Hawking radiation as tunneling from squashed Kaluza-Klein black hole

We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein black hole background.Comment: 16 page

Disruption of Drosophila melanogaster Lipid Metabolism Genes Causes Tissue Overgrowth Associated with Altered Developmental Signaling.

Developmental patterning requires the precise interplay of numerous intercellular signaling pathways to ensure that cells are properly specified during tissue formation and organogenesis. The spatiotemporal function of many developmental pathways is strongly influenced by the biosynthesis and intracellular trafficking of signaling components. Receptors and ligands must be trafficked to the cell surface where they interact, and their subsequent endocytic internalization and endosomal trafficking is critical for both signal propagation and its down-modulation. In a forward genetic screen for mutations that alter intracellular Notch receptor trafficking in Drosophila melanogaster, we recovered mutants that disrupt genes encoding serine palmitoyltransferase and acetyl-CoA carboxylase. Both mutants cause Notch, Wingless, the Epidermal Growth Factor Receptor (EFGR), and Patched to accumulate abnormally in endosomal compartments. In mosaic animals, mutant tissues exhibit an unusual non-cell-autonomous effect whereby mutant cells are functionally rescued by secreted activities emanating from adjacent wildtype tissue. Strikingly, both mutants display prominent tissue overgrowth phenotypes that are partially attributable to altered Notch and Wnt signaling. Our analysis of the mutants demonstrates genetic links between abnormal lipid metabolism, perturbations in developmental signaling, and aberrant cell proliferation

Free field approach to diagonalization of boundary transfer matrix : recent advances

We diagonalize infinitely many commuting operators $T_B(z)$. We call these operators $T_B(z)$ the boundary transfer matrix associated with the quantum group and the elliptic quantum group. The boundary transfer matrix is related to the solvable model with a boundary. When we diagonalize the boundary transfer matrix, we can calculate the correlation functions for the solvable model with a boundary. We review the free field approach to diagonalization of the boundary transfer matrix $T_B(z)$ associated with $U_q(A_2^{(2)})$ and $U_{q,p}(\hat{sl_N})$. We construct the free field realizations of the eigenvectors of the boundary transfer matrix $T_B(z)$. This paper includes new unpublished formula of the eigenvector for $U_q(A_2^{(2)})$. It is thought that this diagonalization method can be extended to more general quantum group $U_q(g)$ and elliptic quantum group $U_{q,p}(g)$.Comment: To appear in Group 28 : Group Theoretical Method in Physic

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

A direct method of solution for the Fokas-Lenells derivative nonlinear Schr\"odinger equation: I. Bright soliton solutions

We develop a direct method of solution for finding the bright $N$-soliton solution of the Fokas-Lenells derivative nonlinear Schr\"odinger equation. The construction of the solution is performed by means of a purely algebraic procedure using an elementary theory of determinants and does not rely on the inverse scattering transform method. We present two different expressions of the solution both of which are expressed as a ratio of determinants. We then investigate the properties of the solutions and find several new features. Specifically, we derive the formula for the phase shift caused by the collisions of bright solitons.Comment: To appear in J. Phys. A: Math. Theor. 45(2012) Ma

Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Charge ordering in the spinels AlV2_2O4_4 and LiV2_2O4_4

We develop a microscopic theory for the charge ordering (CO) transitions in the spinels AlV$_2$O$_4$ and LiV$_2$O$_4$ (under pressure). The high degeneracy of CO states is lifted by a coupling to the rhombohedral lattice deformations which favors transition to a CO state with inequivalent V(1) and V(2) sites forming Kagom\'e and trigonal planes respectively. We construct an extended Hubbard type model including a deformation potential which is treated in unrestricted Hartree Fock approximation and describes correctly the observed first-order CO transition. We also discuss the influence of associated orbital order. Furthermore we suggest that due to different band fillings AlV$_2$O$_4$ should remain metallic while LiV$_2$O$_4$ under pressure should become a semiconductor when charge disproportionation sets in

Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids

Using the Calogero model as an example, we show that the transport in interacting non-dissipative electronic systems is essentially non-linear. Non-linear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for non-linear systems, propagating wave packets are unstable. At finite time shock wave singularities develop, the wave packet collapses, and oscillatory features arise. They evolve into regularly structured localized pulses carrying a fractionally quantized charge - {\it soliton trains}. We briefly discuss perspectives of observation of Quantum Shock Waves in edge states of Fractional Quantum Hall Effect and a direct measurement of the fractional charge

Modified spline-based navigation: Guaranteed safety for obstacle avoidance

© 2017, Springer International Publishing AG. Successful interactive collaboration with a human demands mobile robots to have an advanced level of autonomy, which basic requirements include social interaction, real time path planning and navigation in dynamic environment. For mobile robot path planning, potential function based methods provide classical yet powerful solutions. They are characterized with reactive local obstacle avoidance and implementation simplicity, but suffer from navigation function local minima. In this paper we propose a modification of our original spline-based path planning algorithm, which consists of two levels of planning. At the first level, Voronoi-based approach provides a number sub-optimal paths in different homotopic groups. At the second, these paths are optimized in an iterative manner with regard to selected criteria weights. A new safety criterion is integrated into both levels of path planning to guarantee path safety, while further optimization of a safe path relatively to other criteria is secondary. The modified algorithm was implemented in Matlab environment and demonstrated significant advantages over the original algorithm

Substructure in the stellar halo near the Sun:I. Data-driven clustering in integrals-of-motion space

Aims: Develop a data-driven and statistically based method for finding such clumps in Integrals of Motion space for nearby halo stars and evaluating their significance robustly. Methods: We use data from Gaia EDR3 extended with radial velocities from ground-based spectroscopic surveys to construct a sample of halo stars within 2.5 kpc from the Sun. We apply a hierarchical clustering method that uses the single linkage algorithm in a 3D space defined by the commonly used integrals of motion energy $E$, together with two components of the angular momentum, $L_z$ and $L_\perp$. To evaluate the statistical significance of the clusters found, we compare the density within an ellipsoidal region centered on the cluster to that of random sets with similar global dynamical properties. We pick out the signal at the location of their maximum statistical significance in the hierarchical tree. We estimate the proximity of a star to the cluster center using the Mahalanobis distance. We also apply the HDBSCAN clustering algorithm in velocity space. Results: Our procedure identifies 67 highly significant clusters ($> 3\sigma$), containing 12\% of the sources in our halo set, and in total 232 subgroups or individual streams in velocity space. In total, 13.8\% of the stars in our data set can be confidently associated to a significant cluster based on their Mahalanobis distance. Inspection of our data set reveals a complex web of relationships between the significant clusters, suggesting that they can be tentatively grouped into at least 6 main structures, many of which can be associated to previously identified halo substructures, and a number of independent substructures. This preliminary conclusion is further explored in an accompanying paper by Ruiz-Lara et al., where we also characterize the substructures in terms of their stellar populations. Conclusions: We find... (abridged version)Comment: 16 pages, 14 figures, 2 tables. Accepted for publication in A&A. This is the first in a series of papers, the second (Ruiz-Lara et al.) can be found in https://ui.adsabs.harvard.edu/abs/2022arXiv220102405R/abstract Code of the clustering algorithm can be found in https://github.com/SofieLovdal/IOM_clusterin