Three ways of treating a linear delay differential equation

This work concerns the occurrence of Hopf bifurcations in delay differential equations (DDE). Such bifurcations are associated with the occurrence of pure imaginary characteristic roots in a linearized DDE. In this work we seek the exact analytical conditions for pure imaginary roots, and we compare them with the approximate conditions obtained by using the two variable expansion perturbation method. This method characteristically gives rise to a “slow flow” which contains delayed variables. In analyzing such approximate slow flows, we compare the exact treatment of the slow flow with a further approximation based on replacing the delayed variables in the slow flow with non-delayed variables, thereby reducing the DDE slow flow to an ODE. By comparing these three approaches we are able to assess the accuracy of making the various approximations. We apply this comparison to a linear harmonic oscillator with delayed self-feedback

HALOGAS: HI Observations and Modeling of the Nearby Edge-on Spiral Galaxy NGC 4565

We present 21-cm observations and models of the neutral hydrogen in NGC 4565, a nearby, edge-on spiral galaxy, as part of the Westerbork Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey. These models provide insight concerning both the morphology and kinematics of HI above, as well as within, the disk. NGC 4565 exhibits a distinctly warped and asymmetric disk with a flaring layer. Our modeling provides no evidence for a massive, extended HI halo. We see evidence for a bar and associated radial motions. Additionally, there are indications of radial motions within the disk, possibly associated with a ring of higher density. We see a substantial decrease in rotational velocity with height above the plane of the disk (a lag) of -40 +5/-20 km/s/kpc and -30 +5/-30 km s/kpc in the approaching and receding halves, respectively. This lag is only seen within the inner ~4.75' (14.9 kpc) on the approaching half and ~4.25' (13.4 kpc) on the receding, making this a radially shallowing lag, which is now seen in the HI layers of several galaxies. When comparing results for NGC 4565 and those for other galaxies, there are tentative indications of high star formation rate per unit area being associated with the presence of a halo. Finally, HI is found in two companion galaxies, one of which is clearly interacting with NGC 4565.Comment: 17 pages, 16 figures, accepted for publication in the Astrophysical Journal, modified affiliatio

Synchronization in pairs of opto-thermally driven mechanically coupled micro-oscillators

We study the phenomenon of synchronization in pairs of doubly clamped, mechanically coupled silicon micro-oscillators. A continuous-wave laser beam is used to drive the micro-beams into limit cycle oscillations and to detect the oscillations using interferometry. Devices of different dimensions are used to introduce frequency detuning, and short silicon bridges connecting the micro-beams are used as mechanical coupling between the oscillators. The region of synchronization is plotted for the MEMS system in the detuning vs. coupling parameter space and compared with the numerical analysis of a corresponding, lumped-parameter model. Three states of oscillations are observed i.e. the drift state, quasi-periodic state, and the synchronized state. The numerical model also distinguishes between in-phase and out-of-phase synchronization where out-of-phase synchronization is observed at low coupling strengths and low frequency detuning. We also show that the experimentally measured frequency fluctuations of the system reduce with an increase in coupling strength.Comment: 8 pages, 7 figure

“My Future is Now”: A Qualitative Study of Persons Living With Advanced Cancer

Objectives: Advance care planning (ACP) enables individuals to deliberate about future preferences for care based upon their values and beliefs about what is important in life. For many patients with advanced cancer, however, these critical conversations do not occur. A growing body of literature has examined the end-of-life wishes of seriously ill patients. Few studies have explored what is important to persons as they live with advanced cancer. The aim of the current study was to address this gap and to understand how clinicians can support patients’ efforts to live in the present and plan for the future. Methods: Transcriptions of interviews conducted with 36 patients diagnosed with advanced cancer were analyzed using immersion–crystallization, a qualitative research technique. Results: Four overarching themes were identified: (I) living in the face of death, (II) who I am, (III) my experience of cancer, and (IV) impact of my illness on others. Twelve subthemes are also reported. Significance of Results: These findings have significant implications for clinicians as they partner with patients to plan for the future. Our data suggest that clinicians consider the following 4 prompts: (1) “What is important to you now, knowing that you will die sooner than you want or expected?” (2) “Tell me about yourself.” (3) “Tell me in your own words about your experience with cancer care and treatment.” (4) “What impact has your illness had on others?” In honoring patients’ lived experiences, we may establish the mutual understanding necessary to providing high-quality care that supports patients’ priorities for life

HALOGAS: HI Observations and Modeling of the Nearby Edge-on Spiral Galaxy NGC 4244

We present 21-cm observations and models of the HI kinematics and distribution of NGC 4244, a nearby edge-on Scd galaxy observed as part of the Westerbork Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey. Our models give insight into the HI kinematics and distribution with an emphasis on the potential existence of extra-planar gas as well as a negative gradient in rotational velocity with height above the plane of the disk (a lag). Our models yield strong evidence against a significantly extended halo and instead favor a warp component along the line of sight as an explanation for some of the observed thickening of the disk. Based on these models, we detect a lag of -9 +3/-2 km s-1 kpc-1 in the approaching half and -9 +/-2 km s-1 kpc-1 in the receding half. This lag decreases in magnitude to -5+/-2 km s-1 kpc-1 and -4+/-2 km s-1 kpc-1 near a radius of 10 kpc in the approaching and receding halves respectively. Additionally, we detect several distinct morphological and kinematic features including a shell that is probably driven by star formation within the disk.Comment: 18 pages, 14 figures, Full resolution version may be found at: http://www.astron.nl/halogas/papers/NGC4244.Zschaechner.arXiv.p

Imaging Fabry-Perot Spectroscopy of NGC 5775: Kinematics of the Diffuse Ionized Gas Halo

We present imaging Fabry-Perot observations of Halpha emission in the nearly edge-on spiral galaxy NGC 5775. We have derived a rotation curve and a radial density profile along the major axis by examining position-velocity (PV) diagrams from the Fabry-Perot data cube as well as a CO 2-1 data cube from the literature. PV diagrams constructed parallel to the major axis are used to examine changes in azimuthal velocity as a function of height above the midplane. The results of this analysis reveal the presence of a vertical gradient in azimuthal velocity. The magnitude of this gradient is approximately 1 km/s/arcsec, or about 8 km/s/kpc, though a higher value of the gradient may be appropriate in localized regions of the halo. The evidence for an azimuthal velocity gradient is much stronger for the approaching half of the galaxy, although earlier slit spectra are consistent with a gradient on both sides. There is evidence for an outward radial redistribution of gas in the halo. The form of the rotation curve may also change with height, but this is not certain. We compare these results with those of an entirely ballistic model of a disk-halo flow. The model predicts a vertical gradient in azimuthal velocity which is shallower than the observed gradient, indicating that an additional mechanism is required to further slow the rotation speeds in the halo.Comment: 18 pages, 18 figures. Uses emulateapj.cls. Accepted for publication in Ap

Integral Field Unit Observations of NGC 891: Kinematics of the Diffuse Ionized Gas Halo

We present high and moderate spectral resolution spectroscopy of diffuse ionized gas (DIG) emission in the halo of NGC 891. The data were obtained with the SparsePak integral field unit at the WIYN Observatory. The wavelength coverage includes the [NII]6548,6583, Halpha, and [SII]6716,6731 emission lines. Position-velocity (PV) diagrams, constructed using spectra extracted from four SparsePak pointings in the halo, are used to examine the kinematics of the DIG. Using two independent methods, a vertical gradient in azimuthal velocity is found to be present in the northeast quadrant of the halo, with magnitude approximately 15-18 km/s/kpc, in agreement with results from HI observations. The kinematics of the DIG suggest that this gradient begins at approximately 1 kpc above the midplane. In another part of the halo, the southeast quadrant, the kinematics are markedly different, and suggest rotation at about 175 km/s, much slower than the disk but with no vertical gradient. We utilize an entirely ballistic model of disk-halo flow in an attempt to reproduce the kinematics observed in the northeast quadrant. Analysis shows that the velocity gradient predicted by the ballistic model is far too shallow. Based on intensity cuts made parallel to the major axis in the ballistic model and an Halpha image of NGC 891 from the literature, we conclude that the DIG halo is much more centrally concentrated than the model, suggesting that hydrodynamics dominate over ballistic motion in shaping the density structure of the halo. Velocity dispersion measurements along the minor axis of NGC 891 seem to indicate a lack of radial motions in the halo, but the uncertainties do not allow us to set firm limits.Comment: 31 pages, 10 figures. Accepted for publication in the Astrophysical Journa