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 Anisotropy of Spherical Spaces

The first-year WMAP data taken at their face value hint that the Universe might be slightly positively curved and therefore necessarily finite, since all spherical (Clifford-Klein) space forms M^3 = S^3/Gamma, given by the quotient of S^3 by a group Gamma of covering transformations, possess this property. We examine the anisotropy of the cosmic microwave background (CMB) for all typical groups Gamma corresponding to homogeneous universes. The CMB angular power spectrum and the temperature correlation function are computed for the homogeneous spaces as a function of the total energy density parameter Omega_tot in the large range [1.01, 1.20] and are compared with the WMAP data. We find that out of the infinitely many homogeneous spaces only the three corresponding to the binary dihedral group T*, the binary octahedral group O*, and the binary icosahedral group I* are in agreement with the WMAP observations. Furthermore, if Omega_tot is restricted to the interval [1.00, 1.04], the space described by T* is excluded since it requires a value of Omega_tot which is probably too large being in the range [1.06, 1.07]. We thus conclude that there remain only the two homogeneous spherical spaces S^3/O* and S^3/I* with Omega_tot of about 1.038 and 1.018, respectively, as possible topologies for our Universe.Comment: A version with high resolution sky maps can be obtained at http://www.physik.uni-ulm.de/theo/qc

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

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

Characterization of a trimeric light-harvesting complex in the diatom Phaeodactylum tricornutum built of FcpA and FcpE proteins

Fucoxanthin chlorophyll proteins (Fcps), the light-harvesting antennas of heterokont algae, are encoded by a multigene family and are highly similar with respect to their molecular masses as well as to their pigmentation, making it difficult to purify single Fcps. In this study, a hexa-histidine tag was genetically added to the C-terminus of the FcpA protein of the pennate diatom Phaeodactylum tricornutum. A transgenic strain expressing the recombinant His-tagged FcpA protein in addition to the endogenous wild type Fcps was created. This strategy allowed, for the first time, the purification of a specific, stable trimeric Fcp complex. In addition, a pool of various trimeric Fcps was also purified from the wild-type cells using sucrose density gradient ultracentrifugation and gel filtration. In both the His-tagged and the wild-type Fcps, excitation energy coupling between fucoxanthin and chlorophyll a was intact and the existence of a chlorophyll a/fucoxanthin excitonic dimer was demonstrated using circular dichroism spectroscopy. Mass spectrometric analyses of the trimeric His-tagged complex indicated that it is composed of FcpA and FcpE polypeptides. It is confirmed here that a trimer is the basic organizational unit of Fcps in P. tricornutum. From circular dichroism spectra, it is proposed that the organization of the pigments on the polypeptide backbone of Fcps is a conserved feature in the case of chlorophyll a/c containing algae

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

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

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