scholarly journals Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion

2006 ◽  
Vol 74 (24) ◽  
Author(s):  
A. V. Rozhkov
Keyword(s):  
Nonlinear Dispersion ◽  
One Dimensional ◽  
Exactly Soluble Models ◽  
Luttinger Hamiltonian

Nonlinear Spectral Properties of Elastic Waves Propagating Along a Pantographic Metamaterial With Local Inertia Amplifiers

2021 ◽  
Author(s):  
Valeria Settimi ◽  
Marco Lepidi ◽  
Andrea Bacigalupo
Keyword(s):  
Elastic Waves ◽  
Degrees Of Freedom ◽  
Invariant Manifolds ◽  
Nonlinear Effects ◽  
Harmonic Waves ◽  
Nonlinear Dispersion ◽  
Asymptotic Approach ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Atomic Cell

Abstract Pantographic mechanisms can be introduced in the cellular periodic microstructure of architected metamaterials to achieve functional effects of local inertia amplification. The paper presents a one-dimensional pantographic metamaterial, characterized by an inertially amplified tetra-atomic cell. An internally constrained two-degrees-of-freedom model is formulated to describe the undamped free propagation of harmonic waves in the weakly nonlinear regime. A general asymptotic approach is employed to analytically determine the linear and nonlinear dispersion properties. Analytical, although asymptotically approximate, functions are obtained for the nonlinear wavefrequencies and waveforms, which show significant nonlinear effects including softening/hardening bending of the backbone curves and synclastic/anticlastic curvatures of the invariant manifolds.

scholarly journals Exactly Soluble Models of One-Dimensional Disordered Systems

1971 ◽  
Vol 45 (5) ◽  
pp. 1713-1715 ◽  
Author(s):  
T\=oru Hirota ◽  
Kazushige Ishii
Keyword(s):  
Disordered Systems ◽  
One Dimensional ◽  
Exactly Soluble Models

scholarly journals Electron-plasmon scattering in chiral one-dimensional systems with nonlinear dispersion

2010 ◽  
Vol 82 (3) ◽  
Author(s):  
M. Heyl ◽  
S. Kehrein ◽  
F. Marquardt ◽  
C. Neuenhahn
Keyword(s):  
Nonlinear Dispersion ◽  
One Dimensional

scholarly journals Elastic wave dispersion equation considering material and geometric nonlinearities

2021 ◽  
Author(s):  
xiangyang li ◽  
Na Li ◽  
Bin Zheng ◽  
Jianqiang Bao ◽  
Yan Wang ◽  
...  
Keyword(s):  
Geometric Nonlinearity ◽  
Fourier Spectrum ◽  
Wave Dispersion ◽  
Nonlinear Dispersion ◽  
Geometric Nonlinearities ◽  
Longitudinal Waves ◽  
One Dimensional ◽  
Nonlinear Dispersion Relation ◽  
Nonlinear Elastic ◽  
Relationship Of

Abstract In this letter, we describe the propagation of longitudinal waves in one-dimensional nonlinear elastic thin rods with material nonlinearity and geometric nonlinearity. Mathematical analysis is used to derive the analytical dispersion relationship of longitudinal waves; subsequently, the numerical Fourier spectrum method is used to solve the nonlinear wave equation directly and the results are used to verify the correctness of the derived nonlinear dispersion relation.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

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