Size-dependent Effects Research Articles

Size-dependency and lattice-discreetness effect on fracture toughness in 2D crystals under antiplanar loading

AbstractFracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here numerical simulations of crack propagation in two-dimensional fuse networks of different periodic geometries, which are electrical analogs of bidimensional brittle crystals under antiplanar loading. Fracture energy is determined from Griffith’s analysis of energy balance during crack propagation, and fracture toughness is determined from fits of the displacement fields with Williams’ asymptotic solutions. Significant size dependencies are evidenced in small lattices, with fracture energy and fracture toughness both converging algebraically with system size toward well-defined material-constant values in the limit of infinite system size. The convergence speed depends on the loading conditions and is faster when the symmetry of the considered lattice increases. The material constants at infinity obey Irwin’s relation and properly define the material resistance to failure. Their values are approached up to $$\sim 15\%$$ ∼ 15 % using the recent analytical method proposed in Nguyen and Bonamy (Phys Rev Lett 123:205503, 2019). Nevertheless, the deviation remains finite and does not vanish when the system size goes to infinity. We finally show that this deviation is a consequence of the lattice discreetness and decreases when the super-singular terms of Williams’ solutions (absent in a continuum medium but present here due to lattice discreetness) are taken into account.

The hearts of large mammals generate higher pressures, are less efficient and use more energy than those of small mammals.

A prevailing assumption in the cardiovascular field is that the metabolic rate of the heart is a constant proportion of a mammal's whole-body aerobic metabolic rate. In this Commentary, we assemble previously published cardiovascular, metabolic and body mass data from matched terrestrial mammalian species, at rest and during heavy exercise, and reveal scaling relationships that challenge this assumption. Our analyses indicate that the fractional metabolic cost of systemic perfusion compared with whole-body metabolic rate increases significantly with body size among resting mammals, from ∼2.5% in a mouse to ∼10% in an elephant. We propose that two significant body size-dependent effects contribute to this conclusion; namely, that larger species generate higher mean systemic arterial blood pressure and that their myocardium operates with lower external mechanical efficiencies compared with those of smaller species. We discuss potential physiological and mechanical explanations, including the additional energy needed to support the arterial blood column above the heart in larger species, especially those with long necks, as well as the possible sources of greater internal energy losses from the heart of larger species. Thus, we present an updated view of how increasing blood pressure and decreasing efficiency of the myocardium result in an increasing fractional metabolic cost of perfusion as body size increases among resting mammals.

Size-dependent effects of Cu° nanoparticles on electronic properties and ethanol dehydrogenation catalysis via Cu⁺-O-Cu⁺ species

Copper (Cu) nanoparticles, widely utilized as catalysts in industrial applications, exhibit intriguing behavior in structure-sensitive reactions like ethanol dehydrogenation. Contrary to expectations, the catalytic activity does not consistently increase as the size of Cu nanoparticles decreases. In Cu catalysts, the particle size significantly effects the Cu0/Cu+ ratio on the nanoparticle surface. Decreasing the size of Cu nanoparticles promotes their oxidation, leading to the formation of Cu+ and O2− species. This alteration subsequently influences the structural and electronic properties of the catalytic Cu sites. Through Cu nanoparticle calculations, the presence of an O ad-atom was identified to modify the electron density at the Cu site, thereby altering the ethanol adsorption energy and impacting the overall catalytic activity. The increase in O coverage, due to size effects, resulted in a notable decrease in the heat of adsorption on Cu nanoparticles (by approximately 20 kJ mol− 1). The observed high ΔEads indicates that more ethanol molecules could reach the transition state for the reaction, subsequently augmenting turnover rates (TOF) and reducing the apparent activation energy (Eaap) concerning Cu particle size.

Integrated transcriptomics and proteomics analyses reveal the ameliorative effect of hepatic damage in tilapia caused by polystyrene microplastics with chlorella addition

Fish exhibit varying responses to polystyrene microplastics (MPs) depending on particle size. Previous studies suggested that microorganisms adhering to the surface of MPs can induce toxic effects. In this study, Tilapia were exposed to MPs of control (group A), 75 nm (B), 7.5 μm (C), 750 μm (D), as well as combinations of all sizes (E) and 75 nm MPs with Chlorella vulgaris addition (F) for 7, 10 and 14 days. Histopathological changes in liver of tilapia were assessed using enzyme activities, transcriptomics and proteomics. The results showed that in groups combined MPs of different particle sizes and those supplemented with chlorella, MPs were localized on the surface of goblet cells, leading to vacuoles, constricted hepatic sinuses and nuclei displacement. Exposure to 7.5 and 750 μm MPs significantly increased the contents of fatty acid synthase (FAS), adenosine triphosphate (ATP), acetyl-CoA carboxylase (ACC), lipoprotein lipase (LPL), total cholesterol (TC), total triglyceride (TG) contents at 7 and 10 days. In particular, cytochrome p450 1a1 (EROD), reactive oxygen species (ROS) and superoxide dismutase (SOD) were markedly elevated following exposure to MPs. Apoptotic markers caspase-3, and inflammatory markers, including tumor necrosis factor α (TNF-α) and interleukin-1β (IL-1β), had a similar upward trend in comparisons of group C vs A at 7 d, group D vs A at 14 d. The peroxisome proliferator activated receptor (PPAR) signaling pathway, spliceosome, was highly enriched during the 7-day exposure of medium sized MPs, while largest MPs in the comparison of group D vs A at 14 d activated pathways such as phagosome, apoptosis, salmonella infection. Transcriptomic analysis revealed that after 14 days, the kyoto encyclopedia of genes and genomes (KEGG) pathways associated with protein processing in endoplasmic reticulum and the PPAR signaling has been significantly enriched in the Chlorella-supplemented group, which was further confirmed via the proteomic analysis. Overall, the findings highlight the size-dependent effects of MPs on histopathological changes, gene and protein expression in the liver of tilapia, and C. vulgaris effectively attenuated liver damages, likely through modulation of endoplasmic reticulum protein processing and PPAR signaling pathways.

A meshfree formulation for size-dependent thermal buckling and post-buckling behaviour of porous microplates on elastic foundation subjected to localized heating

The semi-analytical framework is developed for in-plane thermal stresses within the microplates under localized heating. Localized heating is modelled using Fourier Series expansions over the complete domain of the plate. These stresses within the plate are estimated after solving the in-plane thermoelasticity problem using Airy's stress approach. Utilizing these stresses, present work also studies the buckling and post-buckling behaviour of a porous metal foam microplate resting on Winkler and Pasternak elastic foundations. The plate is modelled using Reddy's third-order shear deformation theory (TSDT) and von Kármán geometric nonlinearity, and the size-dependent effects are included using the modified strain gradient theory (MSGT). Galerkin's weighted residual method converts the partial differential equations (PDEs) into algebraic equations. The post-buckling equilibrium path is obtained using the modified Newton-Raphson method. The mode shapes of the microplate for the various configurations of the plate with different boundary conditions due to localized thermal loading are plotted. Also, these mode shapes are compared with the mode shapes of the microplate due to in-plane mechanical loading. The parametric effect of porosity, elastic foundation parameters, thickness of plate, size of plate, boundary conditions and loading concentrations on the buckling and post-buckling behaviour of the plate is studied.

Green synthesis of copper oxide nanoparticles using walnut shell and their size dependent anticancer effects on breast and colorectal cancer cell lines

Metal oxide nanoparticles(NPs) contain unique properties which have made them attractive agents in cancer treatment. The CuO nanoparticles were green synthesized using walnut shell powder in different calcination temperatures (400°, 500°, 700°, and 900 °C). The CuO nanoparticles are characterized by FTIR, XRD, BET, SEM and DLS analyses. SEM and DLS analyses showed that by increasing the required calcination temperature for synthesizing the NPs, their size was increased. DPPH analysis displayed no significant anti-oxidative properties of the CuO NPs. The MTT analysis showed that all synthesized CuO NPs exhibited cytotoxic effects on MCF-7, HCT-116, and HEK-293 cell lines. Among the CuO NPs, the CuO-900 NPs showed the least cytotoxic effect on the HEK-293 cell line (IC50 = 330.8 µg/ml). Hoechst staining and real-time analysis suggested that the CuO-900 NPs induced apoptosis by elevation of p53 and Bax genes expression levels. Also, the CuO-900 NPs increased the Nrf-2 gene expression level in MCF-7 cells, despite the HCT-116 cells. As can be concluded from the results, the CuO-900 NPs exerted promising cytotoxic effects on breast and colon cancer cells.

Influence of nonlinear heat accumulation characteristics in laser powder bed fusion (LPBF) and its effect on the shape memory bone implant

This study investigated the complex thermal accumulation characteristics and their effects in the time and spatial domains during the preparation of complex Nitinol (NiTi) alloy structures using laser powder bed fusion (LPBF) technology. The findings reveal a pronounced size dependency phenomenon when the formed dimensions fall below 2 mm. Specifically, a reduction in formed size leads to a marked surge in element loss, a heightened prevalence of internal defects, and a corresponding decline in both mechanical and functional properties. Small-sized (<0.5 mm) samples have significant thermal accumulation due to their fast heating and slow cooling rates, requiring control of heat input. Medium sized (0.5–2 mm) samples have significant temperature gradients as a result of their rapid heating and cooling rates, requiring control of high-temperature residence time. Large sized (> 2 mm) samples necessitate the insulation measures to reduce thermal stress, owing to their sluggish heating and rapid cooling characteristics. Therefore, we developed a model to evaluate the thermal history characteristics of parameters or design schemes and compensate or eliminate heat accumulation during the machining process to balance the thermal history characteristics. This model can also be combined with a thermal field detection system to develop real-time thermal management and control modules for processing. The key to eliminating size-dependency effects is to homogenize the microstructure. A single aging heat treatment (773 K for 0.5 h with air cooling) can effectively homogenize the structure and eliminate size dependence.

Analysis of the magnetic-thermal response of viscoelastic rotating nanobeams based on nonlocal theory and memory effect

Size-dependent effects in elastic deformation and thermal hysteresis effects in the heat transfer process are significant for small-size structures or devices. As an important component of micro- and nanoelectromechanical systems, the analysis of the thermodynamic properties of rotating nanobeams is crucial for the safe operation of the system. This work aims to construct a new nonlocal thermo-viscoelastic model and use this model to analyze the thermodynamic behavior of rotating nanobeams at the microscale. In this work, fractional order Kelvin-Voigt theory describes the viscoelasticity of materials. Moreover, the theory of continuous medium mechanics is improved by introducing nonlocal parameters to capture the size effect during deformation. Based on the generalized thermoelasticity theory, memory-dependent derivatives predict hysteresis effects during heat transfer. Nanobeams are placed in a longitudinal magnetic field. Graphene strips connected to a power supply are used as the nanobeam heat source. The effects of nonlocal parameters, damping coefficients, and fractional order parameters on the dynamic response of the system are analyzed. In addition, a new comparative study of the effects of voltage and resistance on the system is made in the context of the nonlocal generalized thermoelasticity theory.

Size-dependent effects of dams on river ecosystems and implications for dam removal outcomes.

Understanding the relationship between a dam's size and its ecological effects is important for prioritization of river restoration efforts based on dam removal. Although much is known about the effects of large storage dams, this information may not be applicable to small dams, which represent the vast majority of dams being considered for removal. To better understand how dam effects vary with size, we conducted a multidisciplinary study of the downstream effect of dams on a range of ecological characteristics including geomorphology, water chemistry, periphyton, riparian vegetation, benthic macroinvertebrates, and fish. We related dam size variables to the downstream-upstream fractional difference in measured ecological characteristics for 16 dams in the mid-Atlantic region ranging from 0.9 to 57 m high, with hydraulic residence times (HRTs) ranging from 30 min to 1.5 years. For a range of physical attributes, larger dams had larger effects. For example, the water surface width below dams was greater below large dams. By contrast, there was no effect of dam size on sediment grain size, though the fraction of fine-grained bed material was lower below dams independently of dam size. Larger dams tended to reduce water quality more, with decreased downstream dissolved oxygen and increased temperature. Larger dams decreased inorganic nutrients (N, P, Si), but increased particulate nutrients (N, P) in downstream reaches. Aquatic organisms tended to have greater dissimilarity in species composition below larger dams (for fish and periphyton), lower taxonomic diversity (for macroinvertebrates), and greater pollution tolerance (for periphyton and macroinvertebrates). Plants responded differently below large and small dams, with fewer invasive species below large dams, but more below small dams. Overall, these results demonstrate that larger dams have much greater impact on the ecosystem components we measured, and hence their removal has the greatest potential for restoring river ecosystems.

Size-dependent effect on controllable release and field insecticidal efficacy of diamide insecticide polylactic acid microspheres delivery systems against Ostrinia nubilalis

New nano/microcarriers of pesticides represent a highly promising novel field for sustainable pest management. However, despite extensive laboratory research, few studies on the design and evaluation of nanopesticides for field applications exist. In this study, we present a straightforward and green synthetic method of ultrasonic-assisted and hydrogen-bonded self-assembly at the oil-water interface for the synthesis of polylactic acid (PLA) microspheres encapsulating chlorantraniliprole (CAP), with precise control over the size of the microspheres. The resulting CAP-loaded PLA microspheres (CAP-PLA MS) exhibit both high pesticide encapsulation efficiency and stability in natural environments. It has been determined that non-Fickian diffusion mainly controls pesticide release, thus enabling dynamic control over molecular transport speeds. Importantly, our functional CAP-PLA MS demonstrates superior sustained pesticide release performance under both laboratory and field conditions while maintaining better exceptional insecticidal efficacy than normal CAP in controlling O. nubilalis at a concentration of 30 or 45 g/ha. Consequently, we propose that our functional PLA microspheres could serve as ideal pesticide carriers in the sustained treatment of O. nubilalis.

Influence of Particle Size on Mass Transport during the Oxygen Reduction Reaction at Single Silver Particles Using Scanning Electrochemical Cell Microscopy.

Single entity electrochemical measurements enable insight into the electrocatalytic activity of individual particles based on composition, shape, and crystallographic orientation. In addition to structural effects, particle size can further influence electrocatalytic activity and reaction mechanisms through mass transport effects. In this work, electrodeposition was used to grow well-separated silver particles of varying sizes from 100 to 500 nm in radius. Using a multimicroscopy approach of scanning electrochemical cell microscopy combined with scanning electron microscopy, the electrocatalytic current of individual silver particles toward the oxygen reduction reaction was evaluated as a function of their size. It was found that the current density increased with decreasing particle radius, which was correlated to the mass transport of oxygen to the silver particle, demonstrating the importance of size dependent mass transport effects that can occur at the single particle level using scanning electrochemical cell microscopy and opening new opportunities for quantitative electrocatalysis measurements.

Effect of Field Size Dependence on Dose Rate on Co-60 Teletherapy Unit at BINOR

Background: Cancer, defined as the uncontrolled proliferation of malignant cells, is a serious hazard. Radiotherapy, which employs high-energy radiation, seeks to break cancer cell DNA. Due to the significant consequences involved, accuracy is of utmost importance. Before commencing radiation therapy, thorough quality assurance procedures are carried out. The Percentage Depth Dose (PDD) is employed to ensure accurate dose measurement. The research utilized Cobalt-60 Teletherapy, which produces gamma radiation at energy levels of 1.17 MeV and 1.33 MeV, to assess the various field widths observed in PDD. In this experiment, the percentage depth dose (PDD) was evaluated by using a Farmer chamber, water phantom, PC electrometer, ionization chamber, computer software and barometer. The chamber was used throughout a range of field sizes, which varied from 5x5cm2 to 20x20cm2.The TRS-398 approach was employed to assess the radiation dose. Comparable findings were observed when conducting comparisons with published PDD data for cobalt-60 beams. The accumulation dose zone was found to be located approximately 0.5 cm below the surface, coinciding with the maximum (Zmax) dose site. The absorbed amount of radiation resulted in a decrease in the percentage depth dose (PDD) below the given depth. DOI: https://doi.org/10.52783/pst.643

A modified couple stress model to analyze the effect of size dependence on thermal interactions in rotating nanobeams whose properties change with temperature

A modified couple stress model to analyze the effect of size dependence on thermal interactions in rotating nanobeams whose properties change with temperature

High-thermal free vibration analysis of functionally graded microplates using a new finite element formulation based on TSDT and MSCT

Recent advancements in additive manufacturing (AM) have revolutionized the design and production of complex engineering microstructures. Despite these advancements, their mathematical modeling and computational analysis remain significant challenges. This research aims to develop an effective computational method for analyzing the free vibration of functionally graded (FG) microplates under high temperatures while resting on a Pasternak foundation (PF). This formulation leverages a new third-order shear deformation theory (new TSDT) for improved accuracy without requiring shear correction factors. Additionally, the modified couple stress theory (MCST) is incorporated to account for size-dependent effects in microplates. The PF is characterized by two parameters including spring stiffness () and shear layer stiffness (). To validate the proposed method, the results obtained are compared with those of the existing literature. Furthermore, numerical examples explore the influence of various factors on the high-temperature free vibration of FG microplates. These factors include the length scale parameter (), geometric dimensions, material properties, and the presence of the elastic foundation. The findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the findings significantly enhance our comprehension of the free vibration of FG microplates in high thermal environments. In addition, the results of this research will have great potential in military and defense applications such as components of submarines, fighter aircraft, and missiles.

Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures

The underlying size-dependent mechanism of viscoelastic porous metamaterial structures is still unclear, and the solution to their response using the high-fidelity numerical method is time-consuming, even prohibitive. This paper explores how the size-dependent effect of metamaterial structures emerges from the underlying nonlocal interactions in metamaterial microstructures, and then develops an accurate but efficient homogenization method for analyzing their size-dependent and time-dependent mechanical behaviors of viscoelastic porous metamaterial structures. By accounting for the nonlocal interaction between different representative volume elements and the history-dependent effect, a spatiotemporally nonlocal discrete element model is developed to analyze the mechanical behavior of viscoelastic porous metamaterial structures. With the help of the spatiotemporally nonlocal discrete element model, a spatiotemporally nonlocal homogenization method is proposed to accurately yet efficiently assess the size-dependent mechanical behavior of the porous metamaterial structure. The remarkable potential of the spatiotemporally nonlocal homogenization method is illustrated by simulating the stress relaxation of a viscoelastic porous metamaterial structure under axial strain. Results indicate that the size-dependent phenomenon can be significant, and the spatiotemporally nonlocal homogenization model can efficiently capture the size-dependent relaxation stress evaluated by the high-fidelity finite element model without loss of accuracy.

Wafer-scale bonded GaN–AlN with high interface thermal conductance

Wide and ultrawide bandgap semiconductors, such as GaN, play a crucial role in high-power applications, yet their performance is often constrained by thermal management challenges. In this work, we introduce a high-quality interface between GaN and AlN, prepared through wafer-scale bonding and verified via high-resolution transmission electron microscopy and transport experiments. We experimentally measured the thermal boundary conductance of the GaN–AlN interface, achieving up to 320 MW/m2K at room temperature using an ultrafast optical technique and sensitivity examinations. Non-equilibrium atomistic Green's functions and density functional theory simulations were conducted to model the interface phonon modes and their contributions to thermal transport, demonstrating good agreement with the experimental results from 80 to 300 K. Additionally, we observed a size-dependent effect on the thermal boundary conductance related to the GaN film thickness from 180 to 450 nm, which we attributed to quasi-ballistic thermal transport through molecular dynamics simulations. Our study has demonstrated a scalable processing route for wafer-sized chip packaging and provides fundamental insights to mitigate near-junction thermal resistance. Further exploration of interface engineering could facilitate co-design strategies to advanced thermal management technologies.

A comprehensive investigation of the bending and vibration behavior of size-dependent functionally graded nanoplates via an enhanced nonlocal finite element shear model

This research paper conducts a comprehensive investigation into the linear bending and free vibration of size-dependent functionally graded (FG) nanoplates using an improved first-order shear deformation theory (IFSDT). The present IFSDT offers an enhanced representation and precise computation of normal and shear stresses across the thickness of the nanoplates. Notably, it not only ensures compliance with free conditions on both the upper and lower surfaces but also eliminates the need for a conventional correction factor commonly employed in the first-order shear deformation theory (FSDT). To transcend the assumptions of classical continuum mechanics and address the impacts of small-scale effects in discrete nanoplates, Eringen’s nonlocal elasticity theory is applied. The formulation of the governing equation for the bending and free vibration analyses of the FG nanoplates is achieved through the application of Hamilton’s principle. The proposed IFSDT is implemented with an efficient C0-continuous quadrilateral element which is suitable for analysis of structures with arbitrary shapes and complex forces. The model’s performance is showcased through a comparative evaluation against literature predictions, highlighting its high accuracy and rapid convergence. Additionally, the research scrutinizes the effects of various parameters, such as plate thickness, boundary conditions, aspect ratio, nonlocal parameter, different material compositions, and power-law index on the deflections, stresses, and naturel frequencies of the FG nanoplates. The results underscore the significant impact of size-dependent effects on the linear bending and vibration behaviors of the nanoplates.

Concurrent multiscale topology optimization for size-dependent structures incorporating multiple-phase materials

The significant progress in additive manufacturing has resulted in the development of well-engineered microstructures with innovative topological configurations, showcasing exceptional performance across diverse fields. Topology optimization is widely recognized as an advanced design tool that provides engineers with new insights for creating lightweight structures. As integration devices continue to trend towards miniaturization, the size effect in small-scale structures remains a persistent challenge. The absence of characteristic parameters to describe this size effect hinders proper explanation through traditional multiscale topology optimization based on classical mechanics. Therefore, we propose a size-dependent topology optimization framework for concurrent multiscale design involving multiple-phase materials. The modified couple stress theory is proposed to account for the size effect in small-scale structures. The numerical findings suggest that the size effect is significantly influenced by the ratio of elastic modulus, volume fraction, and width-to-length ratio of the representative volume element as its characteristic size approaches the length of the material. These results highlight the importance of considering size-dependent effects in topology optimization for multiscale design and provide valuable insights for engineers and researchers in this field.

تأثيرات التكنولوجيا النانوية على الخواص الميكانيكية والفيزيائية للمعادن في أنظمة التبريد

Nanotechnology has revolutionized various scientific and engineering fields, including materials science. In this investigation, the focus is on examining the influence of titanium nanoparticle size on the mechanical and physical properties of metal. Incorporating nanoparticles into metal matrices presents an exciting opportunity to enhance material performance through size-dependent effects. Titanium nanoparticles have been chosen as the primary focus due to their unique properties and extensive applications. To assess the impact of nanoparticle size on mechanical properties, a series of experiments were conducted involving the production of metal composites with varying sizes of titanium nanoparticles. Mechanical properties, including yield strength and hardness, were measured using standard testing methods such as tensile testing and nanoindentation. The results indicate that smaller titanium nanoparticles contributed to improve mechanical properties, increased yield strength and hardness compared to the bulk metal. Additionally, the investigation explored the effects of titanium nanoparticle size on the physical properties of the metal composite. Thermal conductivity and coefficient of thermal expansion were measured to evaluate the thermal behavior of the composites. The findings demonstrate that the incorporation of titanium nanoparticles influences thermal conductivity and coefficient of thermal expansion, with variations that depend on nanoparticle size. Keywords: Nanotechnology, Titanium Nanoparticles, Mechanical Properties, Physical Properties, Metal Composites.

BYORP and Dissipation in Binary Asteroids: Lessons from DART

The near-Earth binary asteroid Didymos was the target of the planetary defense demonstration mission DART in 2022 September. The smaller binary component, Dimorphos, was impacted by the spacecraft in order to measure momentum transfer in kinetic impacts into rubble piles. DART and associated Earth-based observation campaigns have provided a wealth of scientific data on the Didymos–Dimorphos binary. DART revealed the largely oblate and ellipsoidal shape of Dimorphos before the impact, while the postimpact observations suggest that Dimorphos now has a prolate shape. Here we add those data points to the known properties of small binary asteroids and propose new paradigms of the radiative binary Yarkovsky–O’Keefe–Radzievskii–Paddack (BYORP) effect as well as tidal dissipation in small binaries. We find that relatively spheroidal bodies like Dimorphos made of small debris may experience a weaker and more size-dependent BYORP effect than previously thought. This could explain the observed values of period drift in several well-characterized binaries. We also propose that energy dissipation in small binaries is dominated by relatively brief episodes of large-scale movement of (likely surface) materials, rather than long-term steady-state tidal dissipation. We propose that one such episode was triggered on Dimorphos by the DART impact. Depending on the longevity of this high-dissipation regime, it is possible that Dimorphos will be more dynamically relaxed in time for the Hera mission than it was in the weeks following the impact.