A gradient method for the quantitative analysis of cell movement and tissue flow and its application to the analysis of multicellular Dictyostelium development

We describe the application of a novel image processing method, which allows quantitative analysis of cell and tissue movement in a series of digitized video images. The result is a vector velocity field showing average direction and velocity of movement for every pixel in the frame. We apply this method to the analysis of cell movement during different stages of the Dictyostelium developmental cycle. We analysed time-lapse video recordings of cell movement in single cells, mounds and slugs. The program can correctly assess the speed and direction of movement of either unlabelled or labelled cells in a time series of video images depending on the illumination conditions. Our analysis of cell movement during multicellular development shows that the entire morphogenesis of Dictyostelium is characterized by rotational cell movement. The analysis of cell and tissue movement by the velocity field method should be applicable to the analysis of morphogenetic processes in other systems such as gastrulation and neurulation in vertebrate embryos

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.Comment: 21 pages, 9 figures, references and supplementary sections added, accepted for publication in PAS

4D topology optimization: Integrated optimization of the structure and self-actuation of soft bodies for dynamic motions

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynamics problems involving large deformations and intricate contact interactions. Moreover, the optimal structure depends on the object's motion, necessitating a simultaneous design approach. To address these challenges, we propose "4D topology optimization," an extension of density-based topology optimization that incorporates the time dimension. This enables the simultaneous optimization of both the structure and self-actuation of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed and hierarchized density variables distributed over the spatiotemporal design domain, representing the material layout, actuator layout, and time-varying actuation. These variables are efficiently optimized using gradient-based methods. Forward and backward simulations of soft bodies are done using the material point method, a Lagrangian-Eulerian hybrid approach, implemented on a recent automatic differentiation framework. We present several numerical examples of self-actuating soft body designs aimed at achieving locomotion, posture control, and rotation tasks. The results demonstrate the effectiveness of our method in successfully designing soft bodies with complex structures and biomimetic movements, benefiting from its high degree of design freedom.Comment: 36 pages, 27 figures; for supplementary video, see https://youtu.be/sPY2jcAsNY