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All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
The natural gradient descent optimisation technique is an efficient optimising protocol for broad classes of classical and quantum systems that takes the underlying geometry of the parameter manifold into account by means of using either…
We extend the definition of generalized coherent states to include the case of time-dependent dispersion. We introduce a suitable operator providing displacement and dynamical rescaling from an arbitrary ground state. As a consequence,…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…
A geometric understanding of entanglement is proposed based on local measurements. Taking recourse to the general structure of density matrices in the framework of Euclidean geometry, we first illustrate our approach for bipartite Werner…
An effective description of an initial state is a method for representing the signatures of new physics in the short-distance structure of a quantum state. The expectation value of the energy-momentum tensor for a field in such a state…
We describe a method to track particles undergoing large displacements. Starting with a list of particle positions sampled at different time points, we assign particle identities by minimizing the sum across all particles of the trace of…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
In this paper, we revisit the notion of quantum entanglement induced by the deformation of phase-space through noncommutative space (NC) parameters. The geometric structure of the state space for Gaussian states in NC-space is illustrated…
A dynamical system is defined in terms of the gradient of a payoff function. Dynamical variables are of two types, ascent and descent. The ascent variables move in the direction of the gradient, while the descent variables move in the…
Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. Up to now, spectral nudging was applied for empirical…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti-)persistence. We present an…
The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state…
The displacement and deviation vectors in spaces (manifolds), the tangent bundle of which is endowed with a transport along paths, are introduced. In case these spaces are equipped with a linear connection, the deviation equations (between…
Standard quantum mechanics and gravity are used to estimate the mass and size of idealized gravitating systems where position states of matter and geometry become indeterminate. It is proposed that well-known inconsistencies of standard…
The vast combination of material properties seen in nature are achieved by the complexity of the material microstructure. Advanced characterization and physics based simulation techniques have led to generation of extremely large…
It is proposed to identify damage variables and their growth with loading in two dimensions by only using full-field displacement measurements. The equilibrium gap method is used to estimate the damage field during a biaxial experiment on a…