Oscillatory and localized perturbations of periodic structures and the bifurcation of defect modes

Let $Q(x)$ denote a periodic function on the real line. The Schr\"odinger operator, $H_Q=-\partial_x^2+Q(x)$, has $L^2(\mathbb{R})-$ spectrum equal to the union of closed real intervals separated by open spectral gaps. In this article we study the bifurcation of discrete eigenvalues (point spectrum) into the spectral gaps for the operator $H_{Q+q_\epsilon}$, where $q_\epsilon$ is spatially localized and highly oscillatory in the sense that its Fourier transform, $\widehat{q}_\epsilon$ is concentrated at high frequencies. Our assumptions imply that $q_\epsilon$ may be pointwise large but $q_\epsilon$ is small in an average sense. For the special case where $q_\epsilon(x)=q(x,x/\epsilon)$ with $q(x,y)$ smooth, real-valued, localized in $x$, and periodic or almost periodic in $y$, the bifurcating eigenvalues are at a distance of order $\epsilon^4$ from the lower edge of the spectral gap. We obtain the leading order asymptotics of the bifurcating eigenvalues and eigenfunctions. Underlying this bifurcation is an effective Hamiltonian associated with the lower edge of the $(b_*)^{\rm th}$ spectral band: $H^\epsilon_{\rm eff}=-\partial_x A_{b_*,\rm eff}\partial_x - \epsilon^2 B_{b_*,\rm eff} \times \delta(x)$ where $\delta(x)$ is the Dirac distribution, and effective-medium parameters $A_{b_*,\rm eff},B_{b_*,\rm eff}>0$ are explicit and independent of $\epsilon$. The potentials we consider are a natural model for wave propagation in a medium with localized, high-contrast and rapid fluctuations in material parameters about a background periodic medium.Comment: To appear in SIAM Journal on Mathematical Analysi

Homogenized description of defect modes in periodic structures with localized defects

A spatially localized initial condition for an energy-conserving wave equation with periodic coefficients disperses (spatially spreads) and decays in amplitude as time advances. This dispersion is associated with the continuous spectrum of the underlying differential operator and the absence of discrete eigenvalues. The introduction of spatially localized perturbations in a periodic medium leads to defect modes, states in which energy remains trapped and spatially localized. In this paper we study weak, localized perturbations of one-dimensional periodic Schr\"odinger operators. Such perturbations give rise to such defect modes, and are associated with the emergence of discrete eigenvalues from the continuous spectrum. Since these isolated eigenvalues are located near a spectral band edge, there is strong scale-separation between the medium period and the localization length of the defect mode. Bound states therefore have a multi-scale structure: a "carrier Bloch wave" times a "wave envelope", which is governed by a homogenized Schr\"odinger operator with associated effective mass, depending on the spectral band edge which is the site of the bifurcation. Our analysis is based on a reformulation of the eigenvalue problem in Bloch quasi-momentum space, using the Gelfand-Bloch transform and a Lyapunov-Schmidt reduction to a closed equation for the near-band-edge frequency components of the bound state. A rescaling of the latter equation yields the homogenized effective equation for the wave envelope, and approximations to bifurcating eigenvalues and eigenfunctions.Comment: The title differs from version 1. To appear in Communications in Mathematical Science

Acanthamoeba castellanii : growth on human cell layers reactivates attenuated properties after prolonged axenic culture

The free-living, but potentially pathogenic, bacteriovorous amoebae of the genus Acanthamoeba can be easily grown axenically in a laboratory culture. This, however, often leads to considerable losses in virulence, and encystment capacity, and to changes in drug susceptibility. We evaluated potential options for a reactivation of a number of physiological properties, attenuated by prolonged axenic laboratory culture, including encystment potential, protease activity, heat resistance, growth rates and drug susceptibility against N-chlorotaurine (NCT). Toward this end, a strain that had been grown axenically for 10 years was repeatedly passaged on human HEp-2 cell monolayers or treated with 5′-azacytidine (AzaC), a methyltransferase inhibitor, and trichostatin A (TSA), a histone deacetylase inhibitor, in order to uplift epigenetic gene regulation. Culture on human cell monolayers resulted in significantly enhanced encystment potentials and protease activities, and higher susceptibility against NCT, whereas the resistance against heat shock was not altered. Treatment with AzaC/TSA resulted in increased encystment rates and protease activities, indicating the participation of epigenetic mechanisms. However, lowered resistances against heat shock indicate that possible stress responses to AzaC/TSA have to be taken into account. Repeated growth on human cell monolayers appears to be a potential method to reactivate attenuated characteristics in Acanthamoeba

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Wave operator bounds for one-dimensional Schrödinger operators with singular potentials and applications

Boundedness of wave operators for Schrödinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds

An Adaptive Optics Survey for Close Protostellar Binaries

In order to test the hypothesis that Class I protostellar binary stars are a product of ejections during the dynamical decay of non-hierarchical multiple systems, we combined the results of new adaptive optics (AO) observations of Class I protostars with our previously published AO data to investigate whether Class I protostars with a widely separated companion (r>200 AU) are more likely to also have a close companion (r<200 AU). In total, we observed 47 embedded young stellar objects (YSOs) with either the Subaru natural guide star AO system or the Keck laser guide star AO system. We found that targets with a widely separated companion within 5,000 AU are not more likely to have a close companion. However, targets with another YSO within a projected separation of 25,000 AU are much more likely to have a close companion. Most importantly, every target with a close companion has another YSO within a projected separation of 25,000 AU. We came to the same conclusions after considering a restricted sample of targets within 500 pc and close companions wider than 50 AU to minimize incompleteness effects. The Orion star forming region was found to have an excess of both close binaries and YSOs within 25,000 AU compared to other star forming regions. We interpret these observations as strong evidence that many close Class I binary stars form via ejections and that many of the ejected stars become unbound during the Class I phase.Comment: 22 pages, 3 figures, 2 table

The Evolution of the Multiplicity of Embedded Protostars II: Binary Separation Distribution & Analysis

We present the Class I protostellar binary separation distribution based on the data tabulated in the companion paper. We verify the excess of Class I binary stars over solar-type main-sequence stars, especially at separations beyond 500 AU. Although our sources are in nearby star forming regions distributed across the entire sky (including Orion), none of our objects are in a high stellar density environment. The binary separation distribution changes significantly during the Class I phase, and the binary frequency at separations greater than 1000 AU declines steadily with respect to spectral index. Despite these changes, the binary frequency remains constant until the end of the Class I phase, when it drops sharply. We propose a scenario to account for the changes in the Class I binary separation distribution. This scenario postulates that companions with a separation greater than ~1000 AU were ejected during the Class 0 phase, but remain gravitationally bound due to the mass of the envelope. As the envelope dissipates, these companions become unbound and the binary frequency at wide separations declines. This scenario predicts that a large number of Class 0 objects should be non-hierarchical multiple systems, and that many Class I YSOs with a widely separated companion should also have a very close companion. We also find that Class I protostars are not dynamically pristine, and have experienced dynamical evolution before they are visible as Class I objects. For the first time, evidence is presented showing that the Class I binary frequency and the binary separation distribution strongly depend on the star forming environment. The reason for this dependence remains unclear.Comment: 33 pages, 16 figures, accepted by the Astronomical Journa

Disk and Envelope Structure in Class 0 Protostars: I. The Resolved Massive Disk in Serpens FIRS 1

We present the first results of a program to characterize the disk and envelope structure of typical Class 0 protostars in nearby low-mass star forming regions. We use Spitzer IRS mid-infrared spectra, high resolution CARMA 230 GHz continuum imaging, and 2-D radiative transfer models to constrain the envelope structure, as well as the size and mass of the circum-protostellar disk in Serpens FIRS 1. The primary envelope parameters (centrifugal radius, outer radius, outflow opening angle, and inclination) are well constrained by the spectral energy distribution (SED), including Spitzer IRAC and MIPS photometry, IRS spectra, and 1.1 mm Bolocam photometry. These together with the excellent uv-coverage (4.5-500 klam) of multiple antenna configurations with CARMA allow for a robust separation of the envelope and a resolved disk. The SED of Serpens FIRS 1 is best fit by an envelope with the density profile of a rotating, collapsing spheroid with an inner (centrifugal) radius of approximately 600 AU, and the millimeter data by a large resolved disk with Mdisk~1.0 Msun and Rdisk~300 AU. These results suggest that large, massive disks can be present early in the main accretion phase. Results for the larger, unbiased sample of Class~0 sources in the Perseus, Serpens, and Ophiuchus molecular clouds are needed to determine if relatively massive disks are typical in the Class 0 stage.Comment: Comments: 13 pages, 8 figures, 3 tables; accepted for publication in the Ap