Burning velocity measurements of fluoropropanes by the spherical-vessel method

Burning velocity measurements of six types of fluoropropanes including structural isomers were carried out in order to understand the flammability of hydrofluorocarbons (HFC). The burning velocity (S_u) was determined by applying a spherical flame model to the pressure rise during combustion, which was measured at room temperature and at initial pressures of 80-107 kPa over a wide range of HFC/air concentrations. The maximum S_u of 1-fluoropropane (HFC-281fa), 2-fluoropropane (HFC-281ea), 1,3-difluoropropane (HFC-272fa), 2,2-difluoropropane (HFC-272ca), 1,2,3-trifluoropropane (HFC-263ea), and 1,1,1-trifluoropropane (HFC-263fb) was 35.0, 31.8, 31.9, 21.2, 25.7, and 14.5 cm s⁻¹, respectively. Note that the maximum S_u of HFC-263ea was appreciably higher than that of HFC-272ca, which shows the importance of the F-atom distribution, as well as of the F/H ratio in the HFC molecule. The results of equilibrium calculation for these HFCs showed that S_u is positively correlated with the flame temperature and the concentrations of the active chain carriers H and OH in the flame. We conducted a trial to interpret the magnitude of S_u by means of the effects of substituents for C₁-C₃ HFCs. As a result, it has been found that the order of inhibition efficiency for S_u decreases in the order of CF₃ > CF₂ > CF.     

Characterizations of function spaces on the sphere using frames

In this paper we introduce a polynomial frame on the unit sphere of , for which every distribution has a wavelet-type decomposition. More importantly, we prove that many function spaces on the sphere , such as , and Besov spaces, can be characterized in terms of the coefficients in the wavelet decompositions, as in the usual Euclidean case . We also study a related nonlinear -term approximation problem on . In particular, we prove both a Jackson-type inequality and a Bernstein-type inequality associated to wavelet decompositions, which extend the corresponding results obtained by R. A. DeVore, B. Jawerth and V. Popov (``Compression of wavelet decompositions', Amer. J. Math. 114 (1992), no. 4, 737-785).

     

Synthesis of spherical nanoparticles of Cu2L2O5 (L=Ho, Er) from W/O microemulsions

Nanoparticles of Cu₂L₂O₅ (L=Ho, Er) (15–25 nm in size) were synthesised by the intermediate use of W/O microemulsions. In this process the aqueous cores of water/cetyltrimethylammonium bromide/n-octane/1-butanol microemulsions were used as microreactors for the precipitation of Cu₂Ho₂(CO₃)₄(OH)₂ (25–30 nm) and Cu₂Er₂(CO₃)₄(OH)₂ (10–40 nm) as precursors. These mixed salts were separated and further decomposed to the corresponding mixed oxides at 900°C for 16 h. All solids were characterised by scanning and transmission electron microscopy, IR, XRPD, ICP-OES, TGA, XPS measurements and elemental analyses.     

HITTING TIME AND PLACE TO A SPHERE OR SPHERICAL SHELL FOR BROWNIAN MOTION

61.IntroductionLetX~{X,(w),t20}beastandardd-dimensionalBrownianmotioninR'(d22).ThefirsthittingtimeofXforaBorelsetBinRdisdefinedtobeThefirsthittingplaceisX(TB).InthispapergwemainlyconsiderthesphereZ'--,(0,r)~{x:xERd,lxl~r}andthesphericalshellZ'--,(0,a)UZ'--,(0,b)~{x.xER',lxl=aorlxl~b},wherer>0,a>0,b>0anda相似文献   

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.     

Gent models for the inflation of spherical balloons

We revisit an iconic deformation of non-linear elasticity: the inflation of a rubber spherical thin shell. We use the 3-parameter Mooney and Gent-Gent (GG) phenomenological models to explain the stretch–strain curve of a typical inflation, as these two models cover a wide spectrum of known models for rubber, including the Varga, Mooney–Rivlin, one-term Ogden, Gent-Thomas and Gent models. We find that the basic physics of inflation exclude the Varga, one-term Ogden and Gent-Thomas models. We find the link between the exact solution of non-linear elasticity and the membrane and Young–Laplace theories often used a priori in the literature. We compare the performance of both models on fitting the data for experiments on rubber balloons and animal bladder. We conclude that the GG model is the most accurate and versatile model on offer for the modelling of rubber balloon inflation.     

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.     

Picard iteration methods for a spherical atmosphere

Several methods for solving the radiative transfer equation in a spherical atmosphere are presented. These methods include the long characteristic Picard iteration, and the conventional and the accelerated short characteristic Picard iteration. Approximate methods as for instance the Picard iteration methods with open boundaries are also discussed. The analysis is focussed on the computational efficiency and accuracy of the proposed method and their applicability to atmospheric remote sensing.     

Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system

This paper employs a hybrid numerical method combining the differential transformation method and the finite difference method to study the nonlinear dynamic behavior of a flexible rotor supported by a spherical gas-lubricated bearing system. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and quasi-periodic responses of the rotor center and the journal center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased. The current analytical results are found to be in good agreement with those from other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of spherical gas film rotor–bearing systems.     

A variational characterisation of spherical designs

In this paper we first establish a new variational characterisation of spherical designs: it is shown that a set , where , is a spherical L-design if and only if a certain non-negative quantity A_L,N(X_N) vanishes. By combining this result with a known “sampling theorem” for the sphere, we obtain the main result, which is that if is a stationary point set of A_L,N whose “mesh norm” satisfies h_XN<1/(L+1), then X_N is a spherical L-design. The latter result seems to open a pathway to the elusive problem of proving (for fixed d) the existence of a spherical L-design with a number of points N of order (L+1)^d. A numerical example with d=2 and L=19 suggests that computational minimisation of A_L,N can be a valuable tool for the discovery of new spherical designs for moderate and large values of L.