相关论文: Enumeration of Polyominoes & Polycubes Composed of…

This paper introduces a method to generate highly selective encodings that can be magnetically "programmed" onto physical modules to enable them to self-assemble in chosen configurations. We generate these encodings based on Hadamard…

We describe a framework to assemble permanent-magnet cubes in 3D-printed frames to construct dipole, quadrupole, and solenoid magnets, whose field, in the absence of iron, can be calculated analytically in three spatial dimensions. Rotating…

In this paper we study polycubes: orthogonal polyhedra with axis-aligned quadrilateral faces. We present a complete characterization of polycubes of any genus based on their dual structure: a collection of oriented loops which run in each…

We study the problem of folding a polyomino $P$ into a polycube $Q$, allowing faces of $Q$ to be covered multiple times. First, we define a variety of folding models according to whether the folds (a) must be along grid lines of $P$ or can…

Which polyominoes can be folded into a cube, using only creases along edges of the square lattice underlying the polyomino, with fold angles of $\pm 90^\circ$ and $\pm 180^\circ$, and allowing faces of the cube to be covered multiple times?…

Manipulating the way in which colloidal particles self-organise is a central challenge in the design of functional soft materials. Meeting this challenge requires the use of building blocks that interact with one another in a highly…

We introduce and analyze a model for self-reconfigurable robots made up of unit-cube modules. Compared to past models, our model aims to newly capture two important practical aspects of real-world robots. First, modules often do not occupy…

Altermagnetism, as an unconventional antiferromagnetism, exhibits collinear-compensated magnetic order in real space and spin-splitting band structure in reciprocal space. In this work, we propose a general approach to generating…

We model the stabilization of clusters and lattices of cuboidal particles with long-ranged magnetic dipolar and short-ranged surface interactions. Two realistic systems were considered: one with magnetization orientated in the [001]…

Through rational chemical design, and thanks to the hybrid nature of metal-organic frameworks (MOFs), it is possible to prepare molecule-based 2D magnetic materials stable at ambient conditions. Here, we illustrate the versatility of this…

There are 6 types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations…

Modular small-scale robots offer the potential for on-demand assembly and disassembly, enabling task-specific adaptation in dynamic and constrained environments. However, existing modular magnetic platforms often depend on workspace…

We report a detailed investigation of the magnetic order in 192 stable magnetic two-dimensional materials from the Computational 2D Materials Database having one magnetic atom in the unit cell. The calculations are based on a systematic…

Earlier investigations showed local minima in the monopole-antimonopole potential in U(1) gauge theory on the lattice. In this paper we localize monopoles of Monte-Carlo configurations. A statistical analysis of localization measurements…

Shape morphing magnetic soft materials, composed of magnetic particles in a soft polymer matrix, can transform shapes reversibly, remotely, and rapidly, finding diverse applications in actuators, soft robotics, and biomedical devices. To…

By using two different invariants for the Rubik's Magic puzzle, one of metric type, the other of topological type, we can dramatically reduce the universe of constructible configurations of the puzzle. Finding the set of actually…

External magnetic fields are known to attract and orient magnetically responsive colloidal particles. In the case of 2D microplatelets, rotating magnetic fields are typically used to orient them parallel to each other in a brick-and-mortar…

Motivated by the idea of using simple macroscopic examples to illustrate the physics of complex systems, we modify a historic experimental setup in which interacting floating magnets spontaneously self-assemble into ordered clusters. By…

Magnetic gels and elastomers are promising candidates to construct reversibly excitable soft actuators, triggered from outside by magnetic fields. These magnetic fields induce or alter the magnetic interactions between discrete rigid…

We study the problem of whether rectangular polyominoes with holes are cube-foldable, that is, whether they can be folded into a cube, if creases are only allowed along grid lines. It is known that holes of sufficient size guarantee that…