189 citations · 1.6k across the 88 of their papers we have counts for
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An inclusive curvature-like framework for describing dissipation: metriplectic 4-bracket dynamics
Philip J. Morrison, Michael H. Updike
An inclusive framework for joined Hamiltonian and dissipative dynamical systems, which preserve energy and produce entropy, is given. The dissipative dynamics of the framework is b…
A Hamiltonian and geometric formulation of general Vlasov-Maxwell-type models
William Barham, Philip J. Morrison, Eric Sonnendrücker
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, an…
Charged Particle Motion in Spherically Symmetric Distributions of Magnetic Monopoles
Robert Littlejohn, Philip Morrison, Jeffrey Heninger
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby…
A Hamiltonian model for the macroscopic Maxwell equations using exterior calculus
William Barham, Philip J. Morrison, Eric Sonnendrücker
A Hamiltonian field theory for the macroscopic Maxwell equations with fully general polarization and magnetization is stated in the language of differential forms. The precise proc…
Clebsch Canonization of Lie-Poisson Systems
Buddhika Jayawardana, Philip J. Morrison, Tomoki Ohsawa
We propose a systematic procedure called the Clebsch canonization for obtaining a canonical Hamiltonian system that is related to a given Lie-Poisson equation via a momentum map. W…
Deformation of Lie-Poisson algebras and chirality
Zensho Yoshida, Philip J. Morrison
Linearization of a Hamiltonian system around an equilibrium point yields a set of Hamiltonian-symmetric spectra: If is an eigenvalue of the linearized generator, and $\bar…
Computing Casimir invariants from Pfaffian systems
T. W. Yudichak, Benito Hernández-Bermejo, P. J. Morrison
We describe a method for computing Casimir invariants that is applicable to both finite and infinite-dimensional Poisson brackets. We apply the method to various finite and infinit…
Hamiltonian Nature of Monopole Dynamics
J. M. Heninger, P. J. Morrison
Classical electromagnetism with magnetic monopoles is not a Hamiltonian field theory because the Jacobi identity for the Poisson bracket fails. The Jacobi identity is recovered onl…
Rattleback: a model of how geometric singularity induces dynamic chirality
Zensho Yoshida, Tadashi Tokieda, Philip J. Morrison
The rattleback is a boat-shaped top with an asymmetric preference in spin. Its dynamics can be described by nonlinearly coupled pitching, rolling, and spinning modes. The chirality…
Hierarchical structure of noncanonical Hamiltonian systems
Z. Yoshida, P. J. Morrison
Topological constraints play a key role in the self-organizing processes that create structures in macro systems. In fact, if all possible degrees of freedom are actualized on equa…
A hierarchy of noncanonical Hamiltonian systems: circulation laws in an extended phase space
Z. Yoshida, P. J. Morrison
The dynamics of an ideal fluid or plasma is constrained by topological invariants such as the circulation of (canonical) momentum or, equivalently, the flux of the vorticity or mag…
Continuum Hamiltonian Hopf Bifurcation II
G. I. Hagstrom, P. J. Morrison
Building on the development of [MOR13], bifurcation of unstable modes that emerge from continuous spectra in a class of infinite-dimensional noncanonical Hamiltonian systems is inv…
Continuum Hamiltonian Hopf Bifurcation I
Philip J. Morrison, George I. Hagstrom
Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These m…
Unfreezing Casimir invariants: singular perturbations giving rise to forbidden instabilities
Z. Yoshida, P. J. Morrison
The infinite-dimensional mechanics of fluids and plasmas can be formulated as "noncanonical" Hamiltonian systems on a phase space of Eulerian variables. Singularities of the Poisso…
Gradient flows in the normal and Kähler metrics and triple bracket generated metriplectic systems
Anthony M. Bloch, Philip J. Morrison, Tudor S. Ratiu
The dynamics of gradient and Hamiltonian flows with particular application to flows on adjoint orbits of a Lie group and the extension of this setting to flows on a loop group are…
Singular Casimir Elements of the Euler Equation and Equilibrium Points
Zensho Yoshida, Philip J. Morrison, Fernando Dobarro
The problem of the nonequivalence of the sets of equilibrium points and energy-Casimir extremal points, which occurs in the noncanonical Hamiltonian formulation of equations descri…
On Krein-like theorems for noncanonical Hamiltonian systems with continuous spectra: application to Vlasov-Poisson
George I. Hagstrom, Philip J. Morrison
The notions of spectral stability and the spectrum for the Vlasov-Poisson system linearized about homogeneous equilibria, f_0(v), are reviewed. Structural stability is reviewed and…
Classification and Casimir Invariants of Lie-Poisson Brackets
Jean-Luc Thiffeault, P. J. Morrison
We classify Lie-Poisson brackets that are formed from Lie algebra extensions. The problem is relevant because many physical systems owe their Hamiltonian structure to such brackets…