Curvature estimates for submanifolds in warped products

We give estimates on the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.Comment: 21 page

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late

Fingerprinting the magnetic behavior of antiferromagnetic nanostructures using remanent magnetization curves

Antiferromagnetic (AF) nanostructures from Co3O4, CoO and Cr2O3 were prepared by the nanocasting method and were characterized magnetometrically. The field and temperature dependent magnetization data suggests that the nanostructures consist of a core-shell structure. The core behaves as a regular antiferromagnet and the shell as a two-dimensional diluted antiferromagnet in a field (2d DAFF) as previously shown on Co3O4 nanowires [Benitez et al., Phys. Rev. Lett. 101, 097206 (2008)]. Here we present a more general picture on three different material systems, i.e. Co3O4, CoO and Cr2O3. In particular we consider the thermoremanent (TRM) and the isothermoremanent (IRM) magnetization curves as "fingerprints" in order to identify the irreversible magnetization contribution originating from the shells. The TRM/IRM fingerprints are compared to those of superparamagnetic systems, superspin glasses and 3d DAFFs. We demonstrate that TRM/IRM vs. H plots are generally useful fingerprints to identify irreversible magnetization contributions encountered in particular in nanomagnets.Comment: submitted to PR

Effects of Liposomes Contained in Thermosensitive Hydrogels as Biomaterials Useful in Neural Tissue Engineering

Indexación: Scopus.Advances in the generation of suitable thermosensitive hydrogels for the delivery of cells in neural tissue engineering demonstrate a delicate relationship between physical properties and capabilities to promote cell proliferation and differentiation. To improve the properties of these materials, it is possible to add liposomes for the controlled release of bioactive elements, which in turn can affect the physical and biological properties of the hydrogels. In the present investigation, different hydrogels based on Pluronic F127 have been formulated with the incorporation of chitosan and two types of liposomes of two different sizes. The rheological and thermal properties and their relation with the neurite proliferation and growth of the PC12 cell line were evaluated. Our results show that the incorporation of liposomes modifies the properties of the hydrogels dependent on the concentration of chitosan and the lipid type in the liposomes, which directly affect the capabilities of the hydrogels to promote the viability and differentiation of PC12 cells. © 2017 by the authors.http://www.mdpi.com/1996-1944/10/10/112

Ordering in the dilute weakly-anisotropic antiferromagnet Mn(0.35)Zn(0.65)F2

The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering in zero field. The Bragg peaks observed below the Neel temperature TN (approximately 10.9 K) indicate stable antiferromagnetic long-range ordering at low temperature. The critical behavior is governed by random-exchange Ising model critical exponents (nu approximately 0.69 and gamma approximately 1.31), as reported for Mn(x)Zn(1-x)F2 with higher x and for the isostructural compound Fe(x)Zn(1-x)F2. However, in addition to the Bragg peaks, unusual scattering behavior appears for |q|>0 below a glassy temperature Tg approximately 7.0 K. The glassy region T<Tg corresponds to that of noticeable frequency dependence in earlier zero-field ac susceptibility measurements on this sample. These results indicate that long-range order coexists with short-range nonequilibrium clusters in this highly diluted magnet.Comment: 7 pages, 5 figure

Physics of Rheologically-Enhanced Propulsion: Different Strokes in Generalized Stokes

Shear-thinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shear-thinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shear-thinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in two-dimensional, inertialess Carreau fluid: shear-thinning "Generalized Stokes" flow. Swimmers are modeled, using the method of femlets, by a set of immersed, regularized forces. The equations governing the fluid dynamics are then discretized over a body-fitted mesh and solved with the finite element method. We analyze the locomotion of three distinct classes of microswimmer: (1) conceptual swimmers comprising sliding spheres employing both one- and two-dimensional strokes, (2) slip-velocity envelope models of ciliates commonly referred to as "squirmers" and (3) monoflagellate pushers, such as sperm. We find that morphologically identical swimmers with different strokes may swim either faster or slower in shear-thinning fluids than in Newtonian fluids. We explain this kinematic sensitivity by considering differences in the viscosity of the fluid surrounding propulsive and payload elements of the swimmer, and using this insight suggest two reciprocal sliding sphere swimmers which violate Purcell's Scallop theorem in shear-thinning fluids. We also show that an increased flow decay rate arising from shear-thinning rheology is associated with a reduction in the swimming speed of slip-velocity squirmers. For sperm-like swimmers, a gradient of thick to thin fluid along the flagellum alters the force it exerts upon the fluid, flattening trajectories and increasing instantaneous swimming speed.Comment: 22 pages, 28 figure

d=3 random field behavior near percolation

The highly diluted antiferromagnet Mn(0.35)Zn(0.65)F2 has been investigated by neutron scattering for H>0. A low-temperature (T<11K), low-field (H<1T) pseudophase transition boundary separates a partially antiferromagnetically ordered phase from the paramagnetic one. For 1<H<7T at low temperatures, a region of antiferromagnetic order is field induced but is not enclosed within a transition boundary.Comment: 9 pages, 4 figure

Non-linear Dependence of L(B) on L(FIR) and M(H2) among Spiral Galaxies and Effects of Tidal Interaction

Through the study of a carefully selected sample of isolated spiral galaxies, we have established that two important global physical quantities for tracing star forming activities, L(FIR) and M(H2), have non-linear dependence on another commonly cited global quantity L(B). Furthermore we show that simple power law relations can effectively describe these non-linear relations for spiral galaxies spanning four orders of magnitude in FIR and M(H2) and nearly three orders of magnitude in L(B). While the existence of non-linear dependence of M(H2) (assuming a constant CO-to-H2 conversion) and L(FIR) on optical luminosity L(B) has been previously noted in the literature, an improper normalization of simple scaling by L(B) has been commonly used in many previous studies to claim enhanced molecular gas content and induced activities among tidally interacting and other types of galaxies. We remove these non-linear effects using the template relations derived from the isolated galaxy sample and conclude that strongly interacting galaxies do not have enhanced molecular gas content, contrary to previous claims. With these non-linear relations among L(B), L(FIR) and M(H2) properly taken into account, we confirm again that the FIR emission and the star formation efficiency L(FIR)/M(H2) are indeed enhanced by tidal interactions. Virgo galaxies show the same level of M(H2) and L(FIR) as isolated galaxies. We do not find any evidence for enhanced star forming activity among barred galaxies.Comment: 19 pages and 5 figures, requires AAS style files, ApJ, accepte

The AMIGA sample of isolated galaxies. IV. A catalogue of neighbours around isolated galaxies

Studies of the effects of environment on galaxy properties and evolution require well defined control samples. Such isolated galaxy samples have up to now been small or poorly defined. The AMIGA project (Analysis of the interstellar Medium of Isolated GAlaxies) represents an attempt to define a statistically useful sample of the most isolated galaxies in the local (z < 0.05) Universe. A suitable large sample for the AMIGA project already exists, the Catalogue of Isolated Galaxies (CIG, Karachentseva 1973; 1050 galaxies), and we use this sample as a starting point to refine and perform a better quantification of its isolation properties. Digitised POSS-I E images were analysed out to a minimum projected radius R > 0.5 Mpc around 950 CIG galaxies (those within Vr = 1500 km s-1 were excluded). We identified all galaxy candidates in each field brighter than B = 17.5 with a high degree of confidence using the LMORPHO software. We generated a catalogue of approximately 54 000 potential neighbours (redshifts exist for 30% of this sample). Six hundred sixty-six galaxies pass and two hundred eighty-four fail the original CIG isolation criterion. The available redshift data confirm that our catalogue involves a largely background population rather than physically associated neighbours. We find that the exclusion of neighbours within a factor of four in size around each CIG galaxy, employed in the original isolation criterion, corresponds to Delta Vr ~ 18000 km s-1 indicating that it was a conservative limit. Galaxies in the CIG have been found to show different degrees of isolation. We conclude that a quantitative measure of this is mandatory. It will be the subject of future work based on the catalogue of neighbours obtained here.Comment: Accepted by A&A, 10 pages, 8 figures, 4 table