Related papers: Flow Equations and Normal Ordering. A Survey
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
The isolation of pure samples of quark and gluon jets is of key interest at hadron colliders. Recent work has employed topic modeling to disentangle the underlying distributions in mixed samples obtained from experiments. However, current…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
Normalizing flows are constructed from a base distribution with a known density and a diffeomorphism with a tractable Jacobian. The base density of a normalizing flow can be parameterised by a different normalizing flow, thus allowing maps…
This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton--Jacobi theory. The relation with the "classical" Hamiltonian approach using canonical transformations is also…
In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions or interacting theories in spacetime dimensions lower than four. In this paper we address the Hamiltonian…
In addition to the diagonalization of a normal matrix by a unitary similarity transformation, there are two other types of diagonalization procedures that sometimes arise in quantum theory applications -- the singular value decomposition…
Scale separation is an important physical principle that has previously enabled algorithmic advances such as multigrid solvers. Previous work on normalizing flows has been able to utilize scale separation in the context of scalar field…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the…
The growing complexity of decision-making in public health and health care has motivated an increasing use of mathematical modeling. An important line of health modeling is based on stock & flow diagrams. Such modeling elevates transparency…
We consider a wide class of semi linear Hamiltonian partial differential equa- tions and their approximation by time splitting methods. We assume that the nonlinearity is polynomial, and that the numerical tra jectory remains at least uni-…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the…
Brownian and fractional processes are useful computational tools for the modelling of physical phenomena. Here, modelling linear homopolymers in solution as Brownian or fractional processes, we develop a formalism to take into account both…
We briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we…
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulations. Geometric integrators are widely used for this purpose,…
This article studies canonical forms derived from the finest simultaneous block diagonalization of a set of symmetric matrices via congruence. Our technique relies on Harrison's center theory, which is extended from a single higher degree…