Delocalized nonlinear vibrational modes in fcc metals Shcherbinin, S.A.; Krylova, K.A.; Chechin, G.M. ...
Communications in nonlinear science & numerical simulation,
January 2022, 2022-01-00, 20220101, Letnik:
104
Journal Article
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Nonlinear lattices support delocalized nonlinear vibrational modes (DNVMs) that are exact solutions to the dynamical equations of motion dictated by the lattice symmetry. Since only lattice symmetry ...is taken into consideration for derivation of DNVMs, they exist regardless the type of interaction between lattice points, and for arbitrary large amplitude. Here, considering space symmetry group of the fcc lattice, we derive all one-component DNVMs, whose dynamics can be described by single equation of motion. Twelve such modes are found and their dynamics are analyzed for Cu, Ni, and Al based on ab initio and molecular dynamics simulations with the use of two different interatomic potentials. Time evolution of atomic displacements, kinetic and potential energy of atoms, and stress components are reported. Frequency–amplitude dependencies of DNVMs obtained in ab initio simulations are used to assess the accuracy of the interatomic potentials. Considered interatomic potentials (by Mendelev et al. and Zhou et al.) for Al are not as accurate as for Cu and Ni. Potentials by Mendelev can be used for relatively small vibration amplitudes, not exceeding 0.1 Å, while potentials by Zhou are valid for larger amplitudes. Overall, the presented family of exact solutions of the equations of atomic motion can be used to estimate the accuracy of the interatomic potentials of fcc metals at large displacements of atoms.
•Delocalized nonlinear vibrational modes (DNVMs) of the fcc lattice are presented.•Dynamics of DNVMs are analyzed numerically for Cu, Ni, and Al.•Comparison of ab initio and MD results helps to assess the interatomic potentials.
The elastically-anisotropic octet truss lattice exhibits high specific stiffness due to its stretching-dominated mechanical behavior. Here, elastically-isotropic truss lattices are designed in a way ...that the constituent beams respond in a stretching-dominated manner instead of bending. Topology constraints ensuring an isotropic elastic response at the macroscopic level are derived from a detailed theoretical analysis of generic periodic truss structures. Specific elastically-isotropic structures are designed by combining elementary cubic truss lattices including the Simple Cubic (SC), Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices. It is shown through periodic homogenization that these isotropic truss lattice compositions exhibit less initial yield anisotropy than the octet truss lattice. For example, the ratio of maximum to minimum yield stress of an SC-BCC-FCC truss lattice composition is 1.4 as compared to 2 for the octet truss lattice. Computational unit cell analysis is carried out to confirm the analytical Young's modulus and yield stress estimates. Selected isotropic structures of 20% relative density are built from a photopolymer using stereolithography. The Young's modulus and Poison's ratio measurements on specimens with different lattice orientations confirm the validity of the design constraints. In addition, the trends regarding the plastic anisotropy are confirmed by the experimental results.
Twisted bilayer graphene has recently attracted a lot of attention for its rich electronic properties and tunability. Here we show that for very small twist angles, α≪1°, the application of a ...perpendicular electric field is mathematically equivalent to a new kind of artificial gauge field. This identification opens the door for the generation and detection of pseudo-Landau levels in graphene platforms within robust setups, which do not depend on strain engineering and therefore can be realistically harvested for technological applications. Furthermore, this new artificial gauge field leads to the development of highly localized modes associated with flat bands close to charge neutrality, which form an emergent kagome lattice in real space. Our findings indicate that for tiny angles biased twisted bilayer graphene is a promising platform that can realize frustrated lattices of highly localized states, opening a new direction for the investigation of strongly correlated phases of matter.
Kirchhoff's law shows that reciprocal materials have equal spectral emissivity at two symmetric polar angles, which is a fundamental limit for a thermal emitter to achieve a small angular divergence ...in the normal direction. Nonreciprocal materials allow violation of Kirchhoff's law as the emissivity at the two symmetric polar angles can be different. However, achieving strong nonreciprocal thermal radiation near zero angle is challenging. In this work, to reduce the power consumption of a light source for e.g. gas sensing, an ultra‐high‐directional nonreciprocal thermal vertical emitter is proposed, with a periodic structure of magneto‐optical material. When B = 3 T or 1.5 T, magneto‐optical lattice resonances enable the near‐perfect emissivity at 22.36 µm or 22.99 µm at zero angle. The strong nonreciprocity contributed by the collective modes allows for a near‐complete violation of Kirchhoff's law at small angles of ±1°. The nonreciprocal emitters have a very small angular divergence (≈1°), which is better than that of the state‐of‐the‐art thermal emitters. The highly directional nonreciprocal thermal emission is robust despite ±25% change in material loss and ±5% fluctuation in structural parameters. This work should inspire the design of high‐directional nonreciprocal thermal emitters and their applications in high‐resolution thermal imaging, infrared gas sensing, biomedical breath monitoring, and so on.
Magneto‐optical lattice resonances are supported by a periodic grating structure. These collective modes can realize near‐perfect emissivity in the vertical direction at the mid‐ and far‐infrared and allow for near‐complete violation of Kirchhoff's law at small polar angles of ±1°. The nonreciprocal emitters have a small angular divergence (≈1°), which is better than that of the state‐of‐the‐art thermal emitters.
Let
n
denote a positive integer. We describe the absolute retracts for the following five categories of finite lattices: (1) slim semimodular lattices, which were introduced by G. Grätzer and E. ...Knapp in (
Acta. Sci. Math. (Szeged)
,
73
445–462
2007
), and they have been intensively studied since then, (2) finite distributive lattices (3) at most
n
-dimensional finite distributive lattices, (4) at most
n
-dimensional finite distributive lattices with cover-preserving {0,1}-homomorphisms, and (5) finite distributive lattices with cover-preserving {0,1}-homomorphisms. Although the singleton lattice is the only absolute retract for the first category, this result has paved the way to some other classes. For the second category, we prove that the absolute retracts are exactly the finite boolean lattices; this generalizes a 1979 result of J. Schmid. For the third category and also for the fourth, the absolute retracts are the finite boolean lattices of dimension at most
n
and the direct products of
n
nontrivial finite chains. For the fifth category, the absolute retracts are the same as those for the second category. Also, we point out that in each of these classes, the algebraically closed lattices and the strongly algebraically closed lattices (investigated by J. Schmid and, in several papers, by A. Molkhasi) are the same as the absolute retracts.
Semiorthomodular BZ⁎–lattices Giuntini, Roberto; Mureşan, Claudia; Paoli, Francesco
Fuzzy sets and systems,
07/2023, Letnik:
463
Journal Article
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Paraorthomodular BZ⁎-lattices, for short PBZ⁎-lattices, were introduced in 8 as an abstraction from the lattice of effects of a complex separable Hilbert space, endowed with the spectral ordering. ...These structures were meant to be a first approximation to a complete description of the equational theory of such lattices of effects. A better approximation is introduced here, together with a preliminary investigation of its properties.
Abstract
We conduct an extensive study of nonlinear localized modes (NLMs), which are temporally periodic and spatially localized structures, in a two-dimensional array of repelling magnets. In our ...experiments, we arrange a lattice in a hexagonal configuration with a light-mass defect, and we harmonically drive the center of the chain with a tunable excitation frequency, amplitude, and angle. We use a damped, driven variant of a vector Fermi–Pasta–Ulam–Tsingou lattice to model our experimental setup. Despite the idealized nature of this model, we obtain good qualitative agreement between theory and experiments for a variety of dynamical behaviors. We find that the spatial decay is direction-dependent and that drive amplitudes along fundamental displacement axes lead to nonlinear resonant peaks in frequency continuations that are similar to those that occur in one-dimensional damped, driven lattices. However, we observe numerically that driving along other directions results in asymmetric NLMs that bifurcate from the main solution branch, which consists of symmetric NLMs. We also demonstrate both experimentally and numerically that solutions that appear to be time-quasiperiodic bifurcate from the branch of symmetric time-periodic NLMs.
Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ...ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually doing a simulation, descriptions of common strategies to connect simulation results to predictions of physical quantities, and a discussion of uncertainties in lattice simulations. More importantly, while lattice QCD is a well-defined field in its own right, it has many connections to continuum field theory and elementary particle physics phenomenology, which are carefully elucidated in this book.
Hansen and Sharpe Phys. Rev. D 92, 114509 (2015) derived a relation between the scattering amplitude of three identical bosons, M3, and a real function referred to as the divergence-free K matrix and ...denoted Kdf,3. The result arose in the context of a relation between finite-volume energies and Kdf,3, derived to all orders in the perturbative expansion of a generic low-energy effective field theory. In this work we set aside the role of the finite volume and focus on the infinite-volume relation between Kdf,3 and M3. We show that, for any real choice of Kdf,3, M3 satisfies the three-particle unitarity constraint to all orders. Given that Kdf,3 is also free of a class of kinematic divergences, the function may provide a useful tool for parametrizing three-body scattering data. Applications include the phenomenological analysis of experimental data (where the connection to the finite volume is irrelevant) as well as calculations in lattice quantum chromodynamics (where the volume plays a key role).
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