21 research outputs found
Self-induced topological transition in phononic crystals by nonlinearity management
A new design paradigm of topology has recently emerged to manipulate the flow
of phonons. At its heart lies a topological transition to a nontrivial state
with exotic properties. This framework has been limited to linear lattice
dynamics so far. Here we show a topological transition in a nonlinear regime
and its implication in emerging nonlinear solutions. We employ nonlinearity
management such that the system consists of masses connected with two types of
nonlinear springs, "stiffening" and "softening" types, alternating along the
length. We show, analytically and numerically, that the lattice makes a
topological transition simply by changing the excitation amplitude and invoking
nonlinear dynamics. Consequently, we witness the emergence of a new family of
finite-frequency edge modes, not observed in linear phononic systems. We also
report the existence of kink solitons at the topological transition point.
These correspond to heteroclinic orbits that form a closed curve in the phase
portrait separating the two topologically-distinct regimes. These findings
suggest that nonlinearity can be used as a strategic tuning knob to alter
topological characteristics of phononic crystals. These also provide fresh
perspectives towards understanding a new family of nonlinear solutions in light
of topology.Comment: 14 pages, 8 figure
Dirac Solitons and Topological Edge States in the -Fermi-Pasta-Ulam-Tsingou dimer lattice
We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type,
where alternating linear couplings have a controllably small difference, and
the cubic nonlinearity (-FPUT) is the same for all interaction pairs. We
use a weakly nonlinear formal reduction within the lattice bandgap to obtain a
continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles
and the model's conservation laws analytically. We then examine the cases of
the semi-infinite and the finite domains and illustrate how the soliton
solutions of the bulk problem can be ``glued'' to the boundaries for different
types of boundary conditions. We thus explain the existence of various kinds of
nonlinear edge states in the system, of which only one leads to the standard
topological edge states observed in the linear limit. We finally examine the
stability of bulk and edge states and verify them through direct numerical
simulations, in which we observe a solitary wave setting into motion due to the
instability.Comment: 13 pages, 9 figures (Multiscale analysis is updated
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Dirac Solitons and Topological Edge States in the β-Fermi-Pasta-Ulam-Tsingou dimer lattice
We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference, and the cubic nonlinearity (β-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice bandgap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model\u27s conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be ``glued\u27\u27 to the boundaries for different types of boundary conditions. We thus explain the existence of various kinds of nonlinear edge states in the system, of which only one leads to the standard topological edge states observed in the linear limit. We finally examine the stability of bulk and edge states and verify them through direct numerical simulations, in which we observe a solitary wave setting into motion due to the instability