This study examines the mechanical behavior of a novel class of mechanical metamaterials alternating pentamode lattices and stiffening plates. The unit cell of such lattices consists of a sub-lattice ...of the face cubic-centered unit cell typically analyzed in the current literature on pentamode materials. The studied systems exhibit only three soft deformation modes in the infinitesimal stretch-dominated regime, as opposed to the five zero-energy modes of unconfined pentamode lattices. We develop analytical formulae for the vertical and bending stiffness properties and study the dependence of such quantities on the main design parameters: the lattice constant, the solid volume fraction, the cross-section area of the rods, and the layer thickness. A noteworthy result is that the effective compression modulus of the analyzed structures is equal to two thirds of the Young modulus of the stiffest isotropic elastic networks currently available in the literature, being accompanied by zero-rigidity against infinitesimal shear and twisting mechanisms. The use of the proposed metamaterials as novel seismic-isolation devices and impact-protection equipment is discussed by drawing comparisons with the response of alternative devices already available or under development.
We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge invariant by construction. We demonstrate the application of this framework to U(1) gauge ...theory in two spacetime dimensions, and find that, at small bare coupling, the approach is orders of magnitude more efficient at sampling topological quantities than more traditional sampling procedures such as hybrid Monte Carlo and heat bath.
In this paper, a new type of three-dimensional (3D) truss-lattice structures for low-frequency and broadband elastic wave absorption is proposed. The local resonance mechanism used in ...acoustic/elastic metamaterials (AMs) for generating low-frequency bandgaps, in which elastic waves cannot pass through, is introduced into the continuous body-centered cubic lattice structures by only making the cross-struts in each unit-cell have a radius jump discontinuity. This method is easy to realize for practical engineering compared with the conventional acoustic metamaterials usually made of different materials. The band structures of the 3D AM-based lattice structures are calculated and the edge modes of each bandgap are analyzed to understand the effects of each component of the unit-cell on the bandgap formation. The effects of the structural and material parameters on the bandgaps are investigated and two kinds of composite AM-based lattice structures are suggested for broadening the bandgap width based on the parametric study. As the design is based on increasing the radii of some parts of the cross-struts inside the unit-cell, the mechanical properties are enhanced. The limiting conditions of the static properties of the 3D AM-based lattice structures for broadening the bandgaps are illustrated. Finally, experiments were carried out to validate the results. This design strategy provides new possibilities for the development of lattice truss structures with both bearing and vibration reduction requirements.
We discuss a general framework for the realization of a family of Abelian lattice gauge theories, i.e., link models or gauge magnets, in optical lattices. We analyze the properties of these models ...that make them suitable for quantum simulations. Within this class, we study in detail the phases of a U(1)-invariant lattice gauge theory in 2+1 dimensions, originally proposed by P. Orland. By using exact diagonalization, we extract the low-energy states for small lattices, up to 4×4. We confirm that the model has two phases, with the confined entangled one characterized by strings wrapping around the whole lattice. We explain how to study larger lattices by using either tensor network techniques or digital quantum simulations with Rydberg atoms loaded in optical lattices, where we discuss in detail a protocol for the preparation of the ground-state. We propose two key experimental tests that can be used as smoking gun of the proper implementation of a gauge theory in optical lattices. These tests consist in verifying the absence of spontaneous (gauge) symmetry breaking of the ground-state and the presence of charge confinement. We also comment on the relation between standard compact U(1) lattice gauge theory and the model considered in this paper.
► We study the quantum simulation of dynamical gauge theories in optical lattices. ► We focus on digital simulation of abelian lattice gauge theory. ► We rediscover and discuss the puzzling phase diagram of gauge magnets. ► We detail the protocol for time evolution and ground-state preparation in any phase. ► We provide two experimental tests to validate gauge theory quantum simulators.
After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide ...resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with constant negative curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space.
A pseudosymmetric description of the crystal lattice derived from a single wide‐angle Kikuchi pattern can have several causes. The small size (<15%) of the sector covered by an electron backscatter ...diffraction pattern, the limited precision of the projection centre position and the Kikuchi band definition are crucial. Inherent pseudosymmetries of the crystal lattice and/or structure also pose a challenge in the analysis of Kikuchi patterns. To eliminate experimental errors as much as possible, simulated Kikuchi patterns of 350 phases have been analysed using the software CALM Nolze et al. (2021). J. Appl. Cryst.54, 1012–1022 in order to estimate the frequency of and reasons for pseudosymmetric crystal lattice descriptions. Misinterpretations occur in particular when the atomic scattering factors of non‐equivalent positions are too similar and reciprocal‐lattice points are systematically missing. As an example, a pseudosymmetry prediction depending on the elements involved is discussed for binary AB compounds with B1 and B2 structure types. However, since this is impossible for more complicated phases, this approach cannot be directly applied to compounds of arbitrary composition and structure.
Distinguishing between actual and apparent pseudosymmetry in electron backscatter diffraction patterns is nearly impossible, even for simulated patterns. However, the resulting lattice is always a superlattice as long as the signal is not a superposition of multiple patterns.
Lattice Boltzmann models have a remarkable ability to simulate single- and multi-phase fluids and transport processes within them. A rich variety of behaviors, including higher Reynolds numbers ...flows, phase separation, evaporation, condensation, cavitation, buoyancy, and interactions with surfaces can readily be simulated. This book provides a basic introduction that emphasizes intuition and simplistic conceptualization of processes. It avoids the more difficult mathematics that underlies LB models. The model is viewed from a particle perspective where collisions, streaming, and particle-particle/particle-surface interactions constitute the entire conceptual framework. Beginners and those with more interest in model application than detailed mathematical foundations will find this a powerful 'quick start' guide. Example simulations, exercises, and computer codes are included. Working code is provided on the Internet.
PDF
