scholarly journals Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations

2020 ◽  
Vol 132 (1) ◽  
pp. 1-82 ◽  
Author(s):  
Helge Ruddat ◽  
Bernd Siebert
Keyword(s):  
Mirror Symmetry ◽  
Canonical Coordinates ◽  
Wall Structures ◽  
Toric Degenerations

scholarly journals Newton–Okounkov Bodies of Flag Varieties and Combinatorial Mutations

2020 ◽  
Author(s):  
Naoki Fujita ◽  
Akihiro Higashitani
Keyword(s):  
Mirror Symmetry ◽  
Projective Variety ◽  
Fundamental Problem ◽  
Flag Varieties ◽  
Systematic Method ◽  
Fano Manifolds ◽  
Projective Varieties ◽  
Combinatorial Properties ◽  
Toric Degenerations ◽  
Higher Rank

Abstract A Newton–Okounkov body is a convex body constructed from a projective variety with a globally generated line bundle and with a higher rank valuation on the function field, which gives a systematic method of constructing toric degenerations of projective varieties. Its combinatorial properties heavily depend on the choice of a valuation, and it is a fundamental problem to relate Newton–Okounkov bodies associated with different kinds of valuations. In this paper, we address this problem for flag varieties using the framework of combinatorial mutations, which was introduced in the context of mirror symmetry for Fano manifolds. By applying iterated combinatorial mutations, we connect specific Newton–Okounkov bodies of flag varieties including string polytopes, Nakashima–Zelevinsky polytopes, and Feigin–Fourier–Littelmann–Vinberg polytopes.

scholarly journals Mirror symmetry and toric degenerations of partial flag manifolds

2000 ◽  
Vol 184 (1) ◽  
pp. 1-39 ◽  
Author(s):  
Victor V. Batyrev ◽  
Ionuţ Ciocan-Fontanine ◽  
Bumsig Kim ◽  
Duco Straten
Keyword(s):  
Mirror Symmetry ◽  
Flag Manifolds ◽  
Toric Degenerations

scholarly journals Toric degenerations of cluster varieties and cluster duality

2020 ◽  
Vol 156 (10) ◽  
pp. 2149-2206
Author(s):  
Lara Bossinger ◽  
Bosco Frías-Medina ◽  
Timothy Magee ◽  
Alfredo Nájera Chávez
Keyword(s):  
Toric Variety ◽  
Mirror Symmetry ◽  
Duke Math ◽  
Cluster Algebras ◽  
Canonical Bases ◽  
Toric Degeneration ◽  
The Family ◽  
Toric Degenerations ◽  
Cluster Varieties ◽  
Natural Way

We introduce the notion of a $Y$-pattern with coefficients and its geometric counterpart: an $\mathcal {X}$-cluster variety with coefficients. We use these constructions to build a flat degeneration of every skew-symmetrizable specially completed $\mathcal {X}$-cluster variety $\widehat {\mathcal {X} }$ to the toric variety associated to its g-fan. Moreover, we show that the fibers of this family are stratified in a natural way, with strata the specially completed $\mathcal {X}$-varieties encoded by $\operatorname {Star}(\tau )$ for each cone $\tau$ of the $\mathbf {g}$-fan. These strata degenerate to the associated toric strata of the central fiber. We further show that the family is cluster dual to $\mathcal {A}_{\mathrm {prin}}$ of Gross, Hacking, Keel and Kontsevich [Canonical bases for cluster algebras, J. Amer. Math. Soc. 31 (2018), 497–608], and the fibers cluster dual to $\mathcal {A} _t$. Finally, we give two applications. First, we use our construction to identify the toric degeneration of Grassmannians from Rietsch and Williams [Newton-Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians, Duke Math. J. 168 (2019), 3437–3527] with the Gross–Hacking–Keel–Kontsevich degeneration in the case of $\operatorname {Gr}_2(\mathbb {C} ^{5})$. Next, we use it to link cluster duality to Batyrev–Borisov duality of Gorenstein toric Fanos in the context of mirror symmetry.

Temperature Dependence of Magnetic Domains and Wall Structures

1972 ◽  
Vol 30 ◽  
pp. 496-497
Author(s):  
Sonoko Tsukahara ◽  
Tadami Taoka ◽  
Hisao Nishizawa
Keyword(s):  
Temperature Dependence ◽  
Domain Walls ◽  
Magnetic Domain ◽  
Iron Film ◽  
Objective Lens ◽  
Lorentz Microscopy ◽  
Domain Structures ◽  
Wall Structures ◽  
Crystal Films ◽  
Metallurgical Structure

The high voltage Lorentz microscopy was successfully used to observe changes with temperature; of domain structures and metallurgical structures in an iron film set on the hot stage combined with a goniometer. The microscope used was the JEM-1000 EM which was operated with the objective lens current cut off to eliminate the magnetic field in the specimen position. Single crystal films with an (001) plane were prepared by the epitaxial growth of evaporated iron on a cleaved (001) plane of a rocksalt substrate. They had a uniform thickness from 1000 to 7000 Å.The figure shows the temperature dependence of magnetic domain structure with its corresponding deflection pattern and metallurgical structure observed in a 4500 Å iron film. In general, with increase of temperature, the straight domain walls decrease in their width (at 400°C), curve in an iregular shape (600°C) and then vanish (790°C). The ripple structures with cross-tie walls are observed below the Curie temperature.

Ruthenium red and alcian blue effects on outer structures of methanotrophic bacteria

1988 ◽  
Vol 46 ◽  
pp. 72-73
Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
C.C. Remsen
Keyword(s):  
Research Effort ◽  
Ruthenium Red ◽  
Outer Cell ◽  
Methanotrophic Bacteria ◽  
En Bloc ◽  
Methylosinus Trichosporium ◽  
Wall Structures ◽  
Methylomonas Albus ◽  
Type Strains ◽  
Outer Cell Wall

Methane, a contributor to the “greenhouse effect”, is oxidized in the natural environment by methanotrophic bacteria. As part of a comprehensive research effort, we have been examining the ultrastructure of methanotrophs. These microorganisms have complex outer cell wall structures similar to those frequently found in other chemol itho- trophic bacteria. (1,2)In our work, we have focused on the “type” strains of Methylomonas albus BG8 and Methylosinus trichosporium OB3b. Between Spurr and LR White embedding resins, we found a difference 1n the preservation of an outer cup layer of BG8 external to the peripheral membranes. Cells from the same sample embedded in Spurr consistently lacked this feature (FIG. 1). This effect was overcome by an en bloc ruthenium red (RR) protocol that resulted in successful retention of the cup layer in Spurr resin (FIG. 2). For OB3b cells, the en bloc RR protocol resulted in an exterior bead feature distinguishable in thin section (FIG. 4) that previously was seen only by SEM.

Architecture of Radiolitid Rudist (Mollusca) Shell-Wall Structures and its Phylogenetic Implications

1975 ◽  
Vol 33 ◽  
pp. 686-687
Author(s):  
David H. Sturm ◽  
Bob F. Perkins
Keyword(s):  
Phylogenetic Relationships ◽  
Outer Wall ◽  
Shell Microstructure ◽  
Shell Wall ◽  
Wall Structures ◽  
Phylogenetic Implications ◽  
Cellular Wall ◽  
Superfamily Analysis ◽  
Central Texas

Each of the seven families of rudists (Mollusca, Bivalvia, Hippuritacea) is characterized by distinctive shell-wall architectures which reflect phylogenetic relationships within the superfamily. Analysis of the complex, calcareous, cellular wall of the attached valve of the radiolite rudist Eoradiolites davidsoni (Hill) from the Comanche Cretaceous of Central Texas indicates that its wall architecture is an elaboration of the simpler monopleurid rudist wall and supports possible radiolite-monopleurid relationships.Several well-preserved specimens of E. davidsoni were sectioned, polished, etched, and carbon and gold coated for SEM examination. Maximum shell microstructure detail was displayed by etching with a 0.7% HC1 solution from 80 to 100 seconds.The shell of E. davidsoni comprises a large, thick-walled, conical, attached valve (AV) and a small, very thin, operculate, free valve (FV) (Fig. 1a). The AV shell is two-layered with a thin inner wall, in which original structures are usually obliterated by recrystallization, and a thick, cellular, outer wall.

Comparative surface and ultrastructural views of methylotrophic bacteria by TEM, STEM, SE, and freeze-etch electron microscopy.

1987 ◽  
Vol 45 ◽  
pp. 792-793
Author(s):  
T.A. Fassel ◽  
M.J. Schaller ◽  
M.E. Lidstrom ◽  
C.C. Remsen
Keyword(s):  
Cytoplasmic Membrane ◽  
Structural Features ◽  
Methylotrophic Bacteria ◽  
Type I ◽  
Type Ii ◽  
Membrane Complex ◽  
Oxidation Of Methane ◽  
Methane Oxidizing Bacteria ◽  
Wall Structures ◽  
Methylomonas Albus

Methylotrophic bacteria play an Important role in the environment in the oxidation of methane and methanol. Extensive intracytoplasmic membranes (ICM) have been associated with the oxidation processes in methylotrophs and chemolithotrophic bacteria. Classification on the basis of ICM arrangement distinguishes 2 types of methylotrophs. Bundles or vesicular stacks of ICM located away from the cytoplasmic membrane and extending into the cytoplasm are present in Type I methylotrophs. In Type II methylotrophs, the ICM form pairs of peripheral membranes located parallel to the cytoplasmic membrane. Complex cell wall structures of tightly packed cup-shaped subunits have been described in strains of marine and freshwater phototrophic sulfur bacteria and several strains of methane oxidizing bacteria. We examined the ultrastructure of the methylotrophs with particular view of the ICM and surface structural features, between representatives of the Type I Methylomonas albus (BG8), and Type II Methylosinus trichosporium (OB-36).

High Resolution Electron Microscopy of internal interfaces in layered materials

1990 ◽  
Vol 48 (4) ◽  
pp. 320-321
Author(s):  
Yoichi Ishida ◽  
Hideki Ichinose ◽  
Yutaka Takahashi ◽  
Jin-yeh Wang
Keyword(s):  
Grain Boundaries ◽  
Mirror Symmetry ◽  
Functional Materials ◽  
High Resolution Electron Microscopy ◽  
Layered Materials ◽  
Plane Boundary ◽  
Chemical Information ◽  
Layer Plane ◽  
High Tc ◽  
Cubic Metals

Layered materials draw attention in recent years in response to the world-wide drive to discover new functional materials. High-Tc superconducting oxide is one example. Internal interfaces in such layered materials differ significantly from those of cubic metals. They are often parallel to the layer of the neighboring crystals in sintered samples(layer plane boundary), while periodically ordered interfaces with the two neighboring crystals in mirror symmetry to each other are relatively rare. Consequently, the atomistic features of the interface differ significantly from those of cubic metals. In this paper grain boundaries in sintered high-Tc superconducting oxides, joined interfaces between engineering ceramics with metals, and polytype interfaces in vapor-deposited bicrystal are examined to collect atomic information of the interfaces in layered materials. The analysis proved that they are not neccessarily more complicated than that of simple grain boundaries in cubic metals. The interfaces are majorly layer plane type which is parallel to the compound layer. Secondly, chemical information is often available, which helps the interpretation of the interface atomic structure.

SEM and fluorescence imaging of callose deposition in root hair tips and suspension cultures of Streptanthus tortuosus

1990 ◽  
Vol 48 (3) ◽  
pp. 698-699
Author(s):  
K.S. Walters ◽  
R.D. Sjolund ◽  
K.C. Moore
Keyword(s):  
Cell Wall ◽  
Root Hair ◽  
Cultured Cells ◽  
Root Hairs ◽  
Callus Cultures ◽  
Callose Deposition ◽  
Culture Cells ◽  
Wall Structures ◽  
Ultraviolet Illumination ◽  
Callose Formation

Callose, B-1,3-glucan, a component of cell walls, is associated with phloem sieve plates, plasmodesmata, and other cell wall structures that are formed in response to wounding or infection. Callose reacts with aniline blue to form a fluorescent complex that can be recognized in the light microscope with ultraviolet illumination. We have identified callose in cell wall protuberances that are formed spontaneously in suspension-cultured cells of S. tortuosus and in the tips of root hairs formed in sterile callus cultures of S. tortuosus. Callose deposits in root hairs are restricted to root hair tips which appear to be damaged or deformed, while normal root hair tips lack callose deposits. The callose deposits found in suspension culture cells are restricted to regions where unusual outgrowths or protuberances are formed on the cell surfaces, specifically regions that are the sites of new cell wall formation.Callose formation has been shown to be regulated by intracellular calcium levels.

The limits of strain and lattice parameter measurements by CBED

1989 ◽  
Vol 47 ◽  
pp. 518-519
Author(s):  
Hamish L. Fraser
Keyword(s):  
Electron Beam ◽  
Mirror Symmetry ◽  
Local Symmetry ◽  
Lattice Parameter ◽  
Growth Direction ◽  
Surface Relaxation ◽  
Strained Layer ◽  
Axis Parallel ◽  
Local Lattice ◽  
Strained Layer Superlattice

The topic of strain and lattice parameter measurements using CBED is discussed by reference to several examples. In this paper, only one of these examples is referenced because of the limitation of length. In this technique, scattering in the higher order Laue zones is used to determine local lattice parameters. Work (e.g. 1) has concentrated on a model strained-layer superlattice, namely Si/Gex-Si1-x. In bulk samples, the strain is expected to be tetragonal in nature with the unique axis parallel to [100], the growth direction. When CBED patterns are recorded from the alloy epi-layers, the symmetries exhibited by the patterns are not tetragonal, but are in fact distorted from this to lower symmetries. The spatial variation of the distortion close to a strained-layer interface has been assessed. This is most readily noted by consideration of Fig. 1(a-c), which show enlargements of CBED patterns for various locations and compositions of Ge. Thus, Fig. 1(a) was obtained with the electron beam positioned in the center of a 5Ge epilayer and the distortion is consistent with an orthorhombic distortion. When the beam is situated at about 150 nm from the interface, the same part of the CBED pattern is shown in Fig. 1(b); clearly, the symmetry exhibited by the mirror planes in Fig. 1 is broken. Finally, when the electron beam is positioned in the center of a 10Ge epilayer, the CBED pattern yields the result shown in Fig. 1(c). In this case, the break in the mirror symmetry is independent of distance form the heterointerface, as might be expected from the increase in the mismatch between 5 and 10%Ge, i.e. 0.2 to 0.4%, respectively. From computer simulation, Fig.2, the apparent monocline distortion corresponding to the 5Ge epilayer is quantified as a100 = 0.5443 nm, a010 = 0.5429 nm and a001 = 0.5440 nm (all ± 0.0001 nm), and α = β = 90°, γ = 89.96 ± 0.02°. These local symmetry changes are most likely due to surface relaxation phenomena.

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