A Nonsteady Heat Diffusion Problem with Spherical Symmetry

A solution in successive approximations is presented for the heat diffusion across a spherical boundary with radial motion. The approximation procedure converges rapidly provided the temperature variations are appreciable only in a thin layer adjacent to the spherical boundary. An explicit solution for the temperature field is given in the zero order when the temperature at infinity and the temperature gradient at the spherical boundary are specified. The first-order correction for the temperature field may also be found. It may be noted that the requirements for rapid convergence of the approximate solution are satisfied for the particular problem of the growth or collapse of a spherical vapor bubble in a liquid when the translational motion of the bubble is neglected

On the Dynamics of Small Vapor Bubbles in Liquids

When a vapor bubble in a liquid changes size, evaporation or condensation of the vapor takes place at the surface of the bubble. Because of the latent heat requirement of evaporation, a change in bubble size must therefore be accompanied by a heat transfer across the bubble wall, such as to cool the surrounding liquid when the bubble grows (or heat it when the bubble becomes smaller). Since the vapor pressure at the bubble wall is determined by the temperature there, the result of a cooling of the liquid is a decrease of the vapor pressure, and this causes a decrease in the rate of bubble growth. A similar effect occurs during the collapse of a bubble which tends to slow down the collapse. In order to obtain a satisfactory theory of the behavior of a vapor bubble in a liquid, these heat transfer effects must be taken into account. In this paper, the equations of motion for a spherical vapor bubble will be derived and applied to the case of a bubble expanding in superheated liquid and a bubble collapsing in liquid below its boiling point. Because of the inclusion of the heat transfer effects, the equations are nonlinear, integro-differential equations. In the case of the collapsing bubble, large temperature variations occur; therefore, tabulated vapor pressure data were used, and the equations of motion were integrated numerically. Analytic solutions are obtainable for the case of the expanding bubble if the period of growth is subdivided into several regimes and the simplifications possible in each regime are utilized. The growth is considered here only during the time that the bubble is small. An asymptotic solution of the equations of motion, valid when the bubble becomes large (i.e. observable), has been presented previously, together with experimental verification. We shall be specifically concerned in the following discussion with the dynamics of vapor bubbles in water. This restriction was made for convenience only, since the theory is applicable without modification to many other liquids

Functional stability of HIV-1 envelope trimer affects accessibility to broadly neutralizing antibodies at its apex

ABSTRACT The trimeric envelope glycoprotein spike (Env) of HIV-1 is the target of vaccine development to elicit broadly neutralizing antibodies (bnAbs). Env trimer instability and heterogeneity in principle make subunit interfaces inconsistent targets for the immune response. Here, we investigate how functional stability of Env relates to neutralization sensitivity to V2 bnAbs and V3 crown antibodies that engage subunit interfaces upon binding to unliganded Env. Env heterogeneity was inferred when antibodies neutralized a mutant Env with a plateau of less than 100% neutralization. A statistically significant correlation was found between the stability of mutant Envs and the MPN of V2 bnAb, PG9, as well as an inverse correlation between stability of Env and neutralization by V3 crown antibody, 447-52D. A number of Env-stabilizing mutations and V2 bnAb-enhancing mutations were identified in Env, but they did not always overlap, indicating distinct requirements of functional stabilization versus antibody recognition. Blocking complex glycosylation of Env affected V2 bnAb recognition, as previously described, but also notably increased functional stability of Env. This study shows how instability and heterogeneity affect antibody sensitivity of HIV-1 Env, which is relevant to vaccine design involving its dynamic apex. IMPORTANCE The Env trimer is the only viral protein on the surface of HIV-1 and is the target of neutralizing antibodies that reduce viral infectivity. Quaternary epitopes at the apex of the spike are recognized by some of the most potent and broadly neutralizing antibodies to date. Being that their glycan-protein hybrid epitopes are at subunit interfaces, the resulting heterogeneity can lead to partial neutralization. Here, we screened for mutations in Env that allowed for complete neutralization by the bnAbs. We found that when mutations outside V2 increased V2 bnAb recognition, they often also increased Env stability-of-function and decreased binding by narrowly neutralizing antibodies to the V3 crown. Three mutations together increased neutralization by V2 bnAb and eliminated binding by V3 crown antibodies. These results may aid the design of immunogens that elicit antibodies to the trimer apex. </jats:p

Optimization of suppression for two-element treatment liners for turbomachinery exhaust ducts

Sound wave propagation in a soft-walled rectangular duct with steady uniform flow was investigated at exhaust conditions, incorporating the solution equations for sound wave propagation in a rectangular duct with multiple longitudinal wall treatment segments. Modal analysis was employed to find the solution equations and to study the effectiveness of a uniform and of a two-sectional liner in attenuating sound power in a treated rectangular duct without flow (M = 0) and with uniform flow of Mach 0.3. Two-segment liners were shown to increase the attenuation of sound as compared to a uniform liner. The predicted sound attenuation was compared with measured laboratory results for an optimized two-segment suppressor. Good correlation was obtained between the measured and predicted suppressions when practical variations in the modal content and impedance were taken into account. Two parametric studies were also completed

Long quantum channels for high-quality entanglement transfer

High-quality quantum-state and entanglement transfer can be achieved in an unmodulated spin bus operating in the ballistic regime, which occurs when the endpoint qubits A and B are coupled to the chain by an exchange interaction $j_0$ comparable with the intrachain exchange. Indeed, the transition amplitude characterizing the transfer quality exhibits a maximum for a finite optimal value $j_0^{opt}(N)$, where $N$ is the channel length. We show that $j_0^{opt}(N)$ scales as $N^{-1/6}$ for large $N$ and that it ensures a high-quality entanglement transfer even in the limit of arbitrarily long channels, almost independently of the channel initialization. For instance, the average quantum-state transmission fidelity exceeds 90% for any chain length. We emphasize that, taking the reverse point of view, should $j_0$ be experimentally constrained, high-quality transfer can still be obtained by adjusting the channel length to its optimal value.Comment: 12 pages, 9 figure

A clinical-molecular update on azanucleoside-based therapy for the treatment of hematologic cancers

The azanucleosides azacitidine and decitabine are currently used for the treatment of acute myeloid leukemia (AML) and myelodysplastic syndromes (MDS) in patients not only eligible for intensive chemotherapy but are also being explored in other hematologic and solid cancers. Based on their capacity to interfere with the DNA methylation machinery, these drugs are also referred to as hypomethylating agents (HMAs). As DNA methylation contributes to epigenetic regulation, azanucleosides are further considered to be among the first true "epigenetic drugs" that have reached clinical application. However, intriguing new evidence suggests that DNA hypomethylation is not the only mechanism of action for these drugs. This review summarizes the experience from more than 10 years of clinical practice with azanucleosides and discusses their molecular actions, including several not related to DNA methylation. A particular focus is placed on possible causes of primary and acquired resistances to azanucleoside treatment. We highlight current limitations for the success and durability of azanucleoside-based therapy and illustrate that a better understanding of the molecular determinants of drug response holds great potential to overcome resistance

Evolution of the quasiparticle spectral function in cuprates

We analyzed photoemssion data for several doping levels of the Bi_2Sr_2CaCu_2O_{8+x} compounds, ranging from overdoped to underdoped. We show that the high frequency part of the spectra near (0,\pi) can be described by Fermi liquid theory in the overdoped regime, but exhibits a non-Fermi liquid behavior in the underdoped regime. We further demonstrate that this novel behavior fits reasonably well to a 1/\sqrt{\omega} behavior suggested for systems with strong spin fluctuations.Comment: 5 pages, 2 figures (EPS), RevTeX, submitted to Phys Rev B R

Boundary effects on one-particle spectra of Luttinger liquids

We calculate one-particle spectra for a variety of models of Luttinger liquids with open boundary conditions. For the repulsive Hubbard model the spectral weight close to the boundary is enhanced in a large energy range around the chemical potential. A power law suppression, previously predicted by bosonization, only occurs after a crossover at energies very close to the chemical potential. Our comparison with exact spectra shows that the effects of boundaries can partly be understood within the Hartree-Fock approximation.Comment: 4 pages including 4 figures, revised version, to be published in Phys. Rev. B, January 200

Unconventional magnetism in the 4d4^{4} based (S=1S=1) honeycomb system Ag3_{3}LiRu2_{2}O6_{6}

We have investigated the thermodynamic and local magnetic properties of the Mott insulating system Ag$_{3}$LiRu$_{2}$O$_{6}$ containing Ru$^{4+}$ (4$d$$^{4}$) for novel magnetism. The material crystallizes in a monoclinic $C2/m$ structure with RuO$_{6}$ octahedra forming an edge-shared two-dimensional honeycomb lattice with limited stacking order along the $c$-direction. The large negative Curie-Weiss temperature ($\theta_{CW}$ = -57 K) suggests antiferromagnetic interactions among Ru$^{4+}$ ions though magnetic susceptibility and heat capacity show no indication of magnetic long-range order down to 1.8 K and 0.4 K, respectively. $^{7}$Li nuclear magnetic resonance (NMR) shift follows the bulk susceptibility between 120-300 K and levels off below 120 K. Together with a power-law behavior in the temperature dependent spin-lattice relaxation rate between 0.2 and 2 K, it suggest dynamic spin correlations with gapless excitations. Electronic structure calculations suggest an $S = 1$ description of the Ru-moments and the possible importance of further neighbour interactions as also bi-quadratic and ring-exchange terms in determining the magnetic properties. Analysis of our $\mu$SR data indicates spin freezing below 5 K but the spins remain on the borderline between static and dynamic magnetism even at 20 mK.Comment: 10 pages, 11 figures. accepted in Phys. Rev.

The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia