On the dependence of (f2-f1) difference tones on subject and on additional masker

For a group of eight subjects showing stronger than usual irregularities in the level dependence of the quadratic distortion product, the level and phase of the (f2-f1) difference tone were measured using the method of cancellation for three sets of primary frequencies as a function of the primary levels. An additional masker seems to "linearize" the level dependence toward regular behavior. Using data sets produced with and without the additional masker, it is possible to separate two sources of quadratic nonlinearity, one with regular behavior presumably located in the middle ear and another with irregular behavior (similar to that of cubic distortion) presumably located in the characteristics of outer hair cells. Through the "subtraction" of empirically determined patterns from idealized patterns, it is possible to approximate patterns stemming from the inner-ear source alone.     

The effect of nonlinearity of the recording media response on the properties of thick phase holograms

The effect of nonlinearity of a photosensitive medium response on the diffraction properties of thick phase holograms is analyzed on the basis of coupled-wave equations. It is shown that, for a typical dependence of the refractive index on the exposure, the response nonlinearity lowers the diffraction efficiency of a hologram illuminated by an s-polarized light. For the p polarization of the reading beam, the response nonlinearity reduces the hologram efficiency when the angle between the beams diffracted into the zero and second orders (into the minus first and first orders) is smaller than 90°, increases the efficiency for angles larger than 90°, and hardly affects the diffraction efficiency when this angle is close to 90°. The results for p polarization are obtained, to the best of our knowledge, for the first time. The analysis of angular selectivity of the gratings has shown that the effect of nonlinearity becomes particularly important for light waves incident on the hologram at angles close to the Bragg one. It is also found that, for any thickness of the photosensitive medium, there exists an optimum value of the maximum change in the refractive index, for which the diffraction efficiency may be close to 100% in a wide range of exposures. In this case, the nonlinearity for s polarization stabilizes, to some extent, the dependence of the diffraction efficiency on the exposure.     

Texture-induced modulations of friction force: the fingerprint effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.     

On the Strongly Damped Wave Equation

We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in the presence of a quite general nonlinearity of critical growth. When the nonlinearity is subcritical, we prove the existence of an exponential attractor of optimal regularity, having a basin of attraction coinciding with the whole phase-space. As a byproduct, the universal attractor is regular and of finite fractal dimension. Moreover, we carry out a detailed analysis of the asymptotic behavior of the solutions in dependence of the damping coefficient.Research partially supported the Italian MIUR Research Projects Problemi di Frontiera Libera nelle Scienze Applicate, Aspetti Teorici e Applicativi di Equazioni a Derivate Parziali and Metodi Variazionali e Topologici nello Studio dei Fenomeni Nonlineari. The second author was also supported by the Istituto Nazionale di Alta Matematica F. Severi (INdAM).     

Nonlinear response and avalanche behavior in metallic glasses

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd₄₀Ni₄₀P₂₀ metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke’s Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.     

Multigap superconductivity in sesquicarbides La2C3 and Y2C3

A complex structure of the superconducting order parameter in Ln2C3 (Ln=La,Y) is demonstrated by muon spin relaxation measurements in their mixed state. The muon depolarization rate sigma v(T)] exhibits a characteristic temperature dependence that can be perfectly described by a phenomenological double-gap model for nodeless superconductivity. While the magnitude of two gaps is similar between La2C3 and Y2C3, a significant difference in the interband coupling between those two cases is clearly observed in the behavior of sigma v(T).     

Winding numbers for the supercritical sine circle map

The dependence of the winding number on the initial value and on the nonlinearity for the supercritical sine circle map is discussed. Analytical investigations and numerical results show that some scaling behavior for the winding number can be extracted.     

Temperature dependent electrophysical characteristics of GaAs-polymer composite varistors

A composition of GaAs-polymer tiny particles was pressed at a temperature of 130 °C and a pressure of 60 MPa and its current–voltage characteristic was studied. The result shows that the prepared disk has varistor behavior and can therefore be used to protect circuits from low overvoltage transients higher than 62 V. Temperature dependence of current-voltage characteristic and the electrical conductivity of the sample were investigated in the temperature range of 25–100 °C. It has been found that increase in temperature results in lower breakdown voltage and nonlinearity coefficient. At high temperatures, nonlinearity in the I–V characteristic of sample disappears and the conductivity becomes Ohmic in nature. The sample has hysteresis which decreases through increase in temperature. Annealing effect on leakage current and breakdown voltage was both investigated and analyzed using SEM micrographs. Finally, the electrical bandgap of the sample was measured.     

Modeling the combined effects of basilar membrane nonlinearity and roughness on stimulus frequency otoacoustic emission fine structure

A theoretical framework for describing the effects of nonlinear reflection on otoacoustic emission fine structure is presented. The following models of cochlear reflection are analyzed: weak nonlinearity, distributed roughness, and a combination of weak nonlinearity and distributed roughness. In particular, these models are examined in the context of stimulus frequency otoacoustic emissions (SFOAEs). In agreement with previous studies, it is concluded that only linear cochlear reflection can explain the underlying properties of cochlear fine structures. However, it is shown that nonlinearity can unexpectedly, in some cases, significantly modify the level and phase behaviors of the otoacoustic emission fine structure, and actually enhance the pattern of fine structures observed. The implications of these results on the stimulus level dependence of SFOAE fine structure are also explored.     

Temperature dependence of the band gap of semiconducting carbon nanotubes

The temperature dependence of the band gap of semiconducting single-wall carbon nanotubes (SWNTs) is calculated by direct evaluation of electron-phonon couplings within a "frozen-phonon" scheme. An interesting diameter and chirality dependence of E(g)(T) is obtained, including nonmonotonic behavior for certain tubes and distinct "family" behavior. These results are traced to a strong and complex coupling between band-edge states and the lowest-energy optical phonon modes in SWNTs. The E(g)(T) curves are modeled by an analytic function with diameter- and chirality-dependent parameters; these provide a valuable guide for systematic estimates of E(g)(T) for any given SWNT. The magnitudes of the temperature shifts at 300 K are smaller than 12 meV and should not affect (n,m) assignments based on optical measurements.     

Study of the Nonlinear Response of Superconductors in the Microwave Band Using a Local Technique

Using a local technique, we study the microwave radiation power P₃(T,P,H_dc) at the triple frequency of the main signal as a function of the temperature T, the input power P, and the external magnetic field H_dc perpendicular to the superconductor surface for YBa₂Cu₃O₇ (YBCO) films, monocrystals, and polycrystals and for Nb films. The most distinctive feature of the temperature dependence P₃(T) of nonlinear response of superconductors is a maximum of the nonlinearity near the critical temperature T_c. Spatial distributions of the third-harmonic power are obtained for YBCO films at various temperatures. These distributions are indicative of a nonuniform distribution of T_c over the superconductor surface. Additional nonlinearity maxima are discovered in the dependence P₃(T) for YBCO films and monocrystals at temperatures about 2T_c/3. These maxima are probably related to the existence of several superconducting phases with different critical temperatures. For Nb films, the second nonlinearity maximum in the dependence P₃(T) appears only in the presence of an external magnetic field. The experimental data are interpreted within the framework of a two-fluid model of a superconductor, which takes into account the phenomenological nonlinear relationship between the vector potential A and the supercurrent j_s(A). The origin of nonlinearity in the studied superconductors is discussed.     

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.     

Characteristics of distortion product otoacoustic emissions in the frog from L1,L2 maps

For a given set of stimulus frequencies (f1 ,f2), the level of distortion product otoacoustic emissions (DPOAEs) varies with the levels of the stimulus tones. By variation of the stimulus levels, L1,L2-maps for DPOAEs can be constructed. Here, we report on L1 ,L2-maps for DPOAEs from the frog ear. In general, these maps were similar to those obtained from the mammalian cochlea. We found a conspicuous difference between the equal-level contour lines for low-level and high-level DPOAEs, which could be modeled by a saturating and an expansive nonlinearity, respectively. The transition from the high-level to the low-level response was accompanied by a DPOAE phase-change, which increased from 0 to pi rad with increasing frequency. These results suggest that in the frog low-level and high-level DPOAEs are generated by separate nonlinear mechanisms. Also, there was a conspicuous difference in the growth of the low-level emissions from the two anuran auditory papillae. In the basilar papilla, this growth was expansive for the lowest stimulus levels and saturated for intermediate levels. This is consistent with the behavior of a Boltzman nonlinearity. In the amphibian papilla this growth was compressive, suggesting the additional effect of a compressive amplification mechanism on the generation of DPOAEs.     

Thermal nonlinearity in a photoacoustic cell

The effect of the thermal nonlinearity caused by the temperature dependence of the specific heat and thermal conductivity of a sample, substrate, and air on the temperature field in a photoacoustic cell is stud-ied theoretically. Exact solutions are obtained for a steady temperature field with allowance for thermal nonlin-earity and for a nonsteady field without allowance for this nonlinearity. The nonsteady nonlinear problem was solved numerically. It is shown that, due to thermal nonlinearity, the linear dependence of the temperature of the irradiated surface on the heating beam intensity gradually transforms into a power-law dependence as the beam intensity increases.     

Dynamics of the spectral width of intense laser pulses consisting of several field oscillations in optical waveguides

The dependence of the rms spectral width of a light pulse consisting of several light-field oscillations on the distance passed in an optical waveguide with arbitrary dispersion and nonresonant electronic nonlinearity has been derived. This dependence allows one to rapidly predict the scenarios of the initial evolution of the spectrum (broadening, distance independence, or compression) by using the input pulse parameters and waveguide characteristics. It is shown that the pulse spectral width increases when the enrichment of the spectrum due to the generation of multiple harmonics is taken into account. In this case, for pulses with the spectrum in the region of the anomalous group dispersion of the waveguide, there is the intensity range for which the self-narrowing of the main spectral peak around the central radiation frequency is characteristic.     

Mechanism of formation of nonlinearity in the dose dependence of the thermoluminescence output for anion-defect α-Al2O3 crystals

The mechanism of formation of nonlinearity in the dose dependence of the thermoluminescence output was investigated for anion-defect α-Al₂O₃ single crystals. The experiments revealed a new specific feature: the nonlinearity of the dose dependence of the thermoluminescence output depends on the heating rate of crystals during recording of thermoluminescence. It was established that this effect and other thermoluminescence features studied earlier for anion-defect α-Al₂O₃ crystals are adequately described in the framework of a unified mechanism associated with the interactive interaction of dosimetric and deep traps. Recommendations are given for a decrease in the range of the superlinear portion in the dose dependence of the thermoluminescence output for the crystals under investigation.     

Theory of FID NMR signal dephasing induced by mesoscopic magnetic field inhomogeneities in biological systems.

A theory of the NMR signal dephasing due to the presence of tissue-specific magnetic field inhomogeneities is developed for a two-compartment model. Randomly distributed magnetized objects of finite size embedded in a given media are modeled by ellipsoids of revolution (prolate and oblate spheroids). The model can be applied for describing blood vessels in a tissue, red blood cells in the blood, marrow within trabecular bones, etc. The time dependence of the dephasing function connected with the spins inside of the objects, s(i), is shown to be expressed by Fresnel functions and creates a powder-type signal in the frequency domain. The short-time regime of the dephasing function for spins outside the objects, s(e), is always characterized by Gaussian time dependence, s(e) approximately exp[-zeta(k)(t/tc)2], with zeta being a volume fraction occupied by the objects, t(c) being a characteristic dephasing time, and the coefficient k depending on the ellipsoid's shape through the aspect ratio of its axes (a/c). The long-time asymptotic behavior of s(e) is always "quasispherical"-linear exponential in time, s(e) approximately exp(-zetaCt/tc), with the same "spherical" decay rate for any ellipsoidal shape. For long prolate spheroids (a/c)<1, there exists an intermediate characteristic regime with a linear exponential time behavior and an aspect-ratio-dependent decay rate smaller than (zetaC/tc).     

Energy harvesting in the nonlinear two-masses piezoelastic system driven by harmonic excitations

We examine the energy harvesting system consisted of two different masses (magnets) attached to piezoelastic oscillators, coupled by the electric circuit, and driven by harmonic excitations. The nonlinearity of the system is achieved by variable distance between vibrating magnetic masses and the magnets attached directly to the harvester. We also introduce the mistuning parameter which describes the disproportion of vibrating masses (their ratio). In our work we examine the dependence of output power (in terms of mean squared voltage) generated on electric load on excitation frequencies for different values of mistuning parameter and additionally for different values of system nonlinearity parameter. We compare obtained results with the dia- grams presenting relative displacements of these oscillators (in terms of standard deviation) vs. excitation frequencies. In the second part of this paper we present the phase boundary lines (phase portraits) for selected values of applied frequency to show the complicated behavior of the oscillators in the nonlinear regime when the mistuning appears.     

Synchrony suppression in complex stimulus responses of a biophysical model of the cochlea

A minimal biophysical model of the cochlea is used to investigate the validity of the hypothesis that a single compressive nonlinearity at the hair cell level can explain some of the suppression phenomena in cochlear responses to complex stimuli. The dependencies of the model responses on the amplitudes and frequencies of two-tone stimuli resemble in many respects the behavior of the experimental data, and can be traced to explicit biophysical parameters in the model. Most discrepancies between theory and experiment stem from simplifications in parameters of the minimal model that play no direct role in the hypothesis. The analysis and simulations predict further results which, pending experimental verification, may provide a more direct test of the influence of the compressive nonlinearity on the relative amplitudes of the synchronous response components, and hence of its role in synchrony suppression. For instance, regardless of the overall absolute levels of a two-tone stimulus applied to this type of model, the ratio of the amplitudes at the input and the ratio of the corresponding responses at the output remain approximately constant and equal (the output ratio changes by at most 6 dB in favor of the stronger tone). Other nonlinear responses to multitonal stimuli can also be reproduced, such as "spectral edge enhancement" [Horst et al., Peripheral Auditory Mechanisms (Springer, Berlin, 1985)] and some aspects of three-tone suppression [Javel et al., Mechanisms of Hearing (Monash U.P., Australia, 1983)]. In contrast to the complex behavior of suppression with increasing sound intensity and the drastic influence of the compressive nonlinearity on the absolute response measures on the auditory nerve (e.g., average rate and synchrony profiles), the percepts of complex sounds are relatively stable. This suggests that the invariant relative response measures are more likely used in the encoding and CNS extraction of the spectrum of complex stimuli such as speech.