Amalgams of Inverse Semigroups and C*-algebras

An amalgam of inverse semigroups [S,T,U] is full if U contains all of the idempotents of S and T. We show that for a full amalgam [S,T,U], the C*-algebra of the inverse semigroup amaglam of S and T over U is the C*-algebraic amalgam of C*(S) and C*(T) over C*(U). Using this result, we describe certain amalgamated free products of C*-algebras, including finite-dimensional C*-algebras, the Toeplitz algebra, and the Toeplitz C*-algebras of graphs

Phase behavior and morphology of multicomponent liquid mixtures

Multicomponent systems are ubiquitous in nature and industry. While the physics of few-component liquid mixtures (i.e., binary and ternary ones) is well-understood and routinely taught in undergraduate courses, the thermodynamic and kinetic properties of $N$-component mixtures with $N>3$ have remained relatively unexplored. An example of such a mixture is provided by the intracellular fluid, in which protein-rich droplets phase separate into distinct membraneless organelles. In this work, we investigate equilibrium phase behavior and morphology of $N$-component liquid mixtures within the Flory-Huggins theory of regular solutions. In order to determine the number of coexisting phases and their compositions, we developed a new algorithm for constructing complete phase diagrams, based on numerical convexification of the discretized free energy landscape. Together with a Cahn-Hilliard approach for kinetics, we employ this method to study mixtures with $N=4$ and $5$ components. We report on both the coarsening behavior of such systems, as well as the resulting morphologies in three spatial dimensions. We discuss how the number of coexisting phases and their compositions can be extracted with Principal Component Analysis (PCA) and K-Means clustering algorithms. Finally, we discuss how one can reverse engineer the interaction parameters and volume fractions of components in order to achieve a range of desired packing structures, such as nested `Russian dolls' and encapsulated Janus droplets.Comment: 16 pages, 11 figures + hyperlinks to 7 video

Kuinka pitkään lasten kotihoitoa? : Selvitys äitien lastenhoitojaksoista kotona 2000-luvulla

Äidit käyttävät pääosan lastenhoitoon kotona liittyvistä perhevapaista, minkä seurauksena äideille kasautuvat myös katkot työelämässä lastenhoidon johdosta. Tässä tutkimuksessa tarkastellaan, miten yleisiä ovat yhtäältä pitkät yhtenäiset lastenhoitojaksot ja toisaalta pitkät kotihoidon tukijaksot, miten hoitojaksojen käyttö on kehittynyt ja mitkä tekijät selittävät äitien kotihoidon tuen kestoa 2000-luvun ensimmäisellä vuosikymmenellä. Tutkimusta varten muodostettiin osa-aineisto, joka perustuu Kelan tutkimusosaston Lapsiperhe-hanketta varten koottuun laajaan rekisteripohjaiseen tutkimusaineistoon. Tutkimusaineisto on rajattu äiteihin, jotka saivat esikoisen vuosina 1999–2006 ja joiden viimeinen lapsi syntyi vuonna 2008. Hoitojaksoja voidaan seurata kohorteittain maksettujen vanhempainrahojen ja kotihoidon tukitietojen avulla vuoden 2010 loppuun asti. Tulosten mukaan muutokset äitien käyttäytymisessä ovat olleet 2000-luvulla melko hitaita. Pääosa, noin kolme neljästä ensisynnyttäjien perhevapaaetuuksiin perustuvista yhtenäisistä lapsenhoitojaksoista päättyy esikoiseen, minkä jälkeen hoitojaksoon tulee vähintään kahden kuukauden tauko, vaikka äiti saisi seuraavan lapsen ennen kuin edellinen täyttää kolme vuotta. Peräkkäin vähintään kahta lasta hoitavia äitejä oli kaikkiaan neljännes. Esimerkiksi vuoden 2003 kohortin kaksi lasta saaneista äideistä 70 prosenttia piti tauon ensimmäisen lapsen jälkeen ja 30 prosenttia hoiti molemmat lapset peräkkäin. Isien vapaat selittävät äitien jaksojen päättymisiä tai taukoja useammin nuorimmilla kohorteilla, mutta yhä vain muutaman prosentin. Kotihoidontuen käyttö on 2000-luvulla hieman yleistynyt, mutta pisimmät jaksot ovat vähentyneet vuosina 1999–2006 noin 14 prosentista 10 prosenttiin. Toisaalta yksinhuoltajilla pitkät, noin kolmen vuoden jaksot muodostavat yhä viidenneksen. Tutkimuksessa tarkasteltiin myös sitä, kuinka suurta osaa äitejä koskisi reformi, joka puolittaisi oikeuden kotihoidon tukeen vanhempien kesken. Tuloksena oli, että runsas kolmasosa kaikista ensisynnyttäjistä, mutta yksinhuoltajista yli 40 prosenttia, joutuisi suunnittelemaan lapsenhoitoratkaisunsa uudelleen, jos uudistus olisi koskenut vuoden 2006 ensisynnyttäjiä. Väestötasolle ja kaikille äideille korotettuna uudistus olisi koskenut, kuukausirajasta riippuen, 17 250–21 750 äitiä, joista yksinhuoltajia olisi ollut 2 000–2 240. Ikä, äidin koulutustaso ja pääasiallinen toiminta osoittautuivat voimakkaiksi selittäjiksi sille, pitävätkö äidit lyhyitä vai pitkiä kotihoidon tukijaksoja. Vaikka nämä tekijät ovat yhteydessä äitien tulojen kautta myös kotitalouden tulotasoon, ei talouden tulotasolla ollut yhtä selviä yhteyksiä. Sen sijaan isän kotihoidon tukijaksot, joita oli yhä pieni määrä, lisäsivät selvästi todennäköisyyttä äitien lyhyempiin jaksoihin ja vähensivät todennäköisyyttä pitkiin jaksoihin

Dynamics of driven interfaces in algebraically correlated random media

In this work we consider the dynamics of interfaces embedded in algebraically correlated two-dimensional random media. We study the isotropic percolation and the directed percolation lattice models away from and at their percolation transitions. Away from the transition, the kinetic roughening of an interface in both of these models is consistent with the power-law correlated Kardar-Parisi-Zhang universality class. Moreover, the scaling exponents are found to be in good agreement with existing renormalization-group calculations. At the transition, however, we find different behavior. In analogy to the case of a uniformly random background, the scaling exponents of the interface can be related to those of the underlying percolation transition. For the directed percolation case, both the growth and roughness exponents depend on the strength of correlations, while for the isotropic case the roughness exponent is constant. For both cases, the growth exponent increases with the strength of correlations. Our simulations are in good agreement with theory.Peer reviewe

Hierarchical Self-Assembly of Halogen-Bonded Block Copolymer Complexes into Upright Cylindrical Domains

Self-assembly of block copolymers into well-defined, ordered arrangements of chemically distinct domains is a reliable strategy for preparing tailored nanostructures. Microphase separation results from the system, minimizing repulsive interactions between dissimilar blocks and maximizing attractive interactions between similar blocks. Supramolecular methods have also achieved this separation by introducing small-molecule additives binding specifically to one block by noncovalent interactions. Here, we use halogen bonding as a supramolecular tool that directs the hierarchical self-assembly of low-molecular-weight perfluorinated molecules and diblock copolymers. Microphase separation results in a lamellar-within-cylindrical arrangement and promotes upright cylindrical alignment in films upon rapid casting and without further annealing. Such cylindrical domains with internal lamellar self-assemblies can be cleaved by solvent treatment of bulk films, resulting in separated and segmented cylindrical micelles stabilized by halogen-bond-based supramolecular crosslinks. These features, alongside the reversible nature of halogen bonding, provide a robust modular approach for nanofabricatio

Apparatus for making continuous lengths of composite wood material, the apparatus including rotating circular baffles

Apparatus for forming an elongated loosely felted mat of thin elongated wood flakes with the flakes being aligned in mutually parallel relation and being aligned with the longitudinal direction of the elongated mat. The apparatus comprises a plurality of conveyor belts positioned in closely adjacent side-by-side relation and defining a mat supporting surface adapted to support the aligned wood flakes, the belts being supported on the surface of a cylinder. Wood flakes are deposited in loosely felted relation on the belts, and a plurality of closely spaced parallel planar baffles surround the cylinder, the baffles comprising plates positioned between the belts and functioning to cause alignment of the flakes as they are deposited on the belts. The mat is compressed against the supporting surface by a plurality of belts positioned in adjacent side-by-side relation, the belts being positionable between the baffles and engage- able against the mat.https://digitalcommons.mtu.edu/patents/1108/thumbnail.jp

Multiple funnel flake aligner for making a loosely felted mat of aligned wood flakes

Apparatus for forming a loosely felted mat of thin elongated wood flakes with said flakes being aligned in mutually parallel relation. The apparatus includes a mat supporting surface, a hopper for holding a quantity of wood flakes, and a funnel assembly for receiving wood flakes from the hopper and for causing the flakes to be aligned in substantially parallel side-by-side relation as they are deposited on the supporting surface. The funnel assembly includes a plurality of funnels positioned in adjacent side-by-side relation, the funnels each including inclined walls having lower edges defining an elongated narrow opening adjacent the supporting surface and upper edges defining an opening wider than said narrow opening and for receiving wood flakes from the hopper. The narrow openings of the funnels are parallel and distribute the flakes uniformly across the supporting surface.https://digitalcommons.mtu.edu/patents/1109/thumbnail.jp

Dynamics of Spreading of Chainlike Molecules with Asymmetric Surface Interactions

In this work we study the spreading dynamics of tiny liquid droplets on solid surfaces in the case where the ends of the molecules feel different interactions with respect to the surface. We consider a simple model of dimers and short chainlike molecules that cannot form chemical bonds with the surface. We use constant temperature Molecular Dynamics techniques to examine in detail the microscopic structure of the time dependent precursor film. We find that in some cases it can exhibit a high degree of local order that can persist even for flexible chains. Our model also reproduces the experimentally observed early and late-time spreading regimes where the radius of the film grows proportional to the square root of time. The ratios of the associated transport coefficients are in good overall agreement with experiments. Our density profiles are also in good agreement with measurements on the spreading of molecules on hydrophobic surfaces.Comment: 12 pages, LaTeX with APS macros, 21 figures available by contacting [email protected], to appear in Phys. Rev.