Related papers: When scale is surplus
The Hamiltonian dynamics of spherically symmetric massive thin shells in the general relativity is studied. Two different constraint dynamical systems representing this dynamics have been described recently; the relation of these two…
We consider general infinite-dimensional dynamical systems with the Galilean and spatiotemporal scaling symmetry groups. Introducing the equivalence relation with respect to temporal scalings and Galilean transformations, we define a…
The dynamical equations describing the evolution of a physical system generally have a freedom in the choice of units, where different choices correspond to different physical systems that are described by the same equations. Since there…
We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$…
One of the interesting aspects in the study of atomic nuclei is the strikingly regular behaviour many display in spite of being complex quantum-mechanical systems, prompting the universal question of how regularity emerges out of…
The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost…
The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing…
The exploration of teleparallel gravity has been done from a dynamical systems point of view in order to be tested against the cosmological evolution currently observed. So far, the proposed autonomous systems have been restrictive over a…
Understanding under what conditions it is possible to construct equivalent ensembles is key to advancing our ability to connect microscopic and macroscopic properties of non-equilibrium statistical mechanics. In the case of fluid dynamical…
The theory of substitution sequences and their higher-dimensional analogues is intimately connected with symbolic dynamics. By systematically studying the factors (in the sense of dynamical systems theory) of a substitution dynamical…
A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
Dynamical supersymmetry breaking is a fascinating theoretical problem. It is also of phenomenological significance. A better understanding of this phenomenon can help in model building, which in turn is useful in guiding the search for…
We consider symmetries and reduction in non-relativistic many-body quantum mechanics, with the aim of identifying physically meaningful observables in systems such as molecules and crystalline solids. To this end, we propose a unified…
Defining similarity is a fundamental challenge in information science. Watanabe's Ugly Duckling Theorem highlights diversity, while algorithmic information theory emphasizes depth through Information Distance. We propose a…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
Conformal defects -- extended objects in conformal field theories -- carry localised excitations inherited from symmetry currents, known as the displacements and tilts. They capture the linear response of the defect to deformations of its…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…