Related papers: On deforming and breaking integrability
We study disformal transformations of the metric in the cosmological context. We first consider the disformal transformation generated by a scalar field $\phi$ and show that the curvature and tensor perturbations on the uniform $\phi$…
We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation…
We investigate experimentally and numerically the defect configurations emerging when a cholesteric liquid crystal is confined to a spherical shell. We uncover a rich scenario of defect configurations, some of them non-existent in nematic…
Extreme deformation of soft matter is central to our understanding of the effects of shock, fracture, and phase change in a variety of systems. Yet, despite, the increasing interest in this area, far-from-equilibrium behaviours of soft…
The shock wave instability induced when interacting with a small waviness on an interface was investigated analytically and numerically. The perturbation to the shock was phenomenologically treated assuming this as the consequence of the…
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
This paper is the first in a series of articles devoted to the construction and study of synthetic deformations of $\infty$-categories in the unstable context: that is, deformations of $\infty$-categories that categorify spectral sequence…
There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to…
We have examined a class of cohesive-zone models of dynamic mode-I fracture, looking both at steady-state crack propagation and its stability against out-of-plane perturbations. Our work is an extension of that of Ching, Langer, and…
We study quasi-static deformation of dense granular packings. The packing is deformed by imposing external boundary conditions, which model engineering experiments such as shear and compression. We propose a two-dimensional network model of…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
Deformation band patterning in single crystals is investigated using a finite strain crystal viscoplasticity model based on the evolution of dislocation densities. In the presence of strong latent hardening and weak rate dependence, the…
As we enter the age of designer matter - where objects can morph and change shape on command - what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion,…
This work presented a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the…
A class of peridynamic material models known as constitutive correspondence models provide a bridge between classical continuum mechanics and peridynamics. These models are useful because they allow well-established local constitutive…
The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such…
The interplay between dissipation and internal interactions in quantum many-body systems gives rise to a wealth of novel phenomena. Here we investigate spin-1/2 chains with uniform local couplings to a Markovian environment using the…
The generation of coherent superposition of distinct physical systems and the construction of robust entangled states under decoherence are the most experimental challenges of quantum technologies. In this work, we investigate the behaviors…
Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features…