Terrestrial planet formation in low eccentricity warm-Jupiter systems

We examine the effect of giant planet migration on the formation of inner terrestrial planet systems. We consider situations in which the giant planet halts migration at semi-major axes in the range 0.13 - 1.7 AU due to gas disk dispersal. An N-body code is employed that is linked to a viscous gas disk algorithm capable of simulating: gas loss via accretion onto the central star and photoevaporation; gap formation by the giant planet; type II migration of the giant; optional type I migration of protoplanets; gas drag on planetesimals. We find that most of the inner system planetary building blocks survive the passage of the giant planet, either by being shepherded inward or scattered into exterior orbits. Systems of one or more hot-Earths are predicted to form and remain interior to the giant planet, especially if type II migration has been limited, or where type I migration has affected protoplanetary dynamics. Habitable planets in low eccentricity warm-Jupiter systems appear possible if the giant planet makes a limited incursion into the outer regions of the habitable zone (HZ), or traverses its entire width and ceases migrating at a radial distance of less than half that of the HZ's inner edge. We conclude that Type II migration does not prevent terrestrial planet formation.Comment: Accepted for publication in A&A; 18 pages, 12 figures, 2 table

Crumpling transition of the triangular lattice without open edges: effect of a modified folding rule

Folding of the triangular lattice in a discrete three-dimensional space is investigated by means of the transfer-matrix method. This model was introduced by Bowick and co-workers as a discretized version of the polymerized membrane in thermal equilibrium. The folding rule (constraint) is incompatible with the periodic-boundary condition, and the simulation has been made under the open-boundary condition. In this paper, we propose a modified constraint, which is compatible with the periodic-boundary condition; technically, the restoration of translational invariance leads to a substantial reduction of the transfer-matrix size. Treating the cluster sizes L \le 7, we analyze the singularities of the crumpling transitions for a wide range of the bending rigidity K. We observe a series of the crumpling transitions at K=0.206(2), -0.32(1), and -0.76(10). At each transition point, we estimate the latent heat as Q=0.356(30), 0.08(3), and 0.05(5), respectively

The stress-corrosion behavior of Al-Li-Cu alloys: A comparison of test methods

Two powder metallurgy processed (Al-Li-Cu) alloys with and without Mg addition were studied in aqueous 3.5% NaCl solution during the alternate immersion testing of tuning fork specimens, slow crack growth tests using fracture mechanics specimens, and the slow strain rate testing of straining electrode specimens. Scanning electron microscopy and optical metallography were used to demonstrate the character of the interaction between the Al-Li-Cu alloys and the selected environment. Both alloys are susceptible to SC in an aqueous 3.5% NaCl solution under the right electrochemical and microstructural conditions. Each test method yields important information on the character of the SC behavior. Under all conditions investigated, second phase particles strung out in rows along the extrusion direction in the alloys were rapidly attacked, and played principal role in the SC process. With time, larger pits developed from these rows of smaller pits and under certain electrochemical conditions surface cracks initiated from the larger pits and contributed directly to the fracture process. Evidence to support slow crack growth was observed in both the slow strain rate tests and the sustained immersion tests of precracked fracture mechanics specimens. The possible role of H2 in the stress corrosion cracking process is suggested

Stress-corrosion behavior of aluminum-lithium alloys in aqueous environments

The stress corrosion susceptibility of two powder metallurgy (P/M) alloys, Al-Li-Cu and Al-Li-Cu-Mg two mechanically attrited (M/A) alloys, Al-Li-Cu and Al-Li-Mg; and two wrought, ingot alloys, X-2020 and AA7475, are compared. Time-dependent fracture in an aqueous sodium chloride environment under alternate immersion condition was found to vary significantly between alloys. The stress corrosion behavior of the two powder metallurgy processed alloys was studied in detail under conditions of crack initiation, static crack growth, and fatigue crack growth. A variety of stress corrosion tests were performed including smooth surface, time-to-failure tests; potentiostatic tests on smooth surfaces exposed to constant applied strain rates; and fracture mechanics-type tests under static and cyclic loads. Both alloys show surface pitting and subsequent intergranular corrosion. Pitting is more severe in the magnesium-bearing alloy and is associated with stringer particles strung along the extrusion direction as a result of P/M processing

Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions

The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student's t distribution. The coupled Gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the Gaussian. Existing estimators of the scale of the coupled Gaussian have relied on estimates of the full distribution, and they suffer from problems related to outliers in heavy-tailed distributions. In this paper, the scale of a coupled Gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling. From our numerical computations of the scales of coupled Gaussians using the generalized mean of random samples, it is indicated that only samples from a Cauchy distribution (with coupling parameter one) form an unbiased estimate with diminishing variance for large samples. Nevertheless, we also prove that the scale is a function of the geometric mean, the coupling term and a harmonic number. Numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values.Comment: 17 pages, 5 figure

Folding of the triangular lattice in a discrete three-dimensional space: Crumpling transitions in the negative-bending-rigidity regime

Folding of the triangular lattice in a discrete three-dimensional space is studied numerically. Such ``discrete folding'' was introduced by Bowick and co-workers as a simplified version of the polymerized membrane in thermal equilibrium. According to their cluster-variation method (CVM) analysis, there appear various types of phases as the bending rigidity K changes in the range -infty < K < infty. In this paper, we investigate the K<0 regime, for which the CVM analysis with the single-hexagon-cluster approximation predicts two types of (crumpling) transitions of both continuous and discontinuous characters. We diagonalized the transfer matrix for the strip widths up to L=26 with the aid of the density-matrix renormalization group. Thereby, we found that discontinuous transitions occur successively at K=-0.76(1) and -0.32(1). Actually, these transitions are accompanied with distinct hysteresis effects. On the contrary, the latent-heat releases are suppressed considerably as Q=0.03(2) and 0.04(2) for respective transitions. These results indicate that the singularity of crumpling transition can turn into a weak-first-order type by appreciating the fluctuations beyond a meanfield level

Self-interaction in Green's-function theory of the hydrogen atom

Atomic hydrogen provides a unique test case for computational electronic structure methods, since its electronic excitation energies are known analytically. With only one electron, hydrogen contains no electronic correlation and is therefore particularly susceptible to spurious self-interaction errors introduced by certain computational methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's GW approximation. While the Hartree-Fock and the exact MBPT self-energy are free of self-interaction, the correlation part of the GW self-energy does not have this property. Here we use atomic hydrogen as a benchmark system for GW and show that the self-interaction part of the GW self-energy, while non-zero, is small. The effect of calculating the GW self-energy from exact wavefunctions and eigenvalues, as distinct from those from the local-density approximation, is also illuminating

Front Propagation in the Pearling Instability of Tubular Vesicles

Recently Bar-Ziv and Moses discovered a dynamical shape transformation induced in cylindrical lipid bilayer vesicles by the action of laser tweezers. We develop a hydrodynamic theory of fluid bilayers in interaction with the surrounding water and argue that the effect of the laser is to induce a sudden tension in the membrane. We refine our previous analysis to account for the fact that the shape transformation is not uniform but propagates outward from the laser trap. Applying the marginal stability criterion to this situation gives us an improved prediction for the selected initial wavelength and a new prediction for the propagation velocity, both in rough agreement with the experimental values. For example, a tubule of initial radius 0.7\micron\ has a predicted initial sinusoidal perturbation in its diameter with wavelength 5.5\micron, as observed. The perturbation propagates as a front with the qualitatively correct front velocity a bit less than 100\micron/sec. In particular we show why this velocity is initially constant, as observed, and so much smaller than the natural scale set by the tension. We also predict that the front velocity should increase linearly with laser power. Finally we introduce an approximate hydrodynamic model applicable to the fully nonlinear regime. This model exhibits propagating fronts as well as fully-developed ``pearled" vesicles similar to those seen in the experiments.Comment: 42 pages, 6 eps figures included with text in uuencoded file, ps file available from ftp://dept.physics.upenn.edu/pub/Nelson/pearl_propagation.ps submitted to Journal de Physiqu