Nilpotent normal form for divergence-free vector fields and volume-preserving maps

We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vector field in $\mathbb{R}^3$ has nilpotent linearization with maximal Jordan block then, to arbitrary degree, coordinates can be chosen so that the nonlinear terms occur as a single function of two variables in the third component. The analogue for volume-preserving diffeomorphisms gives an optimal normal form in which the truncation of the normal form at any degree gives an exactly volume-preserving map whose inverse is also polynomial inverse with the same degree.Comment: laTeX, 20 pages, 1 figur

Observational Constraints to the Evolution of Massive Stars

We consider some aspects of the evolution of massive stars which can only be elucidated by means of "indirect" observations, i.e. measurements of the effects of massive stars on their environments. We discuss in detail the early evolution of massive stars formed in high metallicity regions as inferred from studies of HII regions in external galaxies.Comment: 6 pages, 1 figure; Invited Paper presented at the Roma-Trieste Workshop 1999 "The Chemical Evolution of the Milky Way: Stars versus Clusters", Vulcano Island (ME, Italy), 20-24 September, 1999, eds. F. Giovannelli & F. Matteucci, Kluwer-Holland (in press

Universality of galactic surface densities within one dark halo scale-length

It was recently discovered that the mean dark matter surface density within one dark halo scale length - the radius within which the volume density profile of dark matter remains approximately flat - is constant across a wide range of galaxies. This scaling relation holds for galaxies spanning a luminosity range of 14 magnitudes and the whole Hubble sequence. Here we report that the luminous matter surface density is also constant within one scale length of the dark halo. This means that the gravitational acceleration generated by the luminous component in galaxies is always the same at this radius. Although the total luminous-to-dark matter ratio is not constant, within one halo scale length it is constant. Our finding can be interpreted as a close correlation between the enclosed surface densities of luminous and dark matter in galaxies.Comment: Accepted as a Letter to Natur

On the Generation of the Hubble Sequence through an Internal Secular Dynamical Process

The secular evolution process, which slowly transforms the morphology of a galaxy over its lifetime, could naturally account for observed properties of the great majority of physical galaxies if both stellar and gaseous accretion processes are taken into account. As an emerging paradigm for galaxy evolution, its dynamical foundation had been established in the past few years, and its observational consequences are yet to be fully explored. The secular evolution picture provides a coherent framework for understanding the extraordinary regularity and the systematic variation of galaxy properties along the Hubble sequence.Comment: 10 pages, 1 figure, invited talk presented at the international conference on "Penetrating Bars through the Masks of Cosmic Dust: The Hubble Tuning Fork Strikes a New Note", June 2004, South Afric

The Distribution of Dark Matter in Galaxies: the Core Radius Issue

I review the up-to-date status on the properties of the Dark Matter density distribution around Galaxies. The rotation curves of spirals all conform to a same Universal profile which can be uniquely decomposed as the sum of an exponential thin stellar disk and a dark halo with a flat density core. From dwarfs to giants galaxies, the halos embedding the stellar component feature a constant density region of size $r_0$ and value $\rho_0$, which are inversely correlated. The fine structure of dark halos in the region of the stellar disk has been derived for a number of low--luminosity disk galaxies: the halo circular velocity increases almost linearly with radius out to the edge of the stellar disk, implying, up there, an almost constant dark matter density. This sets a serious discrepancy between the cuspy density distribution predicted by N-body simulations of $\Lambda$CDM cosmology, and those actually detected around galaxies. The small scatter around the Fundamental Plane (FP) of elliptical galaxies constraints the distribution of dark and luminous matter in these systems. The measured central velocity dispersion $\sigma_0$ in the FP is linked to both photometric and dynamical properties of luminous and dark matter. As a consequence, the well-known features of the FP imply that, inside the effective radius $R_e$, the stellar spheroid must dominate over the dark matter, in contrast with $\Lambda$CDM predictions.Comment: 14 pages, 10 figures, invited talk given at Beyond the Desert '03, Ringberg, 11-15 July 200

Star forming dwarf galaxies

Star forming dwarf galaxies (SFDGs) have a high gas content and low metallicities, reminiscent of the basic entities in hierarchical galaxy formation scenarios. In the young universe they probably also played a major role in the cosmic reionization. Their abundant presence in the local volume and their youthful character make them ideal objects for detailed studies of the initial stellar mass function (IMF), fundamental star formation processes and its feedback to the interstellar medium. Occasionally we witness SFDGs involved in extreme starbursts, giving rise to strongly elevated production of super star clusters and global superwinds, mechanisms yet to be explored in more detail. SFDGs is the initial state of all dwarf galaxies and the relation to the environment provides us with a key to how different types of dwarf galaxies are emerging. In this review we will put the emphasis on the exotic starburst phase, as it seems less important for present day galaxy evolution but perhaps fundamental in the initial phase of galaxy formation.Comment: To appear in JENAM Symposium "Dwarf Galaxies: Keys to Galaxy Formation and Evolution", P. Papaderos, G. Hensler, S. Recchi (eds.). Lisbon, September 2010, Springer Verlag, in pres

Does the galaxy NGC1052-DF2 falsify Milgromian dynamics?

A great challenge in current physics is to understand whether the observed internal dynamics of galaxies is due to dark matter or to a modification of the law of gravity. Recently, van Dokkum et al. reported that the ultra-diffuse dwarf galaxy NGC1052–DF2 lacks dark matter, and they claimed that this would — paradoxically — be problematic for modified gravity theories such as Milgromian dynamics (MOND). However, NGC1052–DF2 is not isolated, so a valid prediction of its internal dynamics in MOND cannot be made without properly accounting for the external gravitational fields from neighbouring galaxies. Including this external field effect, following Haghi et al., shows that NGC1052–DF2 is consistent with MOND.PostprintPeer reviewe

Post-Training Dephosphorylation of eEF-2 Promotes Protein Synthesis for Memory Consolidation

Memory consolidation, which converts acquired information into long-term storage, is new protein synthesis-dependent. As protein synthesis is a dynamic process that is under the control of multiple translational mechanisms, however, it is still elusive how these mechanisms are recruited in response to learning for memory consolidation. Here we found that eukaryotic elongation factor-2 (eEF-2) was dramatically dephosphorylated within 0.5–2 hr in the hippocampus and amygdala of mice following training in a fear-conditioning test, whereas genome-wide microarrays did not reveal any significant change in the expression level of the mRNAs for translational machineries or their related molecules. Moreover, blockade of NMDA receptors with MK-801 immediately following the training significantly impeded both the post-training eEF-2 dephosphorylation and memory retention. Notably, with an elegant sophisticated transgenic strategy, we demonstrated that hippocampus-specific overexpression of eEF-2 kinase, a kinase that specifically phosphorylates and hence inactivates eEF-2, significantly inhibited protein synthesis in the hippocampus, and this effects was more robust during an “ongoing” protein synthesis process. As a result, late phase long-term potentiation (L-LTP) in the hippocampus and long-term hippocampus-dependent memory in the mice were significantly impaired, whereas short-term memory and long-term hippocampus-independent memory remained intact. These results reveal a novel translational underpinning for protein synthesis pertinent to memory consolidation in the mammalian brain

Effects of methylphenidate on attention in Wistar rats treated with the neurotoxin N-(2-chloroethyl)-N-ethyl-2-bromobenzylamine (DSP4)

The aim of this study was to assess the effects of the neurotoxin N-(2-chloroethyl)-N-ethyl-2-bromobenzylamine (DSP4) on attention in rats as measured using the 5-choice-serial-reaction-time task (5CSRTT) and to investigate whether methylphenidate has effects on DSP4-treated rats. Methylphenidate is a noradrenaline and dopamine reuptake inhibitor and commonly used in the pharmacological treatment of individuals with attention deficit/hyperactivity disorder (ADHD). Wistar rats were trained in the 5CSRTT and treated with one of three doses of DSP4 or saline. Following the DSP4 treatment rats were injected with three doses of methylphenidate or saline and again tested in the 5CSRTT. The treatment with DSP4 caused a significant decline of performance in the number of correct responses and a decrease in response accuracy. A reduction in activity could also be observed. Whether or not the cognitive impairments are due to attention deficits or changes in explorative behaviour or activity remains to be investigated. The treatment with methylphenidate had no beneficial effect on the rats’ performance regardless of the DSP4 treatment. In the group without DSP4 treatment, methylphenidate led to a reduction in response accuracy and bidirectional effects in regard to parameters related to attention. These findings support the role of noradrenaline in modulating attention and call for further investigations concerning the effects of methylphenidate on attentional processes in rats

Dark Matter in the Milky Way's Dwarf Spheroidal Satellites

The Milky Way's dwarf spheroidal satellites include the nearest, smallest and least luminous galaxies known. They also exhibit the largest discrepancies between dynamical and luminous masses. This article reviews the development of empirical constraints on the structure and kinematics of dSph stellar populations and discusses how this phenomenology translates into constraints on the amount and distribution of dark matter within dSphs. Some implications for cosmology and the particle nature of dark matter are discussed, and some topics/questions for future study are identified.Comment: A version with full-resolution figures is available at http://www.cfa.harvard.edu/~mwalker/mwdsph_review.pdf; 70 pages, 22 figures; invited review article to be published in Vol. 5 of the book "Planets, Stars, and Stellar Systems", published by Springe