Robust determination of relaxation times spectra of long-time multirelaxation processes.

Long-time relaxation processes occur in numerous physical systems. They are often regarded as multirelaxation processes, which are a superposition of exponential decays with a certain distribution of relaxation times. The relaxation times spectra often convey information about the underlying physics. Extracting the spectrum of relaxation times from experimental data is, however, difficult. This is partly due to the mathematical properties of the problem and partly due to experimental limitations. In this paper, we perform the inversion of time-series relaxation data into a relaxation spectrum using the singular value decomposition accompanied by the Akaike information criterion estimator. We show that this approach does not need any a priori information on the spectral shape and that it delivers a solution that consistently approximates the best one achievable for given experimental dataset. On the contrary, we show that the solution obtained imposing an optimal fit of experimental data is often far from reconstructing well the distribution of relaxation times.

Proof of concept of a frequency-preserving and time-invariant metamaterial-based nonlinear acoustic diode.

Acoustic filters and metamaterials have become essential components for elastic wave control in applications ranging from ultrasonics to noise abatement. Other devices have been designed in this field, emulating their electromagnetic counterparts. One such case is an acoustic diode or rectifier, which enables one-way wave transmission by breaking the wave equation-related reciprocity. Its achievement, however, has proved to be rather problematic, and current realizations display a number of shortcomings in terms of simplicity and versatility. Here, we present the design, fabrication and characterization of a device able to work as an acoustic diode, a switch and a transistor-like apparatus, exploiting symmetry-breaking nonlinear effects like harmonic generation and wave mixing, and the filtering capabilities of metamaterials. This device presents several advantages compared with previous acoustic diode realizations, including versatility, time invariance, frequency preserving characteristics and switchability. We numerically evaluate its efficiency and demonstrate its feasibility in a preliminary experimental realization. This work may provide new opportunities for the practical realization of structural components with one-way wave propagation properties.

Proof of Concept for an Ultrasensitive Technique to Detect and Localize Sources of Elastic Nonlinearity Using Phononic Crystals.

The appearance of nonlinear effects in elastic wave propagation is one of the most reliable and sensitive indicators of the onset of material damage. However, these effects are usually very small and can be detected only using cumbersome digital signal processing techniques. Here, we propose and experimentally validate an alternative approach, using the filtering and focusing properties of phononic crystals to naturally select and reflect the higher harmonics generated by nonlinear effects, enabling the realization of time-reversal procedures for nonlinear elastic source detection. The proposed device demonstrates its potential as an efficient, compact, portable, passive apparatus for nonlinear elastic wave sensing and damage detection.

Modeling dynamic acousto-elastic testing experiments: validation and perspectives.

Materials possessing micro-inhomogeneities often display a nonlinear response to mechanical solicitations, which is sensitive to the confining pressure acting on the sample. Dynamic acoustoelastic testing allows measurement of the instantaneous variations in the elastic modulus due to the change of the dynamic pressure induced by a low-frequency wave. This paper shows that a Preisach-Mayergoyz space based hysteretic multi-state elastic model provides an explanation for experimental observations in consolidated granular media and predicts memory and nonlinear effects comparable to those measured in rocks.

Effects of experimental configuration on the detection threshold of hysteretic elastic nonlinearity.

Nonlinear elastic signature of granular consolidated or damaged media is often very small and might easily fall within the noise level. Therefore, it is important to determine an excitation amplitude threshold above which nonlinear measurements start to be meaningful. In this paper, we analyze the way this threshold is influenced by some parameters of the experimental configuration, such as the receiver position, and of the data analysis, such as the considered reference amplitude. Furthermore, this contribution shows that extracting absolute values of the nonlinear parameters often requires the a priori knowledge of the resonance structure of the medium.

Effects of transducer size on impedance spectroscopy measurements.

The response to an electric field of electrolytic solutions, gels, liquid crystals, and other soft materials is described by the drift-diffusion and Poisson equations. Existing models, used for the interpretation of experimental data, usually consider the system as one dimensional (1D), which is valid only for an infinite electrode size. Here we solve numerically the model equations in 2D, considering a circular electrode with a finite radius, and discuss the limit of validity of the 1D approximation.

Nonequilibrium phenomena in damaged media and their effects on the elastic properties.

Concrete, particularly if damaged, exhibits a peculiar nonlinear elastic behavior, which is mainly due to the coupling between nonequilibrium and nonlinear features, the two of which are intrinsically connected. More specifically, the formulation of a constitutive equation able to properly predict the dynamic behavior of damaged concrete is made difficult by the concomitant presence of two mechanisms: The modification of the microstructure of the medium and the transition to a new elastic state caused by a finite amplitude excitation (conditioning). Memory of that new state is kept when the excitation is removed, before relaxation back to the original elastic state takes place. Indeed, besides accounting for linear and nonlinear parameters, a realistic constitutive equation to be used in reliable prediction models should take into account nonequilibrium effects. Specific parameters, sensitive to finite amplitude excitations, should be introduced to provide information about conditioning effects. In this paper, experimental results indicating that nonlinearity of damaged concrete is memory-dependent will be presented and the implications of such findings in the development of physical models, with relevant outcomes for the characterization of hysteretical features, will be discussed.

Similarities and differences among the models proposed for real electrodes in the Poisson-Nernst-Planck theory.

The ionic distribution induced by an external field is investigated by means of the Poisson-Nernst-Planck model, by taking into account the non-blocking properties of the limiting electrodes. Three types of models proposed for the description of real electrodes are considered. The first two assume an ionic current on the electrodes proportional to the variation of the bulk density of ions and to the surface electric field, respectively. The third model assumes that the sample is limited by perfectly blocking electrodes with a true resistance in parallel to the cell. Here we show that the first two models are equivalent, in the sense that it is possible to find a phenomenological parameter by means of which the predictions of the two models, for what concerns the spectra of the real and imaginary parts of the impedance of the cell, are the same. On the contrary, the third model is equivalent to the others only if the conduction current across the electrodes is small with respect to the displacement current.

Break of reciprocity principle due to localized nonlinearities in concrete.

The effects of localized nonlinearities on the reciprocity principle in the context of ultrasounds and nonlinear elasticity are discussed in this paper. Experiments will be presented to prove that a localized crack in a concrete beam causes a break of reciprocity in the ultrasonic response to a mechanical excitation. The link between non-reciprocity and asymmetry in the nonlinear response will be demonstrated and discussed as a tool for NonDestructive Evaluation.

Detection and location of cracks using loss of reciprocity in ultrasonic waves propagation.

The reciprocity theorem is a general statement valid for elastic media, and it has been applied to the solution of elastic wave equations, transducers calibration, time reversal acoustics, etc. However, localized nonlinear scatterers are expected to break reciprocity even though the effect is, in several cases, negligible. Here the dependence of the reciprocity break on the presence of a localized damage and the influence of its relative position has been experimentally investigated. It will be shown that the break of reciprocity, usually considered a disadvantage, can be exploited as an imaging tool for localized cracks detection.

Behavior of an electrolytic cell containing two groups of ions submitted to a step-like external voltage.

The transient and equilibrium behaviors of an electrolytic cell containing two groups of ions submitted to an external voltage is considered. The analysis is performed analytically and numerically, considering the electrolytic solution as a dispersion of ions in an insulating liquid. According to our results, the dynamic of the system corresponds to a multirelaxation problem and the relaxation time related to a new type of free diffusion is able to capture the essential characteristics of the evolution of the variables of the system. We also show that, contrary to what expected, the relaxation time related to the ambipolar diffusion is not a solution of the eigenvalues equation.

Generalization of Berreman's model to the case of large amplitude of the grooves.

We generalize Berreman's model to the case qA > or = 1 , where q is the wave vector of the surface structure and A its amplitude, to describe the alignment induced by a solid surface on a nematic liquid crystal. We show that, by taking into account correctly the elastic contribution to the surface energy connected with the surface topography, the effective surface energy is smaller than the one determined by Berreman, where the limiting surface is assumed flat and qA << 1 . The analysis is performed by assuming that the anchoring energy on the surface is strong, i.e., nematic molecules in contact with the limiting surface are tangent to it, for any bulk distortion. The generalization to the weak anchoring case is also presented.

Anomalous dependence on the diffusion coefficients of the ionic relaxation time in electrolytes.

We show, by using a numerical analysis, that the dynamic toward equilibrium for an electrolytic cell subject to a step-like external electric field is a multirelaxation process when the diffusion coefficients of positive and negative ions are different. By assuming that the diffusion coefficient of positive ions is constant, we observe that the number of involved relaxation processes increases when the diffusion coefficient of the negative ions diminishes. Furthermore, two of the relaxation times depend nonmonotonically on the ratio of the diffusion coefficients. This result is unexpected, because the ionic drift velocity, by means of which the ions move to reach the equilibrium distribution, increases with increasing ionic mobility.

Relaxation times of an electrolytic cell subject to an external electric field: role of ambipolar and free diffusion phenomena.

We evaluate the relaxation times for an electrolytic cell subject to a step-like external voltage, in the case in which the mobility of negative ions is different from that of positive ions. The electrodes of the cell, in the shape of a slab, are supposed to be perfectly blocking. The theoretical analysis is performed by assuming that the applied voltage is so small that the fundamental equations of the problem can be linearized. In this framework, the eigenvalues equations defining all relaxation times of the problem are deduced. In the numerical analysis, we solve the complete set of equations describing the time evolution of the system under the action of the external voltage. Two relaxation processes, connected with the ambipolar and free diffusion phenomena, are sufficient to describe the dynamics of the system, when the diffusion coefficients are of the same order of magnitude.

Electrical impedance for an electrolytic cell.

We analyze in which experimental conditions the concept of electrical impedance is useful for an electrolytic cell. The analysis is performed by solving numerically the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field and comparing the results with the ones obtained by solving the linear approximation of these equations. The control parameter in our study is the amplitude of the applied voltage, assumed a simple harmonic function of the time. We show that the bulk distribution of ions close to the electrodes differs from the one obtained by means of the linear analysis already for small amplitudes of the applied voltage. Nevertheless, the concept of electrical impedance remains valid. For larger amplitudes, the current in the circuit is no longer harmonic at the same frequency of the applied voltage. Therefore the concept of electrical impedance is no longer meaningful.

Markovian model of growth and histologic progression in prostate cancer.

Models, based on bio-physical and biological considerations, may be very helpful as support tools for traditional diagnostic methodologies and interpretation of statistical data in oncology. This is particularly true when the neoplastic progression and differentiation are rather simple and regular, such as in the case of prostatic adenocarcinomas. Using clinical data as a "statistical ensemble," we propose here a Markovian model to forecast the tumor progression. After validation with clinical data, the model is applied to the determination of the temporal evolution of the risk of metastasis.

Influence of the ions on the dynamical response of a nematic cell submitted to a dc voltage.

The influence of the ions present in a liquid crystal on the dynamical response of a nematic slab submitted to a dc voltage is studied. The evolution of the system toward the equilibrium state is investigated by solving the continuity equation for the electric charge, taking into account the current of drift and of diffusion. Our analysis shows that the formation of the double layers close to the electrodes strongly modifies the distribution of the electric field across the sample. We evaluate the surface polarization due to the ions movements and the contribution to the anisotropic part of the surface energy having a dielectric origin. We show also that, even if the optical response of the liquid crystal is a slow phenomenon, the distribution of the ionic charge is rather fast. Consequently, the presence of the ions cannot be neglected in the determination of the flexoelectric coefficients when the nematic sample is submitted to a square wave having a period of the order of 1 s.

Inhibition of vascularization in tumor growth.

The transition to a vascular phase is a prerequisite for fast tumor growth. During the avascular phase, the neoplasm feeds only from the (relatively few) existing nearby blood vessels. During angiogenesis, the number of capillaries surrounding and infiltrating the tumor increases dramatically. A model which includes physical and biological mechanisms of the interactions between the tumor and vascular growth describes the avascular-vascular transition. Numerical results agree with clinical observations and predict the influence of therapies aiming to inhibit the transition.

Properties of a "phase transition" induced by antiangiogenetic therapeutical protocols.

Inhibiting angiogenesis has been found to be an interesting therapeutical strategy against cancer. In fact, the success of tumor growth is subordinated to the corresponding increase of the vascular system feeding the neoplasm. However, optimization and design of proper antiangiogenetic therapeutical strategies is still an open problem. We apply a recently developed angiogenesis model to study how variations in the relevant parameters, e.g., induced by chemicals, may cause a "phase transition" to a region in the parameter space in which angiogenesis is not succesful. To demonstrate the reliability of our approach and its usefulness, we will study some specific drugs and use our model to investigate the influence of the main variables involved in a clinical treatment: the administration time, the duration of the drug effect, and the drug dose.

Competition effects in the dynamics of tumor cords.

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.