On The Capacity of Surfaces in Manifolds with Nonnegative Scalar Curvature

Given a surface in an asymptotically flat 3-manifold with nonnegative scalar curvature, we derive an upper bound for the capacity of the surface in terms of the area of the surface and the Willmore functional of the surface. The capacity of a surface is defined to be the energy of the harmonic function which equals 0 on the surface and goes to 1 at infinity. Even in the special case of Euclidean space, this is a new estimate. More generally, equality holds precisely for a spherically symmetric sphere in a spatial Schwarzschild 3-manifold. As applications, we obtain inequalities relating the capacity of the surface to the Hawking mass of the surface and the total mass of the asymptotically flat manifold.Comment: 18 page

Absolute Value Boundedness, Operator Decomposition, and Stochastic Media and Equations

The research accomplished during this period is reported. Published abstracts and technical reports are listed. Articles presented include: boundedness of absolute values of generalized Fourier coefficients, propagation in stochastic media, and stationary conditions for stochastic differential equations

A Two-Person Dynamic Equilibrium under Ambiguity

This paper describes a pure-exchange, continuous-time economy with two heterogeneous agents and complete markets. A novel feature of the economy is that agents perceive some security returns as ambiguous in the sense often attributed to frank Knight. The equilibrium is described completely in closed-form. In particular, closed-form solutions are obtained for the equilibrium processes describing individual consumption, the interest rate, the market price of uncertainty, security prices and trading strategies. After identifying agents as countries, the model is applied to address the consumption home-bias puzzles.ambiguity, risk, continuous-time, asset returns, Knightian uncertainty, dynamic equilibrium, home bias

B-Physics Observables and Electroweak Precision Data in the CMSSM, mGMSB and mAMSB

We explore electroweak precision observables (EWPO) and $B$-physics observables (BPO) in the CMSSM, the mGMSB and the mAMSB. We perform a chi^2 analysis based on the combination of current EWPO and BPO data. For the first time this allows the comparison of the mGMSB and mAMSB in terms of EWPO and BPO with the CMSSM. We find that relatively low mass scales in all three scenarios are favored. However, the current data from EWPO and BPO can hardly exclude any parameters at the level of Delta chi^2 = 9. Remarkably the mAMSB scenario, despite having one free GUT scale parameter less than the other two scenarios, has a somewhat lower total minimum chi^2. We present predictions for the lightest Higgs boson mass, based on the chi^2 analysis of current data, where relatively good compatibility with the bounds from Higgs searches at LEP is found. We also present the predictions for other Higgs sector parameters and SUSY mass scales, allowing to compare the reach of the LHC and the ILC in the three scenarios. We furthermore explore the future sensitivities of the EWPO and BPO for the current best-fit results and for a hypothetical point with somewhat higher mass scales that results in a similar Higgs and SUSY spectrum in the three scenarios. We find that the future improvement of the accuracy of the EWPO and BPO will lead to a significant gain in the indirect parameter determination. The improvement is similar in the CMSSM, mGMSB and mAMSB and will yield constraints to the parameter space even for heavy Higgs and SUSY mass scales.Comment: 53 pages, 27 figures, discussion extended. Version to appear in JHE

Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite power series in the auxiliary metric given by ref. \cite{s14}, but just picks out the first term from the series formally. New effective interactions of the theories are revealed. That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinite terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite power series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This non-linearity is inevitable to the requirement the two dual actions are equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions added; v3: concision made; v4: minor modification mad

A Remark on Boundary Effects in Static Vacuum Initial Data sets

Let (M, g) be an asymptotically flat static vacuum initial data set with non-empty compact boundary. We prove that (M, g) is isometric to a spacelike slice of a Schwarzschild spacetime under the mere assumption that the boundary of (M, g) has zero mean curvature, hence generalizing a classic result of Bunting and Masood-ul-Alam. In the case that the boundary has constant positive mean curvature and satisfies a stability condition, we derive an upper bound of the ADM mass of (M, g) in terms of the area and mean curvature of the boundary. Our discussion is motivated by Bartnik's quasi-local mass definition.Comment: 10 pages, to be published in Classical and Quantum Gravit

Quantum ground-state cooling and tripartite entanglement with three-mode optoacoustic interactions

We present a quantum analysis of three-mode optoacoustic parametric interactions in an optical cavity, in which two orthogonal transverse optical-cavity modes are coupled to one acoustic mode through radiation pressure. Due to the optimal frequency matching -- the frequency separation of two cavity modes is equal to the acoustic-mode frequency -- the carrier and sideband fields simultaneously resonate and coherently build up. This mechanism significantly enhances the optoacoustic couplings in the quantum regime. It allows exploration of quantum behavior of optoacoustic interactions in small-scale table-top experiments. We show explicitly that given an experimentally achievable parameter, three-mode scheme can realize quantum ground-state cooling of milligram scale mechanical oscillators and create robust stationary tripartite optoacoustic quantum entanglements.Comment: 20 pages, 5 figure