Auxetic regions in large deformations of periodic frameworks

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions.Comment: Presented at the International Conference on "Interdisciplinary Applications of Kinematics" (IAK18), Lima, Peru, March 201

Root asymptotics of spectral polynomials for the Lame operator

The study of polynomial solutions to the classical Lam\'e equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schr\"odinger equation with finite gap potential given by the Weierstrass $\wp$-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.Comment: final version, to appear in Commun. Math. Phys.; 13 pages, 3 figures, LaTeX2

Spectroscopy of 35^{35}P using the one-proton knockout reaction

The structure of $^{35}$P was studied with a one-proton knockout reaction at88~MeV/u from a $^{36}$S projectile beam at NSCL. The $\gamma$ rays from thedepopulation of excited states in $^{35}$P were detected with GRETINA, whilethe $^{35}$P nuclei were identified event-by-event in the focal plane of theS800 spectrograph. The level scheme of $^{35}$P was deduced up to 7.5 MeV using$\gamma-\gamma$ coincidences. The observed levels were attributed to protonremovals from the $sd$-shell and also from the deeply-bound $p\_{1/2}$ orbital.The orbital angular momentum of each state was derived from the comparisonbetween experimental and calculated shapes of individual ($\gamma$-gated)parallel momentum distributions. Despite the use of different reactions andtheir associate models, spectroscopic factors, $C^2S$, derived from the$^{36}$S $(-1p)$ knockout reaction agree with those obtained earlier from$^{36}$S($d$,\nuc{3}{He}) transfer, if a reduction factor $R\_s$, as deducedfrom inclusive one-nucleon removal cross sections, is applied to the knockout transitions.In addition to the expected proton-hole configurations, other states were observedwith individual cross sections of the order of 0.5~mb. Based on their shiftedparallel momentum distributions, their decay modes to negative parity states,their high excitation energy (around 4.7~MeV) and the fact that they were notobserved in the ($d$,\nuc{3}{He}) reaction, we propose that they may resultfrom a two-step mechanism or a nucleon-exchange reaction with subsequent neutronevaporation. Regardless of the mechanism, that could not yet be clarified, thesestates likely correspond to neutron core excitations in \nuc{35}{P}. Thisnewly-identified pathway, although weak, offers the possibility to selectivelypopulate certain intruder configurations that are otherwise hard to produceand identify.Comment: 5 figures, 1 table, accepted for publication in Physical Review

Generalized Borcea-Voisin Construction

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the mirror pairing is lost.Comment: 15 pages, 2 figures. v2: typos corrected & references adde

Filtering Deterministic Layer Effects in Imaging

Sensor array imaging arises in applications such as nondestructive evaluation of materials with ultrasonic waves, seismic exploration, and radar. The sensors probe a medium with signals and record the resulting echoes, which are then processed to determine the location and reflectivity of remote reflectors. These could be defects in materials such as voids, fault lines or salt bodies in the earth, and cars, buildings, or aircraft in radar applications. Imaging is relatively well understood when the medium through which the signals propagate is smooth, and therefore nonscattering. But in many problems the medium is heterogeneous, with numerous small inhomogeneities that scatter the waves. We refer to the collection of inhomogeneities as clutter, which introduces an uncertainty in imaging because it is unknown and impossible to estimate in detail. We model the clutter as a random process. The array data is measured in one realization of the random medium, and the challenge is to mitigate cumulative clutter scattering so as to obtain robust images that are statistically stable with respect to different realizations of the inhomogeneities. Scatterers that are not buried too deep in clutter can be imaged reliably with the coherent interferometric (CINT) approach. But in heavy clutter the signal-to-noise ratio (SNR) is low and CINT alone does not work. The “signal,” the echoes from the scatterers to be imaged, is overwhelmed by the “noise,” the strong clutter reverberations. There are two existing approaches for imaging at low SNR: The first operates under the premise that data are incoherent so that only the intensity of the scattered field can be used. The unknown coherent scatterers that we want to image are modeled as changes in the coefficients of diffusion or radiative transport equations satisfied by the intensities, and the problem becomes one of parameter estimation. Because the estimation is severely ill-posed, the results have poor resolution, unless very good prior information is available and large arrays are used. The second approach recognizes that if there is some residual coherence in the data, that is, some reliable phase information is available, it is worth trying to extract it and use it with well-posed coherent imaging methods to obtain images with better resolution. This paper takes the latter approach and presents a first attempt at enhancing the SNR of the array data by suppressing medium reverberations. It introduces filters, or annihilators of layer backscatter, that are designed to remove primary echoes from strong, isolated layers in a medium with additional random layering at small, subwavelength scales. These strong layers are called deterministic because they can be imaged from the data. However, our goal is not to image the layers, but to suppress them and thus enhance the echoes from compact scatterers buried deep in the medium. Surprisingly, the layer annihilators work better than intended, in the sense that they suppress not only the echoes from the deterministic layers, but also multiply scattered ones in the randomly layered structure. Following the layer annihilators presented here, other filters of general, nonlayered heavy clutter have been developed. We review these more recent developments and the challenges of imaging in heavy clutter in the introduction in order to place the research presented here in context. We then present in detail the layer annihilators and show with analysis and numerical simulations how they work

The photometric properties of a vast stellar substructure in the outskirts of M33

We have surveyed $\sim40$sq.degrees surrounding M33 with CFHT MegaCam in the g and i filters, as part of the Pan-Andromeda Archaeological Survey. Our observations are deep enough to resolve the top 4mags of the red giant branch population in this galaxy. We have previously shown that the disk of M33 is surrounded by a large, irregular, low-surface brightness substructure. Here, we quantify the stellar populations and structure of this feature using the PAndAS data. We show that the stellar populations of this feature are consistent with an old population with $<[Fe/H]>\sim-1.6$dex and an interquartile range in metallicity of $\sim0.5$dex. We construct a surface brightness map of M33 that traces this feature to $\mu_V\simeq33$mags\,arcsec$^{-2}$. At these low surface brightness levels, the structure extends to projected radii of $\sim40$kpc from the center of M33 in both the north-west and south-east quadrants of the galaxy. Overall, the structure has an "S-shaped" appearance that broadly aligns with the orientation of the HI disk warp. We calculate a lower limit to the integrated luminosity of the structure of $-12.7\pm0.5$mags, comparable to a bright dwarf galaxy such as Fornax or AndII and slightly less than $1\$ of the total luminosity of M33. Further, we show that there is tentative evidence for a distortion in the distribution of young stars near the edge of the HI disk that occurs at similar azimuth to the warp in HI. The data also hint at a low-level, extended stellar component at larger radius that may be a M33 halo component. We revisit studies of M33 and its stellar populations in light of these new results, and we discuss possible formation scenarios for the vast stellar structure. Our favored model is that of the tidal disruption of M33 in its orbit around M31.Comment: Accepted for publication in ApJ. 17 figures. ApJ preprint forma

The nuclear shell effects near the r-process path in the relativistic Hartree-Bogoliubov theory

We have investigated the evolution of the shell structure of nuclei in going from the r-process path to the neutron drip line within the framework of the Relativistic Hartree-Bogoliubov (RHB) theory. By introducing the quartic self-coupling of $\omega$ meson in the RHB theory in addition to the non-linear scalar coupling of $\sigma$ meson, we reproduce the available data on the shell effects about the waiting-point nucleus $^{80}$Zn. With this approach, it is shown that the shell effects at N=82 in the inaccessible region of the r-process path become milder as compared to the Lagrangian with the scalar self-coupling only. However, the shell effects remain stronger as compared to the quenching exhibited by the HFB+SkP approach. It is also shown that in reaching out to the extreme point at the neutron drip line, a terminal situation arises where the shell structure at the magic number is washed out significantly.Comment: 18 pages (revtex), 8 ps figures, to appear in Phys. Rev.

Non-Perturbative Corrections and Modularity in N=1 Type IIB Compactifications

Non-perturbative corrections and modular properties of four-dimensional type IIB Calabi-Yau orientifolds are discussed. It is shown that certain non-perturbative alpha' corrections survive in the large volume limit of the orientifold and periodically correct the Kahler potential. These corrections depend on the NS-NS two form and have to be completed by D-instanton contributions to transform covariantely under symmetries of the type IIB orientifold background. It is shown that generically also the D-instanton superpotential depends on the two-form moduli as well as on the complex dilaton. These contributions can arise through theta-functions with the dilaton as modular parameter. An orientifold of the Enriques Calabi-Yau allows to illustrate these general considerations. It is shown that this compactification leads to a controlled four-dimensional N=1 effective theory due to the absence of various quantum corrections. Making contact to the underlying topological string theory the D-instanton superpotential is proposed to be related to a specific modular form counting D3, D1, D(-1) degeneracies on the Enriques Calabi-Yau.Comment: 35 page