Optical guidelines and signal quality for LDA applications in circular pipes

The optical performance of laser Doppler anemometer (LDA) technology in applications to circular pipes with an external plane wall has been clarified and quantified. It is shown that optical aberration is a persistent feature in such LDA measurements and measurements from each direction along a full pipe diameter are needed to obtain the flow distribution. For measurements of axial velocities in a circular pipe no special care has to be taken, even if the optical plane deviates from the pipe axis. For measurements of tangential and radial velocities detailed operating guidelines have been presented with respect to the shift of the measurement volume, its optical properties and the beam waist dislocations. The analysis reveals the possible influences on both the signal quality and the measurement accurac

Dissipation function of the first-order phase transformation in VO2 ceramics by internal-friction measurements

In order to apply the concept of the dissipation function during the first-order phase transition (FOPT) in solids, we measured the internal friction Q-1 and shear modulus μ for a range of frequencies of polycrystalline ceramics VO2 as the sample passed through a FOPT across the temperature range of 300–420 K. The experiment was repeated for different temperature variation rate Ṫ. We have found that for each frequency, a maximum of Q-1 and a minimum of μ occurred at the same temperature Tp when Ṫ was kept constant. The numerical values of the dissipation function ΔGR plus other FOPT parameters have been deduced using Q-1 data. The general trend of ΔGR-T and other results are found to be consistent with known physical aspects.published_or_final_versio

Giant radiation heat transfer through the micron gaps

Near-field heat transfer between two closely spaced radiating media can exceed in orders radiation through the interface of a single black body. This effect is caused by exponentially decaying (evanescent) waves which form the photon tunnel between two transparent boundaries. However, in the mid-infrared range it holds when the gap between two media is as small as few tens of nanometers. We propose a new paradigm of the radiation heat transfer which makes possible the strong photon tunneling for micron thick gaps. For it the air gap between two media should be modified, so that evanescent waves are transformed inside it into propagating ones. This modification is achievable using a metamaterial so that the direct thermal conductance through the metamaterial is practically absent and the photovoltaic conversion of the transferred heat is not altered by the metamaterial.Comment: 4 pages, 3 figure

Novel critical point drying (CPD) based preparation and transmission electron microscopy (TEM) imaging of protein specific molecularly imprinted polymers (HydroMIPs)

We report the transmission electron microscopy (TEM) imaging of a hydrogel-based molecularly imprinted polymer (HydroMIP) specific to the template molecule bovine haemoglobin (BHb). A novel critical point drying based sample preparation technique was employed to prepare the molecularly imprinted polymer (MIP) samples in a manner that would facilitate the use of TEM to image the imprinted cavities, and provide an appropriate degree of both magnification and resolution to image polymer architecture in the <10 nm range. For the first time, polymer structure has been detailed that clearly displays molecularly imprinted cavities, ranging from 5-50 nm in size, that correlate (in terms of size) with the protein molecule employed as the imprinting template. The modified critical point drying sample preparation technique used may potentially play a key role in the imaging of all molecularly imprinted polymers, particularly those prepared in the aqueous phase

Master equation, design equations and runaway speed of the Kaplan turbine

To make the Kaplan turbine technology comparable to both the Pelton and the Francis turbine, the master equation for the Kaplan turbine has been established by analyses similar to that for the Francis turbine. The analysis begins with the descriptions of free vortex flows at the runner inlet and the swirl flow at the impeller exit. By considering the Euler equation for specific work and by further evaluating the most significant shock and swirling losses, the first and the second energy equations in the form of hydraulic efficiency were formulated. The master equation is then established by combining both energy equations. In addition, three design equations and a new design parameter are presented. The master equation relates the turbine hydromechanics to the geometrical design of both the runner and the guide-vane parameters. It enables the complete hydraulic characteristics of a given Kaplan turbine to be analytically and simply computed. A computation example demonstrates the functionality and applicability of the method. With the reconstructed master equation, the runaway speed of the Kaplan turbine and its dependence on the guide-vane setting can be easily and precisely computed. For bulb turbines with guide vanes directly ahead of the turbine runner in the same tube, all computations are also applicable using another equivalent control parameter

DNS of a diffusional jet flame in turbulent cross-flow using a low Mach number solver

Understanding of flame anchoring in a jet in crossflow (JICF) configuration is vital to the design of fuel injectors in combustion devices. The present study numerically investigates a hydrogen rich jet injecting perpendicularly into hot vitiated crossflow using direct numerical simulation (DNS). Development of the reacting flow field and flame shape along the jet trajectory is scrutinised. The flame is found to be anchored around the jet exit, and downstream only on the windward side. Heat release rate and Chemical Explosive Mode Analysis (CEMA) are used to identify combustion modes. Distinct from flames stabilizing in non-vitiated crossflow where combustion is mainly partially premixed, diffusion flame is significant under the current condition, though some premixed or partially premixed regions are found on the leeward side of the jet due to large scale turbulent mixing

Bifurcation curves of subharmonic solutions

We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves from the nonexistence to the existence of subharmonic solutions. In particular our results apply also when one has degeneracy to first order -- i.e. when the subharmonic Melnikov function vanishes identically. Moreover we can deal as well with the case in which degeneracy persists to arbitrarily high orders, in the sense that suitable generalisations to higher orders of the subharmonic Melnikov function are also identically zero. In general the bifurcation curves are not analytic, and even when they are smooth they can form cusps at the origin: we say in this case that the curves are degenerate as the corresponding tangent lines coincide. The technique we use is completely different from that of Chow and Hale, and it is essentially based on rigorous perturbation theory.Comment: 29 pages, 2 figure

Geometric properties and continuity of the pre-duality mapping in Banach space

We use the preduality mapping in proving characterizations of some geometric properties of Banach spaces. In particular, those include nearly strongly convexity, nearly uniform convexity-a property introduced by K. Goebel and T. Sekowski-, and nearly very convexity.We thank a referee for the careful reading of the manuscript. His/her observations substantially improved the overall aspect of the present work, detected several misprints and made some convenient changes. This work was supported by: (1) The National Natural Science Foundation of China (Grant no. 11271248). (2) Specific Academic Discipline Project of Shanghai Municipal Education Commission (Grant no. B-8932-13-0136). (3) Project MTM2011-22417, Ministerio de Ciencia e Innovacion, Spain (V. Montesinos).Zhang, ZH.; Montesinos Santalucia, V.; Liu, CY.; Gong, WZ. (2015). Geometric properties and continuity of the pre-duality mapping in Banach space. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas. 109(2):407-416. https://doi.org/10.1007/s13398-014-0190-6S4074161092Bandyopadhyay, P., Huang, D., Lin, B.L., Troyanski, S.L.: Some generalizations of local uniform rotundity. J. Math. Anal. Appl. 252, 906–916 (2000)Bandyopadhyay, P., Li, Y., Lin, B., Narayana, D.: Proximinality in Banach spaces. J. Math. Anal. Appl. 341, 309–317 (2008)Diestel, J.: Geometry of Banach Spaces. Selected Topics, LNM, vol. 485. Springer, Berlin (1975)Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V.: Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics. Springer, Berlin (2011)Giles, J.R., Gregory, D.A., Sims, B.: Geometrical implications of upper semi-continuity of the duality mapping on a Banach space. Pacific J. Math. 79(1), 99–109 (1978)Goebel, K., Sekowski, T.: The modulus of non-compact convexity. Ann. Univ. M. Curie-Sklodowska, Sect. A 38, 41–48 (1984)Guirao, A.J., Montesinos, V.: A note in approximative compactness and continuity of metric projections in Banach spaces. J. Convex Anal. 18, 397–401 (2011)Huff, R.: Banach spaces which are nearly uniformly convex. Rocky Mountain J. Math. 10(4), 743–749 (1980)Kutzarova, D., Rolewicz, S.: On nearly uniformly convex sets. Arch. Math. 57, 385–394 (1991)Kutzarova, D., Lin, B.L., Zhang, W.: Some geometrical properties of Banach spaces related to nearly uniform convexity. Contemp. Math. 144, 165–171 (1993)Kutzarova, D., Prus, S.: Operators which factor through nearly uniformly convex spaces. Boll. Un. Mat. Ital. B (7) 9, 2, 479–494 (1995)Montesinos, V.: Drop property equals reflexivity. Studia Math. 87, 93–100 (1987)Phelps, R.R.: Convex Functions, Monotone Operators and Differentiability, LNM, vol. 1364, 2nd edn. Springer, Berlin (1993)Rolewicz, S.: On drop property. Studia Math. 85, 27–37 (1986)Rolewicz, S.: On $$\Delta$$ Δ -uniform convexity and drop property. Studia Math. 87, 181–191 (1987)Wu, C.X., Li, Y.J.: Strong convexity in Banach spaces. J. Math. Wuhan Univ. 13(1), 105–108 (1993)Wang, J.H., Nan, C.X.: The continuity of subdifferential mapping. J. Math. Anal. Appl. 210, 206–214 (1997)Wang, J.H., Zhang, Z.H.: Characterization of the property (C-K). Acta Math. Sci. Ser. A Chin. Ed. 17(A)(3), 280–284 (1997)Zhang, Z.H., Liu, C.Y.: Some generalization of locally and weakly locally uniformly convex space. Nonlinear Anal. 74(12), 3896–3902 (2011)Zhang, Z.H., Liu, C.Y.: Convexity and proximinality in Banach spaces. J. Funct. Spaces Appl. 2012, 11 (2012). doi: 10.1155/2012/724120 . Article ID 724120Zhang, Z.H., Liu, C.Y.: Convexity and existence of the farthest point. Abstract Appl. Anal. 2011, 9 (2011). doi: 10.1155/2011/139597 . Article ID 139597Zhang, Z.H., Shi, Z.R.: Convexities and approximative compactness and continuity of the metric projection in Banach spaces. J. Approx. Theory 161(2), 802–812 (2009)Zhang, Z.H., Zhang, C.J.: On very rotund Banach spaces. Appl. Math. Mech. (English Ed.) 21(8), 965–970 (2000