Network of phase-locking oscillators and a possible model for neural synchronization

In order to model the synchronization of brain signals, a three-node fully-connected network is presented. The nodes are considered to be voltage control oscillator neurons (VCON) allowing to conjecture about how the whole process depends on synaptic gains, free-running frequencies and delays. The VCON, represented by phase-locked loops (PLL), are fully-connected and, as a consequence, an asymptotically stable synchronous state appears. Here, an expression for the synchronous state frequency is derived and the parameter dependence of its stability is discussed. Numerical simulations are performed providing conditions for the use of the derived formulae. Model differential equations are hard to be analytically treated, but some simplifying assumptions combined with simulations provide an alternative formulation for the long-term behavior of the fully-connected VCON network. Regarding this kind of network as models for brain frequency signal processing, with each PLL representing a neuron (VCON), conditions for their synchronization are proposed, considering the different bands of brain activity signals and relating them to synaptic gains, delays and free-running frequencies. For the delta waves, the synchronous state depends strongly on the delays. However, for alpha, beta and theta waves, the free-running individual frequencies determine the synchronous state. (C) 2011 Elsevier B.V. All rights reserved.

Spectral properties of chaotic signals generated by the skew tent map

Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map. From these results, we suggest possible applications in communication systems. (C) 2009 Elsevier B.V. All rights reserved.

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.

Recognition of noisy images by PLL networks

We use networks composed of three phase-locked loops (PLLs), where one of them is the master, for recognizing noisy images. The values of the coupling weights among the PLLs control the noise level which does not affect the successful identification of the input image. Analytical results and numerical tests are presented concerning the scheme performance. (c) 2008 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.

Reachability of the synchronous state in a mutually connected PLL network

Second-order phase locked loops (PLLs) are devices that are able to provide synchronization between the nodes in a network even under severe quality restrictions in the signal propagation. Consequently, they are widely used in telecommunication and control. Conventional master-slave (M-S) clock-distribution systems are being, replaced by mutually connected (MC) ones due to their good potential to be used in new types of application such as wireless sensor networks, distributed computation and communication systems. Here, by using an analytical reasoning, a nonlinear algebraic system of equations is proposed to establish the existence conditions for the synchronous state in an MC PLL network. Numerical experiments confirm the analytical results and provide ideas about how the network parameters affect the reachability of the synchronous state. The phase-difference oscillation amplitudes are related to the node parameters helping to design PLL neural networks. Furthermore, estimation of the acquisition time depending on the node parameters allows the performance evaluation of time distribution systems and neural networks based on phase-locked techniques. (c) 2008 Elsevier GmbH. All rights reserved.

Mutually connected phase-locked loop networks: dynamical models and design parameters

Distribution of timing signals is an essential factor for the development of digital systems for telecommunication networks, integrated circuits and manufacturing automation. Originally, this distribution was implemented by using the master-slave architecture with a precise master clock generator sending signals to phase-locked loops (PLL) working as slave oscillators. Nowadays, wireless networks with dynamical connectivity and the increase in size and operation frequency of the integrated circuits suggest that the distribution of clock signals could be more efficient if mutually connected architectures were used. Here, mutually connected PLL networks are studied and conditions for synchronous states existence are analytically derived, depending on individual node parameters and network connectivity, considering that the nodes are nonlinear oscillators with nonlinear coupling conditions. An expression for the network synchronisation frequency is obtained. The lock-in range and the transmission error bounds are analysed providing hints to the design of this kind of clock distribution system.

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.

Multiple synchronous states in static delay-free mutually connected PLL networks

In many engineering applications, the time coordination of geographically separated events is of fundamental importance, as in digital telecommunications and integrated digital circuits. Mutually connected (MC) networks are very good candidates for some new types of application, such as wireless sensor networks. This paper presents a study on the behavior of MC networks of digital phase-locked loops (DPLLs). Analytical results are derived showing that, even for static networks without delays, different synchronous states may exist for the network. An upper bound for the number of such states is also presented. Numerical simulations are used to show the following results: (i) the synchronization precision in MC DPLLs networks; (ii) the existence of synchronous states for the network does not guarantee its achievement and (iii) different synchronous states may be achieved for different initial conditions. These results are important in the neural computation context. as in this case, each synchronous state may be associated to a different analog memory information. (C) 2010 Elsevier B.V. All rights reserved.

Effect of Charge Asymmetry on Adsorption and Phase Separation of Polyampholytes on Silica and Cellulose Surfaces

The relation between the properties of polyampholytes in aqueous solution and their adsorption behaviors on silica and cellulose surfaces was investigated. Four polyampholytes carrying different charge densities but with the same nominal ratio of positive to negative segments and two structurally similar polyelectrolytes (a polyacid and a polybase) were investigated by using quartz crystal microgravimetry using silica-coated and cellulose-coated quartz resonators. Time-resolved mass and rigidity (or viscoelasticity) of the adsorbed layer was determined from the shifts in frequency (Delta f) and energy dissipation (Delta D) of the respective resonator. Therefore, elucidation of the dynamics and extent of adsorption, as well as the conformational changes of the adsorbed macromolecules, were possible. The charge properties of the solid Surface played a crucial role in the adsorption of the studied polyampholytes, which was explained by the capability of the surface to polarize the polyampholyte at the interface. Under the same experimental conditions, the polyampholytes had a higher nominal charge density phase-separated near the interface, producing a soft, dissipative, and loosely bound layer. In the case of cellulose substrates, where adsorption was limited, electrostatic and polarization effects were concluded to be less significant.

Modeling and measuring double-frequency jitter in one-way master-slave networks

The double-frequency jitter is one of the main problems in clock distribution networks. In previous works, sonic analytical and numerical aspects of this phenomenon were studied and results were obtained for one-way master-slave (OWMS) architectures. Here, an experimental apparatus is implemented, allowing to measure the power of the double-frequency signal and to confirm the theoretical conjectures. (C) 2008 Elsevier B.V. All rights reserved.

CALCINED SLUDGE SINTERING EVALUATION BY HEATING MICROSCOPY THERMAL ANALYSIS

Aiming the use of the sewage sludge produced in one of the largest Brazilian wastewater treatment stations as a raw material for the ceramic industry, the sintering process of the ashes produced from its calcination was evaluated by heating microscopy thermal analysis (HMTA). From the microprocessed images, a method was developed to obtain HMTA dimensional change curves as a function of temperature, equivalent to those usually obtained from dilatometers or by thermomechanical analysis (TMA). The final product after sintering at 1050 degrees C, characterized by X-ray fluorescence spectrometry, scanning electron microscopy and X-ray dispersive energy, indicates the presence of a vitreous phase containing phosphorus, which explains the good sintering properties of the studied calcined sludge, as shown from its HMTA dimensional change curve.

MACRONUTRIENTS UPTAKE BY POTATO (Solanum tuberosum L.) IN SEED-TUBER PRODUCTION

In greenhouse potato cultivation, mineral nutrition is one of the main factors contributing to high yields and better product quality. Knowledge about the amount of nutrients accumulated in the plants at each growing phase provides important information that helps the establishment of a more balanced fertilizer application. The objective of this research was to determine the time course of macronutrients uptake and accumulation in potato plants for seed-tuber production, grown in nutrient solution. The experiment was carried out in a greenhouse, using in vitro material from the pre-basic category of the `Atlantic` variety. The plants were collected weekly from 14 days after transplanting (DAT) until 70 DAT The experimental design was a completely randomized block with 9 treatments to sampling times and four replicates. The highest nutrient requirement in the plant shoot occurred at the periods between 28 and 56 DAT while in the tubers it was after 49 DAT The maximum accumulation sequence of macronutrients was K > N > S > Ca > P > Mg.

Alterations in energy properties of eucalyptus wood and bark subjected to torrefaction: The potential of mass loss as a synthetic indicator

Torrefaction is a mild pyrolysis process (usually up to 300 degrees C) that changes the chemical and physical properties of biomass. This process is a possible pre-treatment prior to further processes (transport, grinding, combustion, gasification, etc) to generate energy or biofuels. In this study, three eucalyptus wood species and bark were subjected to different torrefaction conditions to determine the alterations in their structural and energy properties. The most severe treatment (280 degrees C, 5 h) causes mass losses of more than 35%, with severe damage to anatomical structure, and an increase of about 27% in the specific energy content. Bark is more sensitive to heat than wood. Energy yields are always higher than mass yields, thereby demonstrating the benefits of torrefaction in concentrating biomass energy. The overall mass loss is proposed as a relevant parameter to synthesize the effect of torrefaction conditions (temperature and duration). Accordingly, all results are summarised by analytical expressions able to predict the energy properties as a function of the overall mass loss. These expressions are intended to be used in any optimization procedure, from production in the field to the final use. (c) 2010 Elsevier Ltd. All rights reserved.

Root Water Extraction under Combined Water and Osmotic Stress

Using a numerical implicit model for root water extraction by a single root in a symmetric radial flow problem, based on the Richards equation and the combined convection-dispersion equation, we investigated some aspects of the response of root water uptake to combined water and osmotic stress. The model implicitly incorporates the effect of simultaneous pressure head and osmotic head on root water uptake, and does not require additional assumptions (additive or multiplicative) to derive the combined effect of water and salt stress. Simulation results showed that relative transpiration equals relative matric flux potential, which is defined as the matric flux potential calculated with an osmotic pressure head-dependent lower bound of integration, divided by the matric flux potential at the onset of limiting hydraulic conditions. In the falling rate phase, the osmotic head near the root surface was shown to increase in time due to decreasing root water extraction rates, causing a more gradual decline of relative transpiration than with water stress alone. Results furthermore show that osmotic stress effects on uptake depend on pressure head or water content, allowing a refinement of the approach in which fixed reduction factors based on the electrical conductivity of the saturated soil solution extract are used. One of the consequences is that osmotic stress is predicted to occur in situations not predicted by the saturation extract analysis approach. It is also shown that this way of combining salinity and water as stressors yields results that are different from a purely multiplicative approach. An analytical steady state solution is presented to calculate the solute content at the root surface, and compared with the outputs of the numerical model. Using the analytical solution, a method has been developed to estimate relative transpiration as a function of system parameters, which are often already used in vadose zone models: potential transpiration rate, root length density, minimum root surface pressure head, and soil theta-h and K-h functions.