Newtonian versus relativistic nonlinear cosmology

Both for the background world model and its linear perturbations Newtonian cosmology coincides with the zero-pressure limits of relativistic cosmology. However, such successes in Newtonian cosmology are not purely based on Newton's gravity, but are rather guided ones by previously known results in Einstein's theory. The action-at-a-distance nature of Newton's gravity requires further verification from Einstein's theory for its use in the large-scale nonlinear regimes. We study the domain of validity of the Newtonian cosmology by investigating weakly nonlinear regimes in relativistic cosmology assuming a zero-pressure and irrotational fluid. We show that, first, if we ignore the coupling with gravitational waves the Newtonian cosmology is exactly valid even to the second order in perturbation. Second, the pure relativistic correction terms start appearing from the third order. Third, the correction terms are independent of the horizon scale and are quite small in the large-scale near the horizon. These conclusions are based on our special (and proper) choice of variables and gauge conditions. In a complementary situation where the system is weakly relativistic but fully nonlinear (thus, far inside the horizon) we can employ the post-Newtonian approximation. We also show that in the large-scale structures the post-Newtonian effects are quite small. As a consequence, now we can rely on the Newtonian gravity in analyzing the evolution of nonlinear large-scale structures even near the horizon volume.Comment: 8 pages, no figur

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulator for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site we suggest a possible resolution to the puzzling occurrence of bipolar cells, such we offer an explanation for the development of closed, looped veins. Employing non-linear analysis we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.Comment: 9 pages, 4 figures, supplemental information included, accepted for publication in Eur. Phys. J.

Model Analysis of Time Reversal Symmetry Test in the Caltech Fe-57 Gamma-Transition Experiment

The CALTECH gamma-transition experiment testing time reversal symmetry via the E2/M1 mulipole mixing ratio of the 122 keV gamma-line in Fe-57 has already been performed in 1977. Extending an earlier analysis in terms of an effective one-body potential, this experiment is now analyzed in terms of effective one boson exchange T-odd P-even nucleon nucleon potentials. Within the model space considered for the Fe-57 nucleus no contribution from isovector rho-type exchange is possible. The bound on the coupling strength phi_A from effective short range axial-vector type exchange induced by the experimental bound on sin(eta) leads to phi_A < 10^{-2}.Comment: 5 pages, RevTex 3.

The Sachs-Wolfe Effect: Gauge Independence and a General Expression

In this paper we address two points concerning the Sachs-Wolfe effect: (i) the gauge independence of the observable temperature anisotropy, and (ii) a gauge-invariant expression of the effect considering the most general situation of hydrodynamic perturbations. The first result follows because the gauge transformation of the temperature fluctuation at the observation event only contributes to the isotropic temperature change which, in practice, is absorbed into the definition of the background temperature. Thus, we proceed without fixing the gauge condition, and express the Sachs-Wolfe effect using the gauge-invariant variables.Comment: 5 pages, closer to published versio

Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories

We present cosmological perturbations of kinetic components based on relativistic Boltzmann equations in the context of generalized gravity theories. Our general theory considers an arbitrary number of scalar fields generally coupled with the gravity, an arbitrary number of mutually interacting hydrodynamic fluids, and components described by the relativistic Boltzmann equations like massive/massless collisionless particles and the photon with the accompanying polarizations. We also include direct interactions among fluids and fields. The background FLRW model includes the general spatial curvature and the cosmological constant. We consider three different types of perturbations, and all the scalar-type perturbation equations are arranged in a gauge-ready form so that one can implement easily the convenient gauge conditions depending on the situation. In the numerical calculation of the Boltzmann equations we have implemented four different gauge conditions in a gauge-ready manner where two of them are new. By comparing solutions solved separately in different gauge conditions we can naturally check the numerical accuracy.Comment: 26 pages, 9 figures, revised thoroughly, to appear in Phys. Rev.

Structural Ceramic Components by 3D Printing

The Three Dimensional Printing (3DP) Process hasbe~nadapted for processing of fine ceramic powders to •• prepare structllraLceramic components. Our preliminary study was designed to reveal those aspects ofthe.3DPprocesswhichmust be modified for use with fine ceramic powders. The basic elements of the modified process are to spread submicron alumina powder and printJatex binder. Several methods were used to spread thin layers of submicron powders. Gre.enparts are isostaticaUypressed followed by thermal decomposition prior to sintering to remove the polymer. The fired alumina components are greater than 99.2% dense and have·average flexural strength of324 MPa. This is lower than the best conventionally prepared alumina, but we believe that the strength results will improve as we learn more about the relationship between strength limiting flaws and the 3DP build process.Mechanical Engineerin

Structural Ceramic Components by 3D Printing

Several technical challenges exist in adapting Three Dimensional Printing (3DP) to processing of dense ceramic structures. The sintering rate of particulate bodies depends on the sintering mechanism, average powder size, and initial packing density. Fine powders are necessary to ensure appreciable densification rates from powders which sinter by solid state transport. A critical packing density exists for such powders below which densification does not occur. Special build strategies are, therefore, required for 3DP of ceramic structures. We have successfully demonstrated five approaches to produce dense ceramic components by 3DP. First, spray-dried granules of fine ceramic powders are spread in the existing 3DP equipment and bound using a latex binder through an ink-jet print head. The resulting components are then isostatically pressed to raise the green density to a point that the parts will fully densify when fired. A second approach uses glass powders that sinter by a viscous sintering mechanism. Such bodies sinter to full density at all initial green densities. Spray-dried granules of fine glass powders are spread and bound with latex followed by directly sintering to full density. Both of these approaches produce rather large linear shrinkage because of the low overall packing density. Large glass particles have a much higher packing density and produce bodies that sinter to full density because of the rapid viscous sintering. This third technique produces fully dense parts with linear shrinkage of about 15%. The fourth approach involves glass infiltration of porous ceramic bodies. Our results indicate that this technique can produce dense parts with less than 1% linear shrinkage. Finally, the 3DP process has been modified to permit deposition of fine powders as slurries, rather than dry powders. The resulting process considerably increases the bed density and the resulting fine ceramic parts can be sintered to full density without intermediate isopressing.Mechanical Engineerin