Related papers: Calculation of material properties for arbitrary s…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
Transformation optics constructions have allowed the design of electromagnetic, acoustic and quantum parameters that steer waves around a region without penetrating it, so that the region is hidden from external observations. The material…
Mechanically reconfigurable reflectors can modify their geometries to realize large angle beam scanning. This paper studies a method for reconfiguring a reflector geometry from a standard parabolic shape to offset parabolic shapes with…
We propose a new technique for estimating spatially varying parametric materials from a single image of an object with unknown shape in unknown illumination. Our method uses a low-order parametric reflectance model, and incorporates strong…
The question of interest in the present study is: ``Given a body subject to mechanical loads, how to define the initial geometry so that the deformed one matches precisely a prescribed shape?'' This question is particularly relevant in…
Learning to change shape is a fundamental strategy of adaptation and evolution of living organisms, from bacteria and cells to tissues and animals. Human-made materials can also exhibit advanced shape morphing capabilities, but lack the…
Spatial tailoring of the material constitutive properties is a well-known strategy to mold the local flow of given observables in different physical domains. Coordinate-transformation-based methods (e.g., transformation optics) offer a…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
We define a number of natural (from geometric and combinatorial points of view) deformation spaces of valuations on finite graphs, and study functions over these deformation spaces. These functions include both direct metric invariants…
Any three-dimensional Riemannian metric can be locally obtained by deforming a constant curvature metric along one direction. The general interest of this result, both in geometry and physics, and related open problems are stressed.
An emerging theme across many domains of science and engineering is materials that change shape, often dramatically. Determining their structure involves solving a shape optimization problem where a given energy functional is minimized with…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
We present a new technique for the design of transformation-optics devices based on large-scale optimization to achieve the optimal effective isotropic dielectric materials within prescribed index bounds, which is computationally cheap…
The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact…
By idealizing a general mapping as a series of local affine ones, we derive approximately transformed material parameters necessary to control solid elastic waves within classical elasticity theory. The transformed elastic moduli are…
We describe the Mediatrix filamentation method, an iterative procedure that decomposes image shapes in filaments over their intensity ridgeline along their main direction using perpendicular bisectors. From this decomposition several…
A random medium can serve as a controllable arbitrary spectral filter with spectral resolution determined by the inverse of the interaction time of the light in the medium. We use wavefront shaping to implement an arbitrary spectral…
An inverse way to define the parameters of ideal cylindrical cloaks is developed, in which the interconnection between the parameters is revealed for the first time without knowing a specific coordinate transformation. The required…
We discuss some of the geometric properties, such as the foliated Schwarz symmetry, the monotonicity along the axial and the affine-radial directions, of the first eigenfunctions of the Zaremba problem for the Laplace operator on annular…
In this paper, we derive new shape descriptors based on a directional characterization. The main idea is to study the behavior of the shape neighborhood under family of transformations. We obtain a description invariant with respect to…