Enhanced pulse propagation in non-linear arrays of oscillators

The propagation of a pulse in a nonlinear array of oscillators is influenced by the nature of the array and by its coupling to a thermal environment. For example, in some arrays a pulse can be speeded up while in others a pulse can be slowed down by raising the temperature. We begin by showing that an energy pulse (one dimension) or energy front (two dimensions) travels more rapidly and remains more localized over greater distances in an isolated array (microcanonical) of hard springs than in a harmonic array or in a soft-springed array. Increasing the pulse amplitude causes it to speed up in a hard chain, leaves the pulse speed unchanged in a harmonic system, and slows down the pulse in a soft chain. Connection of each site to a thermal environment (canonical) affects these results very differently in each type of array. In a hard chain the dissipative forces slow down the pulse while raising the temperature speeds it up. In a soft chain the opposite occurs: the dissipative forces actually speed up the pulse, while raising the temperature slows it down. In a harmonic chain neither dissipation nor temperature changes affect the pulse speed. These and other results are explained on the basis of the frequency vs energy relations in the various arrays

Amplitude envelope synchronization in coupled chaotic oscillators.

A peculiar type of synchronization has been found when two Van der PolDuffing oscillators, evolving in different chaotic attractors, are coupled. As the coupling increases, the frequencies of the two oscillators remain different, while a synchronized modulation of the amplitudes of a signal of each system develops, and a null Lyapunov exponent of the uncoupled systems becomes negative and gradually larger in absolute value. This phenomenon is characterized by an appropriate correlation function between the returns of the signals, and interpreted in terms of the mutual excitation of new frequencies in the oscillators power spectra. This form of synchronization also occurs in other systems, but it shows up mixed with or screened by other forms of synchronization, as illustrated in this paper by means of the examples of the dynamic behavior observed for three other different models of chaotic oscillators.

Networks of noisy oscillators with correlated degree and frequency dispersion

We investigate how correlations between the diversity of the connectivity of networks and the dynamics at their nodes affect the macroscopic behavior. In particular, we study the synchronization transition of coupled stochastic phase oscillators that represent the node dynamics. Crucially in our work, the variability in the number of connections of the nodes is correlated with the width of the frequency distribution of the oscillators. By numerical simulations on Erdös-Rényi networks, where the frequencies of the oscillators are Gaussian distributed, we make the counterintuitive observation that an increase in the strength of the correlation is accompanied by an increase in the critical coupling strength for the onset of synchronization. We further observe that the critical coupling can solely depend on the average number of connections or even completely lose its dependence on the network connectivity. Only beyond this state, a weighted mean-field approximation breaks down. If noise is present, the correlations have to be stronger to yield similar observations.

Equivalent representation form of oscillators with elastic and damping nonlinear terms

In this work we consider the nonlinear equivalent representation form of oscillators that exhibit nonlinearities in both the elastic and the damping terms. The nonlinear damping effects are considered to be described by fractional power velocity terms which provide better predictions of the dissipative effects observed in some physical systems. It is shown that their effects on the system dynamics response are equivalent to a shift in the coefficient of the linear damping term of a Duffing oscillator. Then, its numerical integration predictions, based on its equivalent representation form given by the well-known forced, damped Duffing equation, are compared to the numerical integration values of its original equations of motion. The applicability of the proposed procedure is evaluated by studying the dynamics response of four nonlinear oscillators that arise in some engineering applications such as nanoresonators, microresonators, human wrist movements, structural engineering design, and chain dynamics of polymeric materials at high extensibility, among others

Caracterització d'oscil·ladors basats en CMOS-M/NEMS i la seva aplicació com a sensors de massa

El present projecte tracta sobre la caracterització d'oscil·ladors basats en ressonadors micro/nanoelectromecànics (M/NEMS) i la seva aplicació com a sensors de massa. Els oscil·ladors utilitzats es basen en un pont i una palanca ressoants M/NEMS, integrats en tecnologia CMOS. En primer lloc s'ha fet una introducció teòrica als conceptes utilitzats per a entendre el funcionament i la caracterització dels dispositius. A continuació s'han realitzat proves per tal de caracteritzar els paràmetres importants per a l'ús dels oscil·ladors com a sensors de massa, com la seva estabilitat en freqüència. Per acabar s'han aplicat aquests sensors en la caracterització i modelització del flux de massa a través d'obertures de dimensions micromètriques.

Anharmonicity contributions to the vibrational second hyperpolarizability of conjugated oligomers

Restricted Hartree-Fock 6-31G calculations of electrical and mechanical anharmonicity contributions to the longitudinal vibrational second hyperpolarizability have been carried out for eight homologous series of conjugated oligomers - polyacetylene, polyyne, polydiacetylene, polybutatriene, polycumulene, polysilane, polymethineimine, and polypyrrole. To draw conclusions about the limiting infinite polymer behavior, chains containing up to 12 heavy atoms along the conjugated backbone were considered. In general, the vibrational hyperpolarizabilities are substantial in comparison with their static electronic counterparts for the dc-Kerr and degenerate four-wave mixing processes (as well as for static fields) but not for electric field-induced second harmonic generation or third harmonic generation. Anharmonicity terms due to nuclear relaxation are important for the dc-Kerr effect (and for the static hyperpolarizability) in the σ-conjugated polymer, polysilane, as well as the nonplanar π systems polymethineimine and polypyrrole. Restricting polypyrrole to be planar, as it is in the crystal phase, causes these anharmonic terms to become negligible. When the same restriction is applied to polymethineimine the effect is reduced but remains quantitatively significant due to the first-order contribution. We conclude that anharmonicity associated with nuclear relaxation can be ignored, for semiquantitative purposes, in planar π-conjugated polymers. The role of zero-point vibrational averaging remains to be evaluated

Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested

Avoiding transcription factor competition at promoter level increases the chances of obtaining oscillations

Background: The ultimate goal of synthetic biology is the conception and construction of genetic circuits that are reliable with respect to their designed function (e.g. oscillators, switches). This task remains still to be attained due to the inherent synergy of the biological building blocks and to an insufficient feedback between experiments and mathematical models. Nevertheless, the progress in these directions has been substantial. Results: It has been emphasized in the literature that the architecture of a genetic oscillator must include positive (activating) and negative (inhibiting) genetic interactions in order to yield robust oscillations. Our results point out that the oscillatory capacity is not only affected by the interaction polarity but by how it is implemented at promoter level. For a chosen oscillator architecture, we show by means of numerical simulations that the existence or lack of competition between activator and inhibitor at promoter level affects the probability of producing oscillations and also leaves characteristic fingerprints on the associated period/amplitude features. Conclusions: In comparison with non-competitive binding at promoters, competition drastically reduces the region of the parameters space characterized by oscillatory solutions. Moreover, while competition leads to pulse-like oscillations with long-tail distribution in period and amplitude for various parameters or noisy conditions, the non-competitive scenario shows a characteristic frequency and confined amplitude values. Our study also situates the competition mechanism in the context of existing genetic oscillators, with emphasis on the Atkinson oscillator.

Entropy change of martensitic transformations in Cu-based shape-memory alloys

We have investigated the different contributions to the entropy change at the martensitic transition of different families of Cu-based shape-memory alloys. The total entropy change has been obtained through calorimetric measurements. By measuring the evolution of the magnetic susceptibility with temperature, the entropy change associated with conduction electrons has been evaluated. The contribution of the anharmonic vibrations of the lattice has also been estimated using various parameters associated with the anharmonic behavior of these alloys, collected from the literature. The results found in the present work have been compared to values published for the martensitic transition of group-IV metals. For Cu-based alloys, both electron and anharmonic contributions have been shown to be much smaller than the overall entropy change. This finding demonstrates that the harmonic vibrations of the lattice are the most relevant contribution to the stability of the bcc phase in Cu-based alloys.

Third order elastic constants of bcc Cu-Al-Ni

We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.

Exported oscillator competition: A concept to analyse complex rhytms

We study the interaction between two independent nonlinear oscillators competing through a neutral excitable element. The first oscillator, completely deterministic, acts as a normal pacemaker sending pulses to the neutral element which fires when it is excited by these pulses. The second oscillator, endowed with some randomness, though unable to make the excitable element to beat, leads to the occasional suppression of its firing. The missing beats or errors are registered and their statistics analyzed in terms of the noise intensity and the periods of both oscillators. This study is inspired in some complex rhythms such as a particular class of heart arrhythmia.

Self-organized criticality induced by diversity

We have studied the collective behavior of a population of integrate-and-fire oscillators. We show that diversity, introduced in terms of a random distribution of natural periods, is the mechanism that permits one to observe self-organized criticality (SOC) in the long time regime. As diversity increases the system undergoes several transitions from a supercritical regime to a subcritical one, crossing the SOC region. Although there are resemblances with percolation, we give proofs that criticality takes place for a wide range of values of the control parameter instead of a single value.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.