Aerodynamics of thrust vectoring

Thrust vectoring as a means to enhance maneuverability and aerodynamic performane of a tactical aircraft is discussed. This concept usually involves the installation of a multifunction nozzle. With the nozzle, the engine thrust can be changed in direction without changing the attitude of the aircraft. Change in the direction of thrust induces a significant change in the aerodynamic forces on the aircraft. Therefore, this device can be used for lift-augmenting as well as stability and control purposes. When the thrust is deflected in the longitudinal direction, the lift force and the pitching stability can be manipulated, while the yawing stability can be controlled by directing the thrust in the lateral direction

Calculation of aerodynamic characteristics of airplane configurations at high angles of attack

Calculation of longitudinal and lateral directional aerodynamic characteristics of airplanes by the VORSTAB code is examined. The numerical predictions are based on the potential flow theory with corrections of high angle of attack phenomena; namely, vortex flow and boundary layer separation effects. To account for the vortex flow effect, vortex lift, vortex action point, augmented vortex lift and vortex breakdown effect through the method of suction analogy are included. The effect of boundary layer separation is obtained by matching the nonlinear section data with the three dimensional lift characteristics iteratively. Through correlation with results for nine fighter configurations, it is concluded that reasonably accurate prediction of longitudinal and static lateral directional aerodynamics can be obtained with the VORSTAB code up to an angle of attack at which wake interference and forebody vortex effect are not important. Possible reasons for discrepancy at higher angles of attack are discussed

Calculation of aerodynamic characteristics at high angles of attack for airplane configurations

The primary objective is to determine how an airplane configuration should be modeled to predict both longitudinal and lateral aerodynamic characteristics at high angles of attack. A generic fighter model, an F-16 and an F-18 configuration with leading edge flap deflection and an F-106B configuration were investigated. Furthermore, the F-16XL and X-29 configurations were examined. Some calculated results are given

Orbifold cup products and ring structures on Hochschild cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology

Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists

This is the author accepted manuscript. The final version is available from Polskiej Akademii Nauk, Instytut Matematyczny via the DOI in this record.We show that the set of numbers with bounded L uroth expansions (or bounded L uroth series) is winning and strong winning. From either winning property, it immediately follows that the set is dense, has full Hausdor dimension, and satis es a countable intersection property. Our result matches the well-known analogous result for bounded continued fraction expansions or, equivalently, badly approximable numbers. We note that L uroth expansions have a countably in nite Markov partition, which leads to the notion of in nite distortion (in the sense of Markov partitions)

Mobile Paving System (MPS): A New Large Scale Freeform Fabrication Method

In the last decade, significant opportunities for automation have been identified in the area of construction. Soaring labor and material costs have driven multiple research efforts in construction automation. In this paper, we present a novel means for construction automation that involves the fusion of the rapid prototyping, controls and mechatronics technologies. The resultant autonomous construction mechanism has been designed for commercial applications. Mobile Paving System (MPS) is a new freeform fabrication process which is capable of rapidly producing variable profiles such as curbs and sidewalks out of materials like cement and asphalt. Path generation and guidance of the construction operation is controlled by a mobile robot. This article presents an overview of research and development efforts that are aimed at establishing the feasibility and the potential of the process.Mechanical Engineerin

Neutron spin-echo study of the critical dynamics of spin-5/2 antiferromagnets in two and three dimensions

We report a neutron spin-echo study of the critical dynamics in the $S=5/2$ antiferromagnets MnF$_2$ and Rb$_2$MnF$_4$ with three-dimensional (3D) and two-dimensional (2D) spin systems, respectively, in zero external field. Both compounds are Heisenberg antiferromagnets with a small uniaxial anisotropy resulting from dipolar spin-spin interactions, which leads to a crossover in the critical dynamics close to the N\'eel temperature, $T_N$. By taking advantage of the $\mu\text{eV}$ energy resolution of the spin-echo spectrometer, we have determined the dynamical critical exponents $z$ for both longitudinal and transverse fluctuations. In MnF$_2$, both the characteristic temperature for crossover from 3D Heisenberg to 3D Ising behavior and the exponents $z$ in both regimes are consistent with predictions from the dynamical scaling theory. The amplitude ratio of longitudinal and transverse fluctuations also agrees with predictions. In Rb$_2$MnF$_4$, the critical dynamics crosses over from the expected 2D Heisenberg behavior for $T\gg T_N$ to a scaling regime with exponent $z = 1.387(4)$, which has not been predicted by theory and may indicate the influence of long-range dipolar interactions

Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Shadow Cones: Unveiling Partial Orders in Hyperbolic Space

Hyperbolic space has been shown to produce superior low-dimensional embeddings of hierarchical structures that are unattainable in Euclidean space. Building upon this, the entailment cone formulation of Ganea et al. uses geodesically convex cones to embed partial orderings in hyperbolic space. However, these entailment cones lack intuitive interpretations due to their definitions via complex concepts such as tangent vectors and the exponential map in Riemannian space. In this paper, we present shadow cones, an innovative framework that provides a physically intuitive interpretation for defining partial orders on general manifolds. This is achieved through the use of metaphoric light sources and object shadows, inspired by the sun-earth-moon relationship. Shadow cones consist of two primary classes: umbral and penumbral cones. Our results indicate that shadow cones offer robust representation and generalization capabilities across a variety of datasets, such as WordNet and ConceptNet, thereby outperforming the top-performing entailment cones. Our findings indicate that shadow cones offer an innovative, general approach to geometrically encode partial orders, enabling better representation and analysis of datasets with hierarchical structures

Coneheads: Hierarchy Aware Attention

Attention networks such as transformers have achieved state-of-the-art performance in many domains. These networks rely heavily on the dot product attention operator, which computes the similarity between two points by taking their inner product. However, the inner product does not explicitly model the complex structural properties of real world datasets, such as hierarchies between data points. To remedy this, we introduce cone attention, a drop-in replacement for dot product attention based on hyperbolic entailment cones. Cone attention associates two points by the depth of their lowest common ancestor in a hierarchy defined by hyperbolic cones, which intuitively measures the divergence of two points and gives a hierarchy aware similarity score. We test cone attention on a wide variety of models and tasks and show that it improves task-level performance over dot product attention and other baselines, and is able to match dot-product attention with significantly fewer parameters. Our results suggest that cone attention is an effective way to capture hierarchical relationships when calculating attention