Evolution of spherical cavitation bubbles: parametric and closed-form solutions

We present an analysis of the Rayleigh-Plesset equation for a three dimensional vacuous bubble in water. In the simplest case when the effects of surface tension are neglected, the known parametric solutions for the radius and time evolution of the bubble in terms of a hypergeometric function are briefly reviewed. By including the surface tension, we show the connection between the Rayleigh-Plesset equation and Abel's equation, and obtain the parametric rational Weierstrass periodic solutions following the Abel route. In the same Abel approach, we also provide a discussion of the nonintegrable case of nonzero viscosity for which we perform a numerical integrationComment: 9 pages, 5 figures, 14 references, version accepted for publication at Phys. Fluid

Quantum mechanical spectral engineering by scaling intertwining

Using the concept of spectral engineering we explore the possibilities of building potentials with prescribed spectra offered by a modified intertwining technique involving operators which are the product of a standard first-order intertwiner and a unitary scaling. In the same context we study the iterations of such transformations finding that the scaling intertwining provides a different and richer mechanism in designing quantum spectra with respect to that given by the standard intertwiningComment: 8 twocolumn pages, 5 figure

A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements

The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.Comment: 20 pages, 1 figure to appear in Foundations of Physics, Nov. 2006 two more references adde

All-optical switching and strong coupling using tunable whispering-gallery-mode microresonators

We review our recent work on tunable, ultrahigh quality factor whispering-gallery-mode bottle microresonators and highlight their applications in nonlinear optics and in quantum optics experiments. Our resonators combine ultra-high quality factors of up to Q = 3.6 \times 10^8, a small mode volume, and near-lossless fiber coupling, with a simple and customizable mode structure enabling full tunability. We study, theoretically and experimentally, nonlinear all-optical switching via the Kerr effect when the resonator is operated in an add-drop configuration. This allows us to optically route a single-wavelength cw optical signal between two fiber ports with high efficiency. Finally, we report on progress towards strong coupling of single rubidium atoms to an ultra-high Q mode of an actively stabilized bottle microresonator.Comment: 20 pages, 24 figures. Accepted for publication in Applied Physics B. Changes according to referee suggestions: minor corrections to some figures and captions, clarification of some points in the text, added references, added new paragraph with results on atom-resonator interactio

High-fat diet exacerbates SIV pathogenesis and accelerates disease progression

Copyright: © 2019. American Society for Clinical Investigation.Consuming a high-fat diet (HFD) is a risk factor for obesity and diabetes; both of these diseases are also associated with systemic inflammation, similar to HIV infection. A HFD induces intestinal dysbiosis and impairs liver function and coagulation, with a potential negative impact on HIV/SIV pathogenesis. We administered a HFD rich in saturated fats and cholesterol to nonpathogenic (African green monkeys) and pathogenic (pigtailed macaques) SIV hosts. The HFD had a negative impact on SIV disease progression in both species. Thus, increased cell-associated SIV DNA and RNA occurred in the HFD-receiving nonhuman primates, indicating a potential reservoir expansion. The HFD induced prominent immune cell infiltration in the adipose tissue, an important SIV reservoir, and heightened systemic immune activation and inflammation, altering the intestinal immune environment and triggering gut damage and microbial translocation. Furthermore, HFD altered lipid metabolism and HDL oxidation and also induced liver steatosis and fibrosis. These metabolic disturbances triggered incipient atherosclerosis and heightened cardiovascular risk in the SIV-infected HFD-receiving nonhuman primates. Our study demonstrates that dietary intake has a discernable impact on the natural history of HIV/SIV infections and suggests that dietary changes can be used as adjuvant approaches for HIV-infected subjects, to reduce inflammation and the risk of non-AIDS comorbidities and possibly other infectious diseases.This study was funded through NIH/NHLBI/NIAID/NIDDK/ NCRR R01 grants HL117715 (to IP), HL123096 (to IP), AI119346 (to CA), DK113919 (to IP and CA), DK119936 (to CA), RR025781 (to CA and IP), and AI104373 (to RMR). RMR was funded by grant PTDC/ MAT-APL/31602/2017 from the Fundação para a Ciência e Tecnologia (Portugal). DNF and CCW were supported by the University of Colorado GI and Liver Innate Immunity Program. KDR and BBP were partly supported by the NIH Training Grant T32AI065380. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.info:eu-repo/semantics/publishedVersio

Track A Basic Science

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/138319/1/jia218438.pd

One-parameter Darboux-deformed Fibonacci numbers

One-parameter Darboux deformations are effected for the simple ODE satisfied by the continuous generalizations of the Fibonacci sequence recently discussed by Faraoni and Atieh [Symmetry 13, 200 (2021)], who promoted a formal analogy with the Friedmann equation in the FLRW homogeneous cosmology. The method allows the introduction of deformations of the continuous Fibonacci sequences, hence of Darboux-deformed Fibonacci (non integer) numbers. Considering the same ODE as a parametric oscillator equation, the Ermakov-Lewis invariants for these sequences are also discussed

Liouville soliton surfaces obtained using Darboux transformations

We construct parametric Liouville surfaces corresponding to parametric soliton solutions of the Liouville equation and Darboux-transformed counterparts. We also use a modified variation of parameters method together with the elliptic functions method to obtain the traveling wave solutions to Liouville equation and express the centroaffine invariant in terms of the soliton Hamiltonia

Radius evolution for bubbles with elastic shells

We present an analysis of an extended Rayleigh–Plesset (RP) equation for a three dimensional cell of microorganisms such as bacteria or viruses in some liquid, where the cell membrane in bacteria or the envelope (capsid) in viruses possess elastic properties. To account for rapid changes in the shape configuration of such microorganisms, the bubble membrane/envelope must be rigid to resist large pressures while being flexible to adapt to growth or decay. Such properties are embedded in the RP equation by including a pressure bending term that is proportional to the square of the curvature of the elastic wall. Analytical solutions to this extended equation are obtained in terms of elliptic functions