Exact and Asymptotic Conditions on Traveling Wave Solutions of the Navier-Stokes Equations

We derive necessary conditions that traveling wave solutions of the Navier-Stokes equations must satisfy in the pipe, Couette, and channel flow geometries. Some conditions are exact and must hold for any traveling wave solution irrespective of the Reynolds number ($Re$). Other conditions are asymptotic in the limit $Re\to\infty$. The exact conditions are likely to be useful tools in the study of transitional structures. For the pipe flow geometry, we give computations up to $Re=100000$ showing the connection of our asymptotic conditions to critical layers that accompany vortex structures at high $Re$

Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from author

E-mail address categorization based on semantics of surnames

Surname (family name) analysis is used in geography to understand population origins, migration, identity, social norms and cultural customs. Some of these are supposedly evolved over generations. Surnames exhibit good statistical properties that can be used to extract information in names data set such as automatic detection of ethnic or community groups in names. An e-mail address, often contains surname as a substring. This containment may be full or partial. An e-mail address categorization based on semantics of surnames is the objective of this paper. This is achieved in two phases. First phase deals with surname representation and clustering. Here, a vector space model is proposed where latent semantic analysis is performed. Clustering is done using the method called averagelinkage method. In the second phase, an email is categorized as belonging to one of the categories (discovered in first phase). For this, substring matching is required, which is done in an efficient way by using suffix tree data structure. We perform experimental evaluation for the 500 most frequently occurring surnames in India and United Kingdom. Also, we categorize the e-mail addresses that have these surnames as substrings

Specific IgE Response to Purified and Recombinant Allergens in Latex Allergy

Background In recent years, allergy to natural rubber latex has emerged as a major allergy among certain occupational groups and patients with underlying diseases. The sensitization and development of latex allergy has been attributed to exposure to products containing residual latex proteins. Although improved manufacturing procedures resulted in a considerable reduction of new cases, the potential risk for some patient groups is still great. In addition the prevalent cross-reactivity of latex proteins with other food allergens poses a major concern. A number of purified allergens and a few commercial kits are currently available, but no concerted effort was undertaken to evaluate them. Methods We studied 11 purified latex allergens, Hev b 1 to Hev b 10, and Hev b 13 along with several crude allergen extracts and two commercial ImmunoCAP assays to evaluate specific IgE antibody in the sera from latex allergic patients and controls. Health care workers and spina bifida patients with clinical symptoms of latex allergy, spina bifida patients without latex allergy, and non-atopic health care workers have been studied. Results The results suggest that Hev b 2, 5, 6, and 13 together identified over 80 percent health care workers with latex allergy, while Hev b 6 along with Hev b 1 or 3 detected specific IgE antibody in all sera studied from patients with spina bifida and latex allergy. The ImmunoCAP results using both Hev b 5 amplified and non-amplified closely agreed with the clinical diagnosis of latex allergy in health care workers and in spina bifida. Conclusion Although the purified allergens and crude extracts reacted diversely with IgE from different patient groups, the results indicated that use of certain combinations of purified recombinant antigens will be useful in commercial kits or in in-house assays for detecting specific IgE antibody in the sera. The results suggest that a combination of Hev b 2, 3, 5, 6, and 13 together detected specific IgE in 80% of the sera from latex allergic patients. Both ImmunoCAPs correctly identified over 95% of latex allergic patients, however, showed reactivity with a few normal control subject

Silver nanowire array-polymer composite as thermal interface material

Silver nanowire arrays embedded inside polycarbonate templates are investigated as a viable thermal interface material for electronic cooling applications. The composite shows an average thermal diffusivity value of 1.89x10(-5) m(2) s(-1), which resulted in an intrinsic thermal conductivity of 30.3 W m(-1) K(-1). The nanowires' protrusion from the film surface enables it to conform to the surface roughness to make a better thermal contact. This resulted in a 61% reduction in thermal impedance when compared with blank polymer. An similar to 30 nm Au film on the top of the composite was found to act as a heat spreader, reducing the thermal impedance further by 35%. A contact impedance model was employed to compare the contact impedance of aligned silver nanowire-polymer composites with that of aligned carbon nanotubes, which showed that the Young's modulus of the composite is the defining factor in the overall thermal impedance of these composites

Effect of pH and temperature on the morphology and phases of co-precipitated hydroxyapatite

This paper reports a high-yield process to fabricate biomimetic hydroxyapatite nano-particles or nano-plates. Hydroxyapatite is obtained by simultaneous dripping of calcium chloride and ammonium hydrogen phosphate solutions into a reaction vessel. Reactions were carried out under various pH and temperature conditions. The morphology and phase composition of the precipitates were investigated using scanning electron microscope and X-ray diffraction. The analyses showed that large plates of calcium hydrophosphate are formed at neutral or acidic pH condition. Nanoparticles of hydroxyapatite were obtained in precipitates prepared at pH 9–11. Hydroxyapatite plates akin to seashell nacre were obtained at 40 °C and pH 9. This material holds promise to improve the strength of hydroxyapatite containing composites for bone implant or bone cement used in orthopaedic surgeries. The thermodynamics of the crystal growth under these conditions was discussed. An assembly mechanism of the hydroxyapatite plates was proposed according to the nanostructure observations

Dynamical mean-field theory of the small polaron

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion (CFE), both at zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground state properties such as the effective polaron mass, which have a smooth behaviour, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more and more open in the density of states at low energy, while the high energy part of the spectrum is broad and can be explained by a strong coupling adiabatic approximation. As a consequence narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum has always a multipeaked structure.Comment: 21 Pages Latex, 19 PostScript figure

Theories for influencer identification in complex networks

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks and socioeconomic systems.Comment: 24 pages, 6 figure

Order-of-magnitude speedup for steady states and traveling waves via Stokes preconditioning in Channelflow and Openpipeflow

Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent wall-bounded shear flows, these states have been hypothesized to be saddle points organizing the trajectories within a chaotic attractor. These states must be computed with Newton's method or one of its generalizations, since time-integration cannot converge to unstable equilibria. The bottleneck is the solution of linear systems involving the Jacobian of the Navier-Stokes or Boussinesq equations. Originally such computations were carried out by constructing and directly inverting the Jacobian, but this is unfeasible for the matrices arising from three-dimensional hydrodynamic configurations in large domains. A popular method is to seek states that are invariant under numerical time integration. Surprisingly, equilibria may also be found by seeking flows that are invariant under a single very large Backwards-Euler Forwards-Euler timestep. We show that this method, called Stokes preconditioning, is 10 to 50 times faster at computing steady states in plane Couette flow and traveling waves in pipe flow. Moreover, it can be carried out using Channelflow (by Gibson) and Openpipeflow (by Willis) without any changes to these popular spectral codes. We explain the convergence rate as a function of the integration period and Reynolds number by computing the full spectra of the operators corresponding to the Jacobians of both methods.Comment: in Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, ed. Alexander Gelfgat (Springer, 2018