Largeeddy simulation was used to model turbulent atmospheric surface layer (ASL) flow over canopies composed of streamwisealigned rows of synthetic trees of height,
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Electrophoresis is the motion of a charged colloidal particle in an electrolyte under an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength
 Award ID(s):
 2002120
 NSFPAR ID:
 10502186
 Publisher / Repository:
 Cambridge University Press
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 968
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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, and systematically arranged to quantify the response to variable streamwise spacing,$h$ , and spanwise spacing,$\delta _1$ , between adjacent trees. The response to spanwise and streamwise heterogeneity has, indeed, been the topic of a sustained research effort: the former resulting in formation of Reynoldsaveraged counterrotating secondary cells, the latter associated with the$\delta _2$  and$k$ type response. No study has addressed the confluence of both, and results herein show secondary flow polarity reversal across ‘critical’ values of$d$ and$\delta _1$ . For$\delta _2$ and$\delta _2/\delta \lesssim 1$ , where$\gtrsim 2$ is the flow depth, the counterrotating secondary cells are aligned such that upwelling and downwelling, respectively, occurs above the elements. The streamwise spacing$\delta$ regulates this transition, with secondary cell reversal occurring first for the largest$\delta _1$ type cases, as elevated turbulence production within the canopy necessitates entrainment of fluid from aloft. The results are interpreted through the lens of a benchmark prognostic closure for effective aerodynamic roughness,$k$ , where$z_{0,{Eff.}} = \alpha \sigma _h$ is a proportionality constant and$\alpha$ is height root mean square. We report$\sigma _h$ , the value reported over many decades for a broad range of rough surfaces, for$\alpha \approx 10^{1}$ type cases at small$k$ , whereas the transition to$\delta _2$ type arrangements necessitates larger$d$ . Though preliminary, results highlight the nontrivial response to variation of streamwise and spanwise spacing.$\delta _2$ 
Abstract We study the locations of complex zeroes of independence polynomials of boundeddegree hypergraphs. For graphs, this is a longstudied subject with applications to statistical physics, algorithms, and combinatorics. Results on zerofree regions for boundeddegree graphs include Shearer’s result on the optimal zerofree disc, along with several recent results on other zerofree regions. Much less is known for hypergraphs. We make some steps towards an understanding of zerofree regions for boundeddegree hypergaphs by proving that all hypergraphs of maximum degree
have a zerofree disc almost as large as the optimal disc for graphs of maximum degree$\Delta$ established by Shearer (of radius$\Delta$ ). Up to logarithmic factors in$\sim 1/(e \Delta )$ this is optimal, even for hypergraphs with all edge sizes strictly greater than$\Delta$ . We conjecture that for$2$ ,$k\ge 3$ uniform$k$ linear hypergraphs have a much larger zerofree disc of radius . We establish this in the case of linear hypertrees.$\Omega (\Delta ^{ \frac{1}{k1}} )$ 
Abstract This paper will study almost everywhere behaviors of functions on partition spaces of cardinals possessing suitable partition properties. Almost everywhere continuity and monotonicity properties for functions on partition spaces will be established. These results will be applied to distinguish the cardinality of certain subsets of the power set of partition cardinals.
The following summarizes the main results proved under suitable partition hypotheses.
If
is a cardinal,$\kappa $ ,$\epsilon < \kappa $ ,${\mathrm {cof}}(\epsilon ) = \omega $ and$\kappa \rightarrow _* (\kappa )^{\epsilon \cdot \epsilon }_2$ , then$\Phi : [\kappa ]^\epsilon _* \rightarrow \mathrm {ON}$ satisfies the almost everywhere short length continuity property: There is a club$\Phi $ and a$C \subseteq \kappa $ so that for all$\delta < \epsilon $ , if$f,g \in [C]^\epsilon _*$ and$f \upharpoonright \delta = g \upharpoonright \delta $ , then$\sup (f) = \sup (g)$ .$\Phi (f) = \Phi (g)$ If
is a cardinal,$\kappa $ is countable,$\epsilon $ holds and$\kappa \rightarrow _* (\kappa )^{\epsilon \cdot \epsilon }_2$ , then$\Phi : [\kappa ]^\epsilon _* \rightarrow \mathrm {ON}$ satisfies the strong almost everywhere short length continuity property: There is a club$\Phi $ and finitely many ordinals$C \subseteq \kappa $ so that for all$\delta _0, ..., \delta _k \leq \epsilon $ , if for all$f,g \in [C]^\epsilon _*$ ,$0 \leq i \leq k$ , then$\sup (f \upharpoonright \delta _i) = \sup (g \upharpoonright \delta _i)$ .$\Phi (f) = \Phi (g)$ If
satisfies$\kappa $ ,$\kappa \rightarrow _* (\kappa )^\kappa _2$ and$\epsilon \leq \kappa $ , then$\Phi : [\kappa ]^\epsilon _* \rightarrow \mathrm {ON}$ satisfies the almost everywhere monotonicity property: There is a club$\Phi $ so that for all$C \subseteq \kappa $ , if for all$f,g \in [C]^\epsilon _*$ ,$\alpha < \epsilon $ , then$f(\alpha ) \leq g(\alpha )$ .$\Phi (f) \leq \Phi (g)$ Suppose dependent choice (
),$\mathsf {DC}$ and the almost everywhere short length club uniformization principle for${\omega _1} \rightarrow _* ({\omega _1})^{\omega _1}_2$ hold. Then every function${\omega _1}$ satisfies a finite continuity property with respect to closure points: Let$\Phi : [{\omega _1}]^{\omega _1}_* \rightarrow {\omega _1}$ be the club of$\mathfrak {C}_f$ so that$\alpha < {\omega _1}$ . There is a club$\sup (f \upharpoonright \alpha ) = \alpha $ and finitely many functions$C \subseteq {\omega _1}$ so that for all$\Upsilon _0, ..., \Upsilon _{n  1} : [C]^{\omega _1}_* \rightarrow {\omega _1}$ , for all$f \in [C]^{\omega _1}_*$ , if$g \in [C]^{\omega _1}_*$ and for all$\mathfrak {C}_g = \mathfrak {C}_f$ ,$i < n$ , then$\sup (g \upharpoonright \Upsilon _i(f)) = \sup (f \upharpoonright \Upsilon _i(f))$ .$\Phi (g) = \Phi (f)$ Suppose
satisfies$\kappa $ for all$\kappa \rightarrow _* (\kappa )^\epsilon _2$ . For all$\epsilon < \kappa $ ,$\chi < \kappa $ does not inject into$[\kappa ]^{<\kappa }$ , the class of${}^\chi \mathrm {ON}$ length sequences of ordinals, and therefore,$\chi $ . As a consequence, under the axiom of determinacy$[\kappa ]^\chi  < [\kappa ]^{<\kappa }$ , these two cardinality results hold when$(\mathsf {AD})$ is one of the following weak or strong partition cardinals of determinacy:$\kappa $ ,${\omega _1}$ ,$\omega _2$ (for all$\boldsymbol {\delta }_n^1$ ) and$1 \leq n < \omega $ (assuming in addition$\boldsymbol {\delta }^2_1$ ).$\mathsf {DC}_{\mathbb {R}}$ 
Abstract For a subgraph
of the blowup of a graph$G$ , we let$F$ be the smallest minimum degree over all of the bipartite subgraphs of$\delta ^*(G)$ induced by pairs of parts that correspond to edges of$G$ . Johansson proved that if$F$ is a spanning subgraph of the blowup of$G$ with parts of size$C_3$ and$n$ , then$\delta ^*(G) \ge \frac{2}{3}n + \sqrt{n}$ contains$G$ vertex disjoint triangles, and presented the following conjecture of Häggkvist. If$n$ is a spanning subgraph of the blowup of$G$ with parts of size$C_k$ and$n$ , then$\delta ^*(G) \ge \left(1 + \frac 1k\right)\frac n2 + 1$ contains$G$ vertex disjoint copies of$n$ such that each$C_k$ intersects each of the$C_k$ parts exactly once. A similar conjecture was also made by Fischer and the case$k$ was proved for large$k=3$ by Magyar and Martin.$n$ In this paper, we prove the conjecture of Häggkvist asymptotically. We also pose a conjecture which generalises this result by allowing the minimum degree conditions in each bipartite subgraph induced by pairs of parts of
to vary. We support this new conjecture by proving the triangle case. This result generalises Johannson’s result asymptotically.$G$ 
We study the spaces of twisted conformal blocks attached to a
curve$\Gamma$ with marked$\Sigma$ orbits and an action of$\Gamma$ on a simple Lie algebra$\Gamma$ , where$\mathfrak {g}$ is a finite group. We prove that if$\Gamma$ stabilizes a Borel subalgebra of$\Gamma$ , then the propagation theorem and factorization theorem hold. We endow a flat projective connection on the sheaf of twisted conformal blocks attached to a smooth family of pointed$\mathfrak {g}$ curves; in particular, it is locally free. We also prove that the sheaf of twisted conformal blocks on the stable compactification of Hurwitz stack is locally free. Let$\Gamma$ be the parahoric Bruhat–Tits group scheme on the quotient curve$\mathscr {G}$ obtained via the$\Sigma /\Gamma$ invariance of Weil restriction associated to$\Gamma$ and the simply connected simple algebraic group$\Sigma$ with Lie algebra$G$ . We prove that the space of twisted conformal blocks can be identified with the space of generalized theta functions on the moduli stack of quasiparabolic$\mathfrak {g}$ torsors on$\mathscr {G}$ when the level$\Sigma /\Gamma$ is divisible by$c$ (establishing a conjecture due to Pappas and Rapoport).$\Gamma $