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

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

Symmetrically coupled higher-order nonlinear Schroedinger equations: singularity analysis and integrability

The integrability of a system of two symmetrically coupled higher-order nonlinear Schr\"{o}dinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlev\'{e} test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the system are uncoupled by a nonlinear transformation.Comment: 12 pages, LaTeX2e, IOP style, final version, to appear in J.Phys.A:Math.Ge

Oral serum-derived bovine immunoglobulin improves duodenal immune reconstitution and absorption function in patients with HIV enteropathy.

ObjectivesTo examine the impact of serum-derived bovine immunoglobulin, an oral medical food known to neutralize bacterial antigen and reduce intestinal inflammation, on restoration of mucosal immunity and gastrointestinal function in individuals with HIV enteropathy.DesignOpen-label trial with intensive 8-week phase of bovine serum immunoglobulin (SBI) 2.5 g twice daily with a 4-week washout period and an optional 9-month extension study.MethodsHIV enteropathy was defined as chronic gastrointestinal symptoms including frequent loose or watery stools despite no identifiable, reversible cause. Upper endoscopy for tissue immunofluorescent antibody assay and disaccharide gut permeability/absorption studies were performed before and after 8 weeks of SBI to test mucosal immunity and gastrointestinal function. Blood was collected for markers of microbial translocation, inflammation, and collagen kinetics. A validated gastrointestinal questionnaire assessed changes in symptoms.ResultsAll eight participants experienced profound improvement in symptoms with reduced bowel movements/day (P = 0.008) and improvements in stool consistency (P = 0.008). Gut permeability was normal before and after the intervention, but D-xylose absorption increased in seven of eight participants. Mucosal CD4 lymphocyte densities increased by a median of 139.5 cells/mm2 from 213 to 322 cells/mm2 (P = 0.016). Intestinal-fatty acid binding protein (I-FABP), a marker of enterocyte damage, initially rose in seven of eight participants after 8 weeks (P = 0.039), and then fell below baseline in four of five who continued receiving SBI (P = 0.12). Baseline serum I-FABP levels were negatively correlated with subsequent rise in mucosal CD4 lymphocyte densities (r = -0.74, P = 0.046).ConclusionSBI significantly increases intestinal mucosal CD4 lymphocyte counts, improves duodenal function, and showed evidence of promoting intestinal repair in the setting of HIV enteropathy

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

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates

We study soliton solutions for the Gross--Pitaevskii equation of the spinor Bose--Einstein condensates with hyperfine spin F=2 in one-dimension. Analyses are made in two ways: by assuming single-mode amplitudes and by generalizing Hirota's direct method for multi-components. We obtain one-solitons of single-peak type in the ferromagnetic, polar and cyclic states, respectively. Moreover, twin-peak type solitons both in the ferromagnetic and the polar state are found.Comment: 15 pages, 8 figure

Reduction of myocardial infarction by postischemic administration of the calpain inhibitor A-705253 in comparison to the Na(+)/H(+) exchange inhibitor Cariporide (R) in isolated perfused rabbit hearts

The calpain inhibitor A-705253 and the Na(+)/H(+) exchange inhibitor Cariporide (R) were studied in isolated perfused rabbit hearts subjected to 60 min occlusion of the ramus interventricularis of the left coronary artery (below the origin of the first diagonal branch), followed by 120 min of reperfusion. The inhibitors were added to the perfusion fluid solely or in combination at the beginning of reperfusion. Hemodynamic monitoring and biochemical analysis of perfusion fluid from the coronary outflow were performed. Myocardial infarct size and area at risk (transiently not perfused myocardium) were determined from left ventricular slices after a special staining procedure with Evans blue and 2,3,5-triphenyltetrazolium chloride. The infarcted area (dead myocardium) was 72.7 +/- 4.0% of the area at risk in untreated controls, but was significantly smaller in the presence of the inhibitors. The largest effect was observed with 10(-6) M A-705253, which reduced the infarcted area to 49.2 +/- 4.1% of the area at risk, corresponding to a reduction of 33.6%. Cariporide (R) at 10(-6) M reduced the infarct size to the same extent. The combination of both inhibitors, however, did not further improve cardioprotection. No significant difference was observed between the experimental groups in coronary perfusion, left ventricular pressure, heart rate, or in the release of lactate dehydrogenase and creatine kinase from heart muscle

Strong Brane Gravity and the Radion at Low Energies

For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for strong gravity, in the low matter density regime, for slowly varying matter sources. This is relevant for astrophysical or cosmological applications. The warped compactification means the radion can not be written as a homogeneous mode in the orbifold coordinate, and we introduce it by extending the coordinate patch approach of the linear theory to the non-linear case. The negative tension brane is taken to be in vacuum. For conformally invariant matter on the positive tension brane, we solve the bulk geometry as a derivative expansion, formally summing the `Kaluza-Klein' contributions to all orders. For general matter we compute the Einstein equations to leading order, finding a scalar-tensor theory with $\omega(\Psi) \propto \Psi / (1 - \Psi)$, and geometrically interpret the radion. We comment that this radion scalar may become large in the context of strong gravity with low density matter. Equations of state allowing $(\rho - 3 P)$ to be negative, can exhibit behavior where the matter decreases the distance between the 2 branes, which we illustrate numerically for static star solutions using an incompressible fluid. For increasing stellar density, the branes become close before the upper mass limit, but after violation of the dominant energy condition. This raises the interesting question of whether astrophysically reasonable matter, and initial data, could cause branes to collide at low energy, such as in dynamical collapse.Comment: 24 pages, 3 figure

Integrable discretizations of derivative nonlinear Schroedinger equations

We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schroedinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa-Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations.Comment: 24 pages, LaTeX2e (IOP style), final versio