Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)

The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = 1/6π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω^2 = ω_0^0(1−0.31W), where ω_0 is the oscillation frequency of a bubble in a quiescent fluid

Bubble dynamics in time-periodic straining flows

The dynamics and breakup of a bubble in an axisymmetric, time-periodic straining flow has been investigated via analysis of an approximate dynamic model and also by time-dependent numerical solutions of the full fluid mechanics problem. The analyses reveal that in the neighbourhood of a stable steady solution, an O(ϵ1/3) time-dependent change of bubble shape can be obtained from an O(ε) resonant forcing. Furthermore, the probability of bubble breakup at subcritical Weber numbers can be maximized by choosing an optimal forcing frequency for a fixed forcing amplitude

Quantum Faraday Effect in Double-Dot Aharonov-Bohm Ring

We investigate Faraday's law of induction manifested in the quantum state of Aharonov-Bohm loops. In particular, we propose a flux-switching experiment for a double-dot AB ring to verify the phase shift induced by Faraday's law. We show that the induced {\em Faraday phase} is geometric and nontopological. Our study demonstrates that the relation between the local phases of a ring at different fluxes is not arbitrary but is instead determined by Faraday's inductive law, which is in strong contrast to the arbitrary local phase of an Aharonov-Bohm ring for a given flux.Comment: Submitted to Phys. Rev. Let

Anomalous Transmission Phase of a Kondo-Correlated Quantum Dot

We study phase evolution of transmission through a quantum dot with Kondo correlations. By considering a model that includes nonresonant transmission as well as the Anderson impurity, we explain unusually large phase evolution of about $\pi$ in the Kondo valley observed in recent experiments. We argue that this anomalous phase evolution is a universal property that can be found in the high-temperature Kondo phase in the presence of the time-reversal symmetry.Comment: 5 pages, 3 figure

Kondo Effect and Josephson Current through a Quantum Dot between Two Superconductors

We investigate the supercurrent through a quantum dot for the whole range of couplings using the numerical renormalization group method. We find that the Josephson current switches abruptly from a $\pi$- to a 0-phase as the coupling increases. At intermediate couplings the total spin in the ground state depends on the phase difference between the two superconductors. Our numerical results can explain the crossover in the conductance observed experimentally by Buitelaar \textit{et al.} [Phys. Rev. Lett. \textbf{89}, 256 801 (2002)].Comment: Fig.2 and corresponding text have been changed; Several other small change

Cascade of Quantum Phase Transitions in Tunnel-Coupled Edge States

We report on the cascade of quantum phase transitions exhibited by tunnel-coupled edge states across a quantum Hall line junction. We identify a series of quantum critical points between successive strong and weak tunneling regimes in the zero-bias conductance. Scaling analysis shows that the conductance near the critical magnetic fields $B_{c}$ is a function of a single scaling argument $|B-B_{c}|T^{-\kappa}$, where the exponent $\kappa = 0.42$. This puzzling resemblance to a quantum Hall-insulator transition points to importance of interedge correlation between the coupled edge states.Comment: 4 pages, 3 figure

NAIP proteins are required for cytosolic detection of specific bacterial ligands in vivo.

NLRs (nucleotide-binding domain [NBD] leucine-rich repeat [LRR]-containing proteins) exhibit diverse functions in innate and adaptive immunity. NAIPs (NLR family, apoptosis inhibitory proteins) are NLRs that appear to function as cytosolic immunoreceptors for specific bacterial proteins, including flagellin and the inner rod and needle proteins of bacterial type III secretion systems (T3SSs). Despite strong biochemical evidence implicating NAIPs in specific detection of bacterial ligands, genetic evidence has been lacking. Here we report the use of CRISPR/Cas9 to generate Naip1(-/-) and Naip2(-/-) mice, as well as Naip1-6(Δ/Δ) mice lacking all functional Naip genes. By challenging Naip1(-/-) or Naip2(-/-) mice with specific bacterial ligands in vivo, we demonstrate that Naip1 is uniquely required to detect T3SS needle protein and Naip2 is uniquely required to detect T3SS inner rod protein, but neither Naip1 nor Naip2 is required for detection of flagellin. Previously generated Naip5(-/-) mice retain some residual responsiveness to flagellin in vivo, whereas Naip1-6(Δ/Δ) mice fail to respond to cytosolic flagellin, consistent with previous biochemical data implicating NAIP6 in flagellin detection. Our results provide genetic evidence that specific NAIP proteins function to detect specific bacterial proteins in vivo

Zero-Bias Anomalies in Narrow Tunnel Junctions in the Quantum Hall Regime

We report on the study of cleaved-edge-overgrown line junctions with a serendipitously created narrow opening in an otherwise thin, precise line barrier. Two sets of zero-bias anomalies are observed with an enhanced conductance for filling factors $\nu > 1$ and a strongly suppressed conductance for $\nu < 1$. A transition between the two behaviors is found near $\nu \approx 1$. The zero-bias anomaly (ZBA) line shapes find explanation in Luttinger liquid models of tunneling between quantum Hall edge states. The ZBA for $\nu < 1$ occurs from strong backscattering induced by suppression of quasiparticle tunneling between the edge channels for the $n = 0$ Landau levels. The ZBA for $\nu > 1$ arises from weak tunneling of quasiparticles between the $n = 1$ edge channels.Comment: version with edits for clarit

Neutrino masses along with fermion mass hierarchy

Recently a new mechanism has been proposed to cure the problem of fermion mass hierarchy in the Standard Model (SM) model. In this scenario, all SM charged fermions other than top quark arise from higher dimensional operators involving the SM Higgs field. This model also predicted some interesting phenomenology of the Higgs boson. We generalize this model to accommodate neutrino masses (Dirac & Majorana) and also obtain the mixing pattern in the leptonic sector. To generate neutrino masses, we add extra three right handed neutrinos $(N_{iR})$ in this model.Comment: 20 pages, the content on results and phenomenology have been expanded, a new section on UV completion of the model has been added and also some new references, this version has been accepted by Physical Review