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Emerging multi-material 3D printing techniques have paved the way for the rational design of metamaterials with not only complex geometries but also arbitrary distributions of multiple materials within those geometries. Varying the spatial…
We perform a duality transformation that allows one to express the partition function of the d-dimensional Ising model with random nearest neighbor coupling in terms of new spin variables defined on the square plaquettes of the lattice. The…
This article presents uniform random generators of plane partitions according to the size (the number of cubes in the 3D interpretation). Combining a bijection of Pak with the method of Boltzmann sampling, we obtain random samplers that are…
A spatial stochastic model is developed which describes the 3D nanomorphology of composite materials, being blends of two different (organic and inorganic) solid phases. Such materials are used, for example, in photoactive layers of hybrid…
Interactions between solitary waves have been pivotal to understanding nonlinear phenomena across various disciplines. The dynamics of rarefaction solitary waves holds great potential, yet their fundamental characteristics and interactions…
Random media introduce large degrees of freedom in device design and can thus address challenges in manipulating optical waves. Wave shaping with metasurfaces has mainly utilized periodic or quasi-periodic grids, and, the potential of…
We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contains isotropic pressures. We develop an algorithm that produces a…
The problem of optimizing over random structures emerges in many areas of science and engineering, ranging from statistical physics to machine learning and artificial intelligence. For many such structures finding optimal solutions by means…
The electronic and structural properties of atomically thin materials can be controllably tuned by assembling them with an interlayer twist. During this process, constituent layers spontaneously rearrange themselves in search of a lowest…
In this work, we consider the approximate reconstruction of high-dimensional periodic functions based on sampling values. As sampling schemes, we utilize so-called reconstructing multiple rank-1 lattices, which combine several preferable…
Sampling-based methods for motion planning, which capture the structure of the robot's free space via (typically random) sampling, have gained popularity due to their scalability, simplicity, and for offering global guarantees, such as…
We report on the development of an original mesoscopic lattice model to predict structural, dynamical and capacitive properties of carbon-carbon supercapacitors. The model uses input from molecular simulations, such as free energy profiles…
The multiple scattering method T-matrix (MSTMM) can be used to solve the electromagnetic response of systems consisting of many compact scatterers, retaining a good level of accuracy while using relatively few degrees of freedom, largely…
Investigating dispersion surface morphology of sonic metamaterials is crucial in providing information on related phenomena as inertial coupling, acoustic transparency, polarisation, and absorption. In the present study, we look into…
A new approach to the nonlinear reponse of a multiplayer structure consisting of alternating dielectric materials with intensity-dependent dielectric constants is considered in both analytical and numerical viewpoints. The nonlinear…
Recent advances in scanning transmission electron and scanning tunneling microscopies allow researchers to measure materials structural and electronic properties, such as atomic displacements and charge density modulations, at an Angstrom…
Geographical data are generally autocorrelated. In this case, it is preferable to select spread units. In this paper, we propose a new method for selecting well-spread samples from a finite spatial population with equal or unequal inclusion…
We study semi-analytically the light emission and absorption properties of arbitrary stratified photonic structures with embedded two-dimensional magnetoelectric point scattering lattices, as used in recent plasmon-enhanced LEDs and solar…
Machine learning potentials (MLPs) developed from extensive datasets constructed from density functional theory (DFT) calculations have become increasingly appealing for many researchers. This paper presents a framework of polynomial-based…
Metasurfaces are generally designed by placing scatterers in a periodic grid. We propose and discuss design rules for efficient random and functional metasurfaces with anisotropic elements. We investigate the impact of the elements density…