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We introduce an adjoint-based aerodynamic shape optimization framework that integrates a diffusion model trained on existing designs to learn a smooth manifold of aerodynamically viable shapes. This manifold is enforced as an equality…

While biological vision systems rely heavily on feedback connections to iteratively refine perception, most artificial neural networks remain purely feedforward, processing input in a single static pass. In this work, we propose a…

This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular…

Biomolecular motor proteins that generate forces by consuming chemical energy obtained from ATP hydrolysis are pivotal for organizing broad cytoskeletal structures in living cells. The control of such cytoskeletal structures benefits…

Eukaryotic cells can move spontaneously without being guided by external cues. For such spontaneous movements, a variety of different modes have been observed, including the amoeboid-like locomotion with protrusion of multiple pseudopods,…

Two phase solid-fluid mixture models are ubiquitous in biological applications. For instance, models for growth of tissues and biofilms combine time dependent and quasi-stationary boundary value problems set in domains whose boundary moves…

Many animal cells change their shape depending on the stiffness of the substrate on which they are cultured: they assume small, rounded shapes in soft ECMs, they elongate within stiffer ECMs, and flatten out on hard substrates. Cells tend…

Mechanically induced unfolding of passive crosslinkers is a fundamental biological phenomenon encountered across the scales from individual macro-molecules to cytoskeletal actin networks. In this paper we study a conceptual model of…

Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…

Growing demands in the semiconductor industry result in the need for enhanced performance of lithographic equipment. However, position tracking accuracy of high precision mechatronics is often limited by the presence of disturbance sources,…

Granular mixtures rapidly segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have…

Biological materials achieve directional reinforcement with oriented assemblies of anisotropic building blocks. One such example is the nanocomposite structure of keratinized epithelium on the toe pad of tree frogs, in which hexagonal…

We present a derivation of a multidomain model for the electric potential in bundles of randomly distributed axons with different radii. The FitzHugh-Nagumo dynamics is assumed on the axons' membrane, and the conductivity depends…

In biological systems, molecular-scale forces and motions are pivotal for enabling processes like motility, shape change, and replication. These forces and motions are organized, amplified, and transmitted across macroscopic scales by…

Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…

Inspired by patterns observed in mixtures of microtubules and molecular motors, we propose continuum equations for the evolution of motor density, and microtubule orientation. The chief ingredients are the transport of motors along tubules,…

The macroscopic behaviour of active matter arises from nonequilibrium microscopic processes. In soft materials, active stresses typically drive macroscopic shape changes, which in turn alter the geometry constraining the microscopic…

The cytoskeleton protein actin assembles into large bundles when supporting stresses in the cell, but grows into a fine branched network to induce cell motion. Such self-organization processes are studied in artificial networks of…

Plant organ outgrowth superficially appears like the continuous mechanical deformation of a sheet of cells. Yet, how precisely cells as individual mechanical entities can act to morph a tissue reliably and efficiently into three dimensions…

Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…