Random Aggregates Research Articles

Characteristic scale of heterogeneity of seismically active fault and its manifestation in scaling of earthquake source spectra

Previously, similarity of source spectra of Kamchatka earthquakes with respect to the common corner frequency fc1 and the expressed deviations from similarity for the second fc2 and the third fc3 corner frequencies were revealed. The value of fc3 reflects the characteristic size Lis of fault surface; correspondingly, Lis ≈ vrTis, where vr is the rupture speed and Tis ≈ 1/fc3 is characteristic time. The estimates of fc3 are used for normalizing fc1 and fc2. In this way one obtains dimensionless rupture temporal parametres τ1 and τ2 and can further study the dependence τ2 (τ1). The growth of a rupture is considered as a process of aggregation of elementary fault spots of the size Lis. The dimensionless width of the random front of aggregation is on the order of τ2. The relationship τ2 (τ1) approximately follows power law with exponent β. The estimates of β derived from earthquake populations of Kamchatka, USA and Central Asia (β = 0.35–0.6) agree with values expected from the known Eden’s theory of random aggregation growth and from its generalizations.

Improved estimates for the effective elastic bulk modulus of random tetragonal crystal aggregates

Particular expressions of upper and lower estimates for the macroscopic elastic bulk modulus of random cell tetragonal polycrystalline materials are derived and computed for a number of practical crystals. The cell-shape-unspecified bounds, based on minimum energy principles and generalized polarization trial fields, appear close to the simple bounds for specific spherical cell polycrystals

New Mineral NamesAntipiniteAnzaite-(Ce)BettertoniteBobshannoniteCalcinaksiteKhvoroviteLeguerniteLukkulaisvaaraiteMinjiangiteMöhniteMoraskoiteNickelpicromeritePilawite-(Ce)RalphcannoniteYeomanite

This New Mineral Names has entries for 15 new minerals, including antipinite, anzaite-(Ce), bettertonite, bobshannonite, calcinaksite, khvorovite, leguernite, lukkulaisvaaraite, minjiangite, mohnite, moraskoite, nickelpicromerite, pilawite-(Ce), ralphcannonite, and yeomanite. # Antipinite* {#article-title-2} N.V. Chukanov, S.M. Aksenov, R.K. Rastsvetaeva, K.A. Lysenko, D.I. Belakovskiy, G. Farber, G. Mohn and K.V. Van (2015) Antipinite, KNa3Cu2(C2O4)4, a new mineral species from a guano deposit at Pabellon de Pica, Chile. Mineralogical Magazine, 79(5), 1111–1121. Antipinite (IMA 2014-027), ideally KNa3Cu2(C2O4)4, was discovered in the guano deposit at the lower part of the northern slope of Pabellon de Pica Mountain, Tarapaca Region, Chile. The new mineral honors Mikhail Yuvenal’evich Antipin (1951–2013), a Russian specialist in the crystallography and crystal chemistry of organometallic and coordination compounds. Antipinite occurs in association with halite, salammoniac, chanabayaite, and joanneumite. The host gabbro consists of amphibole, plagioclase, minor clinochlore, and accessory chalcopyrite. Antipinite forms isometric and short prismatic crystals up to 0.1×0.1×0.15 mm, and random aggregates up to 0.6 mm across. The new mineral is blue, translucent, with pale blue streak and a vitreous luster. It is brittle, with a Mohs hardness ~2. The cleavage is medium in three directions, which were not determined. D meas = 2.53(3) and D calc = 2.549 g/cm3. Antipinite does not fluoresce under UV radiation. It is optically biaxial (+), α = 1.432(2), β = 1.530(2), and γ = 1.698(5) (λ = 589 nm); 2 V meas …

Biofunctionalized Silica Nanoparticles: Standards in Amyloid-β Oligomer-Based Diagnosis of Alzheimer's Disease.

Amyloid-β (Aβ) oligomers represent a promising biomarker for the early diagnosis of Alzheimer's disease (AD). However, state-of-the-art methods for immunodetection of Aβ oligomers in body fluids show a large variability and lack a reliable and stable standard that enables the reproducible quantitation of Aβ oligomers. At present, the only available standard applied in these assays is based on a random aggregation process of synthetic Aβ and has neither a defined size nor a known number of epitopes. In this report, we generated a highly stable standard in the size range of native Aβ oligomers that exposes a defined number of epitopes. The standard consists of a silica nanoparticle (SiNaP), which is functionalized with Aβ peptides on its surface (Aβ-SiNaP). The different steps of Aβ-SiNaP synthesis were followed by microscopic, spectroscopic and biochemical analyses. To investigate the performance of Aβ-SiNaPs as an appropriate standard in Aβ oligomer immunodetection, Aβ-SiNaPs were diluted in cerebrospinal fluid and quantified down to a concentration of 10 fM in the sFIDA (surface-based fluorescence intensity distribution analysis) assay. This detection limit corresponds to an Aβ concentration of 1.9 ng l-1 and lies in the sensitivity range of currently applied diagnostic tools based on Aβ oligomer quantitation. Thus, we developed a highly stable and well-characterized standard for the application in Aβ oligomer immunodetection assays that finally allows the reproducible quantitation of Aβ oligomers down to single molecule level and provides a fundamental improvement for the worldwide standardization process of diagnostic methods in AD research.

Surface-Enhanced Raman Spectroscopy on Liquid Interfacial Nanoparticle Arrays for Multiplex Detecting Drugs in Urine.

The design and application of liquid interfacial plasmonic platform is still in its infancy but is an exciting topic in tunable optical devices, sensors, and catalysis. Here, we developed an interfacial surface-enhanced Raman scattering (SERS) platform through the large-scale self-assembly of gold nanoparticle (GNP) arrays at the cyclohexane (CYH)/water interface for detecting trace drug molecules in the urine of humans. The molecules extracted by the CYH phase from a urine sample were directly localized into the self-organized plasmonic hotspots, yielded excellent Raman enhancement, and realized the substrate-free interfacial SERS detection. Synchrotron radiation small-angle X-ray scattering (SR-SAXS) experiments reveals a good uniformity of approximately 2-3 nm interparticle distance in the GNP arrays. SERS colocalization experiments demonstrated that amphetamine molecules of different concentration levels could be loaded into the interfacial GNP arrays and realized the coassembly together with nanoparticles at the liquid/liquid interface. Interfacial GNP arrays with dynamic nanogaps in liquid interfacial structure can make surrounding molecules easily diffuse into the nanogaps. In contrast, the fixed GNP arrays on Si wafer were more irregular, such as multilayer stack, random aggregates, and voids, during the drying process. When the drugs directly participate in the self-assembly process, it becomes easier for analytes diffusing into the nanogaps of GNP arrays, produces a concentration effect, and amplified the SERS sensitivity. This feature also enables molecules to be adsorbed evenly in the arrays and makes a more uniform distribution of both the analytes and GNPs in the liquid interface and realizes the significant increase in signal reproducibility. Interfacial SERS produced a standard deviation of 12.5% at 1001 cm(-1) peak of methamphetamine (MAMP) molecules under the concentration of 1 ppm, implying a good reproducibility. Moreover, dual-analyte detection at organic and aqueous phases was also realized and confirmed a good capability for analytes detection by liquid interfacial SERS platform, which promises nonengineering detection of analytes dissolved in often-inaccessible environments.

Dilatancy in the Analysis of Interlayer Cyclic Shear Test Results

AbstractDilatancy measurements of double-layer specimens were recorded during cyclic shear tests to derive information on the interface fatigue behavior. Two direct shear testing devices, representing the two most common types of guillotine and inclined configurations, were used. The results clearly highlight a dilatancy variability from the random aggregates distribution at the contact plane, even for specimens prepared in the same way, A saw-chain model is introduced for useful schematization of volumetric expansion during the shear test. Moreover, a new interpretation of the interface fatigue event is presented, based on the trend of dilatancy speed, which shows three stages: (1) important movement perpendicular to the sliding plane; (2) insignificant increase in dilatancy; and (3) crisis and detachment. The number of loading cycles at the beginning (Noverride) and end (Ncrisis) of the dilatancy is introduced as significant moments of the interface fatigue evolution.

Realignment of Nanocrystal Aggregates into Single Crystals as a Result of Inherent Surface Stress

AbstractCrystallization by particle attachment is widely observed in both natural and synthetic environments. Although this form of nonclassical crystallization is generally described by oriented attachment, random aggregation of building blocks to give single‐crystal products is also observed, but the mechanism of crystallographic realignment is unknown. We herein reveal that random attachment during aggregation‐based growth initially produces a nonoriented growth front. Subsequent evolution of the orientation is driven by the inherent surface stress applied by the disordered surface layer and results in single‐crystal formation by grain‐boundary migration. This mechanism is corroborated by measurements of orientation rate versus external stress, which demonstrated a predictive relationship between the two. These findings advance our understandings about aggregation‐based growth via nanocrystal blocks and suggest an approach to material synthesis that takes advantage of stress‐induced coalignment.

Realignment of Nanocrystal Aggregates into Single Crystals as a Result of Inherent Surface Stress.

Crystallization by particle attachment is widely observed in both natural and synthetic environments. Although this form of nonclassical crystallization is generally described by oriented attachment, random aggregation of building blocks to give single-crystal products is also observed, but the mechanism of crystallographic realignment is unknown. We herein reveal that random attachment during aggregation-based growth initially produces a nonoriented growth front. Subsequent evolution of the orientation is driven by the inherent surface stress applied by the disordered surface layer and results in single-crystal formation by grain-boundary migration. This mechanism is corroborated by measurements of orientation rate versus external stress, which demonstrated a predictive relationship between the two. These findings advance our understandings about aggregation-based growth via nanocrystal blocks and suggest an approach to material synthesis that takes advantage of stress-induced coalignment.

An efficient FE–SBFE coupled method for mesoscale cohesive fracture modelling of concrete

This study develops a method coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for efficient meso-scale fracture modelling of concrete for the first time. In this method, the aggregates are modelled by SBFE polygons with boundaries discretised only, while the mortar matrix is modelled by conventional finite elements. The semi-analytical SBFEM is implemented in ABAQUS by a user-defined element subroutine for the first time. Nonlinear cohesive interface elements with normal and shear traction-separation constitutive laws are pre-inserted within the mortar and on the aggregate-mortar interfaces to simulate potential cracks. Various meso-structures generated from both random aggregates and X-ray computed tomography images are modelled. The results demonstrate that the coupled method leads to considerable reductions in degrees of freedom and computational time against the conventional FEM, and these reductions become more significant when the aggregate volume fraction increases. The modelled crack paths and load-carrying capacities of a three-point bending beam and an L-shaped panel are in excellent agreement with the experimental data.

Highly anisotropic P3HT films with enhanced thermoelectric performance via organic small molecule epitaxy

Conducting polymers are potential candidates for thermoelectric (TE) applications owing to their low thermal conductivity, non-toxicity and low cost. However, the coil conformation and random aggregation of polymer chains usually degrade electrical transport properties, thus deteriorating TE performance. In this work, we fabricated poly(3-hexylthiophene) (P3HT) films with highly oriented morphology using 1,3,5-trichlorobenzene (TCB), an organic small-molecule, as a template for polymer epitaxy under a temperature gradient crystallization process. The resulting P3HT molecules, which were confirmed to be highly anisotropic by a combination of scanning electron microscopy, atomic force microscopy, polarizing microscope, polarized Raman spectroscopy, and two-dimensional-grazing incidence X-ray diffraction (GIXRD) analysis, not only markedly reduced the conjugated defects along the polymer backbone, but also effectively increased the degree of electron delocalization. These combined phenomena produced an efficient, 1D path for carrier movement and therefore resulted in enhanced carrier mobility in the TCB-treated P3HT films. The maximum values of the electrical conductivity and Seebeck coefficient were 320 S cm−1 and 269 μV K−1, respectively. Consequently, the maximum TE power factor and ZT value at 365 K reached 62.4 μW mK−2 and 0.1, respectively, in the parallel direction of the TCB-treated P3HT film. To the best of our knowledge, these are the highest values reported for pure P3HT TE materials. The method of using organic small-molecule epitaxy to generate highly anisotropic polymer films is expected to be valid for many conducting polymers. A process for stretching twisted polymer chains into ordered fibers can benefit production of low-cost materials that harvest heat losses. Most thermoelectric energy converters are made from inorganic semiconductors. Conductive polymers, however, are an attractive alternative because of their simple manufacturing requirements and intrinsic thermal insulating properties. Lidong Chen from the Shanghai Institute of Ceramics and co-workers have developed a way to reduce the defects that often plague plastic thermoelectrics with a dissolvable organic template. The team co-crystallized the conductive polymer poly(3-hexylthiophene) with small, trichlorobenzene-based molecules that solidify into needle-like structures under a temperature gradient. The aromatic stacking forces within the trichlorobenzene crystals lock the polymer chains into elongated positions that persist after template removal. Experiments on the resulting poly(3-hexylthiophene) filaments revealed near-record thermoelectric conversion efficiencies for this material. Herein, we fabricated pure poly(3-hexylthiophene) (P3HT) film with highly oriented morphology using a small-molecule 1,3,5-trichlorobenzene (TCB) as the template for polymer epitaxy with a temperature gradient crystallization process. The strong π–π conjugated interactions as well as the very close matching between the repeat distance of the thiophene units in P3HT and the repeat distance of TCB molecules have successfully induced the epitaxy process, allowing the P3HT polymer chains to lock onto the lattice of TCB, forming highly ordered P3HT chains in the direction parallel to the fiber axis. As a result, the electrical conductivity in the direction parallel to the fiber axis was significantly improved. The maximum thermoelectric power factor and ZT value at 365 K reached 62.4 μW mK-2 and 0.1 in the parallel direction of the TCB-treated P3HT film.

Cuboctahedral Sb2O3Mesocrystals Organized from Octahedral Building Blocks: More than Self-Similarity

Assembly of nanoparticle building blocks over multiple length scales into hierarchically ordered structures plays an essential role in the nonclassical crystallization pathway. Although random particle aggregates are constantly observed in crystallization experiments, mesocrystals with well-shaped morphology and ordered hierarchical structure have been seldomly reported. Here, we describe the successful production of remarkable cuboctahedral Sb2O3 mesocrystals with hierarchical three-dimensional superstructures through a simple solution route. This is the first example of well-defined polyhedral mesocrystals with a cuboctahedral external morphology differing from the octahedral morphology of the building subunits. Electrostatic interactions between cetyltrimethylammonium cations (CTA+) and tartrate anions and hydrophobic interactions between the cetyltrimethylammonium bromide tails were supposed to be the driving force for the aggregation-based growth process. This novel mesocrystal formation breaks through the classical crystallization pattern and opens up a new pathway to construct mesoscale-transformed mesocrystals with hierarchical superstructures.

Agarose functionalization: Synthesis of PEG-agarose amino acid nano-conjugate – its structural ramifications and interactions with BSA in a varying pH regime

In a rapid one-step method protein-mimicking large agarose amino acid framework (AAE; GPC 156.7kDa) was conjugated with polyethylene glycol (PEG 9kDa) affording nano-sized PEGylated amphoteric agarose (PEG-AAE; <10nm; DLS) containing amino, carboxyl and ester groups [overall degree of substitution (DS) 0.91]. The PEG groups were at the residual free carboxylic acid groups of succinate half-ester moiety at C-6 positions of the 1, 3 β-d-galactopyranose moieties of AAE. This new nano-sized PEG-AAE performed like a giant protein conjugate (GPC 331.2kDa) and exhibited pH-responsive interconversion between the triple helix and single-stranded random structures (optical rotatory dispersion) presenting a mixed solubility pattern like random coil (soluble), helical (soluble) and aggregate (precipitation) formations. Circular dichroism studies showed its pH-dependent complexation and decomplexation with bovine serum albumin (BSA). Such pH-responsive PEG-conjugate may be of pronounced therapeutic potential in the area of pharmacology as well as in sensing applications.

Estimates for the elastic moduli of d-dimensional random cell polycrystals

Minimum energy principles and generalized polarization trial fields are used to derive bounds on the effective elastic moduli of d-dimensional random cell polycrystals, which are extensions of our earlier 3D (3-dimensional) results. The bounds are specialized to the 2D random aggregates of square-symmetric crystals, with numerical results for a number of particular crystals. Numerical finite element simulations for sufficiently large random aggregate samples of a particular 2D random polycrystal model show convergence toward the possible scatter interval for the effective elastic moduli enveloped by the new bounds, which are tighter than the classical Voigt–Reuss–Hill and Hashin–Shtrikman ones.

Non-Linear Density Dependent Upconversion Luminescence Enhancement of β-NaYF4: Yb3+: Er3+ Nanoparticles on Random Ag Nanowire Aggregates

ABSTRACTSpectroscopic imaging and statistical analysis of NIR-to-visible upconversion luminescence (UCL) from β-NaYF4:Yb3+:Er3+ upconverting nanoparticles (UCNPs) supported on a series of random Ag nanowire aggregates reveals a density dependent UCL enhancement. Statistical analysis of the spectrally resolved upconversion images shows a non-linear dependence of upconversion luminescence enhancement with Ag nanowire surface coverage. A maximum average enhancement of 5.8× was observed for 58% surface coverage. Based on the empirically determined trend with density, it is estimated that up to 20× upconversion luminescence enhancement can be achieved at 100% surface coverage, even at high excitation intensity. This projection is commensurate with the 20× enhancement ratio observed for select locations within the imaged micro-ensemble. Time-resolved emission of the UC luminescence from UCNPs on the Ag nanowire aggregates confirms the surface plasmon effects on the UCNPs kinetics. Such Ag nanowire aggregates show potential as a scalable and relatively simple metal-enhanced upconversion substrate.

Confocal Spectroscopy to Study Dimerization, Oligomerization and Aggregation of Proteins: A Practical Guide.

Protein self-association is a key feature that can modulate the physiological role of proteins or lead to deleterious effects when uncontrolled. Protein oligomerization is a simple way to modify the activity of a protein, as the modulation of binding interfaces allows for self-activation or inhibition, or variation in the selectivity of binding partners. As such, dimerization and higher order oligomerization is a common feature in signaling proteins, for example, and more than 70% of enzymes have the potential to self-associate. On the other hand, protein aggregation can overcome the regulatory mechanisms of the cell and can have disastrous physiological effects. This is the case in a number of neurodegenerative diseases, where proteins, due to mutation or dysregulation later in life, start polymerizing and often fibrillate, leading to the creation of protein inclusion bodies in cells. Dimerization, well-defined oligomerization and random aggregation are often difficult to differentiate and characterize experimentally. Single molecule “counting” methods are particularly well suited to the study of self-oligomerization as they allow observation and quantification of behaviors in heterogeneous conditions. However, the extreme dilution of samples often causes weak complexes to dissociate, and rare events can be overlooked. Here, we discuss a straightforward alternative where the principles of single molecule detection are used at higher protein concentrations to quantify oligomers and aggregates in a background of monomers. We propose a practical guide for the use of confocal spectroscopy to quantify protein oligomerization status and also discuss about its use in monitoring changes in protein aggregation in drug screening assays.

Colloidal Recycling: Reconfiguration of Random Aggregates into Patchy Particles.

The key ingredients to the successful bottom-up construction of complex materials are believed to be colloids with anisotropic shapes and directional, or patchy, interactions. We present an approach for creating such anisotropic patchy particles based on reconfiguring randomly shaped aggregates of colloidal spheres. While colloidal aggregates are often undesirable in colloidal dispersions due to their random shapes, we exploit them as a starting point to synthesize patchy particles. By a deliberate destabilization of the colloidal particles, diffusion-limited aggregation is induced which partitions the particles into randomly shaped aggregates with controlled size distribution. We achieve a reconfiguration of the aggregates into uniform structures by swelling the polymer spheres with an apolar solvent. The swelling lowers the attractive van der Waals forces, lubricates the contact area between the spheres, and drives the reorganization through minimization of the interfacial energy of the swollen polymer network. This reorganization process yields patchy particles whose patch arrangement is uniform for up to five patches. For particles with more patches, we find that the patch orientation depends on the degree of phase separation between the spheres and the monomer. This enables the synthesis of patchy particles with unprecedented patch arrangements. We demonstrate the broad applicability of this recycling strategy for making patchy particles as well as clusters of spheres by varying the swelling ratio, swelling solvent, surfactant concentration, and swelling time.

Efficient and Privacy-Preserving Online Medical Prediagnosis Framework Using Nonlinear SVM.

With the advances of machine learning algorithms and the pervasiveness of network terminals, the online medical prediagnosis system, which can provide the diagnosis of healthcare provider anywhere anytime, has attracted considerable interest recently. However, the flourish of online medical prediagnosis system still faces many challenges including information security and privacy preservation. In this paper, we propose an e fficient and privacy-preserving online medical prediagnosis framework, called eDiag, by using nonlinear kernel support vector machine (SVM). With eDiag, the sensitive personal health information can be processed without privacy disclosure during online prediagnosis service. Specifically, based on an improved expression for the nonlinear SVM, an efficient and privacy-preserving classification scheme is introduced with lightweight multiparty random masking and polynomial aggregation techniques. The encrypted user query is directly operated at the service provider without decryption, and the diagnosis result can only be decrypted by user. Through extensive analysis, we show that eDiag can ensure that users' health information and healthcare provider's prediction model are kept confidential, and has significantly less computation and communication overhead than existing schemes. In addition, performance evaluations via implementing eDiag on smartphone and computer demonstrate eDiag's effectiveness in term of real online environment.

Molecular dynamics simulations of conformation changes of HIV-1 regulatory protein on graphene

The fragment of viral protein R (Vpr), Vpr13-33, plays an important role in regulating nuclear importing of HIV genes through channel formation in which it adopts a leucine-zipper-like alpha-helical conformation. A recent experimental study reported that helical Vpr13-33 would transform to β-sheet or random coil structures and aggregate on the surface of graphene or graphene oxide through hydrophobic interactions. Due to experimental limitations, however, there is still a considerable lack of understanding on the adsorption dynamics at the early stage of the conformational transition at water-graphene interface and the underlying driving force at molecular level. In this study, atomistic molecular dynamics simulations were used to explore the conformation transition phenomena. Vpr13-33 kept α-helical structure in solution, but changed to β-sheet structure when strongly adsorbed onto graphene. Preferential adsorption of Vpr13-33 on graphene is dominated by hydrophobic interactions. The cluster analysis identified the most significant populated conformation and the early stage of structure conversion from α-helical to β-sheet was found, but the full β-sheet propagation was not observed. Free energy landscape analysis further complemented the transformation analysis of peptide conformations. These findings are consistent with experimental results, and give a molecular level interpretation for the reduced cytotoxicity of Vpr13-33 to some extent upon graphene exposure. Meanwhile, this study provides some significant insights into the detailed mechanism of graphene-induced protein conformation transition.

Uniform percolation of inkjet-printed polymer-semiconductor-wrapped carbon nanotube networks by blending with insulating polymer

The enhanced performance uniformity of thin-film transistors (TFTs) fabricated by inkjet printing of polymer-semiconductor-wrapped single-walled carbon nanotube (PSC/SWCNT) networks blended with an insulating polymer binder was investigated. The inkjet-printed PSC/SWCNT network TFTs exhibited varied device performance with a field-effect mobility of 6.15±6.75cm2/V·s; the inkjet-printed TFTs fabricated using the poly(methyl methacrylate) (PMMA)-blended PSC/SWCNT layer as a channel exhibited relatively uniform device performance, with a field-effect mobility of 7.57±3.32cm2/V·s. This notable difference in device performance uniformity is attributed to the blended PMMA, which prevented the PSC/SWCNTs from forming random aggregates and facilitated their uniform percolation when they were inkjet-printed.

RADIATION PRESSURE ON FLUFFY SUBMICRON-SIZED GRAINS

ABSTRACT We investigate the claim that the ratio β of radiation pressure force to gravitational force on a dust grain in our solar system can substantially exceed unity for some grain sizes, provided that grain porosity is high enough. For model grains consisting of random aggregates of silicate spherules, we find that the maximum value of β is almost independent of grain porosity, but for small ( &lt; 0.3 &mgr; m ?> ) grains, β actually decreases with increasing porosity. We also investigate the effect of metallic iron and amorphous carbon inclusions in the dust grains and find that while these inclusions do increase the radiation pressure cross-section, β remains below unity for grains with 3 pg of silicate material. These results affect the interpretation of the grain trajectories estimated from the Stardust mission, which were modeled assuming β values exceeding one. We find that radiation pressure effects are not large enough for particles Orion and Hylabrook captured by Stardust to be of interstellar origin given their reported impact velocities. We also consider the effects of solar radiation on transverse velocities and grain spin, and show that radiation pressure introduces both transverse velocities and equatorial spin velocities of several hundred meters per second for incoming interstellar grains at 2 au. These transverse velocities are not important for modeling trajectories, but such spin rates may result in centrifugal disruption of aggregates.