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In this paper we investigate the degradation of the statistic properties of chaotic maps as consequence of their implementation in a digital media such as Digital Signal Processors (DSP), Field Programmable Gate Arrays (FPGA) or Application-Specific Integrated Circuits (ASIC). In these systems, binary floating- and fixed-point are the numerical representations available. Fixed-point representation is preferred over floating-point when speed, low power and/or small circuit area are necessary. Then, in this paper we compare the degradation of fixed-point binary precision version of chaotic maps with the one obtained by using floating point 754-IEEE standard, to evaluate the feasibility of their FPGA implementation. The specific period that every fixed-point precision produces was investigated in previous reports. Statistical characteristics are also relevant, it has been recently shown that it is convenient to describe the statistical characteristic using both, causal and non-causal quantifiers. In this paper we complement the period analysis by characterizing the behavior of these maps from an statistical point of view using cuantifiers from information theory. Here, rather than reproducing an exact replica of the real system, the aim is to meet certain conditions related to the statistics of systems. Fil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina Fil: Larrondo, Hilda Angela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica; Argentina Fil: Rosso, Osvaldo Aníbal. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidade Federal de Alagoas; Brasil. Hospital Italiano; Argentina. Universidad de Los Andes; Chile

A one-dimensional deterministic continuous dynamical system is studied and shown to exhibit chaotic behavior and complex trans- port properties. Our model is an overdamped rocking ratchet with finite dissipation that is periodically kicked with a delta function driving force, without finite inertia terms or temporal or spatial stochastic forces. This is perhaps the simplest model reported in the literature for a ratchet that exhibits a complex chaotic behavior. We present both numerical and analytical results that predict many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. In particular, we show that alternate positive and negative delta functions as the unbiased driving force on a ratchet potential produces both synchronized and chaotic regions.

This paper deals with a family of interesting 2D-quadratic maps proposed by Sprott, in his seminal paper [1], related to “chaotic art”. Our main interest about these maps is their great potential for using them in digital electronic applications because they present multiple chaotic attractors depending on the selected point in the parameter's space. Only results for the analytical representation of these maps have been published in the open literature. Consequently, the objective of this paper is to extend the analysis to the digital version, to make possible the hardware implementation in a digital medium, like field programmable gate arrays (FPGA) in fixed-point arithmetic. Our main contributions are: (a) the study of the domains of attraction in fixed-point arithmetic, in terms of period lengths and statistical properties; (b) the determination of the threshold of the bus width that preserves the integrity of the domain of attraction and (c) the comparison between two quantifiers based on respective probability distribution functions (PDFs) and the well known maximum Lyapunov exponent (MLE) to detect the above mentioned threshold. Fil: de Micco, Luciana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; Argentina Fil: Antonelli, Maximiliano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; Argentina Fil: Larrondo, Hilda Angela. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Instituto de Investigaciones Científicas y Tecnológicas en Electrónica.; Argentina

We analyze the statistical complexity measure vs. entropy plane-representation of sampled chaotic attractors as a function of the sampling period τ and show that, if the Bandt and Pompe procedure is used to assign a probability distribution function (PDF) to the pertinent time series, the statistical complexity measure (SCM) attains a definite maximum for a specific sampling period t M . On the contrary, the usual histogram approach for assigning PDFs to a time series leads to essentially constant SCM values for any sampling period τ . The significance of t M is further investigated by comparing it with typical times found in the literature for the two main reconstruction processes: the Takens’ one in a delay-time embedding, on one hand, and the exact Nyquist–Shannon reconstruction, on the other one. It is shown that t M is compatible with those times recommended as adequate delay ones in Takens’ reconstruction. The reported results correspond to three representative chaotic systems having correlation dimension 2 D 2 3 . One recent experiment confirms the analysis presented here.

We highlight the potentiality of a special Information Theory (IT) approach in order to unravel the intricacies of nonlinear dynamics, the methodology being illustrated with reference to the logistic map. A rather surprising dynamic feature → plane-topography map becomes available.

Pseudo Random Number Generators (PRNG) have attracted intense attention due to their obvious importance for many branches of science and technology. A randomizing technique is a procedure designed to improve the PRNG randomness degree according the specific requirements. It is obviously important to quantify its effectiveness. In order to classify randomizing techniques based on a symbolic dynamics’ approach, we advance a novel, physically motivated representation based on the statistical properties of chaotic systems. Recourse is made to a plane that has as coordinates (i) the Shannon entropy and (ii) a form of the statistical complexity measure. Each statistical quantifier incorporates a different probability distribution function, generating thus a representation that (i) sheds insight into just how each randomizing technique operates and also (ii) quantifies its effectiveness. Using the Logistic Map and the Three Way Bernoulli Map as typical examples of chaotic dynamics it is shown that our methodology allows for choosing the more convenient randomizing technique in each instance. Comparison with measures of complexity based on diagonal lines on the recurrence plots [N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438 (2007) 237] support the main conclusions of this paper.

Additive White Gaussian Noise (AWGN) generators are a basic tool for the test and measurement of digital systems. One drawback for hardware implementation of the classically used algorithms is that they require the hardware implementation of complex operations (such as sinusoidal and logarithmic functions). In this chapter, a method for the design and hardware implementation of an AWGN generator based on chaotic maps is described. The advantage is that deterministic chaotic systems are described by simple nonlinear equations, and therefore, they are straightforward to implement in hardware. To ensure that the generated sequence has the desired Probability Density Function (PDF), the chaotic map, which is the heart of the system, is synthesized using an approach based on the theory of positive matrices method. The hardware implementation was developed using an Altera Cyclone III FPGA with the 3C120 Development Board.

We present a minimal one-dimensional deterministic continuous dynamical system that exhibits chaotic behavior and complex transport properties. Our model is an overdamped rocking ratchet that is periodically kicked with a delta function potential. We develop an analytical approach that predicts many key features of the system, such as current reversals, as well as the presence of chaotic behavior and bifurcation. We show that our approach can be easily extended to other types of periodic forces, including the square wave., Comment: submitted to Physical Review E

We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test.

A Statistical Complexity measure has been recently proposed to quantify the performance of chaotic Pseudorandom number generators (PRNG) (Physica A 354 (2005) 281). Here we revisit this quantifier and introduce two important improvements: (i) consideration of an intensive statistical complexity (Physica A 334 (2004) 119), and (ii) following the prescription of Brand and Pompe (Phys. Rev. Lett. 88 (2002) 174102-1) in evaluating the probability distribution associated with the PRNG. The ensuing new measure is applied to a very well-tested PRNG advanced by Marsaglia.

Pseudorandom number generators (PRNG) are extensively used in Monte Carlo simulations, gambling machines and cryptography as substitutes of ideal random number generators (RNG). Each application imposes different statistical requirements to PRNGs. As L’Ecuyer clearly states “the main goal for Monte Carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology, observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random”. In accordance with different applications several statistical test suites have been developed to analyze the sequences generated by PRNGs. In a recent paper a new statistical complexity measure [Phys. Lett. A 311 (2003) 126] has been defined. Here we propose this measure, as a randomness quantifier of a PRNGs. The test is applied to three very well known and widely tested PRNGs available in the literature. All of them are based on mathematical algorithms. Another PRNGs based on Lorenz 3D chaotic dynamical system is also analyzed. PRNGs based on chaos may be considered as a model for physical noise sources and important new results are recently reported. All the design steps of this PRNG are described, and each stage increase the PRNG randomness using different strategies. It is shown that the MPR statistical complexity measure is capable to quantify this randomness improvement. The PRNG based on the chaotic 3D Lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison.

The forced and overdamped motion of non-interacting particles in a periodic asymmetric potential is studied. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with non-correlated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters. The mean velocity of the particles and the diffusion coefficient are found to have a non-monotonic dependence on the quenched noise strength. These non-trivial results are explained on the basis of the synchronized motion of the individual particles in the perfect lattice.

Inertia ratchets are characterized by a complex dynamics with multiple current reversals. We recently studied the problem of control of current on inertia ratchets and demonstrated the feasibility of a control method associated with a process of locking to different mean velocity attractors. Here we present the results of a study of the fractal characteristics of basins of attraction for different mean velocities as well as the influence of quenched disorder on the attractors. We find that our previous conjecture that the domains of attraction of the two velocities are intermixed fractals is verified. We also find that the attractor for the negative velocity dissolves as the strength of disorder is increased. These results have important implications for the design of a reliable technique for controlling the particle mean velocities.

This paper deals with the use of Ring Oscillators (ROs) as pseudo random number generators (PRNG). The design, made for ALTERA Cyclone III ©, using low level primitives is explained. Two relevant characteristics of a PRNG are considered to validate the design: 1) the equiprobability of all possible outcomes and 2) the statistical independence of consecutive values. In this work these properties are measured via Information Theory Quantifiers. A dual entropy plane is used to represent the time series and easily visualize the results obtained with different configurations. The quality is also compared with other available PRNGs by means of the dual entropy plane. Our method constitutes an effective reduction of the complete analysis made with test suites like DIEHARD or NIST.

Fil: Larrondo, Hilda Angela. Universidad Nacional de Mar del Plata. Facultad de Ingenieria; Argentina. Consejo Nacional de Investigaciones Cientificas y Tecnicas; Argentina

Polymerization-induced phase separation was described using a phase transformation diagram in conversion vs composition coordinates, where metastable and unstable regions were located. Phase separa...

The present study presents a series of numerical experiments whereby the convergence of the procedure is studied as the number of terms utilized is increased, when considering bare rectangular anisotropic plates

The present study deals with the determination of the lower natural frequencies using two independent techniques. (1) An analytical approach whereby the displacement amplitude is expressed in terms of a truncated double Fourier series which is the exact solution of the vibrating, solid rectangular plate simply supported at its four edges. The frequency determinant is generated using the Rayleigh Ritz method.(2) a finite element method using a standard code

The appearance of a maximum in the intensity of scattered light at a nonzero wave vector for systems undergoing a polymerization-induced phase separation (PIPS) has been considered in the past as conclusive evidence of the presence of a spinodal demixing mechanism. However, recent results from light scattering studies of colloidal aggregation and phase separation in aqueous biopolymers systems and polymer blends prove that the maximum may also be generated by a nucleation-growth process (NG). The origin of this scattering behavior is the presence of a layer surrounding dispersed-phase particles that contains less solute concentration than the bulk (depletion layer). We apply this concept to a system undergoing PIPS through an NG mechanism. The analysis is constrained to the generation of a diluted dispersion of spherical particles where concentration profiles around particles may be analytically derived. Both Rayleigh−Gans and Mie scattering theories are used to describe the patterns of scattered light. I...

Any incident plane polarized beam, after travelling through the fiber, will emerge in a state of general elliptic polarization. The size and shape of the ellipse will depend critically on the total path travelled inside the fiber, which in turn is related to the stresses applied to it. By analyzing the emerging light with a polarizer, one can detect even tiny variations in the fiber length. Using this method in a commercial fiber together with inexpensive equipment, the breaking of individual wires in a multiwired steel rope is detected

An approximate solution to the overall vibrational problem is obtained in the present paper following the approach developed in previous studies which essentially consists of using coordinate functions which yield, in combination with variational methods, very accurate or even exact results in the case where the plate or slab is simply connected. When the slab is traversed by an orifice or hole one simply deducts the strain and kinetic energy corresponding to the non existing portion of the structure

The present study was originated by the dynamic analysis of the foundation of machinery partially embedded in a Winkler type medium and deals with the determination of the lower natural frequencies of transverse vibration corresponding to symmetric and antisymmetric modes

In this paper a hardware implementation of a Maximum Lyapunov Exponent (MLE) quantifier is designed and implemented using a field programmable gate array (FPGA). The design was optimized in terms of accuracy employing floating point architecture to represent the values. The proposed design takes advantage of the underline parallelism of the MLE computation equations and allows its concurrent implementation based on FPGA technology.

By appealing to a long list of different nonlinear maps we review the characterization of time series arising from chaotic maps. The main tool for this characterization is the permutation Bandt-Pompe probability distribution function. We focus attention on both local and global characteristics of the components of this probability distribution function. We show that forbidden ordinal patterns (local quantifiers) exhibit an exponential growth for pattern-length range 3 ≤ D ≤ 8, in the case of finite time series data. Indeed, there is a minimum D; min-value such that forbidden patterns cannot appear for D, Facultad de Ciencias Exactas, Centro de Investigaciones Ópticas, Facultad de Ingeniería, Instituto de Física La Plata

An approximate solution to the title problem is proposed for the case in which the inner boundary of the circular plate is free and the outer edge is elastically restrained against rotation. The displacement amplitude is approximated by means of a superposition of simple polynomial co-ordinate functions, which satisfy identically the boundary conditions at the outer edge only and which yield excellent accuracy in the case of simply connected circular plates. The optimized Rayleigh–Ritz method is then used to generate the frequency determinant minimizing the eigenvalues with respect to an exponential parameter contained in each polynomial co-ordinate function. A comparison with eigenvalues obtained using a finite element solution is also presented and good agreement is shown to exist.

Methods for evaluating the structural health of mechanical cables and detecting their imminent failure could prevent the loss of valuable equipment and, more importantly, the possible loss of human life. The non-destructive test methods available are: thorough visual examination and measurement of the external diameter; X-rays; (induced) wave propagation; acoustic emission; magnetostrictive sensors; infrared detection. A new method which employs a commercial optical fiber for detecting the breakage of individual wires in a rope is proposed in the present paper.

This paper presents some numerical experiments performed on transverse vibrations and the elastic stability of homogeneous, isotropic, clamped circular plates of discontinuously varying thickness. The purpose of the study is threefold: (1) to determine dynamic stiffening situations; (2) to experiment on the effect of optimization with respect to an exponential parameter (non-integer version of the Rayleigh-Ritz method or the ‘optimized Rayleigh-Ritz method’) as opposed to the classical version of the energy method; and (3) to ascertain the relative accuracy of the optimized Rayleigh-Ritz method by comparing eigenvalues determined using this technique and those calculated using a very efficient standard finite element code.

Natural frequencies and buckling loads of circular plates with stepped thickness over a concentric circular region are determined using the optimized Rayleigh-Ritz method. The solution is obtained for the case of edges elastically restrained against rotation and translation.

We deal here with the issue of determinism versus randomness in time series (TS), with the goal of identifying their relative importance in a given TS. To this end we extend (i) the use of ordinal patterns based probability distribution functions associated to a TS [C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002)] and (ii) the so-called Amigo paradigm of forbidden/missing patterns [J.M. Amigo et al., Europhys. Lett. 79, 50001 (2007)], to analyze deterministic finite TS contaminated with strong additive noises of different correlation-degree. Useful information on the deterministic component of the original time series is obtained with the help of the so-called causal entropy-complexity plane [O.A. Rosso et al., Phys. Rev. Lett. 99, 154102 (2007)].

An exact solution of the title problem is rather difficult to obtain. On the other hand, it is not advantageous from a practical viewpoint if one wishes to take into account several parameters that come into play: flexibility of rotational and translational properties at the plate edge; elastic moduli of the plate material; concentrated mass/total plate mass, etc. In view of these considerations an approximate, yet quite accurate solution is obtained by using the optimized Rayleigh-Ritz method and polynomial co-ordinate functions which satisfy identically the governing boundary conditions. Only axisymmetric modes are considered in the present investigation.

Deterministic ratchets, in the inertial and also in the overdamped limit, have a very complex dynamics, including chaotic motion. This deterministically induced chaos mimics, to some extent, the role of noise, changing, on the other hand, some of the basic properties of thermal ratchets; for example, inertial ratchets can exhibit multiple reversals in the current direction. The direction depends on the amount of friction and inertia, which makes it especially interesting for technological applications such as biological particle separation. We overview in this work different strategies to control the current of inertial ratchets. The control parameters analysed are the strength and frequency of the periodic external force, the strength of the quenched noise that models a non-perfectly-periodic potential, and the mass of the particles. Control mechanisms are associated with the fractal nature of the basins of attraction of the mean velocity attractors. The control of the overdamped motion of noninteracting particles in a rocking periodic asymmetric potential is also reviewed. The analysis is focused on synchronization of the motion of the particles with the external sinusoidal driving force. Two cases are considered: a perfect lattice without disorder and a lattice with noncorrelated quenched noise. The amplitude of the driving force and the strength of the quenched noise are used as control parameters.

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the "causal" entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102] and ii) the estimation of the decay rate of missing ordinal patterns [Amig\'o et al. Europhys. Lett. 79 (2007) 50001, and Carpi et al. Physica A 389 (2010) 2020-2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r = 4) to which we added correlated noise (colored noise with f-k Power Spectrum, 0 {\leq} k {\leq} 2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy-complexity plane this goal can be achieved without additional computations., Comment: submitted to Physica A

The dual deterministic-stochastic behavior of chaotic systems (CS) makes them extremely interesting in electronic engineering as CS may replace noise sources in different applications. Consequently it is convenient to have hardware implementations for both, analog and digital versions. Discrete components, Micro Controllers, Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs) are possible choices.

The role of synchronization on the current of particles in periodically‐forced overdamped ratchets is studied. The main goal is to explain the mean velocity and diffusion on the basis of synchronization between the individual particles motion and the driving force. Both normal and anomalous diffusion are considered. Three cases are studied: (1) a perfect lattice with a sinusoidal driving force, (2) a lattice with quenched disorder, and (3) a perfect lattice with a square driving force. In case (1) synchronization is guaranteed over the whole parameter space and the diffusion coefficient is zero. In case (2) a trapping mechanism appears due to partial loss of synchronization. The mean velocity of the particles and the diffusion coefficient are found to have a non‐monotonic dependence on the quenched noise strength. These non‐trivial results are explained on the basis of the synchronized motion of case (1). Finally, in case (3), the system has neither temporal nor quenched noise but the strong nonlinearity ...

The fundamental frequency of vibration of the structural elements described in the title is determined by using the optimized Rayleigh-Ritz method. Polynomial co-ordinate functions which contain an undetermined exponent γ are used in order to approximate the plate response. The eigenvalues are then minimized with respect to γ. It is assumed that the plate is elastically restrained against rotation along the edge, Buckling parameters are also presented.

An exact solution of the title problem is presented. The overall situation is of great interest in many engineering applications. Three combinations of boundary conditions for the structural element are considered: simply supported, simply supported - clamped and clamped at both ends. An analysis of the situation where the spring-mass system acts as a dynamic absorber cancelling out the motion at the point of attachment for certain modes of vibration is presented. An independent solution has also been obtained by means of a finite element code in order to ascertain the validity and accuracy of the results predicted by the exact solution of Timoshenko's dynamic differential system.

A large number of papers and technical reports are available on the technically important problem of structural elements executing transverse vibrations and carrying concentrated masses. In general it is assumed that the attachment is perfectly rigid. On the other hand, a rather limited amount of published work is available when the mass is elastically connected to the structure. The system then exhibits a more complex behavior than in the case of rigid attachment. The present study deals with the solution of the title problem using the well-known normal mode, sinusoidal eigenfunction expansions.

Civil, naval and ocean engineers are frequently confronted with the problem of mounting dynamic, operational units on structural elements. The designer must be able to determine natural frequencies of the coupled system: structure-motor or engine and its elastic mounting. Frequency coefficients are obtained in the present study for three combinations of boundary conditions: simply supported; simply supported and clamped at both ends.