The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows that featur
es without length scales, i.e. topological features, are potentially of central importance. Topology is a natural mathematical tool for the study of shape and we avail ourselves of that tool to examine the relationship between the amino acid sequence and the shapes of protein molecules. We apply what we learn to conjectures about their biological evolution.
LSQ14bdq and SN 2006oz are super-luminous, hydrogen-poor, SNe with double-humped light curves. We show that a Quark-Nova (QN; explosive transition of the neutron star to a quark star) occurring in a massive binary, experiencing two Common Envelope (C
E) phases, can quantitatively explain the light curves of LSQ14bdq and SN 2006oz. The more massive component (A) explodes first as a normal SN, yielding a Neutron Star which ejects the hydrogen envelope of the companion when the system enters its first CE phase. During the second CE phase, the NS spirals into and inflates the second He-rich CE. In the process it gains mass and triggers a Quark-Nova, outside of the CO core, leaving behind a Quark Star. The first hump in our model is the QN shock re-energizing the expanded He-rich CE. The QN occurs when the He-rich envelope is near maximum size (~ 1000R_sun) and imparts enough energy to unbind and eject the envelope. Subsequent merging of the Quark Star with the CO core of component B, driven by gravitational radiation, turns the Quark star to a Black Hole. The ensuing Black Hole accretion provides sufficient power for the second brighter and long lasting hump. Our model suggests a possible connection between SLSNe-I and type Ic-BL SNe which occur when the Quark Nova is triggered inside the CO core. We estimate the rate of QNe in massive binaries during the second CE phase to be ~ 5x10^(-5) of that of core-collapse SNe.
In this paper, the photon stationary transport equation has been extended from $mathbb{R}^3$ to $mathbb{C}^3$. A solution of the inverse problem is obtained on a hyper-sphere and a hyper-cylinder as X-ray and Radon transform, respectively. We show th
at these results can be transformed into each other and they agree with known results.
Hole-doped cuprate high temperature superconductors have ushered in the modern era of high temperature superconductivity (HTS) and have continued to be at center stage in the field. Extensive studies have been made, many compounds discovered, volumin
ous data compiled, numerous models proposed, many review articles written, and various prototype devices made and tested with better performance than their nonsuperconducting counterparts. The field is indeed vast. We have therefore decided to focus on the major cuprate materials systems that have laid the foundation of HTS science and technology and present several simple scaling laws that show the systematic and universal simplicity amid the complexity of these material systems, while referring readers interested in the HTS physics and devices to the review articles. Developments in the field are mostly presented in chronological order, sometimes with anecdotes, in an attempt to share some of the moments of excitement and despair in the history of HTS with readers, especially the younger ones.
In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE($kappa,rho_c$). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we o
btain the long and short time behaviors of the chordal SLE traces. We analyze the solutions of the FP and the corresponding Langevin equations and connect it to the conformal field theory (CFT) and present some exact results. We find the perturbative FP equation of the SLE($kappa,rho_c$) traces and show that it is related to the higher order correlation functions. Using the Langevin equation we find the long-time behaviors in this case. The CFT correspondence of this case is established and some exact results are presented.
Millisecond Pulsars (MSPs) are fast rotating, highly magnetized neutron stars. According to the canonical recycling scenario, MSPs form in binary systems containing a neutron star which is spun up through mass accretion from the evolving companion. T
herefore, the final stage consists of a binary made of a MSP and the core of the deeply peeled companion. In the last years, however an increasing number of systems deviating from these expectations has been discovered, thus strongly indicating that our understanding of MSPs is far to be complete. The identification of the optical companions to binary MSPs is crucial to constrain the formation and evolution of these objects. In dense environments such as Globular Clusters (GCs), it also allows us to get insights on the cluster internal dynamics. By using deep photometric data, acquired both from space and ground-based telescopes, we identified 5 new companions to MSPs. Three of them being located in GCs and two in the Galactic Field. The three new identifications in GCs increased by 50% the number of such objects known before this Thesis. They all are non-degenerate stars, at odds with the expectations of the canonical recycling scenario. These results therefore suggest either that transitory phases should also be taken into account, or that dynamical processes, as exchange interactions, play a crucial role in the evolution of MSPs. We also performed a spectroscopic follow-up of the companion to PSR J1740-5340A in the GC NGC 6397, confirming that it is a deeply peeled star descending from a ~0.8$M_{odot}$ progenitor. This nicely confirms the theoretical expectations about the formation and evolution of MSPs.
The distinctive cometary X-ray morphology of the recently discovered massive galaxy cluster El Gordo (ACT-CT J0102-4915; z=0.87) indicates that an unusually high-speed collision is ongoing between two massive galaxy clusters. A bright X-ray bullet le
ads a twin-tailed wake, with the SZ centroid at the end of the Northern tail. We show how the physical properties of this system can be determined using our FLASH-based, N-body/hydrodynamic model, constrained by detailed X-ray, Sunyaev-Zeldovich (SZ), and Hubble lensing and dynamical data. The X-ray morphology and the location of the two Dark Matter components and the SZ peak are accurately described by a simple binary collision viewed about 480 million years after the first core passage. We derive an impact parameter of ~300 kpc, and a relative initial infall velocity of ~2250 km/sec when separated by the sum of the two virial radii assuming an initial total mass of 2.15x10^(15) Msun and a mass ratio of 1.9. Our model demonstrates that tidally stretched gas accounts for the Northern X-ray tail along the collision axis between the mass peaks, and that the Southern tail lies off axis, comprising compressed and shock heated gas generated as the massive component plunges through the main cluster. The challenge for LCDM will be to find out if this physically extreme event can be plausibly accommodated when combined with the similarly massive, high infall velocity case of the Bullet cluster and other such cases being uncovered in the new SZ based surveys.
The statistical mechanics of polymers grafted on surfaces has been the subject of intense research activity because of many potential applications. In this paper, we analytically investigate the conformational changes caused by a single cross-link on
two ideal (Gaussian) chains grafted on a rigid planar surface. Both the cross-link and the surface reduce the number of allowed configurations. In the absence of the hard substrate, the sole effect of the cross-link is a reduction in the effective Kuhn length of a tethered chain. The cross-link induced shrinkage (collapse) of the grafted chains (mushrooms) turns out to be a reduction in the variance of the distribution of the height of the chain rather than a reduction of the height itself.
We report a multi-wavelength study of four new planetary nebula (PN) candidates selected from the INT/WFC Photometric Ha Survey of the Northern Galactic Plane (IPHAS) and Deep Sky Hunter (DSH) catalogues. We present mid-resolution optical spectra of
these PNs. The PN status of our sample was confirmed by optical narrow-band images and mid-resolution spectra. Based on the locations of these objects in the log (Ha/[N II]) versus log (Ha/[S II]) diagnostic diagram, we conclude that these sources are evolved lowexcitation PNs. The optical and infrared appearances of these newly discovered PNs are discussed. Three of the new nebulae studied here are detected in infrared and have low infrared-to-radio flux ratios, probably suggesting that they are evolved. Furthermore, we derive the dynamical ages and distances of these nebulae and study the spectral energy distribution for one of them with extensive infrared archival data.
We have investigated the X-ray spectral properties of a sample of 138 X-ray sources detected serendipitously in $XMM-Newton$ observations of the Galactic plane, at an intermediate to faint flux level. We divide our sample into 5 subgroups according t
o the spectral hardness of the sources, and stack (i.e. co-add) the individual source spectra within each subgroup. As expected these stacked spectra show a softening trend from the hardest to the softest subgroups, which is reflected in the inferred line-of-sight column density. The spectra of the three hardest subgroups are characterized by a hard continuum plus superimpose Fe-line emission in the 6--7 keV bandpass. The average equivalent width (EW) of the 6.7-keV He-like Fe-K$alpha$ line is 170$^{+35}_{-32}$ eV, whereas the 6.4-keV Fe-K fluorescence line from neutral iron and the 6.9-keV H-like Fe-Ly$alpha$ line have EWs of 89$^{+26}_{-25}$ eV and 81$^{+30}_{-29}$ eV respectively, i.e. roughly half that of the 6.7-keV line. The remaining subgroups exhibit soft thermal spectra. Virtually all of the spectrally-soft X-ray sources can be associated with relatively nearby coronally-active late-type stars, which are evident as bright near-infrared (NIR) objects within the X-ray error circles. On a similar basis only a minority of the spectrally-hard X-ray sources have likely NIR identifications. The average continuum and Fe-line properties of the spectrally-hard sources are consistent with those of magnetic cataclysmic variables but the direct identification of large numbers of such systems in Galactic X-ray surveys, probing intermediate to faint flux levels, remains challenging.
