Singular Laplacian Growth

The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.Comment: 8 pages, Latex, 4 figures, Submitted to Phys. Rev.

Interaction of Supernova Ejecta with Nearby Protoplanetary Disks

The early Solar System contained short-lived radionuclides such as 60Fe (t1/2 = 1.5 Myr) whose most likely source was a nearby supernova. Previous models of Solar System formation considered a supernova shock that triggered the collapse of the Sun's nascent molecular cloud. We advocate an alternative hypothesis, that the Solar System's protoplanetary disk had already formed when a very close (< 1 pc) supernova injected radioactive material directly into the disk. We conduct the first numerical simulations designed to answer two questions related to this hypothesis: will the disk be destroyed by such a close supernova; and will any of the ejecta be mixed into the disk? Our simulations demonstrate that the disk does not absorb enough momentum from the shock to escape the protostar to which it is bound. Only low amounts (< 1%) of mass loss occur, due to stripping by Kelvin-Helmholtz instabilities across the top of the disk, which also mix into the disk about 1% of the intercepted ejecta. These low efficiencies of destruction and injectation are due to the fact that the high disk pressures prevent the ejecta from penetrating far into the disk before stalling. Injection of gas-phase ejecta is too inefficient to be consistent with the abundances of radionuclides inferred from meteorites. On the other hand, the radionuclides found in meteorites would have condensed into dust grains in the supernova ejecta, and we argue that such grains will be injected directly into the disk with nearly 100% efficiency. The meteoritic abundances of the short-lived radionuclides such as 60Fe therefore are consistent with injection of grains condensed from the ejecta of a nearby (< 1 pc) supernova, into an already-formed protoplanetary disk.Comment: 57 pages, 16 figure

Morphological diagram of diffusion driven aggregate growth in plane: competition of anisotropy and adhesion

Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters $D(N)$ as a function of their size $N$. We propose that in the thermodynamic limit of infinite cluster size the aggregates grown with high degree of anisotropy ($N_{fp}=3,4,5$) tend to have fractal dimension $D$ equal to 3/2, while off-lattice aggregates and aggregates with lower anisotropy ($N_{fp}>6$) have $D \approx 1.710$. Noise-reduction procedure results in the change of universality class for DLA. For high enough noise-reduction value clusters with $N_{fp} \ge 6$ have fractal dimension going to $3/2$ when $N\rightarrow\infty$.Comment: 6 pages, 8 figures, conference CCP201

The Crustal Rigidity of a Neutron Star, and Implications for PSR 1828-11 and other Precession Candidates

We calculate the crustal rigidity parameter, b, of a neutron star (NS), and show that b is a factor 40 smaller than the standard estimate due to Baym & Pines (1971). For a NS with a relaxed crust, the NS's free-precession frequency is directly proportional to b. We apply our result for b to PSR 1828-11, a 2.5 Hz pulsar that appears to be precessing with period 511 d. Assuming this 511-d period is set by crustal rigidity, we show that this NS's crust is not relaxed, and that its reference spin (roughly, the spin for which the crust is most relaxed) is 40 Hz, and that the average spindown strain in the crust is 5 \times 10^{-5}. We also briefly describe the implications of our b calculation for other well-known precession candidates.Comment: 44 pages, 10 figures, submitted to Ap

Chandra View of the Dynamically Young Cluster of Galaxies A1367 I. Small-Scale Structures

The 40 ks \emph{Chandra} ACIS-S observation of A1367 provides new insights into small-scale structures and point sources in this dynamically young cluster. Here we concentrate on small-scale extended structures. A ridge-like structure around the center (``the ridge'') is significant in the \chandra\ image. The ridge, with a projected length of $\sim$ 8 arcmin (or 300 h$_{0.5}^{-1}$ kpc), is elongated from northwest (NW) to southeast (SE), as is the X-ray surface brightness distribution on much larger scales ($\sim$ 2 h$_{0.5}^{-1}$ Mpc). The ridge is cooler than its western and southern surroundings while the differences from its eastern and northern surroundings are small. We also searched for small-scale structures with sizes $\sim$ arcmin. Nine extended features, with sizes from $\sim$ 0.5$'$ to 1.5$'$, were detected at significance levels above 4 $\sigma$. Five of the nine features are located in the ridge and form local crests. The nine extended features can be divided into two types. Those associated with galaxies (NGC 3860B, NGC 3860 and UGC 6697) are significantly cooler than their surroundings (0.3 - 0.9 keV vs. 3 - 4.5 keV). The masses of their host galaxies are sufficient to bind the extended gas. These extended features are probably related to thermal halos or galactic superwinds of their host galaxies. The existence of these relatively cold halos imply that galaxy coronae can survive in cluster environment (e.g., Vikhlinin et al. 2001). Features of the second type are not apparently associated with galaxies. Their temperatures may not be significantly different from those of their surroundings. This class of extended features may be related to the ridge. We consider several possibilities for the ridge and the second type of extended features. The merging scenario is preferred.Comment: To appear in ApJ, Vol 576, 2002, Sep., a high-resolution version is in http://cfa160.harvard.edu/~sunm/a1367_a.ps.g

Tails of the Unexpected: The Interaction of an Isothermal Shell with a Cloud

A new mechanism for the formation of cometary tails behind dense clouds or globules is discussed. Numerical hydrodynamical models show that when a dense shell of swept-up matter overruns a cloud, material in the shell is focussed behind the cloud to form a tail. This mode of tail formation is completely distinct from other methods, which involve either the removal of material from the cloud, or shadowing from a strong, nearby source of ionization. This mechanism is relevant to the cometary tails seen in planetary nebulae and to the interaction of superbubble shells with dense clouds.Comment: 6 pages, 6 figures, accepted for publication in MNRAS letter

Morphological properties of projection specific pyramidal neurons of primate anterior cingulate cortex

The anterior cingulate cortex is an important interface of cortical, motor, and limbic networks, and thus is a brain area uniquely situated to affect a wide variety of higher order functions. The aim of this study was to characterize the morphology of two distinct populations of anterior cingulate cortex (ACC) pyramidal neurons, a dorsal-caudal population projecting to the premotor cortex (PMC) and a ventral-rostral population projecting to the amygdala. Retrograde tracers injected into area 6DC of the “cognitive” premotor cortex, and into the basolateral nucleus of the “affective” amygdala were used to label distinct projection neurons in the ACC. Whole-cell patch clamp recording and intracellular filling techniques were used to fill the dendritic arbor of these labeled projection neurons. High resolution confocal microscopy and 3D neuronal reconstructions were used to quantify dendritic morphological parameters. Amygdala projecting neurons were more superficial than premotor projecting neurons, with an average soma-to-pia distance of 498 μm compared to 1,012 μm, respectively (amygdala projecting: 498 ± 139 μm vs. PMC projecting: 1012 ± 113 μm, p<.05). Overall, amygdala and PMC projection neurons had very similar average dendritic lengths, branch points, branch densities, and vertical and horizontal extensions in both apical and basal compartments. Amygdala projecting cells had greater apical tuft branch points than deep PMC projecting cells (8.25 vs. 3.3 apical tuft branch points, p<.05). Superficial PMC projecting cells had smaller total vertical and apical vertical extensions than deep PMC projecting cells (Total vertical: 304.98 vs. 750.96 μm, apical vertical: 241.78 vs 601.95 μm, p<.05). Sholl analyses revealed that the distribution of apical dendritic length as a function of distance from the soma of amygdala projections had bimodal peaks, while that of superficial and deep PMC cells had a single peak. Total spine number of amygdala projecting neurons was greater than PMC projecting cells (~17,000 spines vs. ~2,100 spines). Three major classes of morphology were visualized within the ACC neuron reconstructions dataset: regular-tufted, narrow-tufted, and untufted, with the regular-tufted cells containing more branch points than narrow tufted but less basal branch point density. The work in this study assessing cellular morphological properties of specific amygdala and PMC inputs and outputs within the ACC helps to characterize functional dynamics of both emotional and motor planning networks

Multiscale Finite-Difference-Diffusion-Monte-Carlo Method for Simulating Dendritic Solidification

We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of variation of the surrounding thermal or solutal diffusion field. The first key feature of this method is an efficient multiscale diffusion Monte-Carlo (DMC) algorithm which allows off-lattice random walkers to take longer and concomitantly rarer steps with increasing distance away from the solid-liquid interface. As a result, the computational cost of evolving the large scale diffusion field becomes insignificant when compared to that of calculating the interface evolution. The second key feature is that random walks are only permitted outside of a thin liquid layer surrounding the interface. Inside this layer and in the solid, the diffusion equation is solved using a standard finite-difference algorithm that is interfaced with the DMC algorithm using the local conservation law for the diffusing quantity. Here we combine this algorithm with a previously developed phase-field formulation of the interface dynamics and demonstrate that it can accurately simulate three-dimensional dendritic growth in a previously unreachable range of low undercoolings that is of direct experimental relevance.Comment: RevTeX, 16 pages, 10 eps figures, submitted to J. Comp. Phy

Toroidal Magnetic Fields in Type II Superconducting Neutron Stars

We determine constraints on the form of axisymmetric toroidal magnetic fields dictated by hydrostatic balance in a type II superconducting neutron star with a barotropic equation of state. Using Lagrangian perturbation theory, we find the quadrupolar distortions due to such fields for various models of neutron stars with type II superconducting and normal regions. We find that the star becomes prolate and can be sufficiently distorted to display precession with a period of the order of years. We also study the stability of such fields using an energy principle, which allows us to extend the stability criteria established by R. J. Tayler for normal conductors to more general media with magnetic free energy that depends on density and magnetic induction, such as type II superconductors. We also derive the growth rate and instability conditions for a specific instability of type II superconductors, first discussed by P. Muzikar, C. J. Pethick and P. H. Roberts, using a local analysis based on perturbations around a uniform background.Comment: 32 pages, 6 figures; derivations shortened, comments and references added; accepted for publication in MNRA

New Algorithm for Parallel Laplacian Growth by Iterated Conformal Maps

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth patterns are compared to those obtained by the best algorithms of direct numerical solutions. The fractal dimension of the patterns is discussed.Comment: Sumitted to Phys. Rev. Lett. Further details at http://www.pik-potsdam.de/~ander