arXiv subjects

Mark A. Peterson

Publications and source records attributed to Mark A. Peterson.

8 recordsLinked to original sources

arXiv2015

Model for energy transfer by coherent Fermi pressure fluctuations in quantum soft matter

A 1-dimensional model for coherent quantum energy transfer through a complex of compressible boxes is investigated by numerical integration of the time-dependent Schrödinger equation. Energy is communicated from one box to the next by the resonant fluctuating Fermi pressure of the electrons in each box pushing on the walls and doing work on adjacent boxes. Parameters are chosen similar to the chain molecules of typical light harvesting complexes. For some parameter choices the system is found to have an instability leading to self-induced coherent energy transfer transparency.

physics.chem-ph↗

arXiv2009

The Geometry of Ciliary Dynamics

Cilia are motile biological appendages that are driven to bend by internal shear stresses between tubulin filaments. A continuum model of ciliary material is constructed that incorporates the essential ciliary constraints: (1) one-dimensional inextensibility of filaments, (2) three-dimensional incompressibility, and (3) shear strain only along filaments. This hypothetical ciliary material combines one- and three-dimensional properties in a way that makes it a natural and flexible model for how real cilia convert nanoscopic shear stress into motility on a much larger scale. Without reference to the evolving shape of the cilium, conventional continuum mechanics applied to this hypothetical material leads to the standard model of ciliary dynamics, but with one additional term, required by constraints (2) and (3) above, a model-independent coupling of shear and twist in general ciliary motion.

cond-mat.soft↗

arXiv2009

Lagrangian Crumpling Equations

A concise method for following the evolving geometry of a moving surface using Lagrangian coordinates is described. All computations can be done in the fixed geometry of the initial surface despite the evolving complexity of the moving surface. The method is applied to three problems in nonlinear elasticity: the bulging of a thin plate under pressure (the original motivation for Foeppl-von Karman theory), the buckling of a spherical shell under pressure, and the phenomenon of capillary wrinkles induced by surface tension in a thin film. In this last problem the inclusion of a gravitational potential energy term in the total energy improves the agreement with experiment.

cond-mat.soft↗

arXiv2006

Elliptic function representation of doubly periodic two-dimensional Stokes flows

We construct doubly periodic Stokes flows in two dimensions using elliptic functions. This method has advantages when the doubly periodic lattice of obstacles has less than maximal symmetry. We find the mean flow through an arbitrary lattice in response to a pressure gradient in an arbitrary direction, and show in a typical example that the shorter of the two period lattice vectors is an "easy direction" for the flow, an eigenvector of the conductance tensor corresponding to maximal conductance.

physics.flu-dyn↗

arXiv2005

Crumpling of Curved Sheets: Generalizing Foeppl-von Karman

We generalize the Föppl-von Kármán equations to an initially precurved sheet and present the underlying derivation. A geometrically computed moment of strain replaces the notion of bending moment and results in a geometric formulation of the theory of shells. As the curvature approaches zero, i.e., the sheet becomes flat, the new equations reduce to the classic Föppl-von Kármán ones. The present theory solves the long-standing problem of formulating these equations for an a priori curved shell and applies, for instance, both to shell theory and to strongly curved biomembranes of cells as closed surfaces, exhibiting crumpling as the membrane thickness goes to zero.

cond-mat.soft↗

arXiv2002

Galileo's Discovery of Scaling Laws

Galileo's realization that nature is not scale invariant, motivating his subsequent discovery of scaling laws, is traced to two lectures he gave on the geography of Dante's Inferno.

physics.hist-ph↗

arXiv1997

Nonuniqueness and Turbulence

The possibility is considered that turbulence is described by differential equations for which uniqueness fails maximally, at least in some limit. The inviscid Burgers equation, in the context of Onsager's suggestion that turbulence should be described by a negative absolute temperature, is such a limit. In this picture, the onset of turbulence coincides with the proliferation of singularities which characterizes the failure of uniqueness.

physics.flu-dyn↗

arXiv1997

Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.

cond-mat.stat-mech↗