Diego López González

Nonlinear Dynamics of the Perceived Pitch of Complex Sounds

Institut Mediterrani d’Estudis Avanc¸ats, IMEDEA (CSIC–UIB), E-07071 Palma de Mallorca, Spain(Physical Review Letters, 82, 5389–5392, 1999)We apply results from nonlinear dynamics to an old problem in acoustical physics: the mechanism of theperception of the pitch of sounds, especially the sounds known as complex tones that are important for musicand speech intelligibility.PACS numbers: 05.45.-a, 43.66.+y, 87.19.La

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Brinicles as a case of inverse chemical gardens

Brinicles are hollow tubes of ice from centimeters to meters in length that form under floating sea ice in the polar oceans when dense, cold brine drains downward from sea ice to seawater close to its freezing point. When this extremely cold brine leaves the ice, it freezes the water it comes into contact with: a hollow tube of ice-a brinicle-growing downward around the plume of descending brine. We show that brinicles can be understood as a form of the self-assembled tubular precipitation structures termed chemical gardens, which are plantlike structures formed on placing together a soluble metal salt, often in the form of a seed crystal, and an aqueous solution of one of many anions, often silicate. On one hand, in the case of classical chemical gardens, an osmotic pressure difference across a semipermeable precipitation membrane that filters solutions by rejecting the solute leads to an inflow of water and to its rupture. The internal solution, generally being lighter than the external solution, flows up through the break, and as it does so, a tube grows upward by precipitation around the jet of internal solution. Such chemical-garden tubes can grow to many centimeters in length. In the case of brinicles, on the other hand, in floating sea ice we have porous ice in a mushy layer that filters out water, by freezing it, and allows concentrated brine through. Again there is an osmotic pressure difference leading to a continuing ingress of seawater in a siphon pump mechanism that is sustained as long as the ice continues to freeze. Because the brine that is pumped out is denser than the seawater and descends rather than rises, a brinicle is a downward-growing tube of ice, an inverse chemical garden.

Size dependence of domain pattern transfer in multiferroic heterostructures

Magnetoelectric coupling in multiferroic heterostructures can produce large lateral modulations of magnetic anisotropy enabling the imprinting of ferroelectric domains into ferromagnetic films. Exchange and magnetostatic interactions within ferromagnetic films oppose the formation of such domains. Using micromagnetic simulations and a one-dimensional model, we demonstrate that competing energies lead to the breakdown of domain pattern transfer below a critical domain size. Moreover, rotation of the magnetic field results in abrupt transitions between two scaling regimes with different magnetic anisotropy. The theoretical predictions are confirmed by experiments on CoFeB/BaTiO3 heterostructures.

AESTHETICS, DYNAMICS, AND MUSICAL SCALES: A GOLDEN CONNECTION

Number theory has recently found a quantity of applications in the natural and applied sciences, and in particular in the study of nonlinear dynamical systems. As our sensory systems are highly nonlinear, it is natural to suppose that number theory also plays an important rôle in the description of perception, including aesthetics. Here we present a mathematical construction, based on number-theoretical properties of the golden mean, that generates meaningful musical scales of different numbers of notes. We demonstrate that these numbers coincide with the number of notes that an equal-tempered scale must have in order to optimize its approximation to the currently used harmonic musical intervals. Scales with particular harmonic properties and with more notes than the twelve-note scale now used in Western music can be generated. These scales offer interesting new possibilities for artists in the emerging musical world of microtonality and may be rooted in objective phenomena taking place in the nonlinearities of our perceptual and nervous systems.

Influence of elastically pinned magnetic domain walls on magnetization reversal in multiferroic heterostructures

In elastically coupled multiferroic heterostructures that exhibit full domain correlations between ferroelectric and ferromagnetic sub-systems, magnetic domain walls are firmly pinned on top of ferroelectric domain boundaries. In this work we investigate the influence of pinned magnetic domain walls on the magnetization reversal process in a Co40Fe40B20 wedge film that is coupled to a ferroelectric BaTiO3 substrate via interface strain transfer. We show that the magnetic field direction can be used to select between two distinct magnetization reversal mechanisms, namely (1) double switching events involving alternate stripe domains at a time or (2) synchronized switching of all domains. Furthermore, scaling of the switching fields with domain width and film thickness is also found to depend on field orientation. These results are explained by considering the dissimilar energies of the two types of pinned magnetic domain walls that are formed in the system.

Metallic contact between MoS2 and Ni via Au Nanoglue

A critical factor for electronics based on inorganic layered crystals stems from the electrical contact mode between the semiconducting crystals and the metal counterparts in the electric circuit. Here, a materials tailoring strategy via nanocomposite decoration is carried out to reach metallic contact between MoS2 matrix and transition metal nanoparticles. Nickel nanoparticles (NiNPs) are successfully joined to the sides of a layered MoS2 crystal through gold nanobuffers, forming semiconducting and magnetic NiNPs@MoS2 complexes. The intrinsic semiconducting property of MoS2 remains unchanged, and it can be lowered to only few layers. Chemical bonding of the Ni to the MoS2 host is verified by synchrotron radiation based photoemission electron microscopy, and further proved by first-principles calculations. Following the systems band alignment, new electron migration channels between metal and the semiconducting side contribute to the metallic contact mechanism, while semiconductor-metal heterojunctions enhance the photocatalytic ability.

Two musical paths to the Farey series and devil's staircase

At the 2007 Helmholtz Workshop in Berlin, two seemingly disparate papers were presented. One of these, by Julyan Cartwright, Diego González, and Oreste Piro, dealt with a nonlinear dynamical model for pitch perception based on frequency ratios and forced oscillators, while the other, by Jack Douthett and Richard Krantz, focused on musical scales, maximally even (ME) sets, and their relationship to the one-dimensional antiferromagnetic Ising model. Both these approaches lead to a fractal structure involving Farey series known as a devils staircase. Why is this? What is the connection between them? The ME sets approach is related to the Ising model of statistical physics; on the other hand, the forced oscillator model relates to the circle map of dynamical systems. Thus we find ourselves facing a deeper question: what are the links between these two paradigms, the Ising model and the circle map, that are fundamental to statistical physics on the one hand and to dynamical systems on the other? Here we present the two halves of the work side by side, so that the construction of the two arguments that arrive at a devils staircase in music can be seen together.

Electric-field-driven domain wall dynamics in perpendicularly magnetized multilayers

We report on reversible electric-field-driven magnetic domain wall motion in a Cu/Ni multilayer on a ferroelectric BaTiO3 substrate. In our heterostructure, strain-coupling to ferroelastic domains with in-plane and perpendicular polarization in the BaTiO3 substrate causes the formation of domains with perpendicular and in-plane magnetic anisotropy, respectively, in the Cu/Ni multilayer. Walls that separate magnetic domains are elastically pinned onto ferroelectric domain walls. Using magneto-optical Kerr effect microscopy, we demonstrate that out-of-plane electric field pulses across the BaTiO3 substrate move the magnetic and ferroelectric domain walls in unison. Our experiments indicate an exponential increase of domain wall velocity with electric field strength and opposite domain wall motion for positive and negative field pulses. The application of a magnetic field does not affect the velocity of magnetic domain walls, but independently tailors their internal spin structure, causing a change in domain...

Reconfigurable magnetic logic based on the energetics of pinned domain walls

A magnetic logic concept based on magnetic switching in three stripe domains separated by pinned magnetic domain walls is proposed. The relation between the inputs and the output of the logic operator is determined by the energetics of the domain walls, which can be switched between two distinctive states by an external magnetic field. Together with magnetic read-out along two orthogonal directions, non-volatile AND, OR, NAND, and NOR gates can be created. The logic concept is experimentally demonstrated using CoFeB films on BaTiO3 substrates, and micromagnetic simulations are used to analyze the energetics of the system.