The nonlinear relaxation time and quasideterministic-theory approaches to characterize the decay of unestable states

We present the relationship between nonlinear-relaxation-time (NLRT) and quasideterministic approaches to characterize the decay of an unstable state. The universal character of the NLRT is established. The theoretical results are applied to study the dynamical relaxation of the Landau model in one and n variables and also a laser model.

Confinement of discrete breathers in inhomogeneously profiled nonlinear chains

We investigate numerically the scattering of a moving discrete breather on a pair of junctions in a Fermi-Pasta-Ulam chain. These junctions delimit an extended region with different masses of the particles. We consider (i) a rectangular trap, (ii) a wedge shaped trap, and (iii) a smoothly varying convex or concave mass profile. All three cases lead to DB confinement, with the ease of trapping depending on the profile of the trap. We also study the collision and trapping of two DBs within the profile as a function of trap width, shape, and approach time at the two junctions. The latter controls whether one or both DBs are trapped.

From lattice-gas models to nonlinear diffusion models: A derivation of macroscopic equations and fluctuations

We derive nonlinear diffusion equations and equations containing corrections due to fluctuations for a coarse-grained concentration field. To deal with diffusion coefficients with an explicit dependence on the concentration values, we generalize the Van Kampen method of expansion of the master equation to field variables. We apply these results to the derivation of equations of phase-separation dynamics and interfacial growth instabilities.

Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

Nonlinear filtering in object and Fourier space in a joint transform optical correlator: comparison and experimental realization

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed; their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. All cases are simulated and experimentally implemented by a compact joint transform correlator.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Linear least squares estimation of the first order moving average parameter

We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Nonlinear chemoconvection in the Methylene-blue-glucose system

Interfacial hydrodynamic instabilities arise in a range of chemical systems. One mechanism for instability is the occurrence of unstable density gradients due to the accumulation of reaction products. In this paper we conduct two-dimensional nonlinear numerical simulations for a member of this class of system: the methylene-blue¿glucose reaction. The result of these reactions is the oxidation of glucose to a relatively, but marginally, dense product, gluconic acid, that accumulates at oxygen permeable interfaces, such as the surface open to the atmosphere. The reaction is catalyzed by methylene-blue. We show that simulations help to disassemble the mechanisms responsible for the onset of instability and evolution of patterns, and we demonstrate that some of the results are remarkably consistent with experiments. We probe the impact of the upper oxygen boundary condition, for fixed flux, fixed concentration, or mixed boundary conditions, and find significant qualitative differences in solution behavior; structures either attract or repel one another depending on the boundary condition imposed. We suggest that measurement of the form of the boundary condition is possible via observation of oxygen penetration, and improved product yields may be obtained via proper control of boundary conditions in an engineering setting. We also investigate the dependence on parameters such as the Rayleigh number and depth. Finally, we find that pseudo-steady linear and weakly nonlinear techniques described elsewhere are useful tools for predicting the behavior of instabilities beyond their formal range of validity, as good agreement is obtained with the simulations.

Nonlinear effects in the dynamics of transient pattern formation in nematics

A nonlinear calculation of the dynamics of transient pattern formation in the Fréedericksz transition is presented. A Gaussian decoupling is used to calculate the time dependence of the structure factor. The calculation confirms the range of validity of linear calculations argued in earlier work. In addition, it describes the decay of the transient pattern.

"Suddenly I get into the zone": Examining discontinuities and nonlinear changes in flow experiences at work

Work-related flow is defined as a sudden and enjoyable merging of action and awareness that represents a peak experience in the daily lives of workers. Employees" perceptions of challenge and skill and their subjective experiences in terms of enjoyment, interest and absorption were measured using the experience sampling method, yielding a total of 6981 observations from a sample of 60 employees. Linear and nonlinear approaches were applied in order to model both continuous and sudden changes. According to the R2, AICc and BIC indexes, the nonlinear dynamical systems model (i.e. cusp catastrophe model) fit the data better than the linear and logistic regression models. Likewise, the cusp catastrophe model appears to be especially powerful for modelling those cases of high levels of flow. Overall, flow represents a nonequilibrium condition that combines continuous and abrupt changes across time. Research and intervention efforts concerned with this process should focus on the variable of challenge, which, according to our study, appears to play a key role in the abrupt changes observed in work-related flow.

Dynamics of flow: a nonlinear perspective

The aims of this study are to consider the experience of flow from a nonlinear dynamics perspective. The processes and temporal nature of intrinsic motivation and flow, would suggest that flow experiences fluctuate over time in a dynamical fashion. Thus it can be argued that the potential for chaos is strong. The sample was composed of 20 employees (both full and part time) recruited from a number of different organizations and work backgrounds. The Experience Sampling Method (ESM) was used for data collection. Once obtained the temporal series, they were subjected to various analyses proper to the com- plexity theory (Visual Recurrence Analysis and Surrogate Data Analysis). Results showed that in 80% of the cases, flow presented a chaotic dynamic, in that, flow experiences delineated a complex dynamic whose patterns of change were not easy to predict. Implications of the study, its limitations and future research are discussed.

Estudi comparatiu: errors de les infermeres en la preparació i l'administració de la medicació segons dos sistemes de distribució

Introducció: Els errors de medicació són definits com qualsevol incident prevenible que pot causar dany al pacient o donar lloc a una utilització inapropiada dels medicaments, quan aquests estan sota el control dels professionals sanitaris o del pacient. Els errors en la preparació i l’administració de medicació són els més comuns de l’àrea hospitalària i, tot i la llarga cadena per la qual passa el fàrmac, el professional d’infermeria és el últim responsable de l’acció, tenint així, un paper molt important en la seguretat del pacient. Les infermeres dediquen el 40% del temps de la seva jornada laboral en tasques relacionades amb la medicació. Objectiu: Determinar si les infermeres produeixen més errors si treballen amb sistemes de distribució de medicació de stock o en sistemes de distribució unidosis de medicació. Metodologia: Estudi quantitatiu, observacional i descriptiu, on la notificació d’errors (o oportunitats d’error) realitzats per la infermera, en les fases de preparació i administració de medicació, es farà mitjançant un qüestionari autoelaborat. Els elements a identificar seran: el tipus d’error, les causes que poden haver--‐lo produït, la seva potencial gravetat i qui l’ha pogut evitar; així com el tipus de professional que l’ha produït. Altres dades rellevants són: el medicament implicat junt amb la dosis i la via d’administració i el sistema de distribució utilitzat. Mostreig i mostra: El mostreig serà no probabilístic i per conveniència. S’escolliran aquelles infermeres que l’investigador consideri amb les característiques necessàries per participar en l’estudi, així que la mostra estarà formada per les infermeres les quals treballen a la unitat 40 de l’Hospital del Mar i utilitzen un sistema de distribució de medicació de dosis unitàries i les infermeres que treballen a urgències (concretament a l’àrea de nivell dos) de l’Hospital del Mar les quals treballen amb un sistema de distribució de medicació de stock.

Generation and nonlinear evolution of shore-oblique/transverse sand bars

The coupling between topography, waves and currents in the surf zone may selforganize to produce the formation of shore-transverse or shore-oblique sand bars on an otherwise alongshore uniform beach. In the absence of shore-parallel bars, this has been shown by previous studies of linear stability analysis, but is now extended to the finite-amplitude regime. To this end, a nonlinear model coupling wave transformation and breaking, a shallow-water equations solver, sediment transport and bed updating is developed. The sediment flux consists of a stirring factor multiplied by the depthaveraged current plus a downslope correction. It is found that the cross-shore profile of the ratio of stirring factor to water depth together with the wave incidence angle primarily determine the shape and the type of bars, either transverse or oblique to the shore. In the latter case, they can open an acute angle against the current (upcurrent oriented) or with the current (down-current oriented). At the initial stages of development, both the intensity of the instability which is responsible for the formation of the bars and the damping due to downslope transport grow at a similar rate with bar amplitude, the former being somewhat stronger. As bars keep on growing, their finite-amplitude shape either enhances downslope transport or weakens the instability mechanism so that an equilibrium between both opposing tendencies occurs, leading to a final saturated amplitude. The overall shape of the saturated bars in plan view is similar to that of the small-amplitude ones. However, the final spacings may be up to a factor of 2 larger and final celerities can also be about a factor of 2 smaller or larger. In the case of alongshore migrating bars, the asymmetry of the longshore sections, the lee being steeper than the stoss, is well reproduced. Complex dynamics with merging and splitting of individual bars sometimes occur. Finally, in the case of shore-normal incidence the rip currents in the troughs between the bars are jet-like while the onshore return flow is wider and weaker as is observed in nature.