Reconstructing the global topology of the universe from the cosmic microwave background

If the universe is multiply-connected and sufficiently small, then the last scattering surface wraps around the universe and intersects itself. Each circle of intersection appears as two distinct circles on the microwave sky. The present article shows how to use the matched circles to explicitly reconstruct the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to Class. Quant. Gra

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

Comments on Closed Bianchi Models

We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to show them, we put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. We make clear the relation between the Bianchi type symmetry of space-time and spatial compactness, some part of which seem to be unnoticed in the literature. Especially, it is shown under what conditions class B Bianchi models do not possess compact spatial sections. Finally we briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5

Right-veering diffeomorphisms of compact surfaces with boundary II

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group B_n on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Ro1,Ro2].Comment: 25 pages, 5 figure

Sensorimotor adaptation to auditory perturbation of speech is facilitated by noninvasive brain stimulation

Repeated exposure to disparity between the motor plan and auditory feedback during speech production results in a proportionate change in the motor system’s response called auditory-motor adaptation. Artificially raising F1 in auditory feedback results in a concomitant decrease in F1 during speech production. Transcranial direct current stimulation (tDCS) can be used to alter neuronal excitability in focal areas of the brain. The present experiment explored the effect of noninvasive brain stimulation applied to the speech premotor cortex on the timing and magnitude of adaptation responses to artificially raised F1 in auditory feedback. Participants (N = 18) completed a speaking task in which they read target words aloud. Participants' speech was processed to raise F1 by 30% and played back to them over headphones in real time. A within-subjects design compared acoustics of participants’ speech while receiving anodal (active) tDCS stimulation versus sham (control) stimulation. Participants' speech showed an increasing magnitude of adaptation of F1 over time during anodal stimulation compared to sham. These results indicate that tDCS can affect behavioral response during auditory-motor adaptation, which may have translational implications for sensorimotor training in speech disorders

Quantum creation of an Inhomogeneous universe

In this paper we study a class of inhomogeneous cosmological models which is a modified version of what is usually called the Lema\^itre-Tolman model. We assume that we have a space with 2-dimensional locally homogeneous spacelike surfaces. In addition we assume they are compact. Classically we investigate both homogeneous and inhomogeneous spacetimes which this model describe. For instance one is a quotient of the AdS$_4$ space which resembles the BTZ black hole in AdS$_3$. Due to the complexity of the model we indicate a simpler model which can be quantized easily. This model still has the feature that it is in general inhomogeneous. How this model could describe a spontaneous creation of a universe through a tunneling event is emphasized.Comment: 21 pages, 5 ps figures, REVTeX, new subsection include

Measuring Topological Chaos

The orbits of fluid particles in two dimensions effectively act as topological obstacles to material lines. A spacetime plot of the orbits of such particles can be regarded as a braid whose properties reflect the underlying dynamics. For a chaotic flow, the braid generated by the motion of three or more fluid particles is computed. A ``braiding exponent'' is then defined to characterize the complexity of the braid. This exponent is proportional to the usual Lyapunov exponent of the flow, associated with separation of nearby trajectories. Measuring chaos in this manner has several advantages, especially from the experimental viewpoint, since neither nearby trajectories nor derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro

Twin paradox and space topology

If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than along any other one.Comment: 6 pages, latex, 3 figure

Soft phonons and structural phase transitions in La1.875_{1.875}Ba0.125_{0.125}CuO4_{4}

Soft phonon behavior associated with a structural phase transition from the low-temperature-orthorhombic (LTO) phase ($Bmab$ symmetry) to the low-temperature-tetragonal (LTT) phase ($P4_{2}/ncm$ symmetry) was investigated in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ using neutron scattering. As temperature decreases, the TO-mode at $Z$-point softens and approaches to zero energy around $T_{\rm d2}=62$ K, where the LTO -- LTT transition occurs. Below $T_{\rm d2}$, the phonon hardens quite rapidly and it's energy almost saturates below 50 K. At $T_{\rm d2}$, the energy dispersion of the soft phonon along in-plane direction significantly changes while the dispersion along out-of-plane direction is almost temperature independent. Coexistence between the LTO phase and the LTT phase, seen in both the soft phonon spectra and the peak profiles of Bragg reflection, is discussed in context of the order of structural phase transitions.Comment: 6 pages, 8 figure

Diffusion on a heptagonal lattice

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence the displacement of a classical random walker increases linearly in time. The diffusion of a quantum particle put on the heptagonal lattice is also studied in the framework of the tight-binding model Hamiltonian, and we again find the linear diffusion like the classical random walk. A comparison with diffusion on complex networks is also made.Comment: 5 pages, 6 figure