Measurements of the tip leakage vortex structures and turbulence in the meridional plane of an axial water-jet pump

Particle image velocimetry (PIV) measurements at varying resolutions focus on the flow structures in the tip region of a water-jet pump rotor, including the tip-clearance flow and the rollup process of a tip leakage vortex (TLV). Unobstructed views of these regions are facilitated by matching the optical refractive index of the transparent pump with that of the fluid. High-magnification data reveal the flow non-uniformities and associated turbulence within the tip gap. Instantaneous data and statistics of spatial distributions and strength of vortices in the rotor passage reveal that the leakage flow emerges as a wall jet with a shear layer containing a train of vortex filaments extending from the tip of the blade. These vortices are entrained into the TLV, but do not have time to merge. TLV breakdown in the aft part of the blade passage further fragments these structures, increasing their number and reducing their size. Analogy is made between the circumferential development of the TLV in the blade passage and that of the starting jet vortex ring rollup. Subject to several assumptions, these flows display similar trends, including conditions for TLV separation from the shear layer feeding vorticity into it.     

An algebraic slice in the coadjoint space of the Borel and the Coxeter element

Let g be a complex simple Lie algebra and b a Borel subalgebra. The algebra Y of polynomial semi-invariants on the dual b^? of b is a polynomial algebra on rank g generators (Grothendieck and Dieudonné (1965–1967)) [16]. The analogy with the semisimple case suggests there exists an algebraic slice to coadjoint action, that is an affine translate y+V of a vector subspace of b^? such that the restriction map induces an isomorphism of Y onto the algebra R[y+V] of regular functions on y+V. This holds in type A and even extends to all biparabolic subalgebras (Joseph (2007)) [20]; but the construction fails in general even with respect to the Borel. Moreover already in type C(2) no algebraic slice exists.Very surprisingly the exception of type C(2) is itself an exception. Indeed an algebraic slice for the coadjoint action of the Borel subalgebra is constructed for all simple Lie algebras except those of types B(2m), C(n) and F(4).Outside type A, the slice obtained meets an open dense subset of regular orbits, even though the special point y of the slice is not itself regular. This explains the failure of our previous construction.     

An extension of Alexandrov?s theorem on second derivatives of convex functions

If f is a function of n variables that is locally L¹ approximable by a sequence of smooth functions satisfying local L¹ bounds on the determinants of the minors of the Hessian, then f admits a second order Taylor expansion almost everywhere. This extends a classical theorem of A.D. Alexandrov, covering the special case in which f is locally convex.     

Finite groups with all subgroups not contained in the Frattini subgroup permutable

Let G be a finite group. A subgroup H of G is a permutable subgroup of G if HK = KH for all subgroups K of G. It will be shown that if all subgroups not contained in the Frattini subgroup are permutable in a group G, then all subgroups are permutable in G.     

Asymptotes in SU(2) Recoupling Theory: Wigner Matrices, 3j Symbols, and Character Localization

In this paper, we employ a technique combining the Euler Maclaurin formula with the saddle point approximation method to obtain the asymptotic behavior (in the limit of large representation index J) of generic Wigner matrix elements D^J_MM￠(g){D^{J}_{MM'}(g)} . We use this result to derive asymptotic formulae for the character χ ^J (g) of an SU(2) group element and for Wigner’s 3j symbol. Surprisingly, given that we perform five successive layers of approximations, the asymptotic formula we obtain for χ ^J (g) is in fact exact. The result hints at a “Duistermaat-Heckman like” localization property for discrete sums.     

On the harmonic continued fractions

The Ramanujan Journal - In this paper, we study the harmonic continued fractions. These form an infinite family of ordinary continued fractions with coefficients $$\frac{t}{1}, \frac{t}{2},...     

Connecting mem-models with classical theories

A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histories (e.g., hysteresis). Under the framework of nonlinear state-space representation and hybrid dynamical systems, mem-springs may be formulated to effectively represent an inherent degradation of material state. It is shown in this study, for the first time, how the absement (time integral of strain/displacement), a signature state variable for a mem-spring, can be connected with the damage variable, a key quantity in continuum damage mechanics. The generalized momentum (time integral of stress), on the other hand, is shown to be efficient in modeling strain ratcheting via the concept of mem-dashpot. It is also shown in this study, for the first time, how two formulations of the memcapacitive system models (for mem-springs) are special cases of the Preisach model.

     

Zanthoxylum Species: A Comprehensive Review of Traditional Uses,Phytochemistry, Pharmacological and Nutraceutical Applications

Zanthoxylum species (Syn. Fagara species) of the Rutaceae family are widely used in many countries as food and in trado-medicinal practice due to their wide geographical distribution and medicinal properties. Peer reviewed journal articles and ethnobotanical records that reported the traditional knowledge, phytoconstituents, biological activities and toxicological profiles of Z. species with a focus on metabolic and neuronal health were reviewed. It was observed that many of the plant species are used as food ingredients and in treating inflammation, pain, hypertension and brain diseases. Over 500 compounds have been isolated from Z. species, and the biological activities of both the plant extracts and their phytoconstituents, including their mechanisms of action, are discussed. The phytochemicals responsible for the biological activities of some of the species are yet to be identified. Similarly, biological activities of some isolated compounds remain unknown. Taken together, the Z. species extracts and compounds possess promising biological activities and should be further explored as potential sources of new nutraceuticals and drugs.     

The triplet spectrum of tetramethyl-1,3-cyclobutanedione

The low-temperature single-crystal spectrum of TMCBD has revealed a low-lying triplet state at 25 718 cm^-1 (72·5 kcal/mol). The observed band is ascribed to a ³ A_u (³ A ₂) ← ¹ A_g nπ* transition on the basis of its small singlet-triplet splitting, its polarization behaviour, and its vibrational structure. The ³ A_u state is first-order spin-orbit coupled to either or both of the ¹ B _2u or ¹ B _3u states. No evidence for two or more nπ* transitions was found. Several multi-membered progressions in the carbonyl wagging mode indicate the presence of a distorted excited state, in which the carbonyl carbons attain a pyramidal conformation. Analysis of the site symmetry shows that TMCBD is distorted to a boat-shaped C _2v structure in its triplet nπ* state.