256 research outputs found
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 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 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
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 , lying on a Euclidean two--plane. Then we
outline an alternative proof for . 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
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
Anisotropic Inflation from Extra Dimensions
Vacuum multidimensional cosmological models with internal spaces being
compact -dimensional Lie group manifolds are considered. Products of
3-spheres and 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
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