Statics and kinetics at the nematic­-isotropic interface: effects of biaxiality

We use the Landau-de Gennes theory of a nematic liquid crystal to investigate anew aspects of the properties of the interface between the isotropic and nematic liquid crystal phases of the same fluid. The equations of the static interface have been solved, both numerically and using asymptotic analysis, with an emphasis on the effect of inclusion of the order parameter biaxiality on the physical properties. We have compared the results of the exact solutions to the commonly used de Gennes ansatz, which assumes positive and uniform unixiality through the interface. Although the de Gennes ansatz in general gives good results, when bend and splay elastic constants dominate over the twist constants, it can lead to errors of up to 10% in the surface energy. The asymptotic analysis also shows that, by contrast with the de Gennes ansatz, the order parameter wings in the isotropic phase exhibit negative order parameter, with principal axis perpendicular to the surface. For moving interfaces, using an approximation which at this stage does not yet include hydrodynamic coupling, we have compared our results with the analogue of the de Gennes ansatz used by the present authors in an earlier paper. We find that including biaxiality leads to larger effects in the dynamic than in the static properties, and that whereas this is essentially a perturbation to the energy, the velocity of the moving interface can be significantly slowed down. The slowing down effects are strongly correlated with surface biaxiality, but both effects seem to be diminished when the isotropic phase is advancing

Foam-like structure of the Universe

On the quantum stage spacetime had the foam-like structure. When the Universe cools, the foam structure tempers and does not disappear. We show that effects caused by the foamed structure mimic very well the observed Dark Matter phenomena. Moreover, we show that in a foamed space photons undergo a chaotic scattering and together with every discrete source of radiation we should observe a diffuse halo. We show that the distribution of the diffuse halo of radiation around a point-like source repeats exactly the distribution of dark matter around the same source, i.e. the DM halos are sources of the diffuse radiation

Eutectic colony formation: A phase field study

Eutectic two-phase cells, also known as eutectic colonies, are commonly observed during the solidification of ternary alloys when the composition is close to a binary eutectic valley. In analogy with the solidification cells formed in dilute binary alloys, colony formation is triggered by a morphological instability of a macroscopically planar eutectic solidification front due to the rejection by both solid phases of a ternary impurity that diffuses in the liquid. Here we develop a phase-field model of a binary eutectic with a dilute ternary impurity and we investigate by dynamical simulations both the initial linear regime of this instability, and the subsequent highly nonlinear evolution of the interface that leads to fully developed two-phase cells with a spacing much larger than the lamellar spacing. We find a good overall agreement with our recent linear stability analysis [M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a destabilization of the front by long-wavelength modes that may be stationary or oscillatory. A fine comparison, however, reveals that the assumption commonly attributed to Cahn that lamella grow perpendicular to the envelope of the solidification front is weakly violated in the phase-field simulations. We show that, even though weak, this violation has an important quantitative effect on the stability properties of the eutectic front. We also investigate the dynamics of fully developed colonies and find that the large-scale envelope of the composite eutectic front does not converge to a steady state, but exhibits cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.

The Paradox of Virtual Dipoles in the Einstein Action

The functional integral of pure Einstein 4D quantum gravity admits abnormally large and long-lasting "dipolar fluctuations", generated by virtual sources with the property Int d^4x Sqrt{g(x)} Tr T(x) = 0. These fluctuations would exist also at macroscopic scales, with paradoxical consequences. We set out their general features and give numerical estimates of possible suppression processes.Comment: LaTeX, 5 pages; reference adde

Dark Matter from a gas of wormholes

The simplistic model of the classical spacetime foam is considered, which consists of static wormholes embedded in Minkowski spacetime. We explicitly demonstrate that such a foam structure leads to a topological bias of point-like sources which can equally be interpreted as the presence of a dark halo around any point source. It is shown that a non-trivial halo appears on scales where the topological structure possesses a local inhomogeneity, while the homogeneous structure reduces to a constant renormalization of the intensity of sources. We also show that in general dark halos possess both (positive and negative) signs depending on scales and specific properties of topological structure of space.Comment: minor corrections (eq. 18

Towards a quantitative phase-field model of two-phase solidification

We construct a diffuse-interface model of two-phase solidification that quantitatively reproduces the classic free boundary problem on solid-liquid interfaces in the thin-interface limit. Convergence tests and comparisons with boundary integral simulations of eutectic growth show good accuracy for steady-state lamellae, but the results for limit cycles depend on the interface thickness through the trijunction behavior. This raises the fundamental issue of diffuse multiple-junction dynamics.Comment: 4 pages, 2 figures. Better final discussion. 1 reference adde

Quantum Creation of an Open Inflationary Universe

We discuss a dramatic difference between the description of the quantum creation of an open universe using the Hartle-Hawking wave function and the tunneling wave function. Recently Hawking and Turok have found that the Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is much smaller that the observed value of Omega > 0.3. Galaxies in such a universe would be about $10^{10^8}$ light years away from each other, so the universe would be practically structureless. We will argue that the Hartle-Hawking wave function does not describe the probability of the universe creation. If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Omega = 1, which agrees with the standard expectation that inflation makes the universe flat. The same result can be obtained in the theory of a self-reproducing inflationary universe, independently of the issue of initial conditions. However, there exist two classes of models where Omega may take any value, from Omega > 1 to Omega << 1.Comment: 23 pages, 4 figures. New materials are added. In particular, we show that boundary terms do not help to solve the problem of unacceptably small Omega in the new model proposed by Hawking and Turok in hep-th/9803156. A possibility to solve the cosmological constant problem in this model using the tunneling wave function is discusse

From the Big Bang Theory to the Theory of a Stationary Universe

We consider chaotic inflation in the theories with the effective potentials phi^n and e^{\alpha\phi}. In such theories inflationary domains containing sufficiently large and homogeneous scalar field \phi permanently produce new inflationary domains of a similar type. We show that under certain conditions this process of the self-reproduction of the Universe can be described by a stationary distribution of probability, which means that the fraction of the physical volume of the Universe in a state with given properties (with given values of fields, with a given density of matter, etc.) does not depend on time, both at the stage of inflation and after it. This represents a strong deviation of inflationary cosmology from the standard Big Bang paradigm. We compare our approach with other approaches to quantum cosmology, and illustrate some of the general conclusions mentioned above with the results of a computer simulation of stochastic processes in the inflationary Universe.Comment: No changes to the file, but original figures are included. They substantially help to understand this paper, as well as eternal inflation in general, and what is now called the "multiverse" and the "string theory landscape." High quality figures can be found at http://www.stanford.edu/~alinde/LLMbigfigs