Flow-induced noise of a wall-mounted finite airfoil at low-to-moderate Reynolds number

This paper presents an experimental investigation of the flow-induced noise created by a wall-mounted finite airfoil at low-to-moderate Reynolds number and zero angle of attack. Far-field noise measurements have been taken at a single observer location and with two perpendicular microphone arrays in an anechoic wind tunnel at Reynolds numbers of _Rec=9.2×10⁴–1.6×10⁵${\mathit{Re}}_c=9.2\times {10}^4–1.6\times {10}^5$, based on chord, and for a variety of airfoil aspect ratios (length to chord ratio of L/C=0.2–2$L/C=0.2–2$, corresponding to length to thickness ratio of L/T=1.7–16.7$L/T=1.7–16.7$). Additionally, surface oil-film visualisation images and unsteady velocity measurements taken in the near trailing edge wake are related to far-field noise measurements to determine the flow mechanisms responsible for noise generation. The results show that the wall-mounted finite airfoil radiates noise similar to a two-dimensional airfoil when L/T>8.3$L/T>8.3$. Despite the incoming boundary layer height at the junction being 1.30≤δ/T≤1.46$1.30\le \delta /T\le 1.46$, junction and tip flow suppresses tonal noise production for airfoil?s up to L/T=8.3$L/T=8.3$ at _Rec=9.2×10⁴–1.2×10⁵${\mathit{Re}}_c=9.2\times {10}^4–1.2\times {10}^5$. Trailing edge noise is found to be the dominant airfoil noise generation mechanism at frequencies above 1 kHz with the position of the noise source along the trailing edge determined by the proportion of the airfoil span influenced by flow at the airfoil–wall junction.     

Low temperature properties of the Fermi–Dirac,Boltzmann and Bose–Einstein equations

We investigate low temperature (T  ) properties of three classical quantum statistics models: (I) the Fermi–Dirac equation, (II) the Boltzmann equation, and (III) the Bose–Einstein equation. It is widely assumed that each of these equations is valid for all T>0$T>0$. For each equation we prove that this assumption leads to erroneous predictions as T→0⁺$T\to 0^{+}$. Our approach to correct these errors gives new low temperature predictions which contradict previous theory. We examine a two-state paramagnetism system and show how our new low temperature prediction compares favorably with experimental data.     

On the theory of the dynamical properties of nematics

The Leslie–Ericksen coefficients of a thermotropic nematic are determined by using an approximate solution of the Fokker–Planck equation for the one-particle distribution function over orientations of the nematic molecules. The results show that the well-known Doi–Edwards theory of the dynamical properties of nematics leads to a qualitatively wrong result for the Leslie angle. The “isotropic medium - nematic” (I–N$I–N$) transition induced by the shear flow is considered. When the temperature decreases, the I–N$I–N$ transition in the shear flowing system takes place at the temperature _T1$T_1$ higher than the temperature _Tc$T_c$ of the equilibrium transition in the motionless system. The interface boundary in this case is parallel to the plane formed by the flow velocity and its gradient. When the shear flowing nematic phase is heated, the N–I$N–I$ transition occurs at another temperature _T2$T_2$, and the following inequalities _T1>_T2>_Tc$T_1>T_2>T_c$ hold. In this case the boundary between the isotropic and nematic phases is perpendicular to the flow velocity. Thus, unlike the equilibrium phase transition, a temperature hysteresis of the phase transition is expected.     

Some remarks on special Kähler geometry

Given a special Kähler manifold M$M$, we give a new, direct proof of the relationship between the quaternionic structure on T^∗M$T^{\ast }M$ and the variation of Hodge structures on T^CM$T^{\mathbb{C}}M$.     

Computational analysis of non-isothermal temperature distribution on natural convection in nanofluid filled enclosures

In this study, the problem of steady state natural convection in an enclosure filled with a nanofluid has been analyzed numerically by using heating and cooling by sinusoidal temperature profiles on one side. The governing partial differential equations, in terms of the dimensionless stream function–vorticity and temperature, are solved numerically using the finite volume method for various inclination angles 0^°≤?≤90^°$0^{°}\le ?\le 90^{°}$, different types of nanoparticles (TiO₂ and Al₂O₃) and fractions of nanoparticles 0≤φ≤0.1$0\le \phi \le 0.1$, whereas the range of the Rayleigh number Ra is 10³–10⁵. It is found that the addition of nanoparticles into water affects the fluid flow and temperature distribution especially for higher Rayleigh numbers. An enhancement in heat transfer rate was registered for the whole range of Rayleigh numbers. However, low Rayleigh numbers show more enhancement compared to high Rayleigh numbers.     

Half-monopole in the Weinberg–Salam model

We present new axially symmetric half-monopole configuration of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. The half-monopole configuration possesses net magnetic charge 2π/e$2\pi /e$ which is half the magnetic charge of a Cho–Maison monopole. The electromagnetic gauge potential is singular along the negative z$z$-axis. However the total energy is finite and increases only logarithmically with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$. In the U(1) magnetic field, the half-monopole is just a one dimensional finite length line magnetic charge extending from the origin r=0$r=0$ and lying along the negative z$z$-axis. In the SU(2) ’t Hooft magnetic field, it is a point magnetic charge located at r=0$r=0$. The half-monopole possesses magnetic dipole moment that decreases exponentially fast with increasing Higgs field self-coupling constant λ^1/2${\lambda }^{1/2}$ at sin²θ_W=0.2312${sin}^2{\theta }_W=0.2312$.     

A noncommutative view on topology and order

In this paper we put forward the definition of particular subsets on a unital C^∗$C^{\ast }$-algebra, that we call isocones, and which reduce in the commutative case to the set of continuous non-decreasing functions with real values for a partial order relation defined on the spectrum of the algebra, which satisfies a compatibility condition with the topology (complete separateness). We prove that this space/algebra correspondence is a dual equivalence of categories, which generalizes the Gelfand–Naimark duality. Thus we can expect that general isocones could serve to define a notion of “noncommutative ordered spaces”. We also explore some basic algebraic constructions involving isocones, and classify those which are defined in _M2(C)$M_2\left(\mathbb{C}\right)$.     

Berezinskii–Kosterlitz–Thouless transition close to the percolation threshold

We use Monte Carlo to investigate the Berezinskii–Kosterlitz–Thouless transition close to the site percolation threshold in a square lattice. Several thermodynamic quantities are calculated for lattice sizes L×L$L\times L$, from 16<L<640$16<L<640$. Our results are consistent with an infinite order transition for any value of the concentration of magnetic sites. We found that close to the critical percolation concentration, _pc$p_c$ (0.592746), the Berezinskii–Kosterlitz–Thouless transition temperature goes to zero as _TBKT∝(p−_pc)^0.908$T_{\mathit{BKT}}\propto {(p-p_c)}^{0.908}$ and the specific heat behaves as _Tsh∝p^1.133$T_{sh}\propto p^{1.133}$.