arXiv subjects

Philip J. Morrison

Publications and source records attributed to Philip J. Morrison.

At least 19 recordsLinked to original sources

arXiv2026

Elastoinertial effects govern dynamic response of soft hair beds

Fluid-immersed hair beds are ubiquitous in biology-from the endothelial glycocalyx and primary cilia to intestinal microvilli-where they serve as mechanosensors that transduce dynamic flow signals into biochemical regulatory responses. Despite the inherently dynamic nature of physiological flows, the dynamic mechanical properties of fluid-immersed hair beds under time-varying conditions remain poorly characterized. Here we investigate the transient rheological response of elastic hair beds to large-amplitude oscillatory shear flows at low to intermediate Reynolds number. While the hairs and fluid themselves obey linear constitutive laws, their coupled interaction produces a dynamic nonlinear response that depends sensitively on driving frequency and amplitude. We identify a crossover from a stress-lagging regime to a stress-leading regime, which is governed by an interplay between fluid viscosity, fluid inertia, and hair elasticity. A simplified rigid-beam model qualitatively captures the crossover behavior. Characterizing the dynamic flow response of soft hair beds has direct biological implications, since the lag time sensitively determines the stability of mechanosensory signaling in the feedback loops underlying essential biological processes such as vasodilation, ciliary remodeling, and tubular reabsorption. Our results establish a framework for understanding how the physical properties of biological hair beds optimize dynamic information transmission during mechanotransduction.

cond-mat.soft↗

arXiv2026

Metriplectic dynamical systems on contact manifolds

Flows on symplectic, Poisson, contact, and metriplectic manifolds are reviewed in order to describe our main result, which is to associate a natural metriplectic dynamical system on the general one-jet bundle $J^1N=T^*N\times \mathbb{R}$, which is at once a (trivial) Poisson manifold and a contact manifold. Unlike the standard contact Hamiltonian system, our metriplectic system is thermodynamically consistent in that $$\dot{H} = 0 \quad\mathrm{and}\quad \dot{S} \geq 0$$ under the flow. Here $H$ is the Hamiltonian, while $S$ is the entropy function which is nothing but the $\mathbb{R}$ coordinate function of $J^1N$. As an example we derive the Duffing equation (autonomous and nonautonomous versions) either as a contact Hamiltonian system or as a metriplectic system. We show that for both systems the Duffing equation is a subsystem of three dimensional systems that contain a thermodynamic component, a form that facilitates asymptotic stability analysis of the relevant equilibrium state.

math.SG↗

arXiv2025

On the Poisson brackets of hybrid plasma models with kinetic ions and massless electrons

We investigate the conditions under which the Jacobi identity holds for a class of recently introduced anti-symmetric brackets for the hybrid plasma models with kinetic ions and massless electrons. In particular, we establish the precise conditions under which the brackets for the vector-potential-based formulations satisfy the Jacobi identity, and demonstrate that these conditions are fulfilled by all physically relevant functionals. Moreover, for the magnetic-field-based formulation, we show that the corresponding anti-symmetric bracket constitutes a Poisson bracket under the divergence-free condition of the magnetic field, and we provide a direct proof of the Jacobi identity. These results are further extended to models incorporating electron entropy as well as more general hybrid kinetic-fluid models.

physics.plasm-ph↗

arXiv2025

Semi-Lagrangian methods for a plasma hybrid model with multi-species kinetic ions and massless electrons

The semi-Lagrangian methods with the improved number of one-dimensional advections are proposed for a plasma hybrid model with kinetic ions and mass-less electrons. Two subsystems with mass, momentum, and energy conservation are obtained by a Poisson bracket-based splitting method. For the subsystem in which the distribution functions and the fields are coupled, the second order and reversible modified implicit mid-point rule is used in time with the specially designed mean velocity. The distribution functions are not involved in the iterations and are solved by exact splittings with only one dimensional advections, which makes the proposed schemes efficient. The cancellation problem is overcome by the numerical schemes constructed. Moreover, for the case with a periodic boundary condition, the magnetic field obtained is divergence free, mass, momentum, and energy are conserved. The methods can be extended to cases with multiple ion species.

math.NA↗

arXiv2025

Scattering Theory in Noncanonical Phase Space: A Drift-Kinetic Collision Operator for Weakly Collisional Plasmas

After developing a scattering theory for grazing collisions in general noncanonical phase spaces, we introduce a guiding center collision operator in five-dimensional phase space designed for plasma regimes characterized by long wavelengths (relative to the Larmor radius), low frequencies (relative to the cyclotron frequency), and weak collisionality (where repeated Coulomb collisions induce cumulatively small changes in particle magnetic moment). The collision operator is fully determined by the noncanonical Hamiltonian structure of guiding center dynamics and exhibits a metriplectic structure, ensuring the conservation of particle number, momentum, energy, and interior Casimir invariants. It also satisfies an H-theorem, allowing for deviations from Maxwell-Boltzmann statistics due to the nontrivial kernel of the noncanonical guiding center Poisson tensor, spanned by the magnetic moment. We propose that this collision operator and its underlying mathematical structure may offer valuable insights into the study of turbulence, transport, and self-organizing phenomena in both laboratory and astrophysical plasmas.

physics.plasm-ph↗

arXiv2025

Construction of symplectic systems from parameter-drift Hamiltonian maps

We reveal the symplectic nature of parameter-drift maps by embedding them into extended phase space. Applying the embedding to the parameter-drift standard nontwist map, our construction yields an autonomous symplectic map in extended phase space that preserves key dynamics of the original system. Computing finite time Lyapunov exponents, the symplectic map shows limitations of ensemble-based diagnostics, common in the parameter-drift literature, and provides new insights into transport phenomena in these nonautonomous systems.

nlin.CD↗

arXiv2025

A thermodynamically consistent discretization of 1D thermal-fluid models using their metriplectic 4-bracket structure

Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this modeling formalism to preserve thermodynamic consistency in discretizations of a fluid model. The procedure relies (1) on ensuring that the spatial semi-discretization retains certain symmetries and degeneracies of the Poisson and metriplectic 4-brackets, and (2) on the use of an appropriate energy conserving time-stepping method. The minimally simple yet nontrivial example of a one-dimensional thermal-fluid model is treated. It is found that preservation of the requisite symmetries and degeneracies of the 4-bracket is relatively simple to ensure in Galerkin spatial discretizations, suggesting a path forward for thermodynamically consistent discretizations of more complex fluid models using more specialized Galerkin methods.

physics.comp-ph↗

arXiv2025

Algebra of Invariants for the Vlasov-Maxwell System

The algebra of invariants for both the relativistic and nonrelativistic multispecies Vlasov-Maxwell system is examined, including the case with a fixed ion background. Invariants and their associated fluxes are obtained directly from the Vlasov-Maxwell system. The invariants are shown to Poisson commute with the Hamiltonian and the rest of the Poisson bracket algebra of invariants is identified. Special attention is given to the role played by the monopole condition, $\nabla\cdot \mathbf{B}$.

physics.plasm-ph↗

arXiv2025

Metriplectic 4-bracket algorithm for constructing thermodynamically consistent dynamical systems

A unified thermodynamic algorithm (UTA) is presented for constructing thermodynamically consistent dynamical systems, i.e., systems that have Hamiltonian and dissipative parts that conserve energy while producing entropy. The algorithm is based on the metriplectic 4-bracket given in Morrison and Updike [Phys.\ Rev.\ E 109, 045202 (2024)]. A feature of the UTA is the force-flux relation $\mathbf{J}^α= - L^{αβ}\, \nabla(δH / δξ^β)$ for phenomenological coefficients $L^{αβ}$, Hamiltonian $H$ and dynamical variables $ξ^β$. The algorithm is applied to the Navier-Stokes-Fourier, the Cahn-Hilliard-Navier-Stokes, and and Brenner-Navier-Stokes-Fourier systems, and significant generalizations of these systems are obtained.

physics.flu-dyn↗

arXiv2024

Formulation of a one-dimensional electrostatic plasma model for testing the validity of kinetic theory

We present a one-dimensional (1-D) model composed of aligned, electrostatically interacting charged disks, conceived in order to address in a computable model the validity of the Bogoliubov assumption on the decay of particle correlations in the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy. This assumption is a basic premise of plasma kinetic theory. The disk model exhibits spatially 1-D features at short distances, but retains 3-D features at large distances. Here the collective dynamics of this model plasma is investigated by solving the corresponding Vlasov equation. In addition, the implementation of the model for the numerical validation of the Bogoliubov assumption is formulated.

physics.plasm-ph↗

arXiv2024

A Hamiltonian structure-preserving discretization of Maxwell's equations in nonlinear media

A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a simple Poisson bracket structure with the Hamiltonian encoding all of the nonlinear coupling of the fields. The field-independence of the Poisson bracket facilitates a straightforward Hamiltonian structure-preserving discretization using finite element exterior calculus. The generality and relative simplicity of this Hamiltonian framework makes it amenable for simulating a broad class of time-domain nonlinear optical problems. The main contribution of this work is a finite element discretization of Maxwell's equations in cubicly nonlinear media which is energy-stable and exactly conserves Gauss's laws. Moreover, this approach may be readily adapted to consider more general nonlinear media in subsequent work.

physics.comp-ph↗

arXiv2024

A mimetic discretization of Westervelt's equation

A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which preserve the Hamiltonian structure in the dissipation-free limit, and which achieve the correct dissipation rate in the spatially-discrete dissipative dynamics. Moreover, by using spatial discretizations which preserve the de Rham cohomology, the non-evolving involution constraint for the vorticity may be exactly satisfied for all of time. Numerical examples are given using a mimetic finite difference spatial discretization.

math.NA↗

arXiv2024

On finite-dimensional smoothed-particle Hamiltonian reductions of the Vlasov equation

The inclusion of spatial smoothing in finite-dimensional particle-based Hamiltonian reductions of the Vlasov equation are considered. In the context of the Vlasov-Poisson equation (and other mean-field Lie-Poisson systems), smoothing amounts to a convolutive regularization of the Hamiltonian. This regularization may be interpreted as a change of the inner product structure used to identify the dual space in the Lie-Poisson Hamiltonian formulation. In particular, the shape function used for spatial smoothing may be identified as the kernel function of a reproducing kernel Hilbert space whose inner product is used to define the Lie-Poisson Hamiltonian structure. It is likewise possible to introduce smoothing in the Vlasov-Maxwell system, but in this case the Poisson bracket must be modified rather than the Hamiltonian. The smoothing applied to the Vlasov-Maxwell system is incorporated by inserting smoothing in the map from canonical to kinematic coordinates. In the filtered system, the Lorentz force law and the current, the two terms coupling the Vlasov equation with Maxwell's equations, are spatially smoothed.

math-ph↗

arXiv2024

Some observations regarding brackets and dissipation

Some ideas relating to a bracket formulation for dissipative systems are considered. The formulation involves a bracket that is analogous to a generalized Poisson bracket, but possesses a symmetric component. Such a bracket is presented for the Navier-Stokes equations.

math-ph↗

arXiv2024

A Collision Operator for Describing Dissipation in Noncanonical Phase Space

The phase space of a noncanonical Hamiltonian system is partially inaccessible due to dynamical constraints (Casimir invariants) arising from the kernel of the Poisson tensor. When an ensemble of noncanonical Hamiltonian systems is allowed to interact, dissipative processes eventually break the phase space constraints, resulting in an equilibrium described by a Maxwell-Boltzmann distribution. However, the time scale required to reach Maxwell-Boltzmann statistics is often much longer than the time scale over which a given system achieves a state of thermal equilibrium. Examples include diffusion in rigid mechanical systems, as well as collisionless relaxation in magnetized plasmas and stellar systems, where the interval between binary Coulomb or gravitational collisions can be longer than the time scale over which stable structures are self-organized. Here, we focus on self-organizing phenomena over spacetime scales such that particle interactions respect the noncanonical Hamiltonian structure, but yet act to create a state of thermodynamic equilibrium. We derive a collision operator for general noncanonical Hamiltonian systems, applicable to fast, localized interactions. This collision operator depends on the interaction exchanged by colliding particles and on the Poisson tensor encoding the noncanonical phase space structure, is consistent with entropy growth and conservation of particle number and energy, preserves the interior Casimir invariants, reduces to the Landau collision operator in the limit of grazing binary Coulomb collisions in canonical phase space, and exhibits a metriplectic structure. We further show how thermodynamic equilibria depart from Maxwell-Boltzmann statistics due to the noncanonical phase space structure, and how self-organization and collisionless relaxation in magnetized plasmas and stellar systems can be described through the derived collision operator.

cond-mat.stat-mech↗

arXiv2023

A self-consistent Hamiltonian model of the ponderomotive force and its structure preserving discretization

In the presence of an inhomogeneous oscillatory electric field, charged particles experience a net force, averaged over the oscillatory timescale, known as the ponderomotive force. We derive a one-dimensional Hamiltonian model which self-consistently couples the electromagnetic field to a plasma which experiences the ponderomotive force. We derive a family of structure preserving discretizations of the model of varying order in space and time using conforming and broken finite element exterior calculus spectral element methods. In all variants of our discretization framework, the method is found to conserve the Casimir invariants of the continuous model to machine precision and the energy to the order of the splitting method used.

physics.comp-ph↗

arXiv2023

An inclusive curvature-like framework for describing dissipation: metriplectic 4-bracket dynamics

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 based on the metriplectic 4-bracket, a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes all known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

math-ph↗

arXiv2023

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov-Maxwell equilibria

In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov-Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behavior for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behavior of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

physics.plasm-ph↗