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This is a copy of the slides presented at the meeting but not formally written up for the volume.
Upconverting nanoparticles (UCNs) are modified nanometer-sized composites which generate higher energy visible light from lower energy radiation (usually near-infrared (NIR)) by non-radiative transfer of photons between transition metal, lanthanide, or actinide ions doped into a solid-state host. These nanoparticles offer several advantages as imaging probes for live cells and tissues: high sensitivity of detection due to absence of autofluorescence from tissues, sharp emission peaks, less toxic components (than quantum dots (QDs)) and high depth of penetration and low phototoxicity of NIR light. Although the use of upconverting phosphors in nucleic acid assays, immunohistochemistry and immuno-assays have been demonstrated, no reports exploiting the advantages of these labels in live mammalian cell and tissue imaging have been demonstrated. Moreover, these assays usually utilize large sized reporters (>400nm). In this report, we present the synthesis and characterization of UCN and explore their effectiveness as live cellular and tissue labels. Nanoparticles with a nanocrystalline NaYF4 core doped with Yb3+ and Er3+ and coated with high molecular weight (25 kDa) PEI as surfactant was synthesized using a simple ‘one pot’ hydrothermal method. After characterization and biocompatibility tests, the UCN were conjugated to folic acid and targeted to mammalian breast carcinoma cells. To demonstrate tissue imaging, UCN were injected into live mouse and rat tissues and excited using a simplified NIR laser set-up. The nanoparticles obtained were spherical, about 50nm in diameter and with a narrow size distribution. They demonstrated sharp emission peaks at 653nm and 540nm when excited with a 980nm laser, and excellent stability when stored in phosphate buffered saline or incubated with complete serum at 37 deg C. The particles were found to be biocompatible with different cell types at different concentrations when incubated over varying time periods. Upon incubation, mammalian cancer cells took up the UCN and were imaged with high signal-to-background ratios. Continuous imaging of live cells could be performed without cell damage or death. UCN was injected into mouse skin and leg muscles and excited with NIR laser set at low power to prevent tissue damage. Visible phosphorescence was recorded from both sites. Phosphorescence could also be seen when UCN was injected in the skin and to a small depth of penetration in some muscles of rats.We conclude that these upconverting nanoparticles are promising labels for use in live cell and tissue imaging.
Using basically the impulsive approximation and a modification of the method used by Alladin S.M., (1965, Ap.J.,141, 768), and described in detail in Chatterjee T.K., (1990, IAU Col.,124, 519, 569) we study the evolution of binary interacting galaxies, leading ultimately to mergers. Each collision is characterised by the initial separation between the galaxies and the relative velocity therein. In each case the orbital evolution and largescale structural changes in the galaxies are studied by taking into account the change in relative velocity due to dynamical friction, leading ultimately to mergers. The evolution is considered from a time when the gravitational interaction between the progenitor pairs is physically significant (Chatterjee, 1992, Astroph. Sp.Sc., in press).
We study the stellar orbits, as a function of the binary motion of two identical ellipticals, under initial conditions marginally sufficient for strong interaction. The stars were initially given circularly symmetric velocities. The tidal effects cause a redistribution of stellar orbits, resulting in crowding of stars in shells; the same attaining its maximum intensity slightly after a pericentric passage. As the galaxies recede, the structure disperses gradually by expanding; but is restored, intensified and forms at a shorter radial distance as the galaxies return for a subsequent approach in a shrinking orbit. We give the stellar positions, projected perpendicular to the orbital plane, shortly after the first (t≈0.5) and second (t≈6) pericentric passages in the figures; (time being given in dimensionless units corresponding to mass=l, radius=l, G=4.50). On the basis of the cooling gas inflow model, the gas will be compressed and shocked in these regions of enhanced stellar density, leading to bursts of star formation. The interval between the two successive starbursts is found to be of the same order as the trapping time needed by the galaxy to incorporate the gas ejected by stars in its cooling flow.
Observations indicate that the frequency of merging galaxies in the present epoch is ≈0.3%, and an extrapolation to past yields a frequency ≈5% (Toomre, 1977, Tremaine, 1980). Loosely bound pairs of galaxies that had separated to great distances in the general cosmic expansion and have lately fallen together again in comet-like plunging ellipses seem to be the most lucrative candidates for mergers. But could all ellipticals be merger remnants ? To study this problem we have determined the frequency of merging galaxies on the basis of the collision theory, by studying many collisions with different collision parameters and progenitor pairs (using the impulsive approximation) and compared the values so obtained with the observational ones. The mean values of the collision parameters favourable for mergers for different types of progenitor pairs are segregated from a statistical study of many collisions and are compared to the corresponding values in dense regions where a galaxy and its nearest neighbour can be visualised to form a loosely bound pair, to determine the corresponding frequencies. The theory and method is described in detail in Chatterjee, 1987, 1990, except that subsequently we have studied disk-disk mergers by using basically the same method.
Crystal structures of two fused cyclic compounds, 4-(methyl(sulfonyl)methoxy-2-vinyl)-2S*,3aR*,4S*,5,7aS*-(hexahydro-1H-indan-3a-yl)methylmethanesulfonate (1) and (1S*,2S*,4S*,7R*)-7-(dimethyl(phenyl)silyl)-4′,5′-dihydro-2′H-spiro[bicyclo[2.2.1]heptene-2,3′-furan]-2′-one (2), have been solved from laboratory X-ray powder diffraction data using direct space approach and refined following the Rietveld method. In the absence of strong hydrogen bond donating groups, the crystal packing of 1 and 2 exhibits C–H ⋯ O hydrogen bonds and C–H ⋯ π interactions forming two-dimensional (2D) supramolecular network. The nature of intermolecular interactions in 1 and 2 has been analyzed through the Hirshfeld surface and 2D fingerprint plots. The density functional theory optimized molecular geometries in 1 and 2 agree closely with those obtained from the crystallographic study. Hirshfeld surface analysis of 1, 2 and a few related fused carbocyclic and carbooxacyclic systems retrieved from the Cambridge Structural Database indicates that about 85% of Hirshfeld surface area in these compounds are because of H ⋯ H and O ⋯ H interactions.
Grain-boundary thickness in polycrystalline ice is a function of time (age), salinity, tempera-turf ·, and mode of sample preparation. It is directly proportional to the salinity of the ice and the number-average grain diameter (spheres) or edge-length (cubes). Practically the total salt content resides in the grain boundary for low salinity ice samples. The gram-boundary thickness S is also directly proportional to growth time of the grains raised to a power n(n = 0.25 to 0.3) and increases exponentially with absolute temperature for constant salinity and age. The energy of activation for growth increases with salinity. The results of the grain-boundary thickness calculations are useful for evaluating grain-boundary diffusion coefficients.
Dynamical studies of galactic collisions, conducted previously (Chatterjee, 1992, 1993a, b), indicated that most of the mergers take place in two to three shrinking orbital periods. We extend this line of research work to study induced nuclear activity. We study the binary evolution of a spiral galaxy perturbed by a compact elliptical galaxy of comparable mass and find that each time the perturber penetrates the disk of the spiral, the disk is subjected to an appropriate perturbation, causing inflow of gas towards its nucleus due to loss of angular momentum; there it could activate an inert black hole (consistent with previous studies; e.g. Naguchi, 1988). However a new feature that we find is that repeated episodes of disk penetration by the perturber occur in gradually shorter timescales, causing an overlap of the activity timescale and the dynamical timescale. In fact if the elliptical is very compact and the spiral has a massive bulge, subsequent dynamical timescales reduce by more than an order of magnitude. This periodic increase in the activity of the nucleus is of a secular nature (in contrast to a reactivation process), and could lead to the evolution of the spiral along the following lines, Starburst → Seyfert 2 → Seyfert 1, as interpenetrations follow.
NGC 6369 is a remarkable object, especially in the light of structure and morphology. We studied this object by taking many red plates (103aE), coupled with red filters (F29), of varying exposures using the Schmidt Telescope of the INAOE. The structure brought out by the analysis of the plates indicate that the object consists of a prolate disk sphaped ring nebula with a central hole and featuring huge plumes emanating out of the ring which engulf an outer envelope having a diameter about twice that of the ring. The striking feature of the plumes is that they emanate almost symmetrically out of the two prolate ends of the ring and curve out almost symmetrically along opposite directions.
A comparison of the structures of this object with the temporal evolution of the gas density in the numerical simulations of a purely gaseous self-gravitating polytropic ring is conducted. Features resembling the plumes of this object are found at a certain stage of the simulations. A careful comparison of the observed and computer generated features indicate a marked similarity in the sense that both, the observed and simulated ring appear to be similar to the cross section of a prolate spheroid at the ends of which emanate the plumes. This seems to confirm that the evolution of this object is consistent with its being a planetary nebula having the appearance of a prolate spheroid with a central hole, which is a basic observational feature of most planetary nebulae.
It is significant that the orbits of the planets in the solar system are very nearly circular, except for Mercury and Pluto where, conceivably, due to their comparatively small sizes, the tidal forces have played a less active role. Most of the suspected planets orbiting pulsars have nearly circular orbits. These systems tend to have minimum energy and are subjected to tidal forces. We find that a planet circularizes its orbit, in an effort to attain orbital stability and the ground state. Details can be found in Magalinsky & Chatterjee, 1997, and Magalinsky and Chatterjee, 2000.
The kinetic description of gravitating systems has acquired vital importance in the context of trends in galaxy formation and evolution as evidenced by the existence of the virial and fundamental planes. The fundamental plane deviates for brighter and fainter ellipticals; until the brightest cluster members (BCMs), whose structures have been most modified by interactions, seem to occupy a fundamental plane with a different slope as compared to normal ellipticals. Extending the work of Magalinsky (1972, AZh, 49, 1017; Sov. Astron.-AJ, 16, 830), the Vlasov equation is applied to study small perturbations (considered as protogalaxies) of the exact solution corresponding to a spatially homogeneous medium in expansion. It is found that a perturbation attains a saturated size whose scale length, as a function of a reduced parameter of evolution (in terms of the characteristic frequency of dispersion of momenta, τ), R(τ) ∝ K.E./P.E. ∝ (K.E.)2/σ ∝ (δV)2/Proj.density ∝ σ2/I, which has the parametric form of the virial plane. The subsequent evolution is characterized principally by the variation of the energy due to the gravitational interactions between stars (considered as mass points), given by the potential energy such that the harmonic mean separation scale (between stars) characterizes this evolution. In this stage of the evolution the harmonic scale separation has the parametric form, 〈r−1〉 ∝ (K.E.)1/2, and 〈r−1〉 ∝ (P-E.) such that 〈r−1〉 ∝ (K.E.)1/2/(P.E.) ∝ σ/I. Notice that this is the parametric form of the fundamental plane of evolved ellipticals since the harmonic scale separation determines a physically significant scale.
It is well known that, under favorable conditions, tidal interactions between a spiral galaxy and a more compact elliptical leads to the formation of embedded rings in the disk (e.g. Chatterjee 1979, Bull. Astron. Soc. India, 7, 32); in addition there are also nuclear rings whcih do not seem to have a tidal origin (e.g. Buta 1986, ApJ, 306, 768). The two types of rings occur in different regions of the spirals, which can be explained on the basis of the tidal hypothesis by extending the previous research work of Chatterjee (1984, Ap&SS, 106, 309). In this context, using the same theory, we study many normal on-axis collisions (as rings are best formed for this orientation) between a disk galaxy, modeled as an exponential disk with a polytropic n = 0,3,4, bulge (mass being equally distributed amongst the polytropic indices), and a compact spherical intruder, modeled with a polytropic n = 2, 3, 4, distribution (mass being equally distributed amongst the polytropic indices). The internal energy changes suffered by the disk, have a direct bearing on the sharpness of the rings, and are directly obtained from the relationship, for the fractional change in internal energy of the disk, as fE = γβ, where β is a function of the galactic models and the collision parameter γ = G(σs/V2) ∝ σs/V2 (where σs is the projected velocity of collision). We find that sharp rings form for fE ≥ 0.5; beyond this value of fE the intensity contrast of the rings diminish. However, fairly sharp rings (from an observational point of view) form for fE ≥ 1/3, which corresponds to 7 ≥ 0.01; which corresponds to a density maximum near a region ~ (1/3)R (R being the radius of the disk galaxy), so that rings of tidal origin are not expected to be prominent at a distance interior to ~ 1/3 of the radius of the disk galaxy. They are not expected to form interior to ~ 1/10 of the radius of the disk.
Observations indicate that ring galaxies are more active than spirals (e.g., Ghigo et al., 1983 Appleton and Struck-Marcell, 1987). However, Seyfert activity is noted in only a few ring galaxies, e.g. NGC 985 (de Vaucouleurs & de Vaucouleurs 1975), NGC 1144 = Arp 118 (Huchra et al. 1982), ring galaxy in Sextans-optical counterpart of the IRAS source 09595-0755 (Wakamatus & Nishida). This is indicative of the fact that this type of activity requires favorable circumstances. In this context a previous work on the stellar episode of ring formation, Chatterjee (1984), is extended, including gas and studying the evolution of the ring structure, due to rebounds of the compact elliptical about the plane of the disk.
Using the impulsive approximation to study the velocity changes of stars during disk-sphere collisions and a method due to Bottlinger to study the post collision orbits of stars, the formation of various types of interacting galaxies is studied as a function of the distance of closest approach between the two galaxies.
A study of the expected frequency of merging galaxies is conducted, using the impulsive approximation. Results indicate that if we consider mergers involving galaxy pairs without halos in a single crossing time or orbital period, the expected frequency of mergers is two orders of magnitude below the observed value for the present epoch. If we consider mergers invovling several orbital periods or crossing times, the expected frequency goes up by an order of magnitude. Preliminary calculation indicate that if we consider galaxy mergers between pairs with massive halos, the merger is very much hastened.
Some of the classical seyferts are observed to be prototypical ovals, e.g. NGC 1068 and 4151 (e.g., Bosma 1981; Kormendy 1982; Scoville et al. 1988). Such a non-axisymmetric potential corresponding to an oval disk can produce inward flow of gas and induce mild activity. To test the efficiency of this process, we study a collision between a face-on spiral with a high gaseous content and an equally massive compact elliptical, under marginally bound conditions, as such encounters are most frequent.
We model the spiral galaxy by an exponential model disk (of radius R) with a (static) thickness and scale length α = 4/R and a spherical polytropic bulge (n=0,3,4, equally weighted combination) containing 1/3 of the mass (cf. Chatterjee 1990); about 20% of the mass of the disk contains gas particles. The elliptical is modeled identically as the bulge. The gravitational potential is softened with softening constants of ∊ = r∘/5, r∘/3, and 0.8r∘, for the bulge of the spiral as well as the elliptical, stellar and gaseous components of the disk, respectively. Here r∘ is the radius containing 75% of the total mass of the galaxy in question, while the mutual gravitational interaction is softened with a softening constant of r∘/4.
Observational evidence indicates that the frequency of internal structures (such as rings, bars, spirals, etc.) is preferentially enhanced for spirals in binary systems (e.g. Elmegreen et al. 1990). In this context we study the tidal effects produced due to two spiral galaxies in a near grazing relative orbit with a near parabolic relative velocity, as such barely bound encounters are the most frequent ones. Both the spirals are endowed with an inner and an outer ring.
The spiral galaxies (of radius R) are modeled by an exponential disk of scale length α = 4/R, with a (static) thickness (Chatterjee 1990), and a spherical polytropic bulge (n=0, 3, 4 equally weighted combination) containing 1/3 of the mass; about 10% of the mass of the disk contains gas particles. Two polytropic rings (n=1; Ostriker 1964), are projected on the disk at 1/4 (inner) and 3/4 (outer) of its radius. Though the rings are gaseous, they are here treated as density enhancements. The gravitational potential is softened with softening constants of ∊ = r∘/5, r∘/3, and 0.8r∘, for the bulge, stellar and gaseous components of the disk, respectively. Here r∘ is the radius containing 75% of the total mass of the spiral. The softening constant for the polytropic rings is 0.35, while the mutual gravitational interaction is softened with a softening constant of r∘/4.