Unital hyperarchimedean vector lattices

We prove that the category of unital hyperarchimedean vector lattices is equivalent to the category of Boolean algebras. The key result needed to establish the equivalence is that, via the Yosida representation, such a vector lattice is naturally isomorphic to the vector lattice of all locally constant real-valued continuous functions on a Boolean (=compact Hausdorff totally disconnected) space. We give two applications of our main result.Comment: 15 pages. Submitted pape

The geometry of thresholdless active flow in nematic microfluidics

"Active nematics" are orientationally ordered but apolar fluids composed of interacting constituents individually powered by an internal source of energy. When activity exceeds a system-size dependent threshold, spatially uniform active apolar fluids undergo a hydrodynamic instability leading to spontaneous macroscopic fluid flow. Here, we show that a special class of spatially non-uniform configurations of such active apolar fluids display laminar (i.e., time-independent) flow even for arbitrarily small activity. We also show that two-dimensional active nematics confined on a surface of non-vanishing Gaussian curvature must necessarily experience a non-vanishing active force. This general conclusion follows from a key result of differential geometry: geodesics must converge or diverge on surfaces with non-zero Gaussian curvature. We derive the conditions under which such curvature-induced active forces generate "thresholdless flow" for two-dimensional curved shells. We then extend our analysis to bulk systems and show how to induce thresholdless active flow by controlling the curvature of confining surfaces, external fields, or both. The resulting laminar flow fields are determined analytically in three experimentally realizable configurations that exemplify this general phenomenon: i) toroidal shells with planar alignment, ii) a cylinder with non-planar boundary conditions, and iii) a "Frederiks cell" that functions like a pump without moving parts. Our work suggests a robust design strategy for active microfluidic chips and could be tested with the recently discovered "living liquid crystals".Comment: The rewritten paper has several changes, principally: 1. A separate section III for two-dimensional curved systems, illustrated with an new example. 2. Remarks about the relevance of the frozen director approximation in the case of weak nematic order; and 3. A separate Supplemental Material document, containing material previously in the Appendix, along with additional materia

Asymptotics of surface-plasmon redshift saturation at sub-nanometric separations

Many promising nanophotonics endeavours hinge upon the unique plasmonic properties of nanometallic structures with narrow non-metallic gaps, which support super-concentrated bonding modes that singularly redshift with decreasing separations. In this letter, we present a descriptive physical picture, complemented by elementary asymptotic formulae, of a nonlocal mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manifested as an effective potential discontinuity. For bonding modes in the near-contact limit, the latter discontinuity is shown to be effectively equivalent to a widening of the gap. As a consequence, the resonance-frequency near-contact asymptotics are a renormalisation of the corresponding local ones. Specifically, the renormalisation furnishes an asymptotic plasmon-frequency lower bound that scales with the $1/4$-power of the Fermi wavelength. We demonstrate these remarkable features in the prototypical cases of nanowire and nanosphere dimers, showing agreement between our elementary expressions and previously reported numerical computations

Surface-plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit

According to the hydrodynamic Drude model, surface-plasmon resonances of metallic nanostructures blueshift owing to the nonlocal response of the metal's electron gas. The screening length characterising the nonlocal effect is often small relative to the overall dimensions of the metallic structure, which enables us to derive a coarse-grained nonlocal description using matched asymptotic expansions; a perturbation theory for the blueshifts of arbitrary shaped nanometallic structures is then developed. The effect of nonlocality is not always a perturbation and we present a detailed analysis of the "bonding" modes of a dimer of nearly touching nanowires where the leading-order eigenfrequencies and eigenmode distributions are shown to be a renormalisation of those predicted assuming a local metal permittivity

Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds

We survey physical models which capture the main concepts of double field theory on para-Hermitian manifolds. We show that the geometric theory of Lagrangian and Hamiltonian dynamical systems is an instance of para-Kahler geometry which extends to a natural example of a Born geometry. The corresponding phase space geometry belongs to the family of natural almost para-Kahler structures which we construct explicitly as deformations of the canonical para-Kahler structure by non-linear connections. We extend this framework to a class of non-Lagrangian dynamical systems which naturally encodes the notion of fluxes in para-Hermitian geometry. In this case we describe the emergence of fluxes in terms of weak integrability defined by the D-bracket, and we extend the construction to arbitrary cotangent bundles where we reproduce the standard generalized fluxes of double field theory. We also describe the para-Hermitian geometry of Drinfel'd doubles, which gives an explicit illustration of the interplay between fluxes, D-brackets and different polarizations. The left-invariant para-Hermitian structure on a Drinfel'd double in a Manin triple polarization descends to a doubled twisted torus, which we use to illustrate how changes of polarizations give rise to different fluxes and string backgrounds in para-Hermitian geometry.Comment: 68 pages; v2: typos corrected; Final version to be published in Fortschritte der Physi

Godbillon-Vey Invariants of Non-Lorentzian Spacetimes and Aristotelian Hydrodynamics

We study the geometry of foliated non-Lorentzian spacetimes in terms of the Godbillon-Vey class of the foliation. We relate the intrinsic torsion of a foliated Aristotelian manifold to its Godbillon-Vey class, and interpret it as a measure of the local spin of the spatial leaves in the time direction. With this characterisation, the Godbillon-Vey class is an obstruction to integrability of the $\mathsf{G}$-structure defining the Aristotelian spacetime. We use these notions to formulate a new geometric approach to hydrodynamics of fluid flows by endowing them with Aristotelian structures. We establish conditions under which the Godbillon-Vey class represents an obstruction to steady flow of the fluid and prove new conservation laws.Comment: 41 pages; v2: minor corrections, exposition improved, references added; Final version to be published in Journal of Physics

Intermolecular interaction and solid state characterization of abietic acid/chitosan solid dispersions possessing antimicrobial and antioxidant properties

The aim of this work was to prepare and characterize solid dispersions of abietic acid (AB) and chitosan (CS) to investigate how formulation of the mixture may help in the battle against microbial colonization in different areas, such as the biomedical field or the food industry. Solid dispersions were characterized by differential scanning calorimetry, infrared spectroscopy, Raman spectroscopy, polarized optical microscopy, zeta potential and size analysis. The data showed that the dispersion/solvent evaporation method formed solid dispersions in which abietic acid was molecularly dispersed in the carrier. A synergistic effect between the two components in terms of antioxidant and antimicrobial properties was found, especially in the formulations obtained with 1/1 AB/CS molar ratio. Interestingly, the aggregation state (amorphous/crystalline) of AB seemed to affect the antimicrobial activity of the formulation, suggesting increased bioactivity when the drug was in the amorphous state. These findings, together with the demonstrated biocompatibility of the formulations, seem to open promising perspectives for a successful application of the developed AB/CS formulations in the biomedical field or in the food industry

Co-sputtered amorphous Nb–Ta, Nb–Zr and Ta–Zr coatings for corrosion protection of cyclotron targets for [18F] production

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