152 research outputs found
Exact Polynomial Eigenmodes for Homogeneous Spherical 3-Manifolds
Observational data hints at a finite universe, with spherical manifolds such
as the Poincare dodecahedral space tentatively providing the best fit.
Simulating the physics of a model universe requires knowing the eigenmodes of
the Laplace operator on the space. The present article provides explicit
polynomial eigenmodes for all globally homogeneous 3-manifolds: the Poincare
dodecahedral space S3/I*, the binary octahedral space S3/O*, the binary
tetrahedral space S3/T*, the prism manifolds S3/D_m* and the lens spaces
L(p,1).Comment: v3. Final published version. 27 pages, 1 figur
How well-proportioned are lens and prism spaces?
The CMB anisotropies in spherical 3-spaces with a non-trivial topology are
analysed with a focus on lens and prism shaped fundamental cells. The
conjecture is tested that well proportioned spaces lead to a suppression of
large-scale anisotropies according to the observed cosmic microwave background
(CMB). The focus is put on lens spaces L(p,q) which are supposed to be oddly
proportioned. However, there are inhomogeneous lens spaces whose shape of the
Voronoi domain depends on the position of the observer within the manifold.
Such manifolds possess no fixed measure of well-proportioned and allow a
predestined test of the well-proportioned conjecture. Topologies having the
same Voronoi domain are shown to possess distinct CMB statistics which thus
provide a counter-example to the well-proportioned conjecture. The CMB
properties are analysed in terms of cyclic subgroups Z_p, and new point of view
for the superior behaviour of the Poincar\'e dodecahedron is found
CMB Alignment in Multi-Connected Universes
The low multipoles of the cosmic microwave background (CMB) anisotropy
possess some strange properties like the alignment of the quadrupole and the
octopole, and the extreme planarity or the extreme sphericity of some
multipoles, respectively. In this paper the CMB anisotropy of several
multi-connected space forms is investigated with respect to the maximal angular
momentum dispersion and the Maxwellian multipole vectors in order to settle the
question whether such spaces can explain the low multipole anomalies in the
CMB
Isomorphs in model molecular liquids
Isomorphs are curves in the phase diagram along which a number of static and
dynamic quantities are invariant in reduced units. A liquid has good isomorphs
if and only if it is strongly correlating, i.e., the equilibrium
virial/potential energy fluctuations are more than 90% correlated in the NVT
ensemble. This paper generalizes isomorphs to liquids composed of rigid
molecules and study the isomorphs of two systems of small rigid molecules, the
asymmetric dumbbell model and the Lewis-Wahnstrom OTP model. In particular, for
both systems we find that the isochoric heat capacity, the excess entropy, the
reduced molecular center-of-mass self part of the intermediate scattering
function, the reduced molecular center-of-mass radial distribution function to
a good approximation are invariant along an isomorph. In agreement with theory,
we also find that an instantaneous change of temperature and density from an
equilibrated state point to another isomorphic state point leads to no
relaxation. The isomorphs of the Lewis-Wahnstrom OTP model were found to be
more approximative than those of the asymmetric dumbbell model, which is
consistent with the OTP model being less strongly correlating. For both models
we find "master isomorphs", i.e., isomorphs have identical shape in the
virial/potential energy phase diagram.Comment: 20 page
Cosmic Topology of Polyhedral Double-Action Manifolds
A special class of non-trivial topologies of the spherical space S^3 is
investigated with respect to their cosmic microwave background (CMB)
anisotropies. The observed correlations of the anisotropies on the CMB sky
possess on large separation angles surprising low amplitudes which might be
naturally be explained by models of the Universe having a multiconnected
spatial space. We analysed in CQG 29(2012)215005 the CMB properties of prism
double-action manifolds that are generated by a binary dihedral group D^*_p and
a cyclic group Z_n up to a group order of 180. Here we extend the CMB analysis
to polyhedral double-action manifolds which are generated by the three binary
polyhedral groups (T^*, O^*, I^*) and a cyclic group Z_n up to a group order of
1000. There are 20 such polyhedral double-action manifolds. Some of them turn
out to have even lower CMB correlations on large angles than the Poincare
dodecahedron
A measure on the set of compact Friedmann-Lemaitre-Robertson-Walker models
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently
regained interest as a good fit to the observed cosmic microwave background
temperature fluctuations. However, it is generally thought that a globally,
exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a
probability space on the set F of compact, comoving, 3-spatial sections of FLRW
models, a physically motivated hypothesis is proposed, using the density
parameter Omega as a derived rather than fundamental parameter. We assume that
the processes that select the 3-manifold also select a global mass-energy and a
Hubble parameter. The inferred range in Omega consists of a single real value
for any 3-manifold. Thus, the obvious measure over F is the discrete measure.
Hence, if the global mass-energy and Hubble parameter are a function of
3-manifold choice among compact FLRW models, then probability spaces
parametrised by Omega do not, in general, give a zero probability of a flat
model. Alternatively, parametrisation by the injectivity radius r_inj ("size")
suggests the Lebesgue measure. In this case, the probability space over the
injectivity radius implies that flat models occur almost surely (a.s.), in the
sense of probability theory, and non-flat models a.s. do not occur.Comment: 19 pages, 4 figures; v2: minor language improvements; v3:
generalisation: m, H functions of
Magnetorheology of alginate ferrogels
Magnetorheological (MR) effect is a phenomenon typical of suspensions of magnetizable particles in a liquid carrier, characterized by strong changes of their mechanical properties in response to applied magnetic fields. Its origin is on the migration of magnetized particles and their aggregation into chain-like structures. However, for ferrogels, consisting of dispersions of magnetic particles in a polymer matrix, migration of particles is hindered by the elastic forces of the polymer network, preventing from strong MR effect. Interestingly, we demonstrate in this manuscript that strong MR effect in robustly cross-linked polymer ferrogels is still possible. Experimental results showed enhancement of the storage modulus of more than one order of magnitude for alginate ferrogels containing less than about 10 vol.% of iron particles under moderate magnetic fields. The differential feature of these ferrogels is that, instead of individual particles, the disperse phase consisted of large clusters of iron microparticles homogeneously distributed within the polymer networks. These clusters of magnetic particles were formed at the stage of the preparation of the ferrogels and their presence within the polymer networks had two main consequences. First, the volume fraction of clusters was considerably larger than this of individual particles, resulting in a larger effective volume fraction of solids. Second, since the force of magnetic attraction between magnetic bodies is roughly proportional to the cube of the body size, the existence of such clusters favored inter-cluster interaction under a magnetic field and the appearance of strong MR effect. On this basis, we demonstrated by theoretical modeling that the strong MR effect displayed by the alginate ferrogels of the present work can be quantitatively explained by assuming the existence of large, roughly spherical particle aggregates formed at the stage of the preparation of the ferrogels. Our theoretical model provides a reasonable quantitative prediction of the experimental resultsThis study was supported by project FIS2017-85954-R (Ministerio de Economía, Industria y Competitividad, MINECO, and Agencia Estatal de Investigación, AEI, Spain, cofunded by Fondo Europeo de Desarrollo Regional, FEDER, European Union). CGV acknowledges financial support by Ministerio de Ciencia, Innovación y Universidades and University of Granada, Spain, for her FPU17/00491 grant. AZ is grateful to the Program of the Ministry of Education and Science of the Russian Federation, projects 02.A03.21.0006, 3.1438.2017/4.6, and 3.5214.2017/6.7 and the Russian Fund of Basic Researches, project 18-08-0017
Ascorbic Acid, Alcohol, and Environmental Chemicals a
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73093/1/j.1749-6632.1987.tb23775.x.pd
CMB radiation in an inhomogeneous spherical space
We analyse the CMB radiation in spherical 3-spaces with non-trivial topology.
The focus is put on an inhomogeneous space which possesses observer dependent
CMB properties. The suppression of the CMB anisotropies on large angular scales
is analysed with respect to the position of the CMB observer. The equivalence
of a lens space with a Platonic cubic space is shown and used for the harmonic
analysis. We give the transformation of the CMB multipole radiation amplitude
as a function of the position of the observer. General sum rules are obtained
in terms of the squares of the expansion coefficients for invariant polynomials
on the 3-sphere
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