Enhancement of pupil-masked wavelength-scale gas-filled flat acoustic lens based on anomaly apodization effect

In this letter, the improvement in focus by the use of a pupil mask produced in an acoustic mesoscale cuboid particle filled with CO₂ is reported. Thereby, the result shows that the pupil mask increases the sound intensity and also increases the resolution (or a reduction of the full width at half maximum, FWHM) in focus compared to the non-masked one. These results are important because they confirm the effect of abnormal amplitude apodization for a one-wavelength dimension acoustic lens and demonstrate that it is possible to improve sound focusing of a cuboid gas-filled lens with one wavelength dimension. This is the smallest size of an acoustic lens ever considered in this type of literature, with side dimensions of the cube equal to one wavelength and a diameter to focus ratio of 2.5, the sound amplification in focus is 5.4 dB at 4125 Hz, with the resolution near to the diffraction limit.     

Superradiance with Incoherent Nonradiative Decay

We describe superradiance of a few emitters in a dissipative environment with nonradiative decay in the Schrödinger approach, which is simpler than the density matrix formalism. We find that superradiance increases the quantum efficiency of the radiation if the baths, responsible for dissipation, do not come to equilibrium. The reason is that decoherence destroys Dicke “dark” states, lets emitters radiate, and does not affect the fast radiation from “bright” Dicke states.     

Optimal Control of an Axisymmetric Conical Shell with a Unilateral Elastic Foundation and Rigid Supports

We study an optimal control problem for an elastic conical shell. The displacement vector u =(u,v) is then a function of one variable s∈(a,b), 0<a<b<∞. Here u is the meridional and v the normal displacement. The shell is assumed to be simply supported. Moreover, we consider several unilateral obstacles and an unilateral elastic foundation of Winkler type i.e. the reaction force is proportional of the positive part of the normal displacement. The state problem is formulated in a form of variational inequality for u . The design parameter e =(t,z,F) includes the variable thickness of the shell, the stiffness characteristics of the foundation and the friction coefficient. The existence of the optimal control will be explained. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic resonance imaging of velocity fields, the void fraction and gas dynamics in a cavitating liquid

In acoustic cavitation, the relationship between the bubble dynamics on the microscale and the flow properties on the macroscale is critical in determining sonochemical reaction kinetics. A new technique was developed to measure the void fraction and estimate water mobility in the vicinity of cavitating bubbles using phase-encoded magnetic resonance imaging with short characteristic measurement timescales (0.1–1 ms). The exponential behavior of the NMR signal decay indicated the fast diffusion regime, with the relationship between local mechanical dispersion D _mix and the average bubble radius R, D_mix >> \frac2R²10^-4s, D_{\rm mix}\gg \frac{2R^2}{10^{-4}\hbox{s}}, resulting in dispersion of orders of magnitude greater than diffusion in quiescent water. For two different samples (water and a surfactant solution), the independent measurements of three-dimensional void fraction and velocity fields permitted the calculation of compressibility, divergence and vorticity of the cavitating medium. The measured dynamics of the dissolved gas, compared with that of the surrounding liquid, reflected the difference in the bubble coalescence and lifetimes and correlated with the macroscopic flow parameters.     

Turbulent boundary layer on a plate with transpiration: Dynamical and thermal problems

Scaling laws are established for the profiles of mean velocity and temperature, Reynolds-stress components, turbulent heat flux and mean-square temperature fluctuation, skin friction and wall heat transfer in the turbulent boundary layer on a flat plate with transpiration. In the case of blowing, the velocity and temperature distributions represented in scaling variables outside the viscous sublayer have universal forms known from experimental data for flow over an impermeable flat plate. The turbulent shearing stress and heat flux also can be represented in terms of these two functions. In the case of suction, the mean quantities are described by one-parameter families of curves. Universal skin-friction and heat-transfer laws provide a basis for representation of the skin-friction and heat-flux distributions corresponding to different Reynolds numbers and transpiration velocities in terms of universal functions of one variable. The results are obtained without invoking any special closure hypotheses. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Molecular Structure,Thermodynamic and Spectral Characteristics of Metal-Free and Nickel Complex of Tetrakis(1,2,5-thiadiazolo)porphyrazine

The Knudsen effusion method with mass spectrometric control of the vapor composition was used to study the possibility of a congruent transition to the gas phase and to estimate the enthalpy of sublimation of metal-free tetrakis(1,2,5-thiadiazolo)porphyrazine and its nickel complex (H₂TTDPz and NiTTDPz, respectively). The geometrical and electronic structure of H₂TTDPz and NiTTDPz in ground and low-lying excited electronic states were determined by DFT calculations. The electronic structure of NiTTDPz was studied by the complete active space (CASSCF) method, following accounting dynamic correlation by multiconfigurational quasi-degenerate second-order perturbation theory (MCQDPT2). A geometrical structure of D_2h and D_4h symmetry was obtained for H₂TTDPz and NiTTDPz, respectively. According to data obtained by the MCQDPT2 method, the nickel complex possesses the ground state ¹A_1g, and the wave function of the ground state has the form of a single determinant. Electronic absorption and vibrational (IR and resonance Raman) spectra of H₂TTDPz and NiTTDPz were studied experimentally and simulated theoretically.     

Anhydrous Nitrates and Nitrosonium Nitratometallates of Manganese and Cobalt,M(NO3)2, NO[Mn(NO3)3], and (NO)2[Co(NO3)4]: Synthesis and Crystal Structure

Crystalline NO[Mn(NO₃)₃] ( I ) and (NO)₂[Co(NO₃)₄] ( II ) were synthesized by reaction of the corresponding metal and a liquid N₂O₄/ethylacetate mixture. I is orthorhombic, Pca2₁, a = 9.414(2), b = 15.929(3), c = 10.180(2) Å, Z = 4, R₁ = 0.0286. II is monoclinic, C2/c, a = 14.463(3), b = 19.154(4), c = 13.724(3) Å, β = 120.90(3), Z = 12, R₁ = 0.0890. Structure I consists of [Mn(NO₃)₃]^– sheets with NO⁺ cations between them. Two types of Mn atoms have CN_Mn = 7 and 8. Structure II is ionic containing isolated [Co(NO₃)₄]‐anions and NO⁺ cations with CN_Co = 8. Crystals of Mn(NO₃)₂ ( III ) and Co(NO₃)₂ ( IV ) were obtained by concentration of metal nitrate hydrate solutions in 100% HNO₃ in a desiccator with P₂O₅. III is cubic, Pa 3, a = 7.527(2) Å, Z = 4, R₁ = 0.0987. IV is trigonal, R 3, a = 10.500(2), c = 12.837(3) Å, Z = 12, R₁ = 0.0354. The three dimensional structure III is isotypic to the strontium and barium dinitrates. Structure IV contains a three dimensional network of interconnected Co(NO₃)_6/3 units with a distorted octahedral coordination environment of Co atoms. General correlations between central atom coordination and coordination modes of NO₃ groups are discussed.     

Nonlinear Weakly Curved Rod by Γ-Convergence

We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use an approach analogous to the one for rods and curved rods and start from the strain energy functional of three dimensional nonlinear elasticity. We do not impose any constitutional behavior of the material and work in a general framework. To derive the model, by means of ??-convergence, we need to set the order of strain energy (i.e., its relation to the thickness of the body h). We analyze the situation when the strain energy (divided by the order of volume) is of the order h ⁴. This is the same approach as the one used in F?ppl-von Kármán model for plates and the analogous model for rods. The obtained model is analogous to Marguerre-von Kármán for shallow shells and its linearization is the linear shallow arch model which can be found in the literature.