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We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

We present a simple method for incorporating the surface tension effect into an iterative conformal mapping model of two-dimensional diffusion-limited aggregation. A curvature-dependent growth probability is introduced and the curvature is…

Current understanding of neuronal growth is mostly qualitative, as the staggering number of physical and chemical guidance cues involved prohibit a fully quantitative description of axonal dynamics. We report on a general approach that…

Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…

Tracking of plant cells in images obtained by microscope is a challenging problem due to biological phenomena such as large number of cells, non-uniform growth of different layers of the tightly packed plant cells and cell division.…

We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…

We propose a simple geometrical construction of topological invariants of 3-strand Brownian braids viewed as world lines of 3 particles performing independent Brownian motions in the complex plane z. Our construction is based on the…

In this work a simple problem on 2D optimal shape for body immersed in a viscous flow is analyzed. The body has geometrical constraints and its profile would be found in the class of cubics which satisfy those conditions. The optimal…

We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell…

What are the general principles that allow proper growth of a tissue or an organ? A growing leaf is an example of such a system: it increases its area by orders of magnitude, maintaining a proper (usually flat) shape. How can this be…

Normal surface theory is a central tool in algorithmic three-dimensional topology, and the enumeration of vertex normal surfaces is the computational bottleneck in many important algorithms. However, it is not well understood how the number…

Geometrical cues are known to play a very important role in neuronal growth and the formation of neuronal networks. Here, we present a detailed analysis of axonal growth and dynamics for neuronal cells cultured on patterned…

We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…

The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate…

A topology optimization method is presented and applied to a blazed diffraction grating in reflection under conical incidence. This type of gratings is meant to disperse the incident light on one particular diffraction order and this…

We discuss a way to exploit the conformal mapping to study the response of a finite metallic element of arbitrary shape to an external electromagnetic field at finite frequencies. This provides a simple way to study different physics issues…

The paper deals with three evolution problems arising in the physical modelling of acoustic phenomena of small amplitude in a fluid, bounded by a surface of extended reaction. The first one is the widely studied wave equation with acoustic…