Apparent Horizons with Nontrivial Topology and the Hyperhoop Conjecture in Six-Dimensional Space-Times

We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static, conformally flat initial data sets each describing a gravitational field of uniform massive k-sphere sources, for k=1,2, on the five-dimensional Cauchy surface. The numerical result shows the validity of the hyperhoop conjecture for a wide range of model parameters. We also confirm for the first time the existence of an apparent horizon homeomorphism to S**2 x S**2 or S**1 x S**3, which is a higher-dimensional generalization of the black ring.Comment: 17 pages, 12 figures. to appear in Phys. Rev.

Notch signaling augments the canonical Wnt pathway to specify the size of the otic placode

The inner ear derives from a patch of ectoderm defined by expression of the transcription factor Pax2. We recently showed that this Pax2^+ ectoderm gives rise not only to the otic placode but also to the surrounding cranial epidermis, and that Wnt signaling mediates this placode-epidermis fate decision. We now present evidence for reciprocal interactions between the Wnt and Notch signaling pathways during inner ear induction. Activation of Notch1 in Pax2+ ectoderm expands the placodal epithelium at the expense of cranial epidermis, whereas loss of Notch1 leads to a reduction in the size of the otic placode. We show that Wnt signaling positively regulates Notch pathway genes such as Jag1, Notch1 and Hes1, and we have used transgenic Wnt reporter mice to show that Notch signaling can modulate the canonical Wnt pathway. Gain- and loss-of-function mutations in the Notch and Wnt pathways reveal that some aspects of otic placode development - such as Pax8 expression and the morphological thickening of the placode - can be regulated independently by either Notch or Wnt signals. Our results suggest that Wnt signaling specifies the size of the otic placode in two ways, by directly upregulating a subset of otic genes, and by positively regulating components of the Notch signaling pathway, which then act to augment Wnt signaling

Unwrapping of DNA-protein complexes under external stretching

A DNA-protein complex modelled by a semiflexible chain and an attractive spherical core is studied in the situation when an external stretching force is acting on one end monomer of the chain while the other end monomer is kept fixed in space. Without stretching force, the chain is wrapped around the core. By applying an external stretching force, unwrapping of the complex is induced. We study the statics and the dynamics of the unwrapping process by computer simulation and simple phenomenological theory. We find two different scenarios depending on the chain stiffness: For a flexible chain, the extension of the complex scales linearly with the external force applied. The sphere-chain complex is disordered, i.e. there is no clear winding of the chain around the sphere. For a stiff chain, on the other hand, the complex structure is ordered, which is reminiscent to nucleosome. There is a clear winding number and the unwrapping process under external stretching is discontinuous with jumps of the distance-force curve. This is associated to discrete unwinding processes of the complex. Our predictions are of relevance for experiments, which measure force-extension curves of DNA-protein complexes, such as nucleosome, using optical tweezers.Comment: 8 pages, 7 figure

Quantum-mechanical generation of gravitational waves in braneworld

We study the quantum-mechanical generation of gravitational waves during inflation on a brane embedded in a five-dimensional anti-de Sitter bulk. To make the problem well-posed, we consider the setup in which both initial and final phases are given by a de Sitter brane with different values of the Hubble expansion rate. Assuming that the quantum state is in a de Sitter invariant vacuum in the initial de Sitter phase, we numerically evaluate the amplitude of quantum fluctuations of the growing solution of the zero mode in the final de Sitter phase. We find that the vacuum fluctuations of the initial Kaluza-Klein gravitons as well as of the zero mode gravitons contribute to the final amplitude of the zero mode on small scales, and the power spectrum is quite well approximated by what we call the rescaled spectrum, which is obtained by rescaling the standard four-dimensional calculation following a simple mapping rule. Our results confirm the speculation raised in Ref. \cite{Kobayashi:2003cn} before.Comment: 11 pages, 11 figure

Stochastic Gravitational Wave Background originating from Halo Mergers

The stochastic gravitational wave background (GWB) from halo mergers is investigated by a quasi-analytic method. The method we employ consists of two steps. The first step is to construct a merger tree by using the Extended Press-Schechter formalism or the Sheth & Tormen formalism, with Monte-Carlo realizations. This merger tree provides evolution of halo masses. From $N$-body simulation of two-halo mergers, we can estimate the amount of gravitational wave emission induced by the individual merger process. Therefore the second step is to combine this gravitaional wave emission to the merger tree and obtain the amplitude of GWB. We find $\Omega_{GW}\sim 10^{-19}$ for $f\sim 10^{-17}-10^{-16}$ Hz, where $\Omega_{GW}$ is the energy density of the GWB. It turns out that most of the contribution on the GWB comes from halos with masses below $10^{15} M_\odot$ and mergers at low redshift, i.e., $0<z<0.8$.Comment: 5 pages, 8 figures. Accepted for publication in Physical Review

Nano strain-amplifier: making ultra-sensitive piezoresistance in nanowires possible without the need of quantum and surface charge effects

This paper presents an innovative nano strain-amplifier employed to significantly enhance the sensitivity of piezoresistive strain sensors. Inspired from the dogbone structure, the nano strain-amplifier consists of a nano thin frame released from the substrate, where nanowires were formed at the centre of the frame. Analytical and numerical results indicated that a nano strain-amplifier significantly increases the strain induced into a free standing nanowire, resulting in a large change in their electrical conductance. The proposed structure was demonstrated in p-type cubic silicon carbide nanowires fabricated using a top down process. The experimental data showed that the nano strain-amplifier can enhance the sensitivity of SiC strain sensors at least 5.4 times larger than that of the conventional structures. This result indicates the potential of the proposed strain-amplifier for ultra-sensitive mechanical sensing applications.Comment: 4 pages, 5 figure

Forecasting the Cosmological Constraints with Anisotropic Baryon Acoustic Oscillations from Multipole Expansion

Baryon acoustic oscillations (BAOs) imprinted in the galaxy power spectrum can be used as a standard ruler to determine angular diameter distance and Hubble parameter at high redshift galaxies. Combining redshift distortion effect which apparently distorts the galaxy clustering pattern, we can also constrain the growth rate of large-scale structure formation. Usually, future forecast for constraining these parameters from galaxy redshift surveys has been made with a full 2D power spectrum characterized as function of wavenumber $k$ and directional cosine $\mu$ between line-of-sight direction and wave vector, i.e., $P(k,\mu)$. Here, we apply the multipole expansion to the full 2D power spectrum, and discuss how much cosmological information can be extracted from the lower-multipole spectra, taking a proper account of the non-linear effects on gravitational clustering and redshift distortion. The Fisher matrix analysis reveals that compared to the analysis with full 2D spectrum, a partial information from the monopole and quadrupole spectra generally degrades the constraints by a factor of $\sim1.3$ for each parameter. The additional information from the hexadecapole spectrum helps to improve the constraints, which lead to an almost comparable result expected from the full 2D spectrum.Comment: 12 pages, 6 figure

Heat conduction induced by non-Gaussian athermal fluctuations

We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average and fluctuation are determined not only by the noise intensities but also by the non-Gaussian nature of the noises. Our results explicitly show the absence of the zeroth law of thermodynamics in athermal systems.Comment: 15 pages, 4 figures, PRE in pres

Hamiltonian Derivations of the Generalized Jarzynski Equalities under Feedback Control

In the presence of feedback control by "Maxwell's demon," the second law of thermodynamics and the nonequilibrium equalities such as the Jarzynski equality need to be generalized. In this paper, we derive the generalized Jarzynski equalities for classical Hamiltonian dynamics based on the Liouville's theorem, which is the same approach as the original proof of the Jarzynski equality [Phys. Rev. Lett. 78, 2690 (1997)]. The obtained equalities lead to the generalizations of the second law of thermodynamics for the Hamiltonian systems in the presence of feedback control.Comment: Proceedings of "STATPHYS - Kolkata VII", November 26-30, 2010, Kolkata, Indi

The QCD phase diagram in the space of imaginary chemical potential via 't Hooft anomalies

The QCD phase diagram in the space of temperature and imaginary baryon chemical potential has been an interesting subject in numerical lattice QCD simulations because of the absence of the sign problem and its deep structure related to confinement/deconfinement. We study constraints on the phase diagram by using an 't Hooft anomaly. The relevant anomaly is an anomaly in the space of imaginary chemical potential. We compute it in the UV, and discuss how it is matched by the pion effective field theory at low temperatures. Then we study implications of the anomaly to the phase diagram. There must be a line of phase transition studied in the past by Roberge and Weiss such that the expectation value of the Polyakov loop is not smooth when we cross the line. Moreover, if the greatest common divisor of the color and flavor numbers is greater than one, the phase transition across the Roberge-Weiss line must be either a first order phase transition, or a second order phase transition described by a nontrivial interacting three-dimensional CFT.Comment: 28 pages, 6 figure