Related papers: On anomalies in effective models with nonlinear sy…
First, the properties of a classical model of spontaneous symmetry breakdown are analyzed. Then, the pros and cons of some pedagogical non-relativistic quantum-mechanical models, also used to illustrate spontaneous symmetry breakdown, are…
In real-world control applications, actuator constraints and output constraints (specifically in tracking problems) are inherent and critical to ensuring safe and reliable operation. However, generally, control strategies often neglect…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
In this note we present an example of an extension of the Standard Model where unification of strong and electroweak interactions occurs at a level comparable to that occurring in the minimal supersymmetric standard model.
Nonlinear waves have been observed in synchrotrons for years but have received little attention in the literature. While pathological, these phenomena are worth studying on at least two accounts. First, the formation of solitary waves may…
Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each…
Nonlinear normal modes (NNMs) are widely used as a tool for developing mathematical models of nonlinear structures and understanding their dynamics. NNMs can be identified experimentally through a phase quadrature condition between the…
Nonlinear dynamical systems can be made easier to control by lifting them into the space of observable functions, where their evolution is described by the linear Koopman operator. This paper describes how the Koopman operator can be used…
Applying very small purely radial strains on amorphous solids in radial geometry one observes elastic responses that break the radial symmetry. Without any plasticity involved, the responses indicate nonlinear mode coupling contributions…
The general form of soft supersymmetry breaking terms at one loop for effective supergravity models based on the weakly-coupled heterotic string are presented, with special emphasis on those terms arising from the superconformal anomaly.…
We investigate gauge anomalies in the context of orbifold conformal field theories. Such anomalies manifest as failures of modular invariance in the constituents of the orbifold partition function. We review how this irregularity is…
Metasurfaces enable efficient manipulation of electromagnetic radiation. In particular, control over plane-wave reflection is one of the most useful features in many applications. Extensive research has been done in the field of anomalous…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
We review methods and results for extracting the anomalous dimensions of operators from lattice field theory calculations. The most important application is the anomalous mass dimension in conformal or nearly conformal gauge field theories…
Symmetry breaking of continuous symmetries by extended dynamical defects entails the existence of defect families, which form conformal manifolds in a critical setup. In the presence of bulk 't Hooft anomalies, defects are in fact required…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
This paper considers the observability of nonlinear systems from a Koopman operator theoretic perspective--and in particular--the effect of symmetry on observability. We first examine an infinite-dimensional linear system (constructed using…
For massless $\phi^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the…
A supersymmetry anomaly is found in the presence of non-perturbative fields. When the action is expressed in terms of the correct quantum variables, anomalous surface terms appear in its supersymmetric variation - one per each collective…
Nonlinear topology is an emerging field that combines the intrinsic reconfigurability of nonlinear systems with the robustness of topological protection, offering fertile ground for unconventional phenomena and novel applications. Recently,…