Geometric Stack Research Articles

Representability of derived stacks

AbstractLurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify for many applications. Provided a derived analogue of Schlessinger's condition holds, the theorem reduces to verifying conditions on the underived part and on cohomology groups. Another simplification is that functors need only be defined on nilpotent extensions of discrete rings. Finally, there is a pre-representability theorem, which can be applied to associate explicit geometric stacks to dg-manifolds and related objects.

Characterizing Precipitation Defects in Nickel Based 718 Alloy

In the present study we examine the crystallographic structure of the , ’’ and  phases present in nickel base 718 alloy. The chemical ordering of Nb atoms and possible planar faults that may be observed in ’’ precipitates are detailed. High resolution transmission electron microscopy (HRTEM) observations of various faults are reported. The decomposition of a matrix dislocation to form a locked V shaped configuration is shown. The observation along [110] type direction allows to identify the type of defect, which is observed as a pure geometric stacking fault.

Assembly of NaTaO3 porous microspheres via imperfect oriented attachment mechanism

Spongy-like NaTaO 3 mesoporous microspheres are assembled from nanoparticles via imperfect oriented attachment. Study shows that the NaTaO 3 spongy microspheres with the diameters of ∼1 μm are composed of the fundamental building blocks of ∼50 nm NaTaO 3 nanospheres. The high-resolution transmission electron microscopy further reveals that these fundamental building blocks are assembled from primary building blocks of ∼10 nm NaTaO 3 nanocrystals. The pore diameters of these spongy microspheres are ca. 30 nm and the Brunauer–Emmett–Teller (BET) surface area is calculated to be 57.8 m 2 g −1 . This interesting ternary alkali metal composite oxide of NaTaO 3 spongy microspheres with high specific surface area and strong stability will be favorable for their practical application in photocatalysis. This synthesis route may throw light on the fabrication of the binary or ternary porous metal oxides by geometrical stacking of the nanobuilding blocks via imperfect oriented attachment.

Contamination of Fresh Air Intakes Due to Downwash from a Rooftop Structure

The effect of rooftop structures on the dispersion of building exhaust was evaluated using wind tunnel experiments with an isolated building for four different full-scale equivalent heights varying from 15 to 70 m. The stack was located on the roof of the building downwind of the rooftop structure. In some cases, downwash produced by the rooftop structure caused a significant reduction in dilution (i.e., increased contaminant concentration) compared with results obtained with a flat-roofed model. For the wind normal to the building, the effect of the rooftop structure depended on building height and the crosswind width of the structure. Maximum reduction in dilution occurred for the 15-m building with a wide penthouse. The influence of the rooftop structure on plume behavior for the normal wind diminished as building height increased because of an increase in size of the separated flow region above the roof. On the other hand, for an oblique wind at 45°, the rooftop structure produced low dilution for all building heights. The paper shows that the American Society of Heating, Refrigerating and Air-Conditioning Engineers geometric stack design method and dilution model can lead to an unconservative design.

Homotopical algebraic geometry. II. Geometric stacks and applications

This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category, such as derivations, etale and smooth maps, flat and projective modules, etc. We then use the theory of stacks over model categories introduced in \cite{hagI} in order to define a general notion of geometric stack over a base symmetric monoidal model category C, and prove that this notion satisfies the expected properties. The rest of the paper consists in specializing C to several different contexts. First of all, when C=k-Mod is the category of modules over a ring k, with the trivial model structure, we show that our notion gives back the algebraic n-stacks of C. Simpson. Then we set C=sk-Mod, the model category of simplicial k-modules, and obtain this way a notion of geometric derived stacks which are the main geometric objects of Derived Algebraic Geometry. We give several examples of derived version of classical moduli stacks, as for example the derived stack of local systems on a space, of algebra structures over an operad, of flat bundles on a projective complex manifold, etc. Finally, we present the cases where C=(k) is the model category of unbounded complexes of modules over a char 0 ring k, and C=Sp^{\Sigma} the model category of symmetric spectra. In these two contexts, called respectively Complicial and Brave New Algebraic Geometry, we give some examples of geometric stacks such as the stack of associative dg-algebras, the stack of dg-categories, and a geometric stack constructed using topological modular forms.

Effect of the morphology on thermal stability of the Ba-Ce-Mn-Al-O oxides synthesized in a reverse microemulsion

Ba-Ce-Mn-Al-O (0.5/0.5/1/11, molar ratios) oxides nanorods and nanoparticles were synthesized in reverse microemulsions. The thermal stabilities and catalytic properties of CH4 combustion over Ce-Ba-Mn-Al-O samples with different morphologies were investigated. The results showed that the particle morphology had a significant effect on the properties of the catalysts. The rodlike catalyst had higher thermal stability and catalytic activity for methane combustion than the spherical one. A geometric stacking model was proposed to explain the effect. © 2007 Elsevier B.V. All rights reserved.

Moduli of objects in dg-categories

The purpose of this work is to prove the existence of an algebraic moduli classifying objects in a given triangulated category. To any dg-category T (over some base ring k), we define a D − -stack M T in the sense of [ Toën B., Vezzosi G., Homotopical algebraic geometry II: Geometric stacks and applications, Mem. Amer. Math. Soc., in press], classifying certain T op -dg-modules. When T is saturated, M T classifies compact objects in the triangulated category [ T ] associated to T. The main result of this work states that under certain finiteness conditions on T (e.g. if it is saturated) the D − -stack M T is locally geometric (i.e. union of open and geometric sub-stacks). As a consequence we prove the algebraicity of the group of auto-equivalences of saturated dg-categories. We also obtain the existence of reasonable moduli for perfect complexes on a smooth and proper scheme, as well as complexes of representations of a finite quiver.

Variational analysis of delamination growth for composite laminated cylindrical shells under circumferential concentrated load

The growth of delamination in cylindrical shells under external pressure may lead to structural failure. Based on the variational principle of moving boundary (Qian WC. Variational calculus and finite element. Beijing: Science Press; 1980 [in Chinese].) and considering the contact effect between delamination regions, in this paper, the nonlinear governing equations for the delaminated cylindrical shells are derived, and the corresponding boundary and matching conditions are given. Moreover, according to the Griffith criterion, the formulas of energy release rate along the delamination front are obtained. As the numerical example, the delamination growth of axisymmetrical laminated cylindrical shells is analyzed, and the effects of delamination sizes and depths, geometrical parameters, material properties and laminate stacking sequences on delamination growth are discussed.

Champs affines

The purpose of this work is to introduce a notion of affine stacks, which is a homotopy version of the notion of affine schemes, and to give several applications in the context of algebraic topology and algebraic geometry. As a first application we show how affine stacks can be used in order to give a new point of view (and new proofs) on rational and p-adic homotopy theory. This gives a first solution to A. Grothendieck’s schematization problem described in [18]. We also use affine stacks in order to introduce a notion of schematic homotopy types. We show that schematic homotopy types give a second solution to the schematization problem, which also allows us to go beyond rational and p-adic homotopy theory for spaces with arbitrary fundamental groups. The notion of schematic homotopy types is also used in order to construct various homotopy types of algebraic varieties corresponding to various co-homology theories (Betti, de Rham, l-adic, ...), extending the well known constructions of the various fundamental groups. Finally, just as algebraic stacks are obtained by gluing affine schemes we define $$ \infty $$-geometric stacks as a certain gluing of affine stacks. Examples of $$ \infty $$-geometric stacks in the context of algebraic topology (moduli spaces of dga structures up to quasi-isomorphisms) and Hodge theory (non-abelian periods) are given.

The epidermal permeability barrier: from the early days at Harvard to emerging concepts.

The epidermal permeability barrier: from the early days at Harvard to emerging concepts.

Prediction of Volume and Spatial Distribution of Reservoir Facies, Tiger Ridge Natural Gas Field, Montana: ABSTRACT

Deterministic predictions of the geometry and distribution of subsurface reservoir facies is an exploration and production application of numerical stratigraphic models under development. The models simulate the architecture and facies distributions of offshore marine to coastal-plain strata as discrete time-bounded progradational events or genetic sequences. The Tiger Ridge natural gas field in north-central Montana is productive from upper shoreface facies of the Upper Cretaceous Eagle Sandstone (Campanian). Complex production trends within the field include geographic shifts, gaps, and thickness changes in pay zones. The eagle has been described as consisting of three lithostratigraphic members, and complex production patterns have been explained by diagenetic or structural complications. By contrast, genetic stratigraphic analysis indicates that the Eagle comprises five to seven genetic sequences arranged in the predicted geometric stacking pattern. Isopachs of individual genetic sequences and of reservoir facies indicate that the position and geometry of reservoir facies tracts are predictable in terms of lateral and vertical shifts within the overall genetic stratigraphic framework. This field study illustrates the increased temporal resolution attainable by the method of genetic stratigraphic correlation and documents the ability of the numerical models to predict the distribution of reservoir facies in the subsurface.

Dislocations motion in alloys with a periodic antiphase boundaries structure

Some peculiarities of the propagation of dislocations across a periodic antiphase boundaries structure are discussed. Examination of the effective surface tension acting on each dislocation shows that their equilibrium configuration mainly depends on the relative energies of the geometrical stacking fault and the shear antiphase boundary bounded by a unit dislocation, as well as the average separation of the periodic antiphase boundaries. Such an analysis allows to explain the occurrence of various deformation modes in these alloys: microtwinning in Ni 3 V or propagation of dislocations in planes with disturbed long range order in Cu 3 Pd.