Thermodynamics of Fuzzy Spheres in PP-wave Matrix Model

We discuss thermodynamics of fuzzy spheres in a matrix model on a pp-wave background. The exact free energy in the fuzzy sphere vacuum is computed in the \mu -> \infty limit for an arbitrary matrix size N. The trivial vacuum dominates the fuzzy sphere vacuum at low temperature while the fuzzy sphere vacuum is more stable than the trivial vacuum at sufficiently high temperature. Our result supports that the fluctuations around the trivial vacuum would condense to form an irreducible fuzzy sphere above a certain temperature.Comment: 18 pages, 4 figures, LaTeX2

Membrane Fuzzy Sphere Dynamics in Plane-Wave Matrix Model

In plane-wave matrix model, the membrane fuzzy sphere extended in the SO(3) symmetric space is allowed to have periodic motion on a sub-plane in the SO(6) symmetric space. We consider a background configuration composed of two such fuzzy spheres moving on the same sub-plane and the one-loop quantum corrections to it. The one-loop effective action describing the fuzzy sphere interaction is computed up to the sub-leading order in the limit that the mean distance $r$ between two fuzzy spheres is very large. We show that the leading order interaction is of the 1/r^7 type and thus the membrane fuzzy spheres interpreted as giant gravitons really behave as gravitons.Comment: 28 pages, LaTeX2e, 1 figure, 1 tabl

Thermodynamic Behavior of Fuzzy Membranes in PP-Wave Matrix Model

We discuss a two-body interaction of membrane fuzzy spheres in a pp-wave matrix model at finite temperature by considering a fuzzy sphere rotates with a constant radius r around the other one sitting at the origin in the SO(6) symmetric space. This system of two fuzzy spheres is supersymmetric at zero temperature and there is no interaction between them. Once the system is coupled to the heat bath, supersymmetries are completely broken and non-trivial interaction appears. We numerically show that the potential between fuzzy spheres is attractive and so the rotating fuzzy sphere tends to fall into the origin. The analytic formula of the free energy is also evaluated in the large N limit. It is well approximated by a polylog-function.Comment: 13 pages, 4 figures, LaTe

Glacier dynamics near the calving front of Bowdoin Glacier, northwestern Greenland

To better understand recent rapid recession of marine-terminating glaciers in Greenland, we performed satellite and field observations near the calving front of Bowdoin Glacier, a 3 km wide outlet glacier in northwestern Greenland. Satellite data revealed a clear transition to a rapidly retreating phase in 2008 from a relatively stable glacier condition that lasted for >20 years. Ice radar measurements showed that the glacier front is grounded, but very close to the floating condition. These results, in combination with the results of ocean depth soundings, suggest bed geometry in front of the glacier is the primary control on the rate and pattern of recent rapid retreat. Presumably, glacier thinning due to atmospheric and/or ocean warming triggered the initial retreat. In situ measurements showed complex short-term ice speed variations, which were correlated with air temperature, precipitation and ocean tides. Ice speed quickly responded to temperature rise and a heavy rain event, indicating rapid drainage of surface water to the bed. Semi-diurnal speed peaks coincided with low tides, suggesting the major role of the hydrostatic pressure acting on the calving face in the force balance. These observations demonstrate that the dynamics of Bowdoin Glacier are sensitive to small perturbations occurring near the calving front

Generic Global Rigidity in ℓp\ell_p-Space and the Identifiability of the pp-Cayley-Menger Varieties

The celebrated result of Gortler-Healy-Thurston (independently, Jackson-Jord\'an for $d=2$) shows that the global rigidity of graphs realised in the $d$-dimensional Euclidean space is a generic property. Extending this result to the global rigidity problem in $\ell_p$-spaces remains an open problem. In this paper we affirmatively solve this problem when $d=2$ and $p$ is an even positive integer. A key tool in our proof is a sufficient condition for the $d$-tangentially weakly non-defectiveness of projective varieties due to Bocci, Chiantini, Ottaviani, and Vannieuwenhoven. By specialising the condition to the $p$-Cayley-Menger variety, which is the $\ell_p$-analogue of the Cayley-Menger variety for Euclidean distance, we provide an $\ell_p$-extension of the generic global rigidity theory of Connelly. As a by-product of our proof, we also offer a purely graph-theoretical characterisation of the $2$-identifiability of an orthogonal projection of the $p$-Cayley-Menger variety along a coordinate axis of the ambient affine space

Borehole video observation of Langhovde Glacier, Antarctica

第3回極域科学シンポジウム　横断セッション「海・陸・氷床から探る後期新生代の南極寒冷圏環境変動」11月27日（火） 国立国語研究所 ２階講

The change of terminus and ice velocity field and grounding line estimation in Langhovde Glacier, Antarctica.

第3回極域科学シンポジウム　横断セッション「海・陸・氷床から探る後期新生代の南極寒冷圏環境変動」11月27日（火） 国立国語研究所 ２階講

Hot water drilling and measurements beneath the grounding zone of Langhovde Glacier, East Antarctica

第3回極域科学シンポジウム　横断セッション「海・陸・氷床から探る後期新生代の南極寒冷圏環境変動」11月27日（火） 国立国語研究所 ２階講