The Berlin axisymmetric boundary layer facility

An account is given of the working life of the recently decommissioned axisymmetric turbulent-boundary-layer windtunnel in the Hermann-Föttinger-Institut of the Technische Universität Berlin, and some principal investigations conducted in it.     

Uniqueness of positive solutions of a class of quasilinear ordinary differential equations

Abstract. Uniqueness results are obtained for positive solutions of a class of quasilinear ordi-nary differential equations. The methods rely on the energy analysis and a scale argument.     

LOWER BOUNDS ON THE MAXIMUM GENUS OF LOOPLESS MULTIGRAPHS

§ 1　IntroductionThe maximum genusγM(G) of a graph G is the maximum among the genera,which Ghas a cellularembedding on a sphere with k handles.Since any embedding of G has atleastone face,by Euler polyhedral equation,itcan be obtained thatγM(G)≤β(G) / 2 ,whereβ(G) is the Betti number of G.A graph G is called up-embeddable ifγM(G) =β(G) / 2 .[1 ] has showed that thereare atleasttwo edge-disjointspanning trees in G if G is 4 -edge connected.Let T be a span-ning tree of G.An odd …     

A semi-analytical approach to Biot instability in a growing layer: Strain gradient correction,weakly non-linear analysis and imperfection sensitivity

Many experimental works have recently investigated the dynamics of crease formation during the swelling of long soft slabs attached to a rigid substrate. Mechanically, the spatially constrained growth provokes a residual strain distribution inside the material, and therefore the problem is equivalent to the uniaxial compression of an elastic layer.The aim of this work is to propose a semi-analytical approach to study the non-linear buckling behaviour of a growing soft layer. We consider the presence of a microstructural length, which describes the effect of a simple strain gradient correction in the growing hyperelastic layer, considered as a neo-Hookean material. By introducing a non-linear stream function for enforcing exactly the incompressibility constraint, we develop a variational formulation for performing a stability analysis of the basic homogeneous solution. At the linear order, we derive the corresponding dispersion relation, proving that even a small strain gradient effect allows the system to select a critical dimensionless wavenumber while giving a small correction to the Biot instability threshold. A weakly non-linear analysis is then performed by applying a multiple-scale expansion to the neutrally stable mode. By applying the global conservation of the mechanical energy, we derive the Ginzburg–Landau equation for the critical single mode, identifying a pitchfork bifurcation. Since the bifurcation is found to be subcritical for a small ratio between the microstructural length and the layer׳s thickness, we finally perform a sensitivity analysis to study the effect of the initial presence of a sinusoidal imperfection on the free surface of the layer. In this case, the incremental solution for the stream function is written as a Fourier series, so that the surface imperfection can have a cubic resonance with the linear modes. The solutions indicate the presence of a turning point close to the critical threshold for the perfect system. We also find that the inclusion of higher modes has a steepening effect on the surface profile, indicating the incipient formation of an elastic singularity, possibly a crease.     

Comparison of the texture functions describing the grain alignment in NdFeB magnets

Two types of Gaussian distribution function (`θ type’ and `tan θ type') describing the degree of grain alignment in sintered NdFeB magnets have been compared in the distribution coefficient σ (or σ_g), the distribution probability P(θ) and the grain alignment dependence of coercivity. The results show that when the grain alignment is good (the ratio of remanence-to-saturation polarization J_r/J_s⩾0.90), σ(σ_g) and P(θ) for the two types of Gaussian functions have similar variation tendencies, the calculated values of normalized coercivity based on the starting field theory are basically the same and are consistent with experiments. When the grain alignment is not good (J_r/J_s⩾0.80), the variation tendencies of σ and P(θ) are different. In addition, according to `tan θ type’ Gaussian function, the theoretical values of the normalized coercivity based on the starting field theory are still consistent with the experiments, but according to `θ type’ Gaussian function, the theoretical values seriously deviate from the experiments. This means that the `tan θ type’ Gaussian function is a better texture function for describing the grain alignment.     

一类m-点边值问题的正解

§ 1　 IntroductionIn[1 ] ,Karakostas and Tsamatos studied the existence of positive solutions for two-pointboundary value problemx″+ sign( 1 -c) q( t) f( x,x′) x′=0 ,( 1 .1 )x( 0 ) =0 ,x′( 1 ) =cx′( 0 ) ,( 1 .2 )where c∈ ( 0 ,1 )∪ ( 1 ,∞ ) .By using indices ofconvergence ofthe nonlinearity at0 and +∞and fixed point theorem in cones,they provided a priori upper and lower bounds for theslope of the solutions.The“c∈ ( 0 ,1 ) part”of their results has been extended to the fol-lowing …     

Synthesis and electrical transport properties of Lu2+xTi2−xO7−x/2 oxide-ion conductors

The Lu_2+xTi_2−xO_7−x/2 (x = 0; 0.052; 0.096; 0.286; 0.44; 0.63; 33.3–49 mol% Lu₂O₃) nanoceramics with partly disordered pyrochlore-type structure are prepared by sintering freeze-dried powders obtained by a co-precipitation technique with 1600 °C annealing. Similar to pyrochlore-like compositions in the zirconate system, some of the new titanates are good oxide-ion conductors in air. The new solid-state electrolytes have oxide-ion conductivity in the interval of 1.0 × 10^− 3 – 2.5 × 10^− 3 S/cm at 740 °C in air. This value of conductivity is comparable with that of ZrO₂/Y₂O₃ ceramics. The conductivity of Lu_2+xTi_2−xO_7−x/2 depends on the chemical composition. The highest ionic conductivity is exhibited by nearly stoichiometric Lu_2+xTi_2−xO_7−x/2 (x = 0.096; 35.5 mol% Lu₂O₃) material containing ∼ 4.8 at.% Lu_Ti anti-site defects.