2,193 research outputs found
Splitting fields and general differential Galois theory
An algebraic technique is presented that does not use results of model theory
and makes it possible to construct a general Galois theory of arbitrary
nonlinear systems of partial differential equations. The algebraic technique is
based on the search for prime differential ideals of special form in tensor
products of differential rings. The main results demonstrating the work of the
technique obtained are the theorem on the constructedness of the differential
closure and the general theorem on the Galois correspondence for normal
extensions..Comment: 33 pages, this version coincides with the published on
Models for Chronology Selection
In this paper, we derive an expression for the grand canonical partition
function for a fluid of hot, rotating massless scalar field particles in the
Einstein universe. We consider the number of states with a given energy as one
increases the angular momentum so that the fluid rotates with an increasing
angular velocity. We find that at the critical value when the velocity of the
particles furthest from the origin reaches the speed of light, the number of
states tends to zero. We illustrate how one can also interpret this partition
function as the effective action for a boosted scalar field configuration in
the product of three dimensional de Sitter space and . In this case, we
consider the number of states with a fixed linear momentum around the as
the particles are given more and more boost momentum. At the critical point
when the spacetime is about to develop closed timelike curves, the number of
states again tends to zero. Thus it seems that quantum mechanics naturally
enforces the chronology protection conjecture by superselecting the causality
violating field configurations from the quantum mechanical phase space.Comment: 20 pages, Late
Chronology Protection in Generalized Godel Spacetime
The effective action of a free scalar field propagating in the generalized
Godel spacetime is evaluated by the zeta-function regularization method. From
the result we show that the renormalized stress energy tensor may be divergent
at the chronology horizon. This gives a support to the chronology protection
conjecture.Comment: Latex 6 pages, typos correcte
Rotation and the AdS/CFT correspondence
In asymptotically flat space a rotating black hole cannot be in thermodynamic
equilibrium because the thermal radiation would have to be co-rotating faster
than light far from the black hole. However in asymptotically anti-de Sitter
space such equilibrium is possible for certain ranges of the parameters. We
examine the relationship between conformal field theory in rotating Einstein
universes of dimensions two to four and Kerr anti-de Sitter black holes in
dimensions three to five. The five dimensional solution is new. We find similar
divergences in the partition function of the conformal field theory and the
action of the black hole at the critical angular velocity at which the Einstein
rotates at the speed of light. This should be an interesting limit in which to
study large Yang-Mills.Comment: 24 pages, RevTeX, 1 figure, references adde
Divergences in the Effective Action for Acausal Spacetimes
The 1--loop effective Lagrangian for a massive scalar field on an arbitrary
causality violating spacetime is calculated using the methods of Euclidean
quantum field theory in curved spacetime. Fields of spin 1/2, spin 1 and
twisted field configurations are also considered. In general, we find that the
Lagrangian diverges to minus infinity at each of the nth polarised
hypersurfaces of the spacetime with a structure governed by a DeWitt-Schwinger
type expansion.Comment: 17 pages, Late
Is the Broad-Line Region Clumped or Smooth? Constraints from the H alpha Profile in NGC 4395, the Least Luminous Seyfert 1 Galaxy
The origin and configuration of the gas which emits broad lines in Type I
active galactic nuclei is not established yet. The lack of small-scale
structure in the broad emission-line profiles is consistent with a smooth gas
flow, or a clumped flow with many small clouds. An attractive possibility for
the origin of many small clouds is the atmospheres of bloated stars, an origin
which also provides a natural mechanism for the cloud confinement. Earlier
studies of the broad-line profiles have already put strong lower limits on the
minimum number of such stars, but these limits are sensitive to the assumed
width of the lines produced by each cloud. Here we revisit this problem using
high-resolution Keck spectra of the H alpha line in NGC 4395, which has the
smallest known broad-line region (~10^14 cm). Only a handful of the required
bloated stars (each having r~10^14 cm) could fit into the broad-line region of
NGC 4395, yet the observed smoothness of the H alpha line implies a lower limit
of ~10^4-10^5 on the number of discrete clouds. This rules out conclusively the
bloated-stars scenario, regardless of any plausible line-broadening mechanisms.
The upper limit on the size of the clouds is ~10^12 cm, which is comparable to
the size implied by photoionization models. This strongly suggests that gas in
the broad-line region is structured as a smooth rather than a clumped flow,
most likely in a rotationally dominated thick disk-like configuration. However,
it remains to be clarified why such a smooth, gravity-dominated flow generates
double-peaked emission lines only in a small fraction of active galactic
nuclei.Comment: 12 pages, including 3 figures, accepted for publication in The
Astrophysical Journa
The disengage deficit in hemispatial neglect is restricted to between-object shifts and is abolished by prism adaptation
We sought to determine the effects of prism adaptation on peripherally cued visual attention shifting in patients with spatial neglect, using a task devised by Egly et al. (J Exp Psychol Gen 123:161–177, 1994) based on the classic Posner paradigm. This task allowed a comparison of “within-object” versus “between-object” attention shifts. A display was presented containing two parallel outline rectangles, and subjects were asked to make rapid responses to a target, which would appear at one end of one of the rectangles. The target location was pre-cued with 75% validity: on invalid trials attention was directed either to the other end of the same rectangle, or to the other rectangle. Healthy subjects and right-hemisphere patients without neglect showed a left-right symmetrical pattern, with a larger validity effect when required to shift attention between rectangles, thus indicating a greater difficulty of attention-shifting between than within the respective shapes. The neglect patients showed the typical leftward “disengage deficit” previously observed in neglect, but only for attention shifts between objects, indicating that the effect is object-based rather than purely spatial. A comparison of vertical and horizontal shift costs showed that this attention-shifting deficit for left-hemifield target stimuli was directional rather than hemifield-based: it was absent for vertical shifts of attention within the left hemifield. Finally, we found that prism adaptation abolished the disengage deficit. We found no effects of prism adaptation in the control subjects. We argue that prism adaptation has a powerful effect on one of the fundamental manifestations of the neglect syndrome
Resolved Mid-IR Emission in the Narrow Line Region of NGC 4151
We present subarcsecond resolution mid infrared images of NGC 4151 at 10.8
micron and 18.2 micron. These images were taken with the University of Florida
mid-IR camera/spectrometer OSCIR at the Gemini North 8-m telescope. We resolve
emission at both 10.8 micron and 18.2 micron extending ~ 3.5" across at a P.A.
of ~ 60 degrees. This coincides with the the narrow line region of NGC 4151 as
observed in [OIII] by the Hubble Space Telescope. The most likely explanation
for this extended mid-IR emission is dust in the narrow line region heated by a
central engine. We find no extended emission associated with the proposed torus
and place an upper limit on its mid-IR size of less than or equal to ~ 35 pc.Comment: accepted for publication in the Astrophysical Journal, 19 pages
including 5 figure
Experimental Induction of Odontoblast Differentiation and Stimulation During Preparative Processes
In vivo implantation experiments have shown that ethylenediaminetetraaceticacid(EDTA)-soluble frac tions of dentin stimulate reparative dentinogenesis . When isolated embryonic dental papillae were cultured in the presence of these dentin constituents, odontoblast cytological and functional differentiation could be initiated and maintained in the absence of an enamel organ. These effects were attributed to the presence of TGF-/1- related molecules [TGF-/11 or bone morphogenetic protein -2a (BMP-2a)] which had to be used in combination with an EDT A-soluble fraction of dentin in order to specifically affect competent preodontoblasts . These EDT A-soluble constituents present in dentin could be replaced by heparin or fibronectin which both have been reported to interact with TGF-/1. The association of such defined matrix components with a TGF-/1-related molecule represents a biologically active complex triggering odontoblast functional differentiation.
In response to caries, odontoblasts modulate their secretory activity and are stimulated to elaborate reactionary dentin. This might be induced by active molecules such as IGF, TGF-6 or BMP which are liberated from dentin consecutively to the demineralization process.
Reparative dentinogenesis is distinct from reactionary dentinogenesis and more complex since it implicates the differentiation of precursor cells present in the dental papilla. The developmental history of these cells is different from that of the physiological predontoblasts in developing teeth. The nature of these stem cells and the mechanism of their induction still remain open questions
Threshold for Chaos and Thermalization in One-Dimensional Mean-Field Bose-Hubbard Model
We study the threshold for chaos and its relation to thermalization in the 1D
mean-field Bose-Hubbard model, which in particular describes atoms in optical
lattices. We identify the threshold for chaos, which is finite in the
thermodynamic limit, and show that it is indeed a precursor of thermalization.
Far above the threshold, the state of the system after relaxation is governed
by the usual laws of statistical mechanics.Comment: 4 pages, 3 figures, published versio
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