Harmonical oscillator and electro-mechanical analogy: an interdiscinary experiment to high precision mass variation measurements

In general, the traditional Physics courses needs examples of the aplications of the Physics concepts in other areas such as Chemistry and Biology. This lacks tend to demotivate Chemistry and Biology students regarding to deal with Physical concepts developed in classroom. In this work, the analogy among mechanic and electric oscillators is investigated to be applied in Chemistry and Biology areas, showing to be valuable due to its aplication in techniques that aims to measure mass variation with high precision. This measure could be made in a direct or indirect way. These techniques are known as electrogravimetric techniques and they are important in biosensor aplications. Thus, this paper explores the electromechanic analogy in an interdisciplinary way involving areas like Physics, Chemistry and Biology. Based on this analogy, it is proposed an experiment that can be applied in different ways, i.e. by an basic approach or more deeper, depending on the students specific formation, in other words, Physics, Chemistry or Biology.

An Investigation into Mechanisms of Loss of Safe Basins in a 2 D.O.F. Nonlinear Oscillator

In this work we consider the transient stability of coupled motions of a 2 D.O.F. nonlinear oscillator that can represent, for example, the motions of a sea vessel under the action of trains of regular lateral waves. Instability is studied as the escape of the system from a safe potential well. The set of initial conditions in phase space that lead to acceptable motions constitutes its safe basin. We investigate the evolution of these safe basins under variation of parameters such as frequency and amplitude of waves, and an internal tuning parameter. Complex nonlinear phenomena are known to play an important role in determining the loss of safe basins as, say, wave amplitude is increased. We therefore investigate those processes, and attempt to classify them in terms of their speed relative to changes in parameter values. "Mechanism basins" are produced depicting regions of parameter space in which rapid or slow losses of safe basin are observed. We propose that a comprehensive understanding of mechanisms of loss of safe basins can be a valuable tool in assessing stability properties of these systems, and we give a conceptual view of how such information could be used.

Chaos in a Two-Degree of Freedom Duffing Oscillator

High dimensional dynamical systems has intricate behavior either on temporal or on spatial evolution properties. Nevertheless, most of the work on chaotic dynamics has been concentrated on temporal behavior of low-dimensional systems. This contribution is concerned with the chaotic response of a two-degree of freedom Duffing oscillator. Since the equations of motion are associated with a five-dimensional system, the analysis is performed by considering two Duffing oscillators, both with single-degree of freedom, coupled by a spring-dashpot system. With this assumption, it is possible to analyze the transmissibility of motion between the two oscillators.

Propriedades espectroscópicas e parâmetros ópticos-eletrônicos dos complexos Ln(NO3)3.2DTPO.4H2O (Ln = Nd e Er)

Complexes with the composition Ln(NO3)3.2DTPO.4H2O (Ln = Nd and Er) were synthesized and characterized by infrared and visible absorption spectra (solid state and solution). The results of the absorption spectra in the solid state suggest that metal-ligand bonds are essentially electrostatic in all complexes. The absorption spectra of the nitrate salt solution presented smaller values of the oscillator strength when compared to the spectra of the complexes in the same solvent.

Sintonização de estados quânticos: um estudo numérico do oscilador harmônico quântico

The quantum harmonic oscillator is described by the Hermite equation.¹ The asymptotic solution is predominantly used to obtain its analytical solutions. Wave functions (solutions) are quadratically integrable if taken as the product of the convergent asymptotic solution (Gaussian function) and Hermite polynomial,¹ whose degree provides the associated quantum number. Solving it numerically, quantization is observed when a control real variable is "tuned" to integer values. This can be interpreted by graphical reading of Y(x) and |Y(x)|², without other mathematical analysis, and prove useful for teaching fundamentals of quantum chemistry to undergraduates.

Evolution of circadian organization in vertebrates

Circadian organization means the way in which the entire circadian system above the cellular level is put together physically and the principles and rules that determine the interactions among its component parts which produce overt rhythms of physiology and behavior. Understanding this organization and its evolution is of practical importance as well as of basic interest. The first major problem that we face is the difficulty of making sense of the apparently great diversity that we observe in circadian organization of diverse vertebrates. Some of this diversity falls neatly into place along phylogenetic lines leading to firm generalizations: i) in all vertebrates there is a "circadian axis" consisting of the retinas, the pineal gland and the suprachiasmatic nucleus (SCN), ii) in many non-mammalian vertebrates of all classes (but not in any mammals) the pineal gland is both a photoreceptor and a circadian oscillator, and iii) in all non-mammalian vertebrates (but not in any mammals) there are extraretinal (and extrapineal) circadian photoreceptors. An interesting explanation of some of these facts, especially the differences between mammals and other vertebrates, can be constructed on the assumption that early in their evolution mammals passed through a "nocturnal bottleneck". On the other hand, a good deal of the diversity among the circadian systems of vertebrates does not fall neatly into place along phylogenetic lines. In the present review we will consider how we might better understand such "phylogenetically incoherent" diversity and what sorts of new information may help to further our understanding of the evolution of circadian organization in vertebrates

Effect of age on upper and lower eyelid saccades

To study the effect of age on the metrics of upper and lower eyelid saccades, eyelid movement of two groups of 30 subjects each were measured using computed image analysis. The patients were divided on the basis of age into a younger group (20-30 years) and an older group (60-91 years). Eyelid saccade functions were fitted by the damped harmonic oscillator model. Amplitude and peak velocity were used to compare the effect of age on the saccades of the upper and lower eyelid. There was no statistically significant difference in saccade amplitude between groups for the upper eyelid (mean ± SEM; upward, young = 9.18 ± 0.32 mm, older = 8.93 ± 0.31 mm, t = 0.56, P = 0.58; downward, young = 9.11 ± 0.27 mm, older = 8.86 ± 0.32 mm, t = 0.58, P = 0.56) However, there was a clear decline in the peak velocity of the upper eyelid saccades of older subjects (upward, young = 59.06 ± 2.34 mm/s, older = 50.12 ± 1.95 mm/s, t = 2.93, P = 0.005; downward, young = 71.78 ± 1.78 mm/s, older = 60.29 ± 2.62 mm/s, t = 3.63, P = 0.0006). In contrast, for the lower eyelid there was a clear increase of saccade amplitude in the elderly group (upward, young = 2.27 ± 0.09 mm, older = 2.98 ± 0.15 mm, t = 4.33, P < 0.0001; downward, young = 2.21 ± 0.10 mm, older = 2.96 ± 0.17 mm, t = 3.85, P < 0.001). These data suggest that the aging process affects the metrics of the lid saccades in a different manner according to the eyelid. In the upper eyelid the lower tension exerted by a weak aponeurosis is reflected only on the peak velocity of the saccades. In the lower eyelid, age is accompanied by an increase in saccade amplitude which indicates that the force transmission to the lid is not affected in the elderly.

A simple model for circadian timing by mammals

Circadian timing is structured in such a way as to receive information from the external and internal environments, and its function is the timing organization of the physiological and behavioral processes in a circadian pattern. In mammals, the circadian timing system consists of a group of structures, which includes the suprachiasmatic nucleus (SCN), the intergeniculate leaflet and the pineal gland. Neuron groups working as a biological pacemaker are found in the SCN, forming a biological master clock. We present here a simple model for the circadian timing system of mammals, which is able to reproduce two fundamental characteristics of biological rhythms: the endogenous generation of pulses and synchronization with the light-dark cycle. In this model, the biological pacemaker of the SCN was modeled as a set of 1000 homogeneously distributed coupled oscillators with long-range coupling forming a spherical lattice. The characteristics of the oscillator set were defined taking into account the Kuramoto's oscillator dynamics, but we used a new method for estimating the equilibrium order parameter. Simultaneous activities of the excitatory and inhibitory synapses on the elements of the circadian timing circuit at each instant were modeled by specific equations for synaptic events. All simulation programs were written in Fortran 77, compiled and run on PC DOS computers. Our model exhibited responses in agreement with physiological patterns. The values of output frequency of the oscillator system (maximal value of 3.9 Hz) were of the order of magnitude of the firing frequencies recorded in suprachiasmatic neurons of rodents in vivo and in vitro (from 1.8 to 5.4 Hz).