Granular Crystals Research Articles

Amplitude-dependent phononic processes in a diatomic granular chain in the weakly nonlinear regime

Nonlinear acoustic processes of second harmonic generation and nonlinear resonances in a diatomic granular chain (a granular phononic crystal) with static precompression are reported. The observed nonlinear self-action process which manifests itself as shifts in resonance frequencies of the chain leads to amplitude-dependent band edges: the properties of the phononic crystal change as a function of wave amplitude. Observed nonlinear effects at the band edges are exceptionally strong (self-induced attenuation and self-induced transparency) due to the peculiar frequency dependence of the attenuation in these frequency regions. The reported effects open the way for applications in wave tailoring by nonlinear phononic crystals, using amplitude-dependent processes, such as passive amplitude-dependent attenuators or amplifiers and various logical elements.

Site-Specific Quantification of Bone Quality Using Highly Nonlinear Solitary Waves

Osteoporosis is a well recognized problem affecting millions of individuals worldwide. The ability to diagnose problems in an effective, efficient, and affordable manner and identify individuals at risk is essential. Site-specific assessment of bone mechanical properties is necessary, not only in the process of fracture risk assessment, but may also be desirable for other applications, such as making intraoperative decisions during spine and joint replacement surgeries. The present study evaluates the use of a one-dimensional granular crystal sensor to measure the elastic properties of bone at selected locations via direct mechanical contact. The granular crystal is composed of a tightly packed chain of particles that interact according to the Hertzian contact law. Such chains represent one of the simplest systems to generate and propagate highly nonlinear acoustic signals in the form of compact solitary waves. First, we investigated the sensitivity of the sensor to known variations in bone density using a synthetic cancellous bone substitute, representing clinical bone quality ranging from healthy to osteoporotic. Once the relationship between the signal response and known bone properties was established, the sensor was used to assess the bone quality of ten human cadaveric specimens. The efficacy and accuracy of the sensor was then investigated by comparing the sensor measurements with the bone mineral density (BMD) obtained using dual-energy x-ray absorptiometry (DEXA). The results indicate that the proposed technique is capable of detecting differences in bone quality. The ability to measure site-specific properties without exposure to radiation has the potential to be further developed for clinical applications.

Effects of weak disorder on stress-wave anisotropy in centered square nonlinear granular crystals

The present study describes wave propagation characteristics in a weakly disordered two-dimensional granular media composed of a square array of spheres accommodating interstitial cylindrical intruders. Previous investigations, performed experimentally as well as numerically, emphasized that wave-front shapes in similar systems are tunable via choice of material combinations. Here, we investigate the effects of statistical variation in the particle diameters and compare the effects of the resulting disorder in experiments and numerical simulations, finding good agreement.

Recent analog of gypsified microbial laminites and stromatolites in solar salt works and the Miocene gypsum deposits of Saudi Arabia and Egypt

Accumulation of microbial mats and stromatolites dominate in the crystallization ponds of solar salt works west of Alexandria, Egypt. These microbial mats are laminar in the permanent submerged part of the ponds. The microbial mats commonly form sites for growth of gypsum crystals during periods having higher salinity. In the dominant submerged part of the pond, domal stromatolites are common around groundwater seepage holes. In the shallow, intermittent margin of the ponds, the laminated microbial structure forms laterally close-linked hemispheroidal stromatolite type, with unidirectional and multidirectional ripple mark-like morphology on their surface. The microbial laminite and stromatolite types in the modern solar salt works are similar to the organic-rich Miocene gypsum beds of El-Barqan (west Alexandria, Egypt) and Rabigh (north Jeddah, Saudi Arabia). The Miocene organic-rich beds consist of interlayered dark-colored microbial laminae and light-colored gypsum laminae. These beds may have three different variations: regular even lamination, laterally closed-linked hemispheroidal stromatolites, and/or discrete hemispheroidal stromatolites. Petrographic examination of the microbial laminites and stromatolites in the solar salt works and the Miocene gypsum beds indicate that the dark-colored, organic-rich laminae are composed of micritized microbial laminae and/or brown organic filaments. In El-Barqan area, the light-colored gypsum-rich laminae are composed of either gypsum crystal fragments, or lenticular and prismatic gypsum. These gypsum crystals are either entrapped within the microbial filaments or are nucleated at the surface of the microbial laminae to form a radial pattern, whereas in Rabigh area, the light-colored gypsum-rich laminae are composed of secondary porphyrotopic, poikilotopic, or granular gypsum crystals. By comparison of the microbial structure in the Miocene gypsum beds with the recent occurrence of the microbial laminites and stromatolites in the solar salt works, it is demonstrated that the organic-rich Miocene gypsum beds were formed in a very shallow salina with slightly fluctuating brine levels.

Frequency- and Amplitude-Dependent Transmission of Stress Waves in Curved One-Dimensional Granular Crystals Composed of Diatomic Particles

We study the stress wave propagation in curved chains of particles (granular crystals) confined by bent elastic guides. We report the frequency- and amplitude-dependent filtering of transmitted waves in relation to various impact conditions and geometrical configurations. The granular crystals studied consist of alternating cylindrical and spherical particles pre-compressed with variable static loads. First, we excite the granular crystals with small-amplitude, broadband perturbations using a piezoelectric actuator to generate oscillatory elastic waves. We find that the linear frequency spectrum of the transmitted waves creates pass- and stop-bands in agreement with the theoretical dispersion relation, demonstrating the frequency-dependent filtering of input excitations through the diatomic granular crystals. Next, we excite high-amplitude nonlinear pulses in the crystals using striker impacts. Experimental tests verify the formation and propagation of highly nonlinear solitary waves that exhibit amplitude-dependent attenuation. We show that the wave propagation can be easily tuned by manipulating the pre-compression imposed to the chain or by varying the initial curvature of the granular chains. We use a combined discrete element (DE) and finite element (FE) numerical model to simulate the propagation of both dispersive linear waves and compactly-supported highly nonlinear waves. We find that the tunable, frequency- and amplitude-dependent filtering of the incoming signals results from the close interplay between the granular particles and the soft elastic media. The findings in this study suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of frequencies and amplitudes.

Rapid Materials Degradation Induced by Surfaces and Voids: Ab Initio Modeling of β-Octatetramethylene Tetranitramine

A computational strategy based on coupling density functional theory, variational transition state theory, and a microscale materials morphology description unravels details of the defect-induced effect on the surface decomposition of molecular crystals. The technique allows us to resolve the earliest stages of decomposing solids, even for very complex materials and for ultrafast chemical reactions. A comparative analysis of chemical decomposition reactions in HMX with progressively increasing system complexity (an isolated HMX molecule; a perfect single HMX crystal; a defect-containing, porous, and granular HMX crystal) demonstrates that the initiation of the material's degradation can be effectively manipulated by changing the crystal morphology. The activation barriers, reaction constants, and corresponding reaction rates are obtained as a function of molecular environment (a molecule in a vacuum, in an ideal bulk crystal, on a surface or interface, and on a defect in a solid), and decomposition times are predicted. The computational approach can be applied to any other material and system.

Monitoring the hydration of cement using highly nonlinear solitary waves

In this paper we present a nondestructive evaluation technique based on the propagation of highly nonlinear solitary waves (HNSWs) to monitor the hydration of cement. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, such as one-dimensional chains of contacting spherical particles (i.e., granular crystals). In the present study, we use a granular crystal-based actuator/sensor to observe the solitary waves propagating to and from the mechanical interface between the transducer and a fresh gypsum cement sample. We hypothesize that the reflected HNSWs traveling along the crystal-based transducer are affected by the hydration process of the cement, and we assess the elastic modulus of the specimen in the localized region of the granular crystal contact. To verify the experimental results, we perform numerical simulations based on a simplified finite element model. The elastic properties of the cement specimen measured by the granular crystal transducer are compared with the compressive strength and the elastic modulus measurements obtained from destructive tests, conducted according to the ASTM C109. We observe good agreement between experiments and numerical simulations.

Exploiting pattern transformation to tune phononic band gaps in a two-dimensional granular crystal

The band structure of a two-dimensional granular crystal composed of silicone rubber and polytetrafluoroethylene (PTFE) cylinders is investigated numerically. This system was previously shown to undergo a pattern transformation with uniaxial compression by Göncü et al. [Soft Matter 7, 2321 (2011)]. The dispersion relations of the crystal are computed at different levels of deformation to demonstrate the tunability of the band structure, which is strongly affected by the pattern transformation that induces new band gaps. Replacement of PTFE particles with rubber ones reveals that the change of the band structure is essentially governed by pattern transformation rather than particles' mechanical properties.

Influence of graphite crystallinity on the microtexture of nano-polycrystalline diamond obtained by direct conversion

Nano-polycrystalline diamond (NPD) is a super-hard pure polycrystalline aggregate of nano-diamonds and has a characteristic microtexture composed of a mixture of granular and lamellar crystals. We investigated the origin of the unique microtexture and the influence of the crystallinity of initial graphite sources on the resulting microtexture of NPDs. Polycrystalline graphite rods used for NPD synthesis were found to consist of coke-derived relatively large crystals and pitch-derived nanocrystalline particles. Upon conversion to NPD, the former are converted to cubic and hexagonal diamond mixtures by the martensitic transformation and left a lamellar texture behind, while the latter transform to granular nano-diamonds by diffusion-controlled nucleation and subsequent crystal growth, which initiate preferentially at lattice defects and crystal surfaces. A clear correlation between the crystallite size of the initial graphite and the grain size of the granular nano-diamonds in the NPDs was also found. Our results suggest that the average grain size and the relative abundance of lamellar domains in NPD can potentially be controlled by carefully choosing initial graphite sources based on their crystallinity.

Evolution of the primary pulse in one-dimensional granular crystals subject to on-site perturbations: Analytical study

The propagation of the primary pulse through an uncompressed granular chain subject to external on-site perturbation is studied. An analytical procedure predicting the evolution of the primary pulse is devised for the general form of the on-site perturbation applied on the chain. The validity of the analytical model is confirmed with several specific granular setups, such as chains mounted on the nonlinear elastic foundation, chains perturbed by the dissipative forces, as well as randomly perturbed chains. An additional interesting finding made in the present paper corresponds to the chains subject to a special type of perturbation, including the terms leading to dissipation and those acting as an energy source. In the paper, it is shown that an application of such a perturbation may lead to the formation of stable stationary primary pulses propagating with constant amplitudes and acting as attractors for the initially unperturbed Nesterenko solitary waves. Interestingly enough, the developed analytical procedure provides an extremely close estimation for the amplitudes of these stationary primary pulses as well as predicts zones of their stability. In conclusion, we would like to stress that the developed analytical model has demonstrated spectacular agreement with the results of the direct numerical simulations, and this is for various configurations considered in the current paper.

Defect modes in one-dimensional granular crystals

We study the vibrational spectra of one-dimensional statically compressed granular crystals (arrays of elastic particles in contact) containing light-mass defects. We focus on the prototypical settings of one or two spherical defects (particles of smaller radii) interspersed in a chain of larger uniform spherical particles. We present a systematic measurement, using continuous noise, of the near-linear frequency spectrum within the spatial vicinity of the defect(s). Using this technique, we identify the frequencies of the localized defect modes as a function of the defect size and the position of the defects relative to each other. We also compare the experimentally determined frequencies with those obtained by numerical eigenanalysis and by analytical expressions based on few-site considerations. These approximate analytical expressions, based on normal-mode analysis, are found to be in excellent agreement with numerics for a wide range of mass ratios. We also observe that the experimentally measured frequencies of the localized defect modes are uniformly upshifted, compared to the numerically and theoretically predicted values.

Highly nonlinear solitary wave propagation in Y-shaped granular crystals with variable branch angles

We study the propagation of highly nonlinear waves in a branched (Y-shaped) granular crystal composed of chains of spherical particles of different materials, arranged at variable branch angles. We experimentally test the dynamic behavior of a solitary pulse, or of a train of solitary waves, crossing the Y-junction interface, and splitting between the two branches. We describe the dependence of the split pulses' speed and amplitude on the branch angles. Analytic predictions based on the quasiparticle model and numerical simulations based on Hertzian interactions between the particles are found to be in excellent agreement with the experimental data.

Interaction of highly nonlinear solitary waves with thin plates

We investigate the reflection of highly nonlinear solitary waves in one-dimensional granular crystals interacting with large plates. We observe significant changes in the reflected waves’ properties in terms of wave amplitude and time of flight in association with the intrinsic inelasticity of large plates, which are governed by the plate thickness and the size of the granular constituents. We also study the effects of fixed plate boundaries in the formation of reflected waves, and find the existence of a critical distance, within which the interaction between the granular chain and plate is strongly modified. We explain the effects of intrinsic inelasticity and of boundaries in the large plates by using plate theory and the contact mechanics between a plate and a spherical striker. We find that experimental results are in excellent agreement with the analytical predictions and numerical simulations based on the combined discrete element and spectral element models. The findings in this study can be useful for the nondestructive evaluation of plate structures using granular crystals, which can improve the resolution of in-situ, portable measurement instruments leveraging high acoustic energy and sensitivity of solitary waves.

Self-assembling of non-Brownian magnetized spheres

If we pour spherical beads in a container and then gently shake it to increase the compaction of the system, the packing fraction will converge logarithmically to 0.64, the density of a random close packing. If the system is specially sheared, or tapped through an annealing procedure, lattices may self-organize. In this work we study granular crystallization induced by magnetic cohesion. We observe an interesting granular polymorphism probably due to an effective van der Waals-like interaction.

Mesoscopic approach to granular crystal dynamics

We present a mesoscopic approach to granular crystal dynamics, which comprises a three-dimensional finite-element model and a one-dimensional regularized contact model. The approach investigates the role of vibrational-energy trapping effects in the dynamic behavior of one-dimensional chains of particles in contact (i.e., granular crystals), under small to moderate impact velocities. The only inputs of the models are the geometry and the elastic material properties of the individual particles that form the system. We present detailed verification results and validate the model comparing its predictions with experimental data. This approach provides a physically sound, first-principles description of dissipative losses in granular systems.

New Insights into Ancient Maya Building Materials: Characterization of Mortar, Plaster, and Coquina Flagstones from Toniná

ABSTRACTThis work shows current research on lithic raw material used by the ancient Maya of Toniná. The core of the city of Toniná lies on a steep-sided hill of calcareous sandstones from the shallow marine deposits dated as Oligocene, in the Chiapas Highlands of Southern Mexico. Results of paleontological fieldwork in Toniná show several biostrome sediments mound-like with tabular bafflestones and large coquina flagstones, which are sheet-like rocks enriched with fossil mollusk shells, corals, encrusted organisms, and calcareous debris. The people of Toniná intentionally selected and carved these rocks for use as building blocks and bricks on floors, walls, and stairways. At least two coquina flagstones measuring about 1.90 m long were identified in an archeological context most likely associated with carved stelae. Also non-marine carbonate rocks such as a crudely banded travertine and spongy calcareous tufa from recent sediments of freshwater environments surrounding Toniná were used by the Maya as a raw material on walls, columns, reliefs and murals base.Results of the chemical, mineralogical and micromorphological analysis on plaster and bedding mortars from the walls of Toniná display a slightly interbedded lime of sparry calcite cemented in a highly porous groundmass with silt-to pebble-size of calcareous and siliciclastic rock-crushed aggregates, sand, and soil remains. Lime fabric reveals enclosing quartz grains, granular calcite crystals, and carbonaceous inclusions which may suggest that the lime has been made from a burnt grain-rich limestone with fibrous cement and porous microfabric. WDX analysis in lime lumps of plaster reveal an average amount of 1.37 wt% MgO associated with a limestone source ranging from regular to a magnesium-enriched limestone (1 to 2 wt %). XRF detect a strontium-rich level in the calcite matrix of plaster which is as high as that of fossil shells, tufa, and coquina. Finally, XRD shows that the mean amount of calcite in plaster is 95 wt% and lower amount (2-2.5w%) of siliciclastic minerals: quartz and albite. In contrast, calcite in mortar ranges less than 90.1 wt%. The concentrations of non-carbonate minerals, such as quartz and albite, are higher than those in plaster because mortar incorporates more siliciclastic rock remains, sand and clay.

Nondestructive evaluation of orthopaedic implant stability in THA using highly nonlinear solitary waves

We propose a new biomedical sensing technique based on highly nonlinear solitary waves to assess orthopaedic implant stability in a nondestructive and efficient manner. We assemble a granular crystal actuator consisting of a one-dimensional tightly packed array of spherical particles, to generate acoustic solitary waves. Via direct contact with the specimen, we inject acoustic solitary waves into a biomedical prosthesis, and we nondestructively evaluate the mechanical integrity of the bone–prosthesis interface, studying the properties of the waves reflected from the contact zone between the granular crystal and the implant. The granular crystal contains a piezoelectric sensor to measure the travelling solitary waves, which allows it to function also as a sensor. We perform a feasibility study using total hip arthroplasty (THA) samples made of metallic stems implanted in artificial composite femurs using polymethylmethacrylate for fixation. We first evaluate the sensitivity of the proposed granular crystal sensor to various levels of prosthesis insertion into the composite femur. Then, we impose a sequence of harsh mechanical loading on the THA samples to degrade the mechanical integrity at the stem–cement interfaces, using a femoral load simulator that simulates aggressive, accelerated physiological loading. We investigate the implant stability via the granular crystal sensor–actuator during testing. Preliminary results suggest that the reflected waves respond sensitively to the degree of implant fixation. In particular, the granular crystal sensor–actuator successfully detects implant loosening at the stem–cement interface following violent cyclic loading. This study suggests that the granular crystal sensor and actuator has the potential to detect metal–cement defects in a nondestructive manner for orthopaedic applications.

Study of silicon photomultipliers for the medical imaging systems

Novel photodetectors Silicon Photomultipliers (SiPMs) in combination with scintillation materials as LySO give an impressive progress in the development of the new generation Medical Imaging Systems. The experimental study of the detection system based on highly granular LySO crystals and SiPM is presented in the geometrical configuration of Positron Emission Tomography (PET) systems. An energy resolution of (7.68±0.15)% and a time resolution of (806±26)ps are measured. The experimental results are implemented in the GATE mathematical model of PET system equipped with LySO/SiPM detection block.

Amplitude-dependent attenuation of compressive waves in curved granular crystals constrained by elastic guides

We study the wave propagation in a curved chain of spherical particles constrained by elastic guides under the axial impact of a falling mass. We characterize the force transmission properties of the chain by varying the striker’s mass and the chain’s curvature. Experimental tests demonstrate amplitude-dependent attenuation of compressive waves propagating through the curved chain. In particular, we observe that the curved systems present an improved transmission of small dynamic disturbances relative to that of strong excitations, resulting from the close interplay between the granular particles and the softer elastic medium. We also find that the transmission of the compressive waves through the chains is dependent on the initial curvature imposed to the system. Numerical simulations, based on an approach that combines discrete element and finite element methods, corroborate the experimental results. The findings suggest that hybrid structures composed of granular particles and linear elastic media can be employed as new passive acoustic filtering materials that selectively transmit or mitigate excitations in a desired range of pressure amplitudes.

Study on Membrane Fouling Experiment of Stacked AGMD Module in Low Temperature

In this paper, it has studied membrane fouling experiments at a certain temperature conditions and with untreated tap water as thermal mass, which applied unique multi-layered stacked air-gap membrane distillation module. It has analyzed the original membrane flux and conductivity changes in the experiments, and carried out SEM and EDS analysis before and after acid washed fouling membrane. The results show that: New type membrane module will produce fouling even at lower temperatures. Membrane surface was covered by a lot of uneven accumulation granular pollutants and cuboid crystals, so the mass flux reduced. Fouling membrane washed with 5 % hydrochloric acid solution was removed inorganic scale. The flux recovered to the initial value.