Domain-walls formation in binary nanoscopic finite systems

Using a simple one-dimensional Frenkel-Kontorowa type model, we have demonstrated that finite commensurate chains may undergo the commensurate-incommensurate (C-IC) transition when the chain is contaminated by isolated impurities attached to the chain ends. Monte Carlo (MC) simulation has shown that the same phenomenon appears in two-dimensional systems with impurities located at the peripheries of finite commensurate clusters.Comment: 9 pages, 6 figure

The mechanism of domain-wall structure formation in Ar-Kr submonolayer films on graphite

Using Monte Carlo simulation method in the canonical ensemble, we have studied the commensurate-incommensurate transition in two-dimensional finite mixed clusters of Ar and Kr adsorbed on graphite basal plane at low temperatures. It has been demonstrated that the transition occurs when the argon concentration exceeds the value needed to cover the peripheries of the cluster. The incommensurate phase exhibits a similar domain-wall structure as observed in pure krypton films at the densities exceeding the density of a perfect $(\sqrt{3}\times\sqrt{3})R30^\circ$ commensurate phase, but the size of commensurate domains does not change much with the cluster size. When the argon concentration increases, the composition of domain walls changes while the commensurate domains are made of pure krypton. We have constructed a simple one-dimensional Frenkel-Kontorova-like model that yields the results being in a good qualitative agreement with the Monte Carlo results obtained for two-dimensional systems.Comment: 14 pages, 9 figure

The local and global geometrical aspects of the twin paradox in static spacetimes: I. Three spherically symmetric spacetimes

We investigate local and global properties of timelike geodesics in three static spherically symmetric spacetimes. These properties are of its own mathematical relevance and provide a solution of the physical `twin paradox' problem. The latter means that we focus our studies on the search of the longest timelike geodesics between two given points. Due to problems with solving the geodesic deviation equation we restrict our investigations to radial and circular (if exist) geodesics. On these curves we find general Jacobi vector fields, determine by means of them sequences of conjugate points and with the aid of the comoving coordinate system and the spherical symmetry we determine the cut points. These notions identify segments of radial and circular gepdesics which are locally or globally of maximal length. In de Sitter spacetime all geodesics are globally maximal. In CAdS and Bertotti--Robinson spacetimes the radial geodesics which infinitely many times oscillate between antipodal points in the space contain infinite number of equally separated conjugate points and there are no other cut points. Yet in these two spacetimes each outgoing or ingoing radial geodesic which does not cross the centre is globally of maximal length. Circular geodesics exist only in CAdS spacetime and contain an infinite sequence of equally separated conjugate points. The geodesic curves which intersect the circular ones at these points may either belong to the two-surface $\theta=\pi/2$ or lie outside it.Comment: 27 pages, 0 figures, typos corrected, version published in APP

Jacobi fields, conjugate points and cut points on timelike geodesics in special spacetimes

Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic investigations of the geodesic structure of physically relevant spacetimes. The investigations are focussed on the search of locally and globally maximal timelike geodesics. The method of dealing with the local problem is in a sense algorithmic and is based on the geodesic deviation equation. Yet the search for globally maximal geodesics is non-algorithmic and cannot be treated analytically by solving a differential equation. Here one must apply a mixture of methods: spacetime symmetries (we have effectively employed the spherical symmetry), the use of the comoving coordinates adapted to the given congruence of timelike geodesics and the conjugate points on these geodesics. All these methods have been effectively applied in both the local and global problems in a number of simple and important spacetimes and their outcomes have already been published in three papers. Our approach shows that even in Schwarzschild spacetime (as well as in other static spherically symetric ones) one can find a new unexpected geometrical feature: instead of one there are three different infinite sets of conjugate points on each stable circular timelike geodesic curve. Due to problems with solving differential equations we are dealing solely with radial and circular geodesics.Comment: A revised and expanded version, self-contained and written in an expository style. 36 pages, 0 figures. A substantially abridged version appeared in Acta Physica Polonica

The local and global geometrical aspects of the twin paradox in static spacetimes: II. Reissner--Nordstr\"{o}m and ultrastatic metrics

This is a consecutive paper on the timelike geodesic structure of static spherically symmetric spacetimes. First we show that for a stable circular orbit (if it exists) in any of these spacetimes all the infinitesimally close to it timelike geodesics constructed with the aid of the general geodesic deviation vector have the same length between a pair of conjugate points. In Reissner--Nordstr\"{o}m black hole metric we explicitly find the Jacobi fields on the radial geodesics and show that they are locally (and globally) maximal curves between any pair of their points outside the outer horizon. If a radial and circular geodesics in R--N metric have common endpoints, the radial one is longer. If a static spherically symmetric spacetime is ultrastatic, its gravitational field exerts no force on a free particle which may stay at rest; the free particle in motion has a constant velocity (in this sense the motion is uniform) and its total energy always exceeds the rest energy, i.~e.~it has no gravitational energy. Previously the absence of the gravitational force has been known only for the global Barriola--Vilenkin monopole. In the spacetime of the monopole we explicitly find all timelike geodesics, the Jacobi fields on them and the condition under which a generic geodesic may have conjugate points

Every timelike geodesic in anti--de Sitter spacetime is a circle of the same radius

We refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti--de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by $\Lambda$, lying on a Euclidean two--plane. Then we outline an alternative proof for $AdS_4$. We also make a comment on the shape of timelike geodesics in de Sitter space.Comment: An expanded version of the work published in International Journal of Modern Physics D. 8 pages, 0 figure

Anisotropic Inflation from Extra Dimensions

Vacuum multidimensional cosmological models with internal spaces being compact $n$-dimensional Lie group manifolds are considered. Products of 3-spheres and $SU(3)$ manifold (a novelty in cosmology) are studied. It turns out that the dynamical evolution of the internal space drives an accelerated expansion of the external world (power law inflation). This generic solution (attractor in a phase space) is determined by the Lie group space without any fine tuning or arbitrary inflaton potentials. Matter in the four dimensions appears in the form of a number of scalar fields representing anisotropic scale factors for the internal space. Along the attractor solution the volume of the internal space grows logarithmically in time. This simple and natural model should be completed by mechanisms terminating the inflationary evolution and transforming the geometric scalar fields into ordinary particles.Comment: LaTeX, 11 pages, 5 figures available via fax on request to [email protected], submitted to Phys. Lett.

Changes in the structure of tethered chain molecules as predicted by density functional approach

We use a version of the density functional theory to study the changes in the height of the tethered layer of chains built of jointed spherical segments with the change of the length and surface density of chains. For the model in which the interactions between segments and solvent molecules are the same as between solvent molecules we have discovered two effects that have not been observed in previous studies. Under certain conditions and for low surface concentrations of the chains, the height of the pinned layer may attain a minimum. Moreover, for some systems we observe that when the temperature increases, the height of the layer of chains may decrease.Comment: 13 pages, 7 figure

First-order phase transitions in lattice bilayers of Janus-like particles: Monte Carlo simulations

The first-order phase transitions in the lattice model of Janus-like particles confined in slit-like pores are studied. We assume a cubic lattice with molecules that can freely change their orientation on a lattice site. Moreover, the molecules can interact with the pore walls with orientation-dependent forces. The performed calculations are limited to the cases of bilayers. Our emphasis is on the competition between the fluid-wall and fluid-fluid interactions. The oriented structures formed in the systems in which the fluid-wall interactions acting contrary to the fluid-fluid interactions differ from those appearing in the systems with neutral walls or with walls attracting the repulsive parts of fluid molecules.Comment: 12 pages, 11 figure

Test-field limit of metric nonlinear gravity theories

In the framework of alternative metric gravity theories, it has been shown by several authors that a generic Lagrangian depending on the Riemann tensor describes a theory with 8 degrees of freedom (which reduce to 3 for f(R) Lagrangians depending only on the curvature scalar). This result is often related to a reformulation of the fourth-order equations for the metric into a set of second-order equations for a multiplet of fields, including a massive scalar field and a massive spin-2 field. In this article we investigate an issue which does not seem to have been addressed so far: in ordinary general-relativistic field theories, all fundamental fields (i.e. fields with definite spin and mass) reduce to test fields in some appropriate limit of the model, where they cease to act as sources for the metric curvature. In this limit, each of the fundamental fields can be excited from its ground state independently from the others. The question is: does higher-derivative gravity admit a test-field limit for its fundamental fields? It is easy to show that for a f(R) theory the test-field limit does exist; then, we consider the case of Lagrangians quadratically depending on the full Ricci tensor. We show that the constraint binding together the scalar field and the massive spin-2 field does not disappear in the limit where they should be expected to act as test fields, except for a particular choice of the Lagrangian, which cause the scalar field to disappear (reducing to 7 DOF). We finally consider the addition of an arbitrary function of the quadratic invariant of the Weyl tensor and show that the resulting model still lacks a proper test-field limit. We argue that the lack of a test-field limit for the fundamental fields may constitute a serious drawback of the full 8 DOF higher-order gravity models, which is not encountered in the restricted 7 DOF or 3 DOF cases.Comment: Title and abstract modified to make the content of the paper more clear and readabl