Flora

Abstract

GroundworkAn account of North American flora by common understanding refers to known American plants, native and otherwise, drawing on recorded or remembered information about American plants in addition to their names or locations. Truly comprehensive information about American flora (or the people who have studied it, or lived knowledgably with it in local settings) does not exist; the subject is too vast. That said, American plants are fascinating in their regional and local variety, their histories, their uses and meanings, their names, and the many ways they have always (and for the most part by necessity) captured the attention of people -the same factors that make a comprehensive understanding of American plants elusive.The most ambitious botanical survey to date, comprising botanical information on some 20,000 identified North American species collected over the last 500 years, offers an occasion to consider the difficulty of understanding American flora. The Flora of North America North of Mexico project (FNA 1993-; FNA 2008) is a collaborative effort among hundreds of plant specialists that began in the 1960s, and fewer than half of its thirty projected volumes are complete. It includes native and introduced species as well as extinct species. It explicitly excludes Mexico. Brief information on indigenous expertise comes from ethnobotanical records, which are also not comprehensive, and can't ever be: many American tribes and their languages no longer exist, as a direct result of the same 500 years that gave us American botany. The Flora of North America North of Mexico's first volume has excellent introductory essays on the history of plant collections and botanical books, weeds, indigenous relationships with plants, and conservation of plants, but the flora itself is foremost a list of plants organized taxonomically. Still, the editors are aware that people's interest in plants is A Companion to American Environmental HistoryEdited by Douglas Cazaux Sackman

Spatially Localized Self-Assembly Driven by Electrically Charged Phase Separation

“…a finite domain e↵ect, and in fact understood using by Jacobi elliptic functions as solutions to (23) in vicinity of the onset. The second impact of the finite domain e↵ect is related to branch termination, which happens to be on a periodic solution after the domain gets filled by peaks [12]. However, unlike typical behavior in dissipative models [33], here the branch terminates at a distinct periodic solution, to which we refer as 2⇡ k L = 35 80 2⇡ k c , as shown in Figure 4.…”

“…Following (18), we indeed obtain at γ = γ c the Hamiltonian-Hopf bifurcation, where for < 0 (γ < γ c ) the eigenvalues split on the imaginary axis and for > 0 (γ > γ c ) the eigenvalues upon splitting become complex and form a quartet in the real-imaginary plane [24]. The latter case, designates also temporal stability of the uniform solution and implies a sub-critical bifurcation to localized states, bearing similarity to dissipative systems even in the presence of a double multiplicity of zero eigenvalues which is a characteristic of conservative systems [12].…”

“…Typically, bifurcating localized solutions are unstable near the bifurcation onset and gain stability via saddle node bifurcations [12]. To follow the branch of asymptotic (time independent) localized state, we employ a numerical continuation method using the package AUTO [29].…”

“…In the current form, however, the model does not account for symmetry breaking properties of the coexisting phases, such as asymmetry in the double well potential and permittivity. In what follows, we study an extended version of the OK model and specifically investigate the emergence of spatially localized solutions, having properties as reviewed in [12] and the references therein.…”

“…It would be thus plausible to induce a stable localized self-assembly from a single perturbation as an alternative to multi-step lithography. However, theory of localized states in the context of self-assembly is missing although these attract much of interest in applications, such as nonlinear optics, self-organization of quantum dots, convection, and reaction-diffusion systems, and analysis due to the intriguing phenomena of homoclinic snaking [12]. Specifically, while many insights have been provided via models with local interactions (e.g., the Swift-Hohenberg model [12]), the existence and stability properties of localized states under Coulombic interactions are in general missing [19].…”