Extended Derivative Dispersion Relations

It is shown that, for a wide class of functions with physical interest as forward scattering amplitudes, integral dispersion relations can be replaced by derivative forms without any high-energy approximation. The applicability of these extended derivative relations, in the investigation of forward proton-proton and antiproton-proton elastic scattering, is exemplified by means of a Pomeron-Reggeon model with totally nondegenerate trajectories.Comment: 7 pages, 1 figure, contribution to "Sense of Beauty in Physics", Miniconference in Honor of Adriano Di Giacomo on his 70th Birthday, Pisa, Italy, Jan. 26-27, 200

Derivative dispersion relations above the physical threshold

We discuss some formal and practical aspects related to the replacement of Integral Dispersion Relations (IDR) by derivative forms, without high-energy approximations. We first demonstrate that, for a class of functions with physical interest as forward scattering amplitudes, this replacement can be analytically performed, leading to novel Extended Derivative Dispersion Relations (EDDR), which, in principle, are valid for any energy above the physical threshold. We then verify the equivalence between the IDR and EDDR by means of a popular parametrization for total cross sections from proton-proton and antiproton-proton scattering and compare the results with those obtained through other representations for the derivative relations. Critical aspects on the limitations of the whole analysis, from both formal and practical points of view, are also discussed in some detail.Comment: Final version, published in Brazilian Journal of Physics, V. 37, 358 (2007

High-Energy Proton-Proton Forward Scattering and Derivative Analyticity Relations

We present the results of several parametrizations to two different ensemble of data on $pp$ total cross sections $\sigma_{tot}^{pp}$ at the highest center-of-mass energies (including cosmic-ray information). The results are statistically consistent with two distinct scenarios at high energies. From one ensemble the prediction for the LHC ($\sqrt s = 14$ TeV) is $\sigma_{tot}^{pp} = 113 \pm 5$ mb and from the other, $\sigma_{tot}^{pp}=140 \pm 7$ mb. From each parametrization, and making use of derivative analyticity relations (DAR), we determine $\rho(s)$ (ratio between the forward real and imaginary parts of the elastic scattering amplitude). A discussion on the optimization of the DAR in terms of a free parameter is also presented.In all cases good descriptions of the experimental data are obtained.Comment: One formula added, one unit changed, small misprints corrected, final version to be published in Brazilian Journal of Physics; 13 pages, 8 figures, aps-revte

Numerical investigation of high-speed droplet impact using a multiscale two-fluid approach

A single droplet impact onto solid surfaces remains a fundamental and challenging topic in both experimental and numerical studies with significant importance in a plethora of industrial applications, ranging from printing technologies to fuel injection in internal combustion engines. Under high-speed impact conditions, additional complexities arise as a result of the prompt droplet splashing and the subsequent violent fragmentation; thus, different flow regimes and a vast spectrum of sizes for the produced secondary flow structures coexist in the flow field. The present work introduces a numerical methodology to capture the multiscale processes involved with respect to local topological characteristics. The proposed methodology concerns a compressible Σ-Υ two-fluid model with dynamic interface sharpening based on an advanced flow topology detection algorithm. The model has been developed in OpenFOAM® and provides the flexibility of dealing with the multiscale character of droplet splashing, by switching between a sharp and a diffuse interface within the Eulerian-Eulerian framework in segregated and dispersed flow regions, respectively. An additional transport equation for the interface surface area density (Σ) introduces important information for the sub-grid scale phenomena, which is exploited in the dispersed flow regions to provide an insight into the extended cloud of secondary droplets after impact on the target. A high-speed water droplet impact case has been examined and evaluated against new experimental data; these refer to a millimetre size droplet impacting a solid dry smooth surface at velocity as high as 150m/s, which corresponds to a Weber number of ~7.6×10^5. At the investigated impact conditions compressibility effects dominate the early stages of droplet splashing. A strong shock wave forms and propagates inside the droplet, where transonic Mach numbers occur; local Mach numbers up to 2.5 are observed for the expelled surrounding gas outside the droplet. The proposed numerical approach is found to capture relatively accurately the phenomena and provide significant information regarding the produced flow structure dimensions, which is not available from the experiment

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade

Anomalous infrared spectra of hybridized phonons in type-I clathrate Ba8_8Ga16_{16}Ge30_{30}

The optical conductivity spectra of the rattling phonons in the clathrate Ba$_8$Ga$_{16}$Ge$_{30}$ are investigated in detail by use of the terahertz time-domain spectroscopy. The experiment has revealed that the lowest-lying vibrational mode of a Ba(2)$^{2+}$ ion consists of a sharp Lorentzian peak at 1.2 THz superimposed on a broad tail weighted in the lower frequency regime around 1.0 THz. With decreasing temperature, an unexpected linewidth broadening of the phonon peak is observed, together with monotonic softening of the phonon peak and the enhancement of the tail structure. These observed anomalies are discussed in terms of impurity scattering effects on the hybridized phonon system of rattling and acoustic phonons.Comment: Submitted to JPS

Meson Structure Functions in Valon Model

Parton distributions in a {\it{valon}} in the next-to-leading order is used to determine the patron distributions in pion and kaon. The validity of the valon model is tested and shown that the partonic content of the valon is universal and independent of the valon type. We have evaluated the valon distribution in pion and kaon, and in particular it is shown that the results are in good agreement with the experimental data on pion structure in a wide range of $x=[10^{-4},1]$Comment: 13 pages with 7 figures included, The manuscript is revised, figures are added and some errors are corrected. Accepted for publication in Physical Review