Terrestrial Planet Formation in a protoplanetary disk with a local mass depletion: A successful scenario for the formation of Mars

Models of terrestrial planet formation for our solar system have been successful in producing planets with masses and orbits similar to those of Venus and Earth. However, these models have generally failed to produce Mars-sized objects around 1.5 AU. The body that is usually formed around Mars' semimajor axis is, in general, much more massive than Mars. Only when Jupiter and Saturn are assumed to have initially very eccentric orbits (e $\sim$ 0.1), which seems fairly unlikely for the solar system, or alternately, if the protoplanetary disk is truncated at 1.0 AU, simulations have been able to produce Mars-like bodies in the correct location. In this paper, we examine an alternative scenario for the formation of Mars in which a local depletion in the density of the protosolar nebula results in a non-uniform formation of planetary embryos and ultimately the formation of Mars-sized planets around 1.5 AU. We have carried out extensive numerical simulations of the formation of terrestrial planets in such a disk for different scales of the local density depletion, and for different orbital configurations of the giant planets. Our simulations point to the possibility of the formation of Mars-sized bodies around 1.5 AU, specifically when the scale of the disk local mass-depletion is moderately high (50-75%) and Jupiter and Saturn are initially in their current orbits. In these systems, Mars-analogs are formed from the protoplanetary materials that originate in the regions of disk interior or exterior to the local mass-depletion. Results also indicate that Earth-sized planets can form around 1 AU with a substantial amount of water accreted via primitive water-rich planetesimals and planetary embryos. We present the results of our study and discuss their implications for the formation of terrestrial planets in our solar system.Comment: Accepted for publication in The Astrophysical Journa

Ab initio mass tensor molecular dynamics

Mass tensor molecular dynamics was first introduced by Bennett [J. Comput. Phys. 19, 267 (1975)] for efficient sampling of phase space through the use of generalized atomic masses. Here, we show how to apply this method to ab initio molecular dynamics simulations with minimal computational overhead. Test calculations on liquid water show a threefold reduction in computational effort without making the fixed geometry approximation. We also present a simple recipe for estimating the optimal atomic masses using only the first derivatives of the potential energy.Comment: 19 pages, 5 figure

Coorbital Satellites of Saturn: Congenital Formation

Saturn is the only known planet to have coorbital satellite systems. In the present work we studied the process of mass accretion as a possible mechanism for coorbital satellites formation. The system considered is composed of Saturn, a proto-satellite and a cloud of planetesimals distributed in the coorbital region around a triangular Lagrangian point. The adopted relative mass for the proto-satellite was 10^-6 of Saturn's mass and for each planetesimal of the cloud three cases of relative mass were considered, 10^-14, 10^-13 and 10^-12 masses of Saturn. In the simulations each cloud of planetesimal was composed of 10^3, 5 x 10^3 or 10^4 planetesimals. The results of the simulations show the formation of coorbital satellites with relative masses of the same order of those found in the saturnian system (10^-13 - 10^-9). Most of them present horseshoe type orbits, but a significant part is in tadpole orbit around L_4 or L_5. Therefore, the results indicate that this is a plausible mechanism for the formation of coorbital satellites.Comment: 10 pages, 9 figures, 4 table

Space biology initiative program definition review. Trade study 1: Automation costs versus crew utilization

A significant emphasis upon automation within the Space Biology Initiative hardware appears justified in order to conserve crew labor and crew training effort. Two generic forms of automation were identified: automation of data and information handling and decision making, and the automation of material handling, transfer, and processing. The use of automatic data acquisition, expert systems, robots, and machine vision will increase the volume of experiments and quality of results. The automation described may also influence efforts to miniaturize and modularize the large array of SBI hardware identified to date. The cost and benefit model developed appears to be a useful guideline for SBI equipment specifiers and designers. Additional refinements would enhance the validity of the model. Two NASA automation pilot programs, 'The Principal Investigator in a Box' and 'Rack Mounted Robots' were investigated and found to be quite appropriate for adaptation to the SBI program. There are other in-house NASA efforts that provide technology that may be appropriate for the SBI program. Important data is believed to exist in advanced medical labs throughout the U.S., Japan, and Europe. The information and data processing in medical analysis equipment is highly automated and future trends reveal continued progress in this area. However, automation of material handling and processing has progressed in a limited manner because the medical labs are not affected by the power and space constraints that Space Station medical equipment is faced with. Therefore, NASA's major emphasis in automation will require a lead effort in the automation of material handling to achieve optimal crew utilization

Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates

We propose an integrable model of a multicomponent spinor Bose-Einstein condensate in one dimension, which allows an exact description of the dynamics of bright solitons with spin degrees of freedom. We consider specifically an atomic condensate in the F=1 hyperfine state confined by an optical dipole trap. When the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction of a spinor condensate is ferromagnetic (c_2 < 0), we prove that the system possesses a completely integrable point leading to the existence of multiple bright solitons. By applying results from the inverse scattering method, we analyze a collision law for two-soliton solutions and find that the dynamics can be explained in terms of the spin precession.Comment: 4 pages, 2 figure

A systematic method for constructing time discretizations of integrable lattice systems: local equations of motion

We propose a new method for discretizing the time variable in integrable lattice systems while maintaining the locality of the equations of motion. The method is based on the zero-curvature (Lax pair) representation and the lowest-order "conservation laws". In contrast to the pioneering work of Ablowitz and Ladik, our method allows the auxiliary dependent variables appearing in the stage of time discretization to be expressed locally in terms of the original dependent variables. The time-discretized lattice systems have the same set of conserved quantities and the same structures of the solutions as the continuous-time lattice systems; only the time evolution of the parameters in the solutions that correspond to the angle variables is discretized. The effectiveness of our method is illustrated using examples such as the Toda lattice, the Volterra lattice, the modified Volterra lattice, the Ablowitz-Ladik lattice (an integrable semi-discrete nonlinear Schroedinger system), and the lattice Heisenberg ferromagnet model. For the Volterra lattice and modified Volterra lattice, we also present their ultradiscrete analogues.Comment: 61 pages; (v2)(v3) many minor correction

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem

At what age should screening mammography be recommended for Asian women?

Although regular screening mammography has been suggested to be associated with improvements in the relative survival of breast cancer in recent years, the appropriate age to start screening mammography remains controversial. In November 2009, the United States Preventive Service Task Force published updated guidelines for breast cancer, which no longer support routine screening mammography for women aged 40–49 years, but instead, defer the choice of screening in that age group to the patient and physician. The age to begin screening differs between guidelines, including those from the Task Force, the American Cancer Society and the World Health Organization. It remains unclear how this discrepancy impacts patient survival, especially among certain subpopulations. Although the biological characteristics of breast cancer and peak age of incidence differ among different ethnic populations, there have been few reports that evaluate the starting age for screening mammography based on ethnicity. Here, we discuss the benefits and harm of screening mammography in the fifth decade, and re-evaluate the starting age for screening mammography taking ethnicity into account, focusing on the Asian population. Breast cancer incidence peaked in the fifth decade in Asian women, which has been thought to be due to a combination of biological and environmental factors. Previous reports suggest that Asian women in their 40s may receive more benefit and less harm from screening mammography than the age-matched non-Asian US population. Therefore, starting screening mammography at age 40 may be beneficial for women of Asian ethnicity in well-resourced countries, such as Japanese women who reside in Japan

One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schr\"odinger Equation and Solution of Bogoliubov Equation in These Systems

In this short note, we construct mappings from one-dimensional integrable spinor BECs to matrix nonlinear Schr\"odinger equation, and solve the Bogoliubov equation of these systems. A map of spin-$n$ BEC is constructed from the $2^n$-dimensional spinor representation of irreducible tensor operators of $so(2n+1)$. Solutions of Bogoliubov equation are obtained with the aid of the theory of squared Jost functions.Comment: 2.1 pages, JPSJ shortnote style. Published version. Note and reference adde

Matter-Wave Solitons in an F=1 Spinor Bose-Einstein Condensate

Following our previous work [J. Ieda, T. Miyakawa, M. Wadati, cond-mat/0404569] on a novel integrable model describing soliton dynamics of an F=1 spinor Bose--Einstein condensate, we discuss in detail the properties of the multi-component system with spin-exchange interactions. The exact multiple bright soliton solutions are obtained for the system where the mean-field interaction is attractive (c_0 < 0) and the spin-exchange interaction is ferromagnetic (c_2 < 0). A complete classification of the one-soliton solution with respect to the spin states and an explicit formula of the two-soliton solution are presented. For solitons in polar state, there exists a variety of different shaped solutions including twin peaks. We show that a "singlet pair" density can be used to distinguish those energetically degenerate solitons. We also analyze collisional effects between solitons in the same or different spin state(s) by computing the asymptotic forms of their initial and final states. The result reveals that it is possible to manipulate the spin dynamics by controlling the parameters of colliding solitons.Comment: 12 pages, 9 figures, to appear in J. Phys. Soc. Jpn. Vol.73 No.11 (2004