Related papers: A study of deformation localization in nonlinear e…
We examine the onset of Anderson localization in three-dimensional systems with structural disorder in the form of lattice irregularities and in the absence of any on-site disordered potential. Analyzing two models with distinct types of…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their existence and bifurcation structure are well-understood, the…
We investigate an odd-sized fermionic open tight-binding chain subjected to stochastic projective measurements at its central site, effectively inducing localized dephasing. Focusing initially on the single-particle regime, we demonstrate…
Understanding lattice deformations is crucial in determining the properties of nanomaterials, which can become more prominent in future applications ranging from energy harvesting to electronic devices. However, it remains challenging to…
We study the evolution of a wave packet in a nonlinear Schr\"odinger lattice equation subject to a dc bias. In the absence of nonlinearity all normal modes are spatially localized giving rise to a Stark ladder with an equidistant eigenvalue…
A continuum dynamical model is developed to determine the morphological and compositional instabilities on the free surface of heteroepitaxial alloy films in the absence of growth. We use linear stability analysis to study the early…
Metals deformed at high strain rates can exhibit failure through formation of shear bands, a phenomenon often attributed to Hadamard instability and localization of the strain into an emerging coherent structure. We verify formation of…
We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
Discrete nonlinear systems support a rich variety of localized and extended wave phenomena, with their dynamics sensitively dependent on the symmetries of the underlying interaction forces within the lattice. Odd elasticity, emerging in…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
We experimentally investigate the evolution of linear and nonlinear waves in a realization of the Anderson model using disordered one dimensional waveguide lattices. Two types of localized eigenmodes, flat-phased and staggered, are directly…
We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for…
In a one dimensional lattice thermal fluctuations destroy the long-range order making particles of the lattice move on a scale much larger than the lattice spacing. We discuss the assumption that this motion may be responsible for the…
We describe wave propagation and soliton localization in photonic lattices which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability…
Disorder plays a crucial role in many systems particularly in solid state physics. However, the disorder in a particular system can usually not be chosen or controlled. We show that the unique control available for ultracold atomic gases…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…