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The origin of the indentation size effect has been extensively researched over the last three decades, following the establishment of nanoindentation as a broadly used small-scale mechanical testing technique that enables hardness measurements at submicrometer scales. However, a mechanistic understanding of the indentation size effect based on direct experimental observations at the dislocation level remains limited due to difficulties in observing and quantifying the dislocation structures that form underneath indents using conventional microscopy techniques. Here, we employ precession electron beam diffraction microscopy to “look beneath the surface,” revealing the dislocation characteristics (e.g., distribution and total length) as a function of indentation depth for a single crystal of nickel. At smaller depths, individual dislocation lines can be resolved, and the dislocation distribution is quite diffuse. The indentation size effect deviates from the Nix–Gao model and is controlled by dislocation source starvation, as the dislocations are very mobile and glide away from the indented zone, leaving behind a relatively low dislocation density in the plastically deformed volume. At larger depths, dislocations become highly entangled and self-arrange to form subgrain boundaries. In this depth range, the Nix–Gao model provides a rational description because the entanglements and subgrain boundaries effectively confine dislocation movement to a small hemispherical volume beneath the contact impression, leading to dislocation interaction hardening. The work highlights the critical role of dislocation structural development in the small-scale mechanistic transition in indentation size effect and its importance in understanding the plastic deformation of materials at the submicron scale.

To cope with proteotoxic stress, cells attenuate protein synthesis. However, the precise mechanisms underlying this fundamental adaptation remain poorly defined. Here we report that mTORC1 acts as an immediate cellular sensor of proteotoxic stress. Surprisingly, the multifaceted stress-responsive kinase JNK constitutively associates with mTORC1 under normal growth conditions. On activation by proteotoxic stress, JNK phosphorylates both RAPTOR at S863 and mTOR at S567, causing partial disintegration of mTORC1 and subsequent translation inhibition. Importantly, HSF1, the central player in the proteotoxic stress response (PSR), preserves mTORC1 integrity and function by inactivating JNK, independently of its canonical transcriptional action. Thereby, HSF1 translationally augments the PSR. Beyond promoting stress resistance, this intricate HSF1–JNK–mTORC1 interplay, strikingly, regulates cell, organ and body sizes. Thus, these results illuminate a unifying mechanism that controls stress adaptation and growth. Dai and colleagues reveal that proteotoxic stress causes JNK-mediated disintegration of the mTORC1 complexes, whereas heat shock factor 1 (HSF1) counteracts this response to promote stress resistance and growth.

The interactions between dislocations (dislocations and deformation twins) and boundaries (grain boundaries, twin boundaries and phase interfaces) during deformation at ambient temperatures are reviewed with focuses on interaction behaviors, boundary resistances and energies during the interactions, transmission mechanisms, grain size effects and other primary influencing factors. The structure of boundaries, interactions between dislocations and boundaries in coarse-grained, ultrafine-grained and nano-grained metals during deformation at ambient temperatures are summarized, and the advantages and drawbacks of different in-situ techniques are briefly discussed based on experimental and simulation results. The latest studies as well as fundamental concepts are presented with the aim that this paper can serve as a reference in the interactions between dislocations and boundaries during deformation.

Gold (Au) catalysts exhibit a significant size effect, but its origin has been puzzling for a long time. It is generally believed that supported Au clusters are more or less rigid in working condition, which inevitably leads to the general speculation that the active sites are immobile. Here, by using atomic resolution in situ environmental transmission electron microscopy, we report size-dependent structure dynamics of single Au nanoparticles on ceria (CeO₂) in CO oxidation reaction condition at room temperature. While large Au nanoparticles remain rigid in the catalytic working condition, ultrasmall Au clusters lose their intrinsic structures and become disordered, featuring vigorous structural rearrangements and formation of dynamic low-coordinated atoms on surface. Ab initio molecular-dynamics simulations reveal that the interaction between ultrasmall Au cluster and CO molecules leads to the dynamic structural responses, demonstrating that the shape of the catalytic particle under the working condition may totally differ from the shape under the static condition. The present observation provides insight on the origin of superior catalytic properties of ultrasmall gold clusters.

Structural components with different scales normally show different fatigue behaviors, which are virtually dominated by defects originated from multiple sources, including manufacturing processes. This paper reviews three types of size effects (statistical, geometrical, technological) as well as their recent advances in metal fatigue, aiming to provide a guide for fatigue strength assessment of engineering components containing defects, inclusions and material inhomogeneity. Firstly, the background of inherent defects and defect-based failure mechanism are briefly outlined, and fatigue failure analysis based on fracture mechanics as well as statistics theory are emphasized. Then, two approaches commonly applied in statistical size effect modeling, i.e. critical defect method and weakest link method, are elaborated. In addition, the highly stressed volume method is introduced for considering the geometrical size effects, and the technological (production and surface) size effect is briefly overviewed. Finally, further directions on size effect in metal fatigue under defects are explored.

Twin-field quantum key distribution(TF-QKD) protocol and its variants, such as phase-matching QKD, sending-or-not-sending QKD and no phase post-selection TF-QKD(NPP-TFQKD), are very promising for long-distance applications. However, there are still some gaps between theory and practice in these protocols. Concretely, a finite-key size analysis is still missing, and the intensity fluctuations are not taken into account. To address the finite-key size effect, we first give the key rate of NPP-TFQKD against collective attack in finite-key size region and then prove it can be against coherent attack. To deal with the intensity fluctuations, we present an analytical formula of 4-intensity decoy state NPP-TFQKD and a practical intensity fluctuation model. Finally, through detailed simulations, we show NPP-TFQKD can still keep its superiority of high key rate and long achievable distance.

Up to the beginning of the twenty-first century, most of quasi-brittle structures, in particular the ones composed by concrete or masonry frames and walls, were designed and built according to codes that totally ignored fracture mechanics theory. The structural load capacity predicted by strength-based theories, such as plastic analysis and limit analysis, do not exhibit size-effect. Within the framework of fracture mechanics theory, this paper deals with the analysis of the effect of non proportional loadings on the strength reduction with the structural scaling. In particular, this study investigates the size-effect of quasi-brittle materials subjected to self-weight. Although omnipresent, gravity-load is often considered negligible in most studies in the field of fracture mechanics. This assumption is obviously not valid for large structures and in particular for geometries in which the dead load is a major driving force leading to fracture and structural failure. In this study, an analytical formulation expressing the relation between the strength-reduction and the structural scaling and accounting for self-weight, was derived for both notched and unnotched bodies. More specifically, a closed form expression for size and self-weight effects was first derived for notched specimens from equivalent linear elastic fracture mechanics. Next, equivalent linear elastic fracture mechanics theory being not applicable to unnotched bodies, a cohesive model formulation was considered. Particularly, the cohesive size effect curve and the generalized cohesive size effect curves, originally obtained via cohesive crack analysis for weightless bodies with sharp and blunt/unnotched notches, respectively, were equipped of an additional term to account for the effect of gravity. All the resulting formulas were compared with the predictions of numerical simulation resulting from the adoption of the Lattice Discrete Particle Model. The results point out that the analytical formulas match very well the results of the numerical model for both notched and unnotched samples. Furthermore, the analytical formulas predict a vertical asymptote for increasing size, in the typical double-logarithm strength versus structural size representation. The asymptote corresponds to a characteristic size at which the structure fails under its own weight. For large structural sizes approaching this characteristic size, the newly developed formulas deviate significantly from previously proposed size-effect formulas. The practical relevance of this finding was demonstrated by analyzing size and self-weight effect for several quasi-brittle materials such as concrete, wood, limestone and carbon composites. Most importantly, the proposed formulas were applied to the failure of semi-circular masonry arches under spreading supports with different slenderness ratios. Results show that analytical formulas well predict numerical simulations and, above all, that for vaulted structures it is mandatory accounting for the effect of self-weight.

Particle size strongly influences the shear strength of granular materials. However, previous studies of the particle size effect have focused mainly on the macroscopic behavior of granular materials, neglecting the associated micro-mechanism. In this study, the effect of particle size on the shear strength of uncrushable granular materials in biaxial testing is investigated using the discrete element method (DEM). First, a comprehensive calibration against experimental results is conducted to obtain the DEM parameters for two types of quartz sand. Then, a series of biaxial tests are simulated on sands with parallel particle size distributions to investigate the effect of particle size on macro- and microscopic behaviors. Finally, by adopting the rolling resistance method and the clump method, irregular-shaped particles are simulated to investigate how the particle size effect will be influenced by the particle shape. Simulation results demonstrate that (1) the peak shear strength increases with particle size, whereas the residual shear strength is independent of particle size; (2) the thickness of the shear band increases with the particle size, but its ratio decreases with particle size; (3) the particle size effect can be explained by the increase of friction utilization ratio with particle size; and (4) the particle size effect is more significant in granular materials that consist of particles with higher angularity.

The seminal work of Nix and Gao in (J Mech Phys Solids, 46:411–425, 1998), laid the foundation for quantifying indentation size effect (ISE). Several groups around the world have continued to explore the various factors that influence ISE, through extensive numerical and experimental studies. In this work, a unified approach to quantify ISE is presented, wherein the effects of materials, geometry and other coupled parameters on ISE are incorporated to derive a simple unified model. The model predictions for depth dependence of hardness are validated through experimental studies on pulsed electro-deposited (PED) nickel with varying grain sizes using a Berkovich tip with a finite tip radius. Lower grain sizes, higher statistically stored dislocation densities, blunt tips, lower constraint factors and higher plastic zone sizes are found to reduce ISE. The deviation caused by these parameters from the predictions of the original Nix & Gao model are discussed. Graphical abstract

In prevention science and related fields, large meta-analyses are common, and these analyses often involve dependent effect size estimates. Robust variance estimation (RVE) methods provide a way to include all dependent effect sizes in a single meta-regression model, even when the exact form of the dependence is unknown. RVE uses a working model of the dependence structure, but the two currently available working models are limited to each describing a single type of dependence. Drawing on flexible tools from multilevel and multivariate meta-analysis, this paper describes an expanded range of working models, along with accompanying estimation methods, which offer potential benefits in terms of better capturing the types of data structures that occur in practice and, under some circumstances, improving the efficiency of meta-regression estimates. We describe how the methods can be implemented using existing software (the “metafor” and “clubSandwich” packages for R), illustrate the proposed approach in a meta-analysis of randomized trials on the effects of brief alcohol interventions for adolescents and young adults, and report findings from a simulation study evaluating the performance of the new methods.