Atiyah-Patodi-Singer index on a lattice

We propose a non-perturbative formulation of the Atiyah-Patodi-Singer(APS) index in lattice gauge theory, in which the index is given by the $\eta$ invariant of the domain-wall Dirac operator. Our definition of the index is always an integer with a finite lattice spacing. To verify this proposal, using the eigenmode set of the free domain-wall fermion, we perturbatively show in the continuum limit that the curvature term in the APS theorem appears as the contribution from the massive bulk extended modes, while the boundary $\eta$ invariant comes entirely from the massless edge-localized modes.Comment: 14 pages, appendices added, details of key equations added, typos corrected, to appear in PTE

Estimating the Evaporation from Irrigation Canals in Northwestern China Using the Double-Deck Surface Air Layer Model

The evaporation from irrigation canals was estimated by the aerodynamic method based on the double-deck surface air layer model (called “DSAL model” for short hereafter). The DSAL model describes the surface air layer over a canal as a composite air layer with two sublayers, the lower sublayer and the upper sublayer. The lower sublayer is a few tens of centimeters thick and formed by the flowing water, in which there is no advection; the upper sublayer is over the lower sublayer and formed by the surface wind. The results were compared to those obtained by the heat balance method; field experiments were conducted in the middle reaches of the Heihe River in northwestern China. Results showed that cumulative evaporation instances estimated by the DSAL model were equal in order of magnitude to those by the heat balance method on observed days during the daytime (0700~1900 BST). We infer from these experimental results that the evaporation loss in transport in this region is of the order of one percent at most

Estimating the Evaporation from Irrigation Canals in Northwestern China Using the Double-Deck Surface Air Layer Model

The evaporation from irrigation canals was estimated by the aerodynamic method based on the double-deck surface air layer model (called “DSAL model” for short hereafter). The DSAL model describes the surface air layer over a canal as a composite air layer with two sublayers, the lower sublayer and the upper sublayer. The lower sublayer is a few tens of centimeters thick and formed by the flowing water, in which there is no advection; the upper sublayer is over the lower sublayer and formed by the surface wind. The results were compared to those obtained by the heat balance method; field experiments were conducted in the middle reaches of the Heihe River in northwestern China. Results showed that cumulative evaporation instances estimated by the DSAL model were equal in order of magnitude to those by the heat balance method on observed days during the daytime (0700~1900 BST). We infer from these experimental results that the evaporation loss in transport in this region is of the order of one percent at most