Rate-independent dissipation and loading direction effects in compressed carbon nanotube arrays.

Arrays of nominally-aligned carbon nanotubes (CNTs) under compression deform locally via buckling, exhibit a foam-like, dissipative response, and can often recover most of their original height. We synthesize millimeter-scale CNT arrays and report the results of compression experiments at different strain rates, from 10(-4) to 10(-1) s(-1), and for multiple compressive cycles to different strains. We observe that the stress-strain response proceeds independently of the strain rate for all tests, but that it is highly dependent on loading history. Additionally, we examine the effect of loading direction on the mechanical response of the system. The mechanical behavior is modeled using a multiscale series of bistable springs. This model captures the rate independence of the constitutive response, the local deformation, and the history-dependent effects. We develop here a macroscopic formulation of the model to represent a continuum limit of the mesoscale elements developed previously. Utilizing the model and our experimental observations we discuss various possible physical mechanisms contributing to the system's dissipative response.

Dynamics of time-modulated, nonlinear phononic lattices.

The propagation of acoustic and elastic waves in time-varying, spatially homogeneous media can exhibit different phenomena when compared to traditional spatially varying, temporally homogeneous media. In the present work, the response of a one-dimensional phononic lattice with time-periodic elastic properties is studied with experimental, numerical and theoretical approaches in both linear and nonlinear regimes. The system consists of repelling magnetic masses with grounding stiffness controlled by electrical coils driven with electrical signals that vary periodically in time. For small-amplitude excitation, in agreement with linear theoretical predictions, wave-number band gaps emerge. The underlying instabilities associated to the wave-number band gaps are investigated with Floquet theory and the resulting parametric amplification is observed in both theory and experiments. In contrast to genuinely linear systems, large-amplitude responses are stabilized via the nonlinear nature of the magnetic interactions of the system, and results in a family of nonlinear time-periodic states. The bifurcation structure of the periodic states is studied. It is found the linear theory correctly predicts parameter values from which the time-periodic states bifurcate from the zero state. In the presence of an external drive, the parametric amplification induced by the wave-number band gap can lead to bounded and stable responses that are temporally quasiperiodic. Controlling the propagation of acoustic and elastic waves by balancing nonlinearity and external modulation offers a new dimension in the realization of advanced signal processing and telecommunication devices. For example, it could enable time-varying, cross-frequency operation, mode- and frequency-conversion, and signal-to-noise ratio enhancements.

Bifurcation-based acoustic switching and rectification.

Switches and rectification devices are fundamental components used for controlling the flow of energy in numerous applications. Thermal and acoustic rectifiers have been proposed for use in biomedical ultrasound applications, thermal computers, energy- saving and -harvesting materials, and direction-dependent insulating materials. In all these systems the transition between transmission states is smooth with increasing signal amplitudes. This limits their effectiveness as switching and logic devices, and reduces their sensitivity to external conditions as sensors. Here we overcome these limitations by demonstrating a new mechanism for tunable rectification that uses bifurcations and chaos. This mechanism has a sharp transition between states, which can lead to phononic switching and sensing. We present an experimental demonstration of this mechanism, applied in a mechanical energy rectifier operating at variable sonic frequencies. The rectifier is a granular crystal, composed of a statically compressed one-dimensional array of particles in contact, containing a light mass defect near a boundary. As a result of the defect, vibrations at selected frequencies cause bifurcations and a subsequent jump to quasiperiodic and chaotic states with broadband frequency content. We use this combination of frequency filtering and asymmetrically excited bifurcations to obtain rectification ratios greater than 10(4). We envisage this mechanism to enable the design of advanced photonic, thermal and acoustic materials and devices.

Stress wave anisotropy in centered square highly nonlinear granular systems.

Highly ordered, close packed granular systems present a nonlinear dynamic behavior stemming from the Hertzian contact interaction between particles. We investigated the propagation of elastic stress waves in an uncompressed, centered square array of spherical and cylindrical particles. We show, via experiments and numerical simulations, that systematic variations of the mass and stiffness ratios of the spherical and cylindrical particles lead to large variations in the characteristics of the propagating stress wave fronts traveling through the system. The ability to control the stress wave front properties in these granular systems may allow for the development of new wave-tailoring materials including systems capable of redirecting impact energy.

Effect of density variation and non-covalent functionalization on the compressive behavior of carbon nanotube arrays.

Arrays of aligned carbon nanotubes (CNTs) have been proposed for different applications, including electrochemical energy storage and shock-absorbing materials. Understanding their mechanical response, in relation to their structural characteristics, is important for tailoring the synthesis method to the different operational conditions of the material. In this paper, we grow vertically aligned CNT arrays using a thermal chemical vapor deposition system, and we study the effects of precursor flow on the structural and mechanical properties of the CNT arrays. We show that the CNT growth process is inhomogeneous along the direction of the precursor flow, resulting in varying bulk density at different points on the growth substrate. We also study the effects of non-covalent functionalization of the CNTs after growth, using surfactant and nanoparticles, to vary the effective bulk density and structural arrangement of the arrays. We find that the stiffness and peak stress of the materials increase approximately linearly with increasing bulk density.

Relationships between technical efficiency and the quality and costs of health care in Italy.

OBJECTIVE: This paper reports the measurement of technical efficiency of Tuscan Local Health Authorities and its relationship with quality and appropriateness of care. DESIGN: First, a bias-corrected measure of technical efficiency was developed using the bootstrap technique applied to data envelopment analysis. Then, correlation analysis was used to investigate the relationships among technical efficiency, quality and appropriateness of care. SETTING AND PARTICIPANTS: These analyses have been applied to the Local Health Authorities of Tuscany Region (Italy), which provide not only hospital inpatient services, but also prevention and primary care. All top managers of Tuscan Local Health Authorities were involved in selection of the inputs and outputs for calculating technical efficiency. MAIN OUTCOME MEASURES: The main measure used in this study are volume, quality and appropriateness indicators monitored by the multidimensional performance evaluation system developed in the Tuscany Region. RESULTS: On average, Tuscan Local Health Authorities experienced 14(%) of bias-corrected inefficiency in 2007. Correlation analyses showed a significant negative correlation between per capita costs and overall performance. No correlation was found in 2007 between technical efficiency and overall performance or between technical efficiency and per capita costs. CONCLUSIONS: Technical efficiency cannot be considered as an extensive measure of healthcare performance, but evidence shows that Tuscan Local Health Authorities have room for improvement in productivity levels. Indeed, correlation findings suggest that, to pursue financial sustainability, Local Health Authorities mainly have to improve their performance in terms of quality and appropriateness.

Optimization methods for the imputation of missing values in Educational Institutions Data.

The imputation of missing values in the detail data of Educational Institutions is a difficult task. These data contain multivariate time series, which cannot be satisfactory imputed by many existing imputation techniques. Moreover, almost all the data of an Institution are interconnected: the number of graduates is not independent from the number of students, the expenditure is not independent from the staff, etc. In other words, each imputed value has an impact on the whole set of data of the institution. Therefore, imputation techniques for this specific case should be designed very carefully. We describe here the methods and the codes of the imputation methodology developed to impute the various patterns of missing values which appear in similar interconnected data. In particular, a first part of the proposed methodology, called ``trend smoothing imputation'', is designed to impute missing values in time series by respecting the trend and the other features of an Institution. The second part of the proposed methodology, called ``donor imputation'', is designed to impute larger chunks of missing data by using values taken form similar Institutions in order to respect again their size and trend.•Trend smoothing imputation can handle missing subsequences in time series, and is given by a weighted combination of: (a) weighed average of the other available values of the sequence, and (b) linear regression.•Donor imputation can handle full sequence missing in time series. It imputes the Recipient Institution using the values taken from a similar institution, called Donor, selected using optimization criteria.•The values imputed by our techniques should respect the trend, the size and the ratios of each Institution.

Discrete breathers in one-dimensional diatomic granular crystals.

We report the experimental observation of modulational instability and discrete breathers in a one-dimensional diatomic granular crystal composed of compressed elastic beads that interact via Hertzian contact. We first characterize their effective linear spectrum both theoretically and experimentally. We then illustrate theoretically and numerically the modulational instability of the lower edge of the optical band. This leads to the dynamical formation of long-lived breather structures, whose families of solutions we compute throughout the linear spectral gap. Finally, we experimentally observe the manifestation of the modulational instability and the resulting generation of localized breathing modes with quantitative characteristics that agree with our numerical results.

Nonlinear coherent structures in granular crystals.

The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures-which include traveling solitary waves, dispersive shock waves, and discrete breathers-have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

Room temperature solvent-free synthesis of monodisperse magnetite nanocrystals.

We have successfully demonstrated a facile, solvent-free synthesis of highly crystalline and monodisperse Fe3O4 nanocrystallites at ambient temperature avoiding any heating. Solid state reaction of inorganic Fe(ll) and Fe(ll) salts with NaOH was found to produce highly crystalline Fe3O4 nanoparticles. The reaction, if carried out in the presence of surfactant such as oleic acid-oleylamine adduct, generated monodisperse Fe3O4 nanocrystals extractable directly from the reaction mixture. The extracted nanoparticles were capable of forming self-assembled, two-dimensional and uniform periodic array. The new process utilizes inexpensive and nontoxic starting materials, and does not require a use of high boiling point and toxic solvents, thus is amenable to an environmentally desirable, large-scale synthesis of nanocrystals.

Strongly nonlinear wave dynamics in a chain of polymer coated beads.

Strongly nonlinear phononic crystals were assembled from a chain of Parylene-C coated steel spheres in a polytetrafluoroethylene holder. This system exhibits strongly nonlinear properties and extends the range of materials supporting sonic-vacuum-type behavior. The combination of a high density core and a soft (low elastic modulus) coating ensures a relatively low velocity of wave propagation. The bead contact interaction caused by the deformation of the Parylene coating can be described by classical nonlinear elastic Hertz theory with an effective value of the elastic modulus equal to 15 GPa for the contact interaction. Strongly nonlinear solitary waves excited by impacts were investigated experimentally and compared to chains composed of uniform steel beads. Fracture of the polymer coating was detected under relatively large pulse amplitude.

Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals.

One-dimensional strongly nonlinear phononic crystals were assembled from chains of PTFE (polytetrafluoroethylene) and stainless-steel spheres with gauges installed inside the beads. Trains of strongly nonlinear solitary waves were excited by impacts. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same magnitude of dynamic contact force) were achieved through a noncontact magnetically induced precompression of the chains. The data for the PTFE based chains are presented for the first time and the data for the stainless-steel beads chains are extended into a range of maximum dynamic forces more than one order of magnitude lower than previously reported. Experimental results agreed reasonably well with the long-wave approximation and numerical calculations based on the Hertz interaction law for particles interactions.

Extreme stiffness tunability through the excitation of nonlinear defect modes.

The incremental stiffness characterizes the variation of a material's force response to a small deformation change. In lattices with noninteracting vibrational modes, the excitation of localized states does not have any effect on material properties, such as the incremental stiffness. We report that, in nonlinear lattices, driving a defect mode introduces changes in the static force-displacement relation of the material. By varying the defect excitation frequency and amplitude, the incremental stiffness can be tuned continuously to arbitrarily large positive or negative values. Furthermore, the defect excitation parameters also determine the displacement region at which the force-displacement relation is being tuned. We demonstrate this phenomenon experimentally in a compressed array of spheres tuning its incremental stiffness from a finite positive value to zero and continuously down to negative infinity.

Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains.

This article explores the excitation of different vibrational states in a spatially extended dynamical system through theory and experiment. As a prototypical example, we consider a one-dimensional packing of spherical particles (a so-called granular chain) that is subject to harmonic boundary excitation. The combination of the multimodal nature of the system and the strong coupling between the particles due to the nonlinear Hertzian contact force leads to broad regions in frequency where different vibrational states are possible. In certain parametric regions, we demonstrate that the nonlinear Schrödinger equation predicts the corresponding modes fairly well. The electromechanical model we apply predicts accurately the conversion from the obtained mechanical energy to the electrical energy observed in experiments.

Ultrastructural examination of dentin using focused ion-beam cross-sectioning and transmission electron microscopy.

Focused ion-beam (FIB) milling is a commonly used technique for transmission electron microscopy (TEM) sample preparation of inorganic materials. In this study, we seek to evaluate the FIB as a TEM preparation tool for human dentin. Two particular problems involving dentin, a structural analog of bone that makes up the bulk of the human tooth, are examined. Firstly, the process of aging is studied through an investigation of the mineralization in 'transparent' dentin, which is formed naturally due to the filling up of dentinal tubules with large mineral crystals. Next, the process of fracture is examined to evaluate incipient events that occur at the collagen fiber level. For both these cases, FIB-milling was able to generate high-quality specimens that could be used for subsequent TEM examination. The changes in the mineralization suggested a simple mechanism of mineral 'dissolution and reprecipitation', while examination of the collagen revealed incipient damage in the form of voids within the collagen fibers. These studies help shed light on the process of aging and fracture of mineralized tissues and are useful steps in developing a framework for understanding such processes.

Strongly nonlinear waves in a chain of Teflon beads.

One-dimensional "sonic vacuum" type phononic crystals were assembled from a chain of polytetrafluoroethylene (PTFE,Teflon) spheres with different diameters in a Teflon holder. It was demonstrated that this polymer-based sonic vacuum, with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed. These solitary waves can be described using the classical nonlinear Hertz law despite the viscoelastic nature of the polymer and high strain rate deformation of the contact area. The experimentally measured speeds of solitary waves at high amplitudes are close to the theoretically estimated values with a Young's modulus of 1.46 GPa obtained from shock wave experiments. This is significantly higher than the Young's modulus of PTFE from ultrasonic measurements. Trains of strongly nonlinear solitary waves excited by an impact were investigated experimentally and were found to be in reasonable agreement with numerical calculations based on Hertz interaction law though exhibiting a significant dissipation.

Traveling waves in 2D hexagonal granular crystal lattices.

This study describes the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. The dynamics of the system are modeled using the Hertzian normal contact law. After the initial impact strikes the system, a characteristic wave structure emerges and continuously decays as it propagates through the lattice. Using an extension of the binary collision approximation for one-dimensional chains, we predict its decay rate, which compares well with numerical simulations and experimental data. While the hexagonal lattice does not support constant speed traveling waves, we provide scaling relations that characterize the directional power law decay of the wave velocity for various angles of impact. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates.

Wave transmission in time- and space-variant helicoidal phononic crystals.

We present a dynamically tunable mechanism of wave transmission in one-dimensional helicoidal phononic crystals in a shape similar to DNA structures. These helicoidal architectures allow slanted nonlinear contact among cylindrical constituents, and the relative torsional movements can dynamically tune the contact stiffness between neighboring cylinders. This results in cross-talking between in-plane torsional and out-of-plane longitudinal waves. We numerically demonstrate their versatile wave mixing and controllable dispersion behavior in both wavenumber and frequency domains. Based on this principle, a suggestion toward an acoustic configuration bearing parallels to a transistor is further proposed, in which longitudinal waves can be switched on and off through torsional waves.

Damped-driven granular chains: an ideal playground for dark breathers and multibreathers.

By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory.

Interaction of traveling waves with mass-with-mass defects within a Hertzian chain.

We study the dynamic response of a granular chain of particles with a resonant inclusion (i.e., a particle attached to a harmonic oscillator, or a mass-with-mass defect). We focus on the response of granular chains excited by an impulse, with no static precompression. We find that the presence of the harmonic oscillator can be used to tune the transmitted and reflected energy of a mechanical pulse by adjusting the ratio between the harmonic resonator mass and the bead mass. Furthermore, we find that this system has the capability of asymptotically trapping energy, a feature that is not present in granular chains containing other types of defects. Finally, we study the limits of low and high resonator mass, and the structure of the reflected and transmitted pulses.