Yatian Zhang, Thomas Frauenheim, Traian Dumitrică
et al.
Because of their rapid ionic diffusion, Ag-based argyrodites have great potential as solid-state electrolytes. The fundamental thermal transport in these materials is important for the overall all-solid-state battery design. Using an accurate framework and a unified heat-transport theory, we compute both the particle-like (κp) and the glass-like (κc) components of the lattice thermal conductivity (κL) of Ag8SnSe6 in the orthorhombic phase. Despite being a crystal, Ag8SnSe6 exhibits an exceptionally low room-temperature κL=κp+κc of 0.274 W/mK, which is nearly temperature independent over the 100–350 K range. This unusual behavior is linked to the lonesome Ag atoms, which, in this temperature range, exhibit intense vibrations while remaining weakly bonded to the Sn-Se framework. While their bonding anharmonicity significantly reduces κp, the Ag-dominated extended vibrations make κc the primary heat-transfer mode. By unveiling the role of Ag in the heat transport of Ag8SnSe6, we support the notion that the bonding and structural characteristics responsible for fast ionic conduction can also help identify extreme materials with glass-like thermal transport.
AbstractThe investigation of the mixed convective magnetohydrodynamic (MHD) flow of a couple stress hybrid nanofluid having temperature‐dependent viscosity and thermal conductivity in a vertical channel is dealt with within this paper. The considered hybrid nanofluid is processed by mixing multiwalled carbon nanotubes () and silver (Ag) nanoparticles in a base fluid of ethylene glycol () assuming the base fluid and the nanoparticles to be in a thermal equilibrium state following the Tiwari–Das nanofluid model. The flow is generated by the buoyancy force under the standard Boussinesq approximation and the pressure gradient force. The effect of a uniform transverse magnetic field is considered, and a constant temperature is maintained at the channel walls. The governing momentum and energy equations are nondimensionalized with relevant dimensionless parameters and solved using the homotopy analysis method (HAM) to obtain semi‐analytical solutions. The skin friction coefficient and Nusselt number on the channel walls are derived to analyze the shear stress and heat transfer rate, and to scrutinize the irreversibilities in the system, the entropy generation number and the Bejan number are defined. The emphasis is given to the analysis of velocity and temperature profiles, irreversibilities in the system, shear stresses, and heat transfer rate on the channel walls concerning the volumetric concentration of the nanoparticles, shape factor effect for various nanoparticle shapes, and temperature‐dependent viscosity and thermal conductivity. The analysis reveals that with higher shape factors and enhancement of nanoparticle concentration, both velocity and temperature degrade, and the entropy generation rate escalates with growing heat transfer irreversibility. Moreover, a lower and higher shear stress and heat transfer rate are achieved, respectively. The variable viscosity and thermal conductivity parameters effectively alter the velocity and temperature profiles, irreversibilities, shear stress, and heat transfer rate.
The free-field formalism for quantum groups [preprint ITEP-M3/94, CRM-2202 hep-th/9409093] provides a special choice of coordinates on a quantum group. In these coordinates the construction of associated integrable system [arXiv:1207.1869] is especially simple. This choice also fits into general framework of cluster varieties [math.AG/0311245]—natural changes in coordinates are cluster mutations.
We generalise a formula of Shou-Wu Zhang, which describes local arithmetic intersection numbers of three Cartier divisors with support in the special fibre on a a self-product of a semi-stable arithmetic surface using elementary analysis. By an approximation argument, Zhang extends his formula to a formula for local arithmetic intersection numbers of three adelic metrized line bundles on the self-product of a curve with trivial underlying line bundle. Using the results on intersection theory from arXiv:1404.1623 [math.AG] we generalize these results to d-fold self-products for arbitrary d. For the approximations to converge, we have to assume that d satisfies the vanishing condition 4.7 from arXiv:1404.1623 [math.AG], which is true at least for $d\in \{2,3,4,5\}$.
We present an approach to Green-Lazarsfeld's generic vanishing combining gaussian maps and the Fourier-Mukai transform associated to the Poincar\`e line bundle. As an application we prove the Generic Vanishing Theorem for all normal Cohen-Macaulay subvarieties of abelian varieties over an algebraically closed field. This paper is a reworking of part of arXiv:math/0310026v2 [math.AG], which contained a mistake.
We investigate principal $G$-bundles on a compact K\"ahler manifold, where $G$ is a complex algebraic group such that the connected component of it containing the identity element is reductive. Defining (semi)stability of such bundles, it is shown that a principal $G$-bundle $E_G$ admits an Einstein-Hermitian connection if and only if $E_G$ is polystable. We give an equivalent formulation of the (semi)stability condition. A question is to compare this definition with that of math.AG/0506511.
In this Part II, D(10.2), of D(10), we take D(10.1) (arXiv:1302.2054 [math.AG]) as the foundation to define the notion of $Z$-semistable morphisms from general Azumaya nodal curves, of genus $\ge 2$, with a fundamental module to a projective Calabi-Yau 3-fold and show that the moduli stack of such $Z$-semistable morphisms of a fixed type is compact. This gives us a counter moduli stack to D-strings as the moduli stack of stable maps in Gromov-Witten theory to the fundamental string. It serves and prepares for us the basis toward a new invariant of Calabi-Yau 3-fold that captures soft-D-string world-sheet instanton numbers in superstring theory. This note is written hand-in-hand with D(10.1) and is to be read side-by-side with ibidem.
In a suitable regime of superstring theory, D-branes in a Calabi-Yau space and their most fundamental behaviors can be nicely described mathematically through morphisms from Azumaya spaces with a fundamental module to that Calabi-Yau space. In the earlier work [L-L-S-Y] (D(2): arXiv:0809.2121 [math.AG], with Si Li and Ruifang Song) from the project, we explored this notion for the case of D1-branes (i.e. D-strings) and laid down some basic ingredients toward understanding the notion of D-string world-sheet instantons in this context. In this continuation, D(10), of D(2), we move on to construct a moduli stack of semistable morphisms from Azumaya nodal curves with a fundamental module to a projective Calabi-Yau 3-fold $Y$. In this Part I of the note, D(10.1), we define the notion of twisted central charge $Z$ for Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves and the associated stability condition on such transforms and prove that for a given compact stack of nodal curves $C_{\cal M}/{\cal M}$, the stack $FM^{1,[0];Zss}_{C_{\cal M}/{\cal M}}(Y,c)$ of $Z$-semistable Fourier-Mukai transforms of dimension 1 and width [0] from nodal curves in the family $C_{\cal M}/{\cal M}$ to $Y$ of fixed twisted central charge $c$ is compact. For the application in the sequel D(10.2), $C_{\cal M}/{\cal M}$ will contain $C_{\bar{\cal M}_g}/\bar{\cal M}_g$ as a substack and $FM^{1,[0];Zss}_{C_{\cal M}/{\cal M}}(Y,c)$ in this case will play a key role in defining stability condition for morphisms from arbitrary Azumaya nodal curves (with the underlying nodal curves not necessary in the family $C_{\cal M}/{\cal M}$) to $Y$.
Abstract Supersymmetric heterotic string models, built from a Calabi–Yau threefold X endowed with a stable vector bundle V , usually start from a phenomenologically motivated choice of a bundle V v in the visible sector, the spectral cover construction on an elliptically fibered X being a prominent example. The ensuing anomaly mismatch between c 2 ( V v ) and c 2 ( X ) , or rather the corresponding differential forms, is often ‘solved’, on the cohomological level, by including a fivebrane. This leads to the question whether the difference can be alternatively realized by a further stable bundle. The ‘DRY’-conjecture of Douglas, Reinbacher and Yau in math.AG/0604597 gives a sufficient condition on cohomology classes on X to be realized as the Chern classes of a stable sheaf. In 1010.1644 [hep-th], we showed that infinitely many classes on X exist for which the conjecture is true. In this note, we give the sufficient condition for the mentioned fivebrane classes to be realized by a further stable bundle in the hidden sector. Using a result obtained in 1011.6246 [hep-th], we show that corresponding bundles exist, thereby confirming this version of the DRY-Conjecture.
We show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compactification of S with torsion singularity. This result generalizes our previous result for admissible normal functions on curves [arxiv:math/0604345 [math.AG]]. It has also been obtained by M. Saito using a different method in a recent preprint [arXiv:0803.2771v2].
We introduce and study kernel algebras, i.e., algebras in the category of sheaves on a square of a scheme, where the latter category is equipped with a monoidal structure via a natural convolution operation. We show that many interesting categories, such as D-modules, equivariant sheaves and their twisted versions, arise as categories of modules over kernel algebras. We develop the techniques of constructing derived equivalences between these module categories. As one application we generalize the results of math.AG/9901009 concerning modules over algebras of twisted differential operators on abelian varieties. As another application we recover and generalize the results of Laumon in alg-geom/9603004 concerning an analog of the Fourier transform for derived categories of quasicoherent sheaves on a dual pair of generalized 1-motives.
Abstract We determine the possible Hilbert functions of graded rank one torsion free modules over three dimensional Artin–Schelter regular algebras. It turns out that, as in the commutative case, they are related to Castelnuovo functions. From this we obtain an intrinsic proof that the space of torsion free rank one modules on a non-commutative P 2 is connected. A different proof of this fact, based on deformation theoretic methods and the known commutative case has recently been given by Nevins and Stafford [Sklyanin algebras and Hilbert schemes of points, math.AG/0310045 ]. For the Weyl algebra it was proved by Wilson [Invent. Math. 133 (1) (1998) 1–41].
Let X be a K3 surface with a polarization H with H^2=2rs. Assume that H.N(X)=Z for the Picard lattice N(X). The moduli space Y of sheaves over X with the Mukai vector (r,H,s) is again a K3 surface. We prove that Y\cong X, if there exists h_1\in N(X) with (h_1)^2=f(r,s), H.h_1\equiv 0\mod g(r,s), and h_1 satisfies some condition of primitivity. Existence of such type a criterion is surprising, and also gives some geometric interpretation of elements in N(X) with negative square. We describe all 18-dimensional irreducible components of moduli of the (X,H) with Y\cong X and prove that their number is infinite. These generalizes results of math.AG/0206158, math.AG/0304415 for r=s.
In [Duke Math. J. 55 (1987) 629–659] K. Kato proved, using techniques from K-theory, a formula which compares the dimensions of the spaces of vanishing cycles in a finite morphism between formal germs of curves over a complete discrete valuation ring. To the best of my knowledge Kato's formula is explicit only in the case where this morphism is generically separable on the level of special fibres. In this note we prove, using formal patching techniques a la Harbater, an analogous explicit formula in the case of a Galois cover of degree p between formal germs of curves over a complete discrete valuation ring of unequal characteristic (0,p) which includes the case where we have inseparability on the level of special fibres. The results of this paper play a key role in [math.AG/0106249] where is studied the semi-stable reduction of Galois covers of degree p of curves over a complete discrete valuation ring of unequal characteristics (0,p), as well as the Galois action on these covers.