Cells exploit a phase transition to mechanically remodel the fibrous extracellular matrix

Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers—tracts of high densification and fibre alignment—form between cells, thinner bands emanate from cell clusters. While tethers facilitate cell migration and communication, how they form is unclear. Combining modelling, simulation and experiment, we show that tether formation is a densification phase transition of the extracellular matrix, caused by buckling instability of network fibres under cell-induced compression, featuring unexpected similarities with martensitic microstructures. Multiscale averaging yields a two-phase, bistable continuum energy landscape for fibrous collagen, with a densified/aligned second phase. Simulations predict strain discontinuities between the undensified and densified phase, which localizes within tethers as experimentally observed. In our experiments, active particles induce similar localized patterns as cells. This shows how cells exploit an instability to mechanically remodel the extracellular matrix simply by contracting, thereby facilitating mechanosensing, invasion and metastasis.

Non-Bloch band theory and bulk–edge correspondence in non-Hermitian systems

In this paper, we review our non-Bloch band theory in 1D non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su–Schrieffer–Heeger model, the bulk–edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.

Linear and nonlinear Fano resonance in the main chain-structure of additional defects with an isolated ring composed of defects

As is well known, Fano resonance originates from the interference between a continuum energy band and an embedded discrete energy level. We study transmission properties of the discrete chain-structure of additional defects with an isolated ring composed of N defect states, and obtain the analytical transmission coefficient of similar Fano formula. Using the formula, we reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences. It is found that a nonlinear Kerr-like response leads to bistable transmission, and for either linear cases or nonlinear ones, the defects in main arrays have a major impact on perfect reflections, but has no effect on perfect transmission.

A method to predict fatigue crack initiation in metals using dislocation dynamics

A theory is proposed to predict the initiation of fatigue cracks using cyclic dislocation dynamics (DD) simulations. The evolution of dislocation networks in a grain is simulated over several cycles. It is shown that the dislocation density and the energy stored in the dislocation networks increase with the number of cycles. The results of the DD simulations are used to construct an energy balance expression for crack initiation. A hypothetical crack is inserted into the grain, and the Gibbs energy consisting of the energy of the dislocation structure, the surface energy of the hypothetical crack, and the reduction in continuum energy is evaluated. Once the Gibbs energy attains a maximum, the dislocation structure becomes unstable, and it becomes energetically more favorable to form a real crack. The proposed method is applied to oxygen-free high conductivity copper, and the results are compared against experiments. Finally, it is shown how the method can be amended to account for environmental effects.

Euler elastica as a Γ-limit of discrete bending energies of one-dimensional chains of atoms

In the 1920s, Hencky proposed a discrete elastica model describing a chain of identical rigid bars connected by torsional springs. Hencky observed that this discrete elastica model converges to Euler’s elastica as the number of bars increases while their lengths decrease, and Hencky’s bar-chain model has been used primarily as an approximation of Euler’s elastica. A Hencky-type bar-chain model can also be incorporated into a Frenkel–Kontorova-type discrete atomistic model, where the joints and bars represent the atoms and interatomic bonds, respectively, while the entire chain of atoms interacts with either a substrate or other chains. The energy of a continuum system corresponding to this Frenkel–Kontorova-type model can then be recovered by taking an appropriate discrete-to-continuum limit. Developing a correct limiting procedure for the discrete elastica establishes the bending component of this continuum energy. In this paper we use Γ-convergence to rigorously show that as the bar length in the discrete elastica model we consider goes to 0, the bending energies of the chain Γ-converge to the continuum bending energy associated with Euler’s elastica.

Analyses of the TIARA 43 MeV Proton Benchmark Shielding Experiments Using the ARES Transport Code

ARES is a multidimensional parallel discrete ordinates particle transport code with arbitrary order anisotropic scattering. It can be applied to a wide variety of radiation shielding calculations and reactor physics analysis. To validate the applicability of the code to accelerator shielding problems, ARES is adopted to simulate a series of accelerator shielding experiments for 43 MeV proton-7Li quasi-monoenergetic neutrons, which is performed at Takasaki Ion Accelerator for Advanced Radiation Application. These experiments on iron and concrete were analyzed using the ARES code with FENDL/MG-3.0 multigroup libraries and compared to direct measurements from the BC501A detector. The simulations show good agreement with the experimental data. The ratios of calculated values to experimental data for integrated neutron flux at peak and continuum energy regions are within 64% and 25% discrepancy for the concrete and iron experiments, respectively. The results demonstrate the accuracy and efficiency of ARES code for accelerator shielding calculation.

Sensitivity Analysis for a Quantum Informed Ferroelectric Energy Model

We perform global sensitivity analysis for parameters in a continuum energy model for ferroelectric materials, which is informed by density functional theory (DFT). Specifically, we use global sensitivity analysis to rank the sensitivity of phenomeno-logical parameters governing the Landau and electrostriction energy for single-domain ferroelectric lead titanate. These techniques include Pearson correlations constructed directly from input and output relations, Sobol sensitivity indices, and Morris indices.