Umělé spinové systémy jsou vhodným nástrojem pro zkoumání a ovlivňování neobvyklých exotických nízko-energiových stavů přímo v reálném prostoru. Experimentální realizace těchto systémů jsou založeny na výrobě vzájemně interagujících nano-magnetů uspořádaných do požadované geometrie. Prvním a asi i nejvíce studovaným umělým systémem je prostá čtvercová mřížka. V této práci se zabýváme modifikováním této čtvercové geometrie, které umožní zachycení různých magnetických fází založených na modelech ledu. Výsledky ukazují, že vhodným nastaveném této modifikace lze realizovat různé magnetické fáze, včetně neuspořádané spinové kapalné fáze s uvězněnými magnetickými kvazičásticemi (magnetickými monopóly).

During development of tissues, cells collectively organize to form complex patterns and morphologies. A general feature of many developing epithelia is their distinct organization into cellular compartments of different cell lineages. The interfaces between these compartments, called compartment boundaries, maintain straight and sharp morphologies. The interfaces play key roles in tissue development and pattern formation. An important model system to study the morphology of compartment boundaries during development is the wing disc of the fruit fly. Two compartment boundaries exist in the fly wing disc, the anteroposterior (AP) boundary and the dorsoventral (DV) boundary. A crucial question is how compartment boundaries are shaped and remain stable during growth. In this work, we discuss the dynamics and mechanisms of compartment boundaries in developing epithelia. We analyze the general features of interfacial phenomena in coarse- grained models of passive and active fluids. We introduce a continuum description of tissues with two cell types. This model allows us to study the propagation of interfaces due to the interplay of cell dynamics and tissue mechanics. We also use a vertex model to describe cellular compartments in growing epithelia. The vertex model accounts for cell mechanics and describes a 2D picture of tissues where the network of adherens junctions characterizes cell shapes. We use this model to study the general physical mechanisms by which compartment boundaries are shaped. We quantify the stresses in the cellular network and discuss how cell mechanics and growth influence the stress profile. With the help of the anisotropic stress profile near the interfaces we calculate the interfacial tension. We show that cell area pressure, cell proliferation rate, orientation of cell division, cell elongation created by external stress, and cell bond tension all have distinct effects on the morphology of interfaces during tissue growth. Furthermore, we investigate how much different mechanisms contribute to the effective interfacial tension. We study the mechanisms shaping the DV boundary in wing imaginal disc at different stages during the development. We analyze the images of wing discs to quantify the roughness of the DV boundary and average cell elongation in its vicinity. We quantify increased cell bond tension along the boundary and analyze the role of localized reduction in cell proliferation on the morphology of the DV boundary. We use experimentally determined values for cell bond tension, cell elongation and bias in orientation of cell division in simulations of tissue growth in order to reproduce the main features of the time-evolution of the DV boundary shape.

During development of tissues, cells collectively organize to form complex patterns and morphologies. A general feature of many developing epithelia is their distinct organization into cellular compartments of different cell lineages. The interfaces between these compartments, called compartment boundaries, maintain straight and sharp morphologies. The interfaces play key roles in tissue development and pattern formation. An important model system to study the morphology of compartment boundaries during development is the wing disc of the fruit fly. Two compartment boundaries exist in the fly wing disc, the anteroposterior (AP) boundary and the dorsoventral (DV) boundary. A crucial question is how compartment boundaries are shaped and remain stable during growth. In this work, we discuss the dynamics and mechanisms of compartment boundaries in developing epithelia. We analyze the general features of interfacial phenomena in coarse- grained models of passive and active fluids. We introduce a continuum description of tissues with two cell types. This model allows us to study the propagation of interfaces due to the interplay of cell dynamics and tissue mechanics. We also use a vertex model to describe cellular compartments in growing epithelia. The vertex model accounts for cell mechanics and describes a 2D picture of tissues where the network of adherens junctions characterizes cell shapes. We use this model to study the general physical mechanisms by which compartment boundaries are shaped. We quantify the stresses in the cellular network and discuss how cell mechanics and growth influence the stress profile. With the help of the anisotropic stress profile near the interfaces we calculate the interfacial tension. We show that cell area pressure, cell proliferation rate, orientation of cell division, cell elongation created by external stress, and cell bond tension all have distinct effects on the morphology of interfaces during tissue growth. Furthermore, we investigate how much different mechanisms contribute to the effective interfacial tension. We study the mechanisms shaping the DV boundary in wing imaginal disc at different stages during the development. We analyze the images of wing discs to quantify the roughness of the DV boundary and average cell elongation in its vicinity. We quantify increased cell bond tension along the boundary and analyze the role of localized reduction in cell proliferation on the morphology of the DV boundary. We use experimentally determined values for cell bond tension, cell elongation and bias in orientation of cell division in simulations of tissue growth in order to reproduce the main features of the time-evolution of the DV boundary shape.