modulus hardens below T(MI) much more sharply upon warming, while the cooling and warming curves are reproducible above T(MI). Conversely, for the sample with x - 0.35, s and Q(-1) curves are very similar upon warming and cooling. The results presented here give credence to the proposition that the MI phase transition changes from first to second order with increasing Eu doping. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3549615]