Final Evolution and Delayed Explosions of Spinning White Dwarfs in Single Degenerate Models for Type Ia Supernovae

We study the occurrence of delayed SNe~Ia in the single degenerate (SD) scenario. We assume that a massive carbon-oxygen (CO) white dwarf (WD) accretes matter coming from a companion star, making it to spin at the critical rate. We assume uniform rotation due to magnetic field coupling. The carbon ignition mass for non-rotating WDs is M_{ig}^{NR} \approx 1.38 M_{\odot}; while for the case of uniformly rotating WDs it is a few percent larger (M_{ig}^{R} \approx 1.43 M_{\odot}). When accretion rate decreases, the WD begins to lose angular momentum, shrinks, and spins up; however, it does not overflow its critical rotation rate, avoiding mass shedding. Thus, angular momentum losses can lead the CO WD interior to compression and carbon ignition, which would induce an SN~Ia. The delay, largely due to the angular momentum losses timescale, may be large enough to allow the companion star to evolve to a He WD, becoming undetectable at the moment of explosion. This scenario supports the occurrence of delayed SNe~Ia if the final CO WD mass is 1.38 M_{\odot} < M < 1.43 M_{\odot}. We also find that if the delay is longer than ~3 Gyr, the WD would become too cold to explode, rather undergoing collapse.Comment: 6 pages, 5 figures, published in the Astrophysical Journal Letters, 809, L6 (2015), added some corrections for errat

Gathering an even number of robots in an odd ring without global multiplicity detection

We propose a gathering protocol for an even number of robots in a ring-shaped network that allows symmetric but not periodic configurations as initial configurations, yet uses only local weak multiplicity detection. Robots are assumed to be anonymous and oblivious, and the execution model is the non- atomic CORDA model with asynchronous fair scheduling. In our scheme, the number of robots k must be greater than 8, the number of nodes n on a network must be odd and greater than k+3. The running time of our protocol is O(n2) asynchronous rounds.Comment: arXiv admin note: text overlap with arXiv:1104.566

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure

Ferromagnetism induced in anisotropic stacked kagome-lattice antiferromagnet Cs2_2Cu3_3CeF12_{12}

The magnetic properties of Cs$_2$Cu$_3$CeF$_{12}$ were investigated through magnetization and specific heat measurements. Cs$_2$Cu$_3$CeF$_{12}$ is composed of a buckled kagome lattice of Cu$^{2+}$, which is stacked along the b axis. The exchange network in the buckled kagome lattice is strongly anisotropic. Consequently, Cs$_2$Cu$_3$CeF$_{12}$ can be divided into two subsystems: alternating Heisenberg chains with strong antiferromagnetic exchange interactions and dangling spins. The dangling spins couple with one another via effective exchange interactions, which are mediated by chain spins. The dangling spins are further divided into two subsystems, DS1 and DS2. The dangling spins in DS1 undergo three-dimensional ferromagnetic ordering at 3.14 K, while those in DS2 remain paramagnetic down to 0.35 K. The effective interaction between the DS1 spins is approximately expressed by the ferromagnetic $XXZ$ model with the $z$ direction parallel to the crystallographic c axis. A magnetic phase diagram for $H {\parallel} c$ was obtained and was analyzed within the framework of the molecular field approximation. With increasing magnetic field, the dangling spins are polarized and the magnetization curve exhibits a wide plateau at one-third of the saturation magnetization.Comment: 10 pages, 12 figure

Ghosts in the self-accelerating universe

The self-accelerating universe realizes the accelerated expansion of the universe at late times by large-distance modification of general relativity without a cosmological constant. The Dvali-Gabadadze-Porrati (DGP) braneworld model provides an explicit example of the self-accelerating universe. Recently, the DGP model becomes very popular to study the observational consequences of the modified gravity models as an alternative to dark energy models in GR. However, it has been shown that the self-accelerating universe in the DGP model contains a ghost at the linearized level. The ghost carries negative energy densities and it leads to the instability of the spacetime. In this article, we review the origin of the ghost in the self-accelerating universe and explore the physical implication of the existence of the ghost.Comment: Invited topical review for Classical and Quantum Gravity, 20 pages, 4 figure

Gathering Anonymous, Oblivious Robots on a Grid

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved

Enhancement of magnetoresistance in manganite multilayers

Magnanite multilayers have been fabricated using La0.67Ca0.33MnO3 as the ferromagnetic layer and Pr0.7Ca0.3MnO3 and Nd0.5Ca0.5MnO3 as the spacer layers. All the multilayers were grown on LaAlO3 (100) by pulse laser deposition. An enhanced magnetoresistnace (defined (RH- R0)/R0) of more than 98% is observed in these multilayers. Also a low field magnetoresistance of 41% at 5000 Oe is observed in these multilayer films. The enhanced MR is attributed to the induced double exchange in the spacer layer, which is giving rise to more number of conducting carriers. This is compared by replacing the spacer layer with LaMnO3 where Mn exists only in 3+ state and no enhancement is observed in the La0.67Ca0.33MnO3 / LaMnO3 multilayers as double exchange mechanism can not be induced by external magnetic fields.Comment: 13 pages, 5 Figure

Ghosts in asymmetric brane gravity and the decoupled stealth limit

We study the spectrum of gravitational perturbations around a vacuum de Sitter brane in a 5D asymmetric braneworld model, with induced curvature on the brane. This generalises the stealth acceleration model proposed by Charmousis, Gregory and Padilla (CGP) which realises the Cardassian cosmology in which power law cosmic acceleration can be driven by ordinary matter. Whenever the bulk has infinite volume we find that there is always a perturbative ghost propagating on the de Sitter brane, in contrast to the Minkowski brane case analysed by CGP. We discuss the implication of this ghost for the stealth acceleration model, and identify a limiting case where the ghost decouples as the de Sitter curvature vanishes.Comment: 21 page

Exploration of finite dimensional Kac algebras and lattices of intermediate subfactors of irreducible inclusions

We study the four infinite families KA(n), KB(n), KD(n), KQ(n) of finite dimensional Hopf (in fact Kac) algebras constructed respectively by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal subalgebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along the way, we extend some general results on the Galois correspondence for depth 2 inclusions, and develop some tools and algorithms for the study of twisted group algebras and their lattices of coideal subalgebras. This research was driven by heavy computer exploration, whose tools and methodology we further describe.Comment: v1: 84 pages, 13 figures, submitted. v2: 94 pages, 15 figures, added connections with Masuoka's families KA and KB, description of K3 in KD(n), lattices for KD(8) and KD(15). v3: 93 pages, 15 figures, proven lattice for KD(6), misc improvements, accepted for publication in Journal of Algebra and Its Application