Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh–Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein–Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter (\(\rho _{0}\)) were explicitly plotted. The results show that, when the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter at \(r=1\) (\(\rho _{0}\)) vanish \((\rho _{0}=\epsilon =0)\), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing \(\rho _{0}\), the transition points are shifted to lower entropies. The same thing is observed when increasing \(\epsilon ^{2}\). In the absence of quintessence-like matter (\(\rho _{0}=0\)), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing \(\rho _{0}\) or \((\epsilon ^2)\).     

KB scanning of X‐ray beam for Laue microdiffraction on accelero‐phobic samples: application to in situ mechanically loaded nanowires

A mapping technique has been developed where a sub‐micrometer focused polychromatic X‐ray beam is scanned across a stationary sample instead of scanning the sample in front of the X‐ray microbeam. This method is applied to a gold nanowire during its mechanical loading using the tip of an atomic force microscope. During the loading process, such a sample is `accelero‐phobic', i.e. the sample scanning stages must not to be moved to avoid parasitic additional load. Without beam scanning, only one single position within the sample can be probed during the test. The probed material point may even change because of drifts or movements induced by the test itself. The new scanning approach facilitates the in situ mapping of the entire wire giving access to the evolution of the wire shape as well as to the boundary conditions. This novel scanning technique opens promising perspectives for studies where sample motion is forbidden because of the sample environment.     

A high-order incompressible flow solver with WENO

A numerical method for solving the incompressible Navier–Stokes equations with a 5th-order weighted essentially non-oscillatory (WENO) scheme is presented. The method is not based on artificial compressibility and is free of tunable parameters such as the artificial compressibility parameter. The method makes use of the fractional-step method in conjunction with the low-dissipation and low-dispersion Runge–Kutta (LDDRK) scheme to improve temporal accuracy of the scheme. The use of a WENO scheme makes it possible to obtain stable solutions for discontinuous initial data and resolve difficult applications with strong shear such as Kelvin–Helmholtz instability or turbulence. Good convergence rate is established for the velocity variables and numerical solutions of the present method compare well with exact solutions and other numerical results.     

X-ray attenuation around <Emphasis Type="Italic">K</Emphasis>-edge of Zr,Nb, Mo and Pd: A comparative study using proton-induced X-ray emission and <Superscript>241</Superscript>Am gamma rays

Mass attenuation coefficients (μ/ρ) for Zr, Nb, Mo and Pd elements around their K-edges are measured at 14 energies in the range 15.744–28.564 keV using secondary excitation from thin Zr, Nb, Mo, Rh, Pd, Cd and Sn foils. The measurements were carried out at the K _α and K _β energy values of the target elements by two techniques: (1) Proton-induced X-ray emission (PIXE) and (2) ²⁴¹Am (300 mCi) source. In PIXE, 2 MeV proton-excited X-rays were detected by a Si(Li) detector. In the second case, X-rays excited by 59.54 keV photons from the targets were counted by an HPGe detector under a narrow beam good geometry set-up with sufficient shielding. The results are consistent with theoretical values derived from the XCOM package and indicate that the PIXE data have better statistical accuracy.     

T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

Optimal focusing by spatio-temporal inverse filter. I. Basic principles

A focusing technique based on the inversion of the propagation operator relating an array of transducers to a set of control points inside a medium was proposed in previous work [Tanter et al., J. Acoust. Soc. Am. 108, 223-234 (2000)] and is extended here to the time domain. As the inversion of the propagation operator is achieved both in space and time, this technique allows calculation of the set of temporal signals to be emitted by each element of the array in order to optimally focus on a chosen control point. This broadband inversion process takes advantage of the singular-value decomposition of the propagation operator in the Fourier domain. The physical meaning of this decomposition is explained in a homogeneous medium. In particular, a definition of the number of degrees of freedom necessary to define the acoustic field generated by an array of limited aperture in a focal plane of limited extent is given. This number corresponds to the number of independent signals that can be created in the focal area both in space and time. In this paper, this broadband inverse-focusing technique is compared in homogeneous media with the classical focusing achieved by simple geometrical considerations but also with time-reversal focusing. It is shown that, even in a simple medium, slight differences appear between these three focusing strategies. In the companion paper [Aubry et al., J. Acoust. Soc. Am. 110, 48-58 (2001)] the three focusing techniques are compared in heterogeneous, absorbing, or complex media where classical focusing is strongly degraded. The strong improvement achieved by the spatio-temporal inverse-filter technique emphasizes the great potential of multiple-channel systems having the ability to apply completely different signal waveforms on each transducer of the array. The application of this focusing technique could be of great interest in various ultrasonic fields such as medical imaging, nondestructive testing, and underwater acoustics.     

High-Resolution Infrared Spectra of the ν2, ν3, ν4, and 2ν3 Bands of SO3

New measurements are reported for the infrared spectrum of sulfur trioxide, ³²S¹⁶O₃, with resolutions ranging from 0.0015 cm⁻¹ to 0.0025 cm⁻¹. Rovibrational constants have been measured for the fundamentals ν₂, ν₃, and ν₄ and the overtone band 2ν₃. Comparisons are made with the earlier high-resolution measurements on SO₃, and the high correlation among some of the constants related to the Coriolis coupling of the ν₂ and ν₄ levels is discussed in order to understand the areas of disagreement with the earlier work. Splittings of some of the levels are observed and the splitting constant for K=3 of the ground state is determined for the first time. Other observed splittings include the K=1 levels of 2ν₃ (l=2), the K=2 levels of ν₃ and ν₄, and the K=3 levels of ν₂. The analysis shows that there are level crossings between the l=0 and l=2 states of 2ν₃ that allow one to determine the separation of the subband centers for these two states even though access to the l=0 state from the ground state is electric-dipole forbidden. This is a generalized phenomenon that should be found for many other molecules with the same symmetry. The l-type resonance constant, q₃, that causes the splitting of the l₃=±1, k=±1 levels of ν₃ also couples the l₃=0 and 2 states of 2ν₃.