Axisymmetric bubble pinch-off at high Reynolds numbers

Analytical considerations and potential-flow numerical simulations of the pinch-off of bubbles at high Reynolds numbers reveal that the bubble minimum radius, rn, decreases as tau proportional to r2n sqrt[1lnr2n], where tau is the time to break up, when the local shape of the bubble near the singularity is symmetric. However, if the gas convective terms in the momentum equation become of the order of those of the liquid, the bubble shape is no longer symmetric and the evolution of the neck changes to a rn proportional to tau1/3 power law. These findings are verified experimentally.     

Influence of high magnetic fields on the superconducting transition of one-dimensional Nb and MoGe nanowires

The effects of a strong magnetic field on superconducting Nb and MoGe nanowires with diameter approximately 10 nm have been studied. We have found that the Langer-Ambegaokar-McCumber-Halperin (LAMH) theory of thermally activated phase slips is applicable in a wide range of magnetic fields and describes well the temperature dependence of the wire resistance, over 11 orders of magnitude. The field dependence of the critical temperature, T(c), extracted from the LAMH fits is in good quantitative agreement with the theory of pair-breaking perturbations that takes into account both spin and orbital contributions. The extracted spin-orbit scattering time agrees with an estimate tau(s.o.) approximately tau(variant Planck's over 2pic/Ze(2))(4), where tau is the elastic scattering time and Z is the atomic number.     

Defect production in nonlinear quench across a quantum critical point

We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.     

Complete condensation in a zero range process on scale-free networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.     

Scaling law for second-order hyperpolarizability in poly(triacetylene) molecular wires

Poly(triacetylenes) are rodlike molecules with electrons delocalized over a one-dimensional path. We show that they exhibit a power-law dependence of the second-order hyperpolarizability gamma on the monomer unit n for short molecules and a smooth saturation toward a linear increase in longer molecules. The power law of gamma?n(a) with a approximately 2.5 from dengenerate four-wave mixing and third-harmonic generation measurements is in good agreement with quantum-chemical calculations. The critical conjugation length for saturation in the three cases is shown to be approximately 60 carbon-carbon bonds, which indicates the upper boundary for the electron delocalization in such a one-dimensional molecular wire.     

Sandpile on scale-free networks

We investigate the avalanche dynamics of the Bak-Tang-Wiesenfeld sandpile model on scale-free (SF) networks, where the threshold height of each node is distributed heterogeneously, given as its own degree. We find that the avalanche size distribution follows a power law with an exponent tau. Applying the theory of the multiplicative branching process, we obtain the exponent tau and the dynamic exponent z as a function of the degree exponent gamma of SF networks as tau=gamma divided by (gamma-1) and z=(gamma-1) divided by (gamma-2) in the range 23, with a logarithmic correction at gamma=3. The analytic solution supports our numerical simulation results. We also consider the case of a uniform threshold, finding that the two exponents reduce to the mean-field ones.     

Microwave resonance of the bubble phases in 1/4 and 3/4 filled high Landau levels

We have measured the diagonal conductivity, sigma(xx), in the microwave regime of an ultrahigh mobility two dimensional electron system. We find a sharp resonance in Re[sigma(xx)] versus frequency when nu>4 and the partial filling of the highest Landau level, nu(*), is approximately 1/4 or 3/4 and temperatures <0.1 K. The resonance appears for a range of nu(*) from 0.20 to 0.38 and again from 0.64 to 0.80. The peak frequency f(pk) changes from approximately 500 to approximately 150 MHz as nu(*)=1/2 is approached. This range of f(pk) shows no dependence on nu where the resonance is observed. The quality factor, Q, of the resonance is maximum at about nu(*)=0.25 and 0.74. We interpret the resonance as due to a pinning mode of the bubble phase crystal.     

Quantum correction to conductivity close to a ferromagnetic quantum critical point in two dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the crossover between diffusive and ballistic regimes of quantum interference effects occurs at a temperature T*=1/taugamma(E(F)tau)2, where gamma is the parameter associated with the Landau damping of the spin fluctuations, tau is the impurity scattering time, and E(F) is the Fermi energy. For a generic choice of parameters, T* is smaller than the nominal crossover scale 1/tau. In the ballistic quantum critical regime, the conductivity behaves as T1/3.     

Role of the channel geometry on the bubble pinch-off in flow-focusing devices

The formation of bubbles by flow focusing of a gas and a liquid in a rectangular channel is shown to depend strongly on the channel aspect ratio. Bubble breakup consists in a slow linear 2D collapse of the gas thread, ending in a fast 3D pinch-off. The 2D collapse is predicted to be stable against perturbations of the gas-liquid interface, whereas the 3D pinch-off is unstable, causing bubble polydispersity. During 3D pinch-off, a scaling w_(m) approximately tau(1/3) between the neck width w_(m) and the time tau before breakup indicates that breakup is driven by the inertia of both gas and liquid, not by capillarity.     

Geometry-dependent dephasing in small metallic wires

Temperature dependent weak localization is measured in metallic nanowires in a previously unexplored size regime down to width w = 5 nm. The dephasing time, tau(phi), shows a low temperature T dependence close to quasi-1D theoretical expectations (tau(phi) approximately T(-2/3)) in the narrowest wires, but exhibits a relative saturation as T-->0 for wide samples of the same material, as observed previously. As only sample geometry is varied to exhibit both suppression and divergence of tau(phi), this finding provides a new constraint on models of dephasing phenomena.     

Frustration and sound attenuation in structural glasses

Three classes of harmonic disorder systems (Lennard-Jones-like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation gamma(Q) approximately Qalpha. In particular, alpha decreases from approximately d+1 in low-frustration systems (where d is the spectral dimension) to approximately 2 for high-frustration systems such as the realistic glasses examined.     

Superplasticity of a microcrystalline aluminum-lithium alloy under torsion

The deformation of an aluminum-lithium alloy under torsion in the temperature range 523–673 K at angular velocities of 0.322 and 0.0322 rad/s is studied. The shear strain γ prior to failure is found to increase with decreasing strain rate, and its temperature dependence has a maximum at 553 K (γ≈30). The initial loading-induced jump in the dependence of the torque on the angle of rotation (stress-strain curve) is followed by a softening stage, which changes into a hardening stage or a stage with a constant torque at all temperatures except those near 673 K. The stress distribution over a cross section is analyzed, and the dependence of the shear-strain rate \(\dot \gamma \) on the stress τ and temperature T is found to be \(\dot \gamma \sim \tau ^n \exp ( - {U \mathord{\left/ {\vphantom {U {kT}}} \right. \kern-\nulldelimiterspace} {kT}})\). The results are compared with those obtained earlier from tensile tests of this alloy.     

63Cu nuclear relaxation in the quantum critical point system CeCu5.9Au0.1

63Cu NQR measurements of the 63Cu T1 are reported for the quantum critical point system CeCu5.9Au0.1 over temperatures ranging from 0.1 up to 4.2 K. Below approximately 1 K the magnetization recovery exhibits a stable, nonexponential decay function which we believe signals the onset of 2D quantum critical fluctuations, as has been noted in the literature. We find T1(-1) is proportional to T0.75 for the region T < 1 K. The observed temperature dependence is in agreement with a phenomenological model of non-Fermi liquid behavior based on the uniform susceptibility but is inconsistent with calculations based on susceptibility peaks identified via neutron scattering experiments.     

Localized excitation in the hybridization gap in YbAl3

The intermediate valence compound YbAl3 exhibits a broad magnetic excitation in the inelastic neutron scattering spectrum with characteristic energy E1 approximately 50 meV, equal to the Kondo energy (T(K) approximately 600-700 K). In the low temperature (T < T(coh) approximately 40 K) Fermi liquid state, however, a new peak in the scattering occurs at E2 approximately 33 meV, which lies in the hybridization gap that exists in this compound. We report inelastic neutron scattering results for a single-crystal sample. The scattering at energies near E1 qualitatively has the momentum (Q) dependence expected for interband scattering across the indirect gap. The scattering near E2 has a very different Q dependence: it is a weak function of Q over a large fraction of the Brillouin zone and is smallest near (1/2,1/2, 1/2). A possibility is that the peak at E2 arises from a spatially localized excitation in the hybridization gap.     

Diffusive liquid propagation in porous and elastic materials: the case of foams under microgravity conditions

We report the results of fluid transport experiments in aqueous foams under microgravity. Using optical and electrical methods, the capillary motion of the foam fluid and the local liquid fractions are monitored. We show that foams can be continuously wetted up to high liquid fractions ( approximately 0.3), without any bubble motion instabilities. Data are compared to drainage models: For liquid fractions above 0.2, discrepancies are found and identified. These new results on foam hydrodynamics and structure can be useful for other poroelastic materials, such as plants and biological tissues.     

Enhanced drainage and coarsening in aqueous foams

Experiments are presented elucidating how the evolution of foam microstructure by gas diffusion from high to low pressure bubbles can significantly speed up the rate of gravitational drainage, and vice versa. This includes detailed data on the liquid-fraction dependence of the coarsening rate, and on the liquid-fraction and the bubble-size profiles across a sample. These results can be described by a "coarsening equation" for the increase of bubble growth rate for drier foams. Spatial variation of the average bubble size and liquid fraction can also affect the growth and drainage rates.     

Collective non-Abelian instabilities in a melting color glass condensate

We present first results for (3 + 1)D simulations of SU(2) Yang-Mills equations for matter expanding into the vacuum after a heavy ion collision. Violations of boost invariance cause a non-Abelian Weibel instability leading soft modes to grow with proper time tau as exp(gamma square root(g2 mu tau)), where g2 mu is a scale arising from the saturation of gluons in the nuclear wave function. The scale for the growth rate gamma is set by a plasmon mass, defined as omega(pl) = kappa0 square root(g2 mu/tau)), generated dynamically in the collision. We compare the numerical ratio gamma/kappa0 to the corresponding value predicted by the hard thermal loop formalism for anisotropic plasmas.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

Theory of transport of long polymer molecules through carbon nanotube channels

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using the Fokker-Planck equation and direct molecular dynamics simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, the entropy, and the diffusion coefficient. A power law dependence tau approximately N2 is found, where N is the number of monomers in a molecule. For 10(5)-unit long polyethylene molecules, tau is estimated to be approximately 1 micros. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, is found to be a few orders of magnitude larger than in ordinary silicate based zeolite systems.     

TO ENHANCE THE INTENSITY OF SONOLUMINESCENCE

The transient resonance of a sonoluminescence bubble has been analysed. When the bubble performs its transient resonance at the nth order harmonics of the standing waves in the liquid, the light intensity strongly depends on the amplitude of the driving pressure (proportional to its 2n power, with n=f_r/f, where f_r is Minnaert's linear resonant frequency of the bubble and f is the frequency of driving sound). The kinetic energy of a vibrating bubble becomes maximum approximately when it is in its equilibrium size. For example, when the ambient temperature of a bubble decreases from 34℃ to 4℃, a huge increase of the light intensity emitted by it can be explained. A suggestion was made that, within the limits permitted by the phase diagrams, as high an increase in driving pressure as possible could enhance the light intensity of sonoluminescence up to four orders of magnitude.