Related papers: Fractal space frames and metamaterials for high me…
The usual formulation of time-dependent mechanics implies a given splitting $Y=R\times M$ of an event space $Y$. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The…
In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…
Static structure factors are computed for large-scale, mechanically stable, jammed packings of frictionless spheres (three dimensions) and disks (two dimensions) with broad, power-law size dispersity characterized by the exponent $-\beta$.…
We show that the space charge dynamics of high intensity beams in the plane perpendicular to the magnetic field in cyclotrons is described by the two-dimensional Euler equations for an incompressible fluid. This analogy with fluid dynamics…
Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite…
Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound.…
The elastic properties of a material with spherical voids of equal volume are analysed using a new model, with particular attention paid to the hexagonal close-packed and the face-centred cubic arrangement of voids. Void fractions well…
We study the physical properties derived from interstellar cloud complexes having a fractal structure. We first generate fractal clouds with a given fractal dimension and associate each clump with a maximum in the resulting density field.…
Highly-deformable materials, from synthetic hydrogels to biological tissues, are becoming increasingly important from both fundamental and practical perspectives. Their mechanical behaviors, in particular the dynamics of crack propagation…
A method is proposed for generating compact fractal disordered media, by generalizing the random midpoint displacement algorithm. The obtained structures are invasive stochastic fractals, with the Hurst exponent varying as a continuous…
Geometric fracture assembly presents a challenging practical task in archaeology and 3D computer vision. Previous methods have focused solely on assembling fragments based on semantic information, which has limited the quantity of objects…
The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail…
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a…
We present an analytical model which permits the calculation of effective material parameters for planar metamaterials consisting of arbitrary unit cells (metaatoms) formed by a set of straight wire sections of potentially different shape.…
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer…
Seeing sharper or becoming invisible are visions strongly driving the development of THz metamaterials. Strings are a preferred architecture of metamaterials as they extend continuously along one dimension. Here, we demonstrate that…
Much of the structure in metric spaces that allows for the creation of fractals exists in more generalized non-metrizable spaces. In particular the same theorems regarding the behavior of compact sets can be proven in the more general…
We have developed a simulation technique that uses non-linear finite element analysis and elastic fracture mechanics to compute physically plausible motion for three-dimensional, solid objects as they break, crack, or tear. When these…
The stability, robustness, accuracy, and efficiency of space-time finite element methods crucially depend on the choice of approximation spaces for test and trial functions. This is especially true for high-order, mixed finite element…
There has been substantial interest in miniaturizing optical systems by flat optics. However, one essential optical component, free space, fundamentally cannot be substituted with conventional local flat optics with space-dependent transfer…