Related papers: Modeling Arcs
Advanced spectral and statistical data analysis techniques have greatly contributed to shaping our understanding of microphysical processes in plasmas. We review some of the main techniques that allow for characterising fluctuation…
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation,…
One distinguishing feature of rational curves is that they have algebraic parameterizations. Arc spaces are a way of describing approximations to parameterizations of all curves in some fixed space. Playing on these descriptions, this paper…
The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and…
Geometric modelling has been a crucial component of the design process ever since the introduction of the first Computer-Aided Design (CAD) systems. Additive Manufacturing (AM) pushes design freedom to previously unachievable limits. AM…
Statistical learning algorithms are finding more and more applications in science and technology. Atomic-scale modeling is no exception, with machine learning becoming commonplace as a tool to predict energy, forces and properties of…
Many motivated extensions of the standard model include new light bosons, such as axions and dark photons, which can mix with the ordinary photon. This latter, when in a dilute plasma, can be dressed by an effective plasma mass. If this is…
Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model,…
A challenge in advancing Visual-Language Models (VLMs) is determining whether their failures on abstract reasoning tasks, such as Bongard problems, stem from flawed perception or faulty top-down reasoning. To disentangle these factors, we…
Consider a graph drawn on a surface (for example, the plane minus a finite set of obstacle points), possibly with crossings. We provide an algorithm to decide whether such a drawing can be untangled, namely, if one can slide the vertices…
Many systems in biology, physics and engineering can be described by systems of ordinary differential equation containing many parameters. When studying the dynamic behavior of these large, nonlinear systems, it is useful to identify and…
Plasma wakefield acceleration is a groundbreaking technique for accelerating particles, capable of sustaining gigavolt-per-meter accelerating fields. Understanding the physical mechanisms governing the recovery of plasma accelerating…
Autonomous agents are increasingly expected to operate in complex, dynamic, and uncertain environments, performing tasks such as manipulation, navigation, and decision-making. Achieving these capabilities requires agents to understand the…
Electron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100 terawatt-class lasers. Two different approaches to computationally efficient,…
The positive link prediction (PLP) problem is formulated in a system identification framework: we consider dynamic graphical models for auto-regressive moving-average (ARMA) Gaussian random processes. For the identification of the…
Models of physical systems are used to explain and predict experimental results and observations. When students encounter discrepancies between the actual and expected behavior of a system, they revise their models to include the newly…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
The energy of plasma waves can be moved up and down the spectrum using chirped modulations of plasma parameters, which can be driven by external fields. Depending on whether the wave spectrum is discrete (bounded plasma) or continuous…