Drop deformation and breakup due to shock wave and steady disturbances

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76208/1/AIAA-1994-560-222.pd

Deformation and secondary breakup of drops

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77341/1/AIAA-1993-814-776.pd

Next-to-leading-order corrections to exclusive processes in kTk_T factorization

We calculate next-to-leading-order (NLO) corrections to exclusive processes in $k_T$ factorization theorem, taking $\pi\gamma^*\to\gamma$ as an example. Partons off-shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms $\ln^2k_T$ and $\ln^2 x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation, and the latter absorbed into a jet function and organized by the threshold resummation. The NLO corrections are found to be only few-percent for $\pi\gamma^*\to\gamma$, if setting the factorization scale to the momentum transfer from the virtual photon.Comment: 13 pages; version to appear in Physical Review

Dynamics of drop deformation and formation during secondary breakup in the bag breakup regime

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77016/1/AIAA-1997-797-833.pd

Stochastic Lorentz forces on a point charge moving near the conducting plate

The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the method of Feynman-Vernon influence functional. This stochastic approach incorporates not only the stochastic noise manifested from electromagnetic vacuum fluctuations, but also dissipation backreaction on a charge in the form of the retarded Lorentz forces. Since the imposition of the boundary is expected to anisotropically modify the effects of the fields on the evolution of the particle, we consider the motion of a charge undergoing small-amplitude oscillations in the direction either parallel or normal to the plane boundary. Under the dipole approximation for nonrelativistic motion, velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rather different rate, revealing strong anisotropic behavior. They are then asymptotically saturated as a result of the fluctuation-dissipation relation, and the same saturated value is found for the motion in both directions. The observational consequences are discussed. plane boundary. Velocity fluctuations of the charge are found to grow linearly with time in the early stage of the evolution at the rate given by the relaxation constant, which turns out to be smaller in the parallel case than in the perpendicular one in a similar configuration. Then, they are asymptotically saturated as a result of the fluctuation-dissipation relation. For the electron, the same saturated value is obtained for motion in both directions, and is mainly determined by its oscillatory motion. Possible observational consequences are discussed.Comment: 33 pages, 2 figure

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure

Near-limit drop deformation and secondary breakup

The properties of drop deformation and secondary breakup were observed for shock wave initiated disturbances in air at normal temperature and pressure. Test liquids included water, glycerol solutions, n-heptane, ethyl alcohol and mercury to yield Weber numbers (We) of 0.5-1000, Ohnesorge numbers (Oh) of 0.0006-4, liquid/gas density ratios of 580-12,000 and Reynolds numbers (Re) of 300-16,000. Measurements included pulsed shadowgraphy and holography to find drop deformation properties prior to breakup, as well as drop size distributions after breakup. Drop deformation and breakup regimes were identified in terms of We and Oh: regimes at low Oh include no deformation, nonoscillatory deformation, oscillatory deformation, bag breakup, multimode breakup and shear breakup as We is increased. However, most of these regimes occur at higher We when Oh values are increased, with no breakup observed for Oh > 4 over the present test range. Unified temporal scaling of deformation and breakup processes was observed in terms of a characteristic breakup time that largely was a function of Oh. Prior to breakup, the drag coefficient evolved from the properties of spheres to those of thin disks as drop deformation progressed. The drop size distribution after breakup satisfied Simmons' universal root normal distribution function for the bag and multimode breakup regimes and could be characterized by the Sauter mean diameter (SMD) alone. Drop sizes after shear breakup, however, did not satisfy this distribution function due to the distorting effect of the core or drop-generating drop. Nevertheless, the SMD after secondary breakup could be correlated in terms of a characteristic liquid boundary layer thickness for all breakup regimes, similar to recent results for nonturbulent primary breakup. Drop properties after secondary breakup suggest that both reduced drop sizes and reduced relative velocities play a role in ending the secondary breakup process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29886/1/0000239.pd

Drop properties after secondary breakup

Drop properties during and after secondary breakup in the bag, multimode and shear breakup regimes were observed for shock-wave-initiated disturbances in air at normal temperature and pressure. Test liquids included water, n-heptane, ethyl alcohol and glycerol mixtures to yield Weber numbers of 15-600, Ohnesorge numbers of 0.0025-0.039, liquid/gas density ratios of 579-985 and Reynolds numbers of 1060-15080. Measurements included pulsed shadowgraphy and double-pulsed holography to find drop sizes and velocities after breakup. Drop size distributions after breakup satisfied Simmons' universal root normal distribution in all three breakup regimes, after removing the core (or drop-forming) drop from the drop population for shear breakup. The size and velocity of the core drop after shear breakup was correlated separately based on the observation that the end of drop stripping corresponded to a constant Eotvos number. The relative velocities of the drop liquid were significantly reduced during secondary breakup, due both to the large drag coefficients caused by drop deformation and the reduced relaxation times of smaller drops. These effects were correlated successfully based on a simplified phenomenological theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30567/1/0000200.pd

Vector-pseudoscalar two-meson distribution amplitudes in three-body BB meson decays

We study three-body nonleptonic decays $B\to VVP$ by introducing two-meson distribution amplitudes for the vector-pseudoscalar pair, such that the analysis is simplified into the one for two-body decays. The twist-2 and twist-3 $\phi K$ two-meson distribution amplitudes, associated with longitudinally and transversely polarized $\phi$ mesons, are constrained by the experimental data of the $\tau\to\phi K\nu$ and $B\to\phi K\gamma$ branching ratios. We then predict the $B\to\phi K\gamma$ and $B\to\phi\phi K$ decay spectra in the $\phi K$ invariant mass. Since the resonant contribution in the $\phi K$ channel is negligible, the above decay spectra provide a clean test for the application of two-meson distribution amplitudes to three-body $B$ meson decays.Comment: 9 pages, 1 figure, Revtex4, version to appear in PR