Route to chaos in a third-order phase-locked loop network

Phase-locked loops (PLLs) are widely used in applications related to control systems and telecommunication networks. Here we show that a single-chain master-slave network of third-order PLLs can exhibit stationary, periodic and chaotic behaviors, when the value of a single parameter is varied. Hopf, period-doubling and saddle-saddle bifurcations are found. Chaos appears in dissipative and non-dissipative conditions. Thus, chaotic behaviors with distinct dynamical features can be generated. A way of encoding binary messages using such a chaos-based communication system is suggested. (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.

Comparing lock-in ranges and transient responses of second- and third-order phase-locked loops in master-slave clock distribution networks

The distribution of clock signals throughout the nodes of a network is essential for several applications. in control and communication with the phase-locked loop (PLL) being the component for electronic synchronization process. In systems with master-slave (MS) strategies, the PLLs are the slave nodes responsible for providing reliable clocks in all nodes of the network. As PLLs have nonlinear phase detection, double-frequency terms appear and filtering becomes necessary. Imperfections in filtering process cause oscillations around the synchronous state worsening the performance of the clock distribution process. The behavior of one-way master-slave (OWMS) clock distribution networks is studied and performances of first- and second-order filter processes are compared, concerning lock-in ranges and responses to perturbations of the synchronous state. (c) 2007 Elsevier GmbH. All rights reserved.

Influence of gold nanoparticles on optically stimulated effects in TeO(2)-ZnO and GeO(2)-PbO amorphous thin films

We have found photoinduced second harmonic generation at wavelength 1064 nm during bicolor Nd:YAG laser coherent treatment of TeO(2)-ZnO and GeO(2)-PbO amorphous films. The maximally achieved second order susceptibility was equal to about 1.02 pm/V. Correlation of the induced second order susceptibility with local sample heating and induced birefringence may indicate an occurrence of local phase transitions from amorphous glass-like phase to non-centrosymmetry metastable phases. (C) 2010 Elsevier B.V. All rights reserved.

Heat-moisture treatment and enzymatic digestibility of Peruvian carrot, sweet potato and ginger starches

The aim of this work was to study the effects of heat-moisture treatment (27% moisture, 100 degrees C, 16 h) and of enzymatic digestion (alpha-amylase and glucoamylase) on the properties of sweet potato (SP), Peruvian carrot (PC) and ginger (G) starches. The structural modification with heat-moisture treatment (HMT) affected crystallinity, enzyme susceptibility and viscosity profile. The changes in PC starch were the most pronounced, with a strong decrease of relative crystallinity (from 0.31 to 0.21) and a shift of X-ray pattern from B- to A-type. HMTof SP and G starch did not change the Xray pattern (A-type). The relative crystallinity of these starches changed only slightly, from 0.32 to 0.29 (SP) and from 0.33 to 0.32 (G). The extent of these structural changes (PC > SP > G) altered the susceptibility of the starches to enzymatic attack, but not in same order (PC > G > SP). HMT increased the starches digestion, probably due to rearrangement of disrupted crystallites, increasing accessible areas to attack of enzymes. The viscosity profiles and values changed significantly with HMT, resulting in higher pasting temperatures, decrease of viscosity values and no breakdown, i.e., stability at high temperatures and shear rates. Changes in pasting properties appeared to be more significant for PC and SP starch, whereas the changes for G starch were small. Setback was minimized following HMT in SP and G starches.

Evaluation of algorithms used to order markers on genetic maps

When building genetic maps, it is necessary to choose from several marker ordering algorithms and criteria, and the choice is not always simple. In this study, we evaluate the efficiency of algorithms try (TRY), seriation (SER), rapid chain delineation (RCD), recombination counting and ordering (RECORD) and unidirectional growth (UG), as well as the criteria PARF (product of adjacent recombination fractions), SARF (sum of adjacent recombination fractions), SALOD (sum of adjacent LOD scores) and LHMC (likelihood through hidden Markov chains), used with the RIPPLE algorithm for error verification, in the construction of genetic linkage maps. A linkage map of a hypothetical diploid and monoecious plant species was simulated containing one linkage group and 21 markers with fixed distance of 3 cM between them. In all, 700 F(2) populations were randomly simulated with and 400 individuals with different combinations of dominant and co-dominant markers, as well as 10 and 20% of missing data. The simulations showed that, in the presence of co-dominant markers only, any combination of algorithm and criteria may be used, even for a reduced population size. In the case of a smaller proportion of dominant markers, any of the algorithms and criteria (except SALOD) investigated may be used. In the presence of high proportions of dominant markers and smaller samples (around 100), the probability of repulsion linkage increases between them and, in this case, use of the algorithms TRY and SER associated to RIPPLE with criterion LHMC would provide better results. Heredity (2009) 103, 494-502; doi:10.1038/hdy.2009.96; published online 29 July 2009

Auditory processing disorder in perisylvian syndrome

We hypothesized that the processing of auditory information by the perisylvian polymicrogyric cortex may be different from the normal cortex. To characterize the auditory processing in bilateral perisylvian syndrome, we examined ten patients with perisylvian polymicrogyria (Group 1) and seven control children (Group 11). Group I was composed by four children with bilateral perisylvian polymicrogyria and six children with bilateral posterior perisylvian polymicrogyria. The evaluation included neurological and neuroimaging investigation, intellectual quotient and audiological assessment (audiometry and behavior auditory tests). The results revealed a statistically significant difference between the groups in the behavioral auditory tests, Such as, digits dichotic test, nonverbal dichotic test (specifically in right attention), and random gap detection/random gap detection expanded tests. Our data showed abnormalities in the auditory processing of children with perisylvian polymicrogyria, suggesting that perisylvian polymicrogyric cortex is functionally abnormal. We also found a correlation between the severity of our auditory findings and the extent of the cortical abnormality. (C) 2009 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.

Sensitivity to cisplatin-induced mutations and elevated chromosomal aberrations in lymphocytes from sickle cell disease patients

Sickle cell disease (SCD) is an inherited disorder caused by a single nucleotide substitution in the P-globin gene. The clinical heterogeneity observed in SCD patients has been attributed to environmental and genetic factors. The patients are subjected to increased oxidative stress, particularly during vaso-occlusive crises and acute chest pain. Another possible cause of oxidative stress in SCD is the high concentration of iron in the patients` plasma. The increase in oxidative stress could be a relevant risk factor for mutagenesis and carcinogenesis. Studies on the frequency of basal chromosomal aberrations in cultured lymphocytes from SCD patients have not been reported so far. In order to contribute to the understanding of the role of the different biomarkers and their relationship with the extremely variable clinical manifestation of SCD, we investigated the frequency of chromosome damage in peripheral lymphocytes from sickle cells patients and healthy controls. We found an increased frequency of chromosome damage and percentage of aberrant metaphases in these patients when compared with control subjects, even at basal values (p < 0.05). In the cytogenetic sensitivity assay, the results showed that these patients presented a marked decrease in the mitotic index values compared with healthy controls. Cisplatin-induced chromosomal damage in lymphocytes from these patients was significantly higher than the frequency measured in healthy controls. The results obtained in the present study showed that more investigations are needed in order to elucidate the susceptibility to genomic instability of SCD patients.

Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Spontaneous transitions in the coordination of a whole body task

This paper describes an example of spontaneous transitions between qualitatively different coordination patterns during a cyclic lifting and lowering task. Eleven participants performed 12 trials of repetitive lifting and lowering in a ramp protocol in which the height of the lower shelf was raised or lowered 1 cm per cycle between 10 and 50 cm. Two distinct patterns of coordination were evident: a squat technique in which moderate range of hip, knee and ankle movement was utilised and ankle plantar-flexion occurred simultaneously with knee and hip extension; and a stoop technique in which the range of knee movement was reduced and knee and hip extension was accompanied by simultaneous ankle dorsi-flexion. Abrupt transitions from stoop to squat techniques were observed during descending trials, and from squat to stoop during ascending trials. Indications of hysteresis was observed in that transitions were more frequently observed during descending trials, and the average shelf height at the transition was 5 cm higher during ascending trials. The transitions may be a consequence of a trade-off between the biomechanical advantages of each technique and the influence of the lift height on this trade-off.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

Fixed bed reactors with catalyst poisoning - first order kinetics.

The long performance of an isothermal fixed bed reactor undergoing catalyst poisoning is theoretically analyzed using the dispersion model. First order reaction with dth order deactivation is assumed and the model equations are solved by matched asymptotic expansions for large Peclet number. Simple closed-form solutions, uniformly valid in time, are obtained.

Hysteresis and phase transitions in a single partially internally wetted catalyst pellet: Thermogravimetric studies

The hydrogenation of cyclohexene over palladium supported in a microporous gamma-alumina pellet is studied thermogravimetrically with a view to measuring the extent of partial internal wetting associated with the different steady state branches. As many as three steady state branches having significantly different degrees of internal wetting and reaction rates, with transitions between them, are confirmed from observations of catalyst weight change. It is seen that with reduction in catalyst activity the middle branch, obtained by condensation from a vapor filled pellet, is much more prominent without showing an evaporative transition for the range of hydrogen partial pressures used here. The catalyst activity is therefore an important parameter affecting the structure of the steady state branches. Hysteresis effects are found to occur, and the thermogravimetric results also confirm the importance of history in determining the catalyst state. The measured degree of wetting is in accordance with that estimated from a mathematical model incorporating capillary condensation effects in addition to reaction-diffusion phenomena. The same model also satisfactorily interprets the reaction rate variations and transitions seen in the present work.