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
Recenzirano
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.
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.
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.
This introduction to quantum chromodynamics presents the basic concepts and calculations in a clear and didactic style accessible to those new to the field. Readers will find useful methods for ...obtaining numerical results, including pure gauge theory and quenched spectroscopy.
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.
On the number of atoms in three-generated lattices
Acta litterarum ac scientiarum regiae Universitatis Hungaricae Francisco-Josephinae. Sectio scientiarum mathematicarum/Acta scientiarum mathematicarum,
01/2021
Journal Article
A
bstract
The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is ...strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with
N
f
∈ 2, 8 mass-degenerate flavours on
N
τ
∈ {4
,
6
,
8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with
N
f
≤ 6, and possibly up to the onset of the conformal window at 9 ≲
N
f
∗
≲ 12. A reanalysis of already published
O
(
a
)-improved
N
f
= 3 Wilson data on
N
τ
∈ 4
,
12 is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.
Lattice Boltzmann method (LBM) is a relatively new simulation technique for the modeling of complex fluid systems and has attracted interest from researchers in computational physics. Unlike the ...traditional CFD methods, which solve the conservation equations of macroscopic properties (i.e., mass, momentum, and energy) numerically, LBM models the fluid consisting of fictive particles, and such particles perform consecutive propagation and collision processes over a discrete lattice mesh. This book will cover the fundamental and practical application of LBM. The first part of the book consists of three chapters starting form the theory of LBM, basic models, initial and boundary conditions, theoretical analysis, to improved models. The second part of the book consists of six chapters, address applications of LBM in various aspects of computational fluid dynamic engineering, covering areas, such as thermo-hydrodynamics, compressible flows, multicomponent/multiphase flows, microscale flows, flows in porous media, turbulent flows, and suspensions.
Three-dimensional printed polymeric lattice structures have recently gained interests in several engineering applications owing to their excellent properties such as low-density, energy absorption, ...strength-to-weight ratio, and damping performance. Three-dimensional (3D) lattice structure properties are governed by the topology of the microstructure and the base material that can be tailored to meet the application requirement. In this study, the effect of architected structural member geometry and base material on the viscoelastic response of 3D printed lattice structure has been investigated. The simple cubic lattice structures based on plate-, truss-, and shell-type structural members were used to describe the topology of the cellular solid. The proposed lattice structures were fabricated with two materials, i.e., PLA and ABS using the material extrusion (MEX) process. The quasi-static compression response of lattice structures was investigated, and mechanical properties were obtained. Then, the creep, relaxation and cyclic viscoelastic response of the lattice structure were characterized. Both material and topologies were observed to affect the mechanical properties and time-dependent behavior of lattice structure. Plate-based lattices were found to possess highest stiffness, while the highest viscoelastic behavior belongs to shell-based lattices. Among the studied lattice structures, we found that the plate-lattice is the best candidate to use as a creep-resistant LS and shell-based lattice is ideal for damping applications under quasi-static loading conditions. The proposed analysis approach is a step forward toward understanding the viscoelastic tolerance design of lattice structures.
Materials based on cubic tetrahedrites (Cu12Sb4S13) are useful thermoelectrics with unusual thermal and electrical transport properties, such as very low and nearly temperature-independent lattice ...thermal conductivity (κL). We explain the microscopic origin of the glasslike κL in Cu12Sb4S13 by explicitly treating anharmonicity up to quartic terms for both phonon energies and phonon scattering rates. We show that the strongly unstable phonon modes associated with trigonally coordinated Cu atoms are anharmonically stabilized above approximately 100 K and continue hardening with increasing temperature in accord with experimental data. This temperature-induced hardening effect reduces scattering of heat carrying acoustic modes by reducing the available phase space for three-phonon processes, thereby balancing the conventional ∝ T increase in scattering due to phonon population and yielding nearly temperature-independent κL. Furthermore, we find that very strong phonon broadening leads to a qualitative breakdown of the conventional phonon-gas model and modify the dominant heat transport mechanism from the particlelike phonon wave packet propagation to incoherent contributions described by the off-diagonal terms in the heat-flux operator, which are typically prevailing in glasses and disordered crystals. Our work paves the way to a deeper understanding of glasslike thermal conductivity in complex crystals with strong anharmonicity.
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