Calculations of the moon's heat history at different concentrations of radioactive elements taking account of the material differentiation with melting

A mathematical procedure for analyzing the heat conductivity of the lunar surface is discussed. The solution is based on homogeneous and laminated moon models and considers the effects of radioactive elements conveyed to the lunar surface by melting. The various parameters which introduce uncertainties into the numerical analysis are identified. The application of data obtained from radio astronomy and from analyses of lunar samples returned by the Apollo flights is explained. Tables of data are included to show the types and amounts of radioactive materials which have been identified

Calculations of the moon's thermal history at different concentrations of radioactive elements, taking into account differentiation on melting

Calculations of the thermal history of the moon were done by solving the thermal conductivity equation for the case in which the heat sources are the long lived radioactive elements Th, U, and K-40. The concentrations of these elements were adjusted to give 4 variations of heat flow. Calculations indicated that the moon's interior was heated to melting during the first 0.7 to 2.3 x 10 to the 9th power years. The maximum fusion involved practically the entire moon to a distance from 15 to 45 km beneath the surface, and started 3.5 to 4.0 x 10 to the 9th power years ago, or 2.5 x 3.0 x 10 to the 9th power years ago and continued for 1 to 2 x 10 to the 9th power years. The moon today is cooling. The current thickness of the solid crust is from 150 to 200 km and the heat flow exceeds the stationary value 1.5 fold

Statistical mechanics model of angiogenic tumor growth

We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the supply is correlated with distribution of tumor cells, which as we suggest might mimick the angiogenic growth, the extinction shows different, and most likely novel critical behaviour. Such a correlation affects also the morphology of the growing tumors and drastically raise tumor survival probability.Comment: 4 page

Sequential Quantum Cloning

Not all unitary operations upon a set of qubits can be implemented by sequential interactions between each qubit and an ancillary system. We analyze the specific case of sequential quantum cloning 1->M and prove that the minimal dimension D of the ancilla grows linearly with the number of clones M. In particular, we obtain D = 2M for symmetric universal quantum cloning and D = M+1 for symmetric phase-covariant cloning. Furthermore, we provide a recipe for the required ancilla-qubit interactions in each step of the sequential procedure for both cases.Comment: 4 pages, no figures. New version with changes. Accepted in Physical Review Letter

Cadherin composition and multicellular aggregate invasion in organotypic models of epithelial ovarian cancer intraperitoneal metastasis.

During epithelial ovarian cancer (EOC) progression, intraperitoneally disseminating tumor cells and multicellular aggregates (MCAs) present in ascites fluid adhere to the peritoneum and induce retraction of the peritoneal mesothelial monolayer prior to invasion of the collagen-rich submesothelial matrix and proliferation into macro-metastases. Clinical studies have shown heterogeneity among EOC metastatic units with respect to cadherin expression profiles and invasive behavior; however, the impact of distinct cadherin profiles on peritoneal anchoring of metastatic lesions remains poorly understood. In the current study, we demonstrate that metastasis-associated behaviors of ovarian cancer cells and MCAs are influenced by cellular cadherin composition. Our results show that mesenchymal N-cadherin-expressing (Ncad+) cells and MCAs invade much more efficiently than E-cadherin-expressing (Ecad+) cells. Ncad+ MCAs exhibit rapid lateral dispersal prior to penetration of three-dimensional collagen matrices. When seeded as individual cells, lateral migration and cell-cell junction formation precede matrix invasion. Neutralizing the Ncad extracellular domain with the monoclonal antibody GC-4 suppresses lateral dispersal and cell penetration of collagen gels. In contrast, use of a broad-spectrum matrix metalloproteinase (MMP) inhibitor (GM6001) to block endogenous membrane type 1 matrix metalloproteinase (MT1-MMP) activity does not fully inhibit cell invasion. Using intact tissue explants, Ncad+ MCAs were also shown to efficiently rupture peritoneal mesothelial cells, exposing the submesothelial collagen matrix. Acquisition of Ncad by Ecad+ cells increased mesothelial clearance activity but was not sufficient to induce matrix invasion. Furthermore, co-culture of Ncad+ with Ecad+ cells did not promote a 'leader-follower' mode of collective cell invasion, demonstrating that matrix remodeling and creation of invasive micro-tracks are not sufficient for cell penetration of collagen matrices in the absence of Ncad. Collectively, our data emphasize the role of Ncad in intraperitoneal seeding of EOC and provide the rationale for future studies targeting Ncad in preclinical models of EOC metastasis

Wave Solutions of Evolution Equations and Hamiltonian Flows on Nonlinear Subvarieties of Generalized Jacobians

The algebraic-geometric approach is extended to study solutions of N-component systems associated with the energy dependent Schrodinger operators having potentials with poles in the spectral parameter, in connection with Hamiltonian flows on nonlinear subvariaties of Jacobi varieties. The systems under study include the shallow water equation and Dym type equation. The classes of solutions are described in terms of theta-functions and their singular limits by using new parameterizations. A qualitative description of real valued solutions is provided

Lifetimes and Sizes from Two-Particle Correlation Functions

We discuss the Yano-Koonin-Podgoretskii (YKP) parametrization of the two-particle correlation function for azimuthally symmetric expanding sources. We derive model-independent expressions for the YKP fit parameters and discuss their physical interpretation. We use them to evaluate the YKP fit parameters and their momentum dependence for a simple model for the emission function and propose new strategies for extracting the source lifetime. Longitudinal expansion of the source can be seen directly in the rapidity dependence of the Yano-Koonin velocity.Comment: 15 pages REVTEX, 2 figures included, submitted to Phys. Lett. B, Expanded discussion of disadvantages of standard HBT fit and of Fig.

IgG anti-apolipoprotein A-1 antibodies in patients with systemic lupus erythematosus are associated with disease activity and corticosteroid therapy: an observational study.

IgG anti-apolipoprotein A-1 (IgG anti-apoA-1) antibodies are present in patients with systemic lupus erythematosus (SLE) and may link inflammatory disease activity and the increased risk of developing atherosclerosis and cardiovascular disease (CVD) in these patients. We carried out a rigorous analysis of the associations between IgG anti-apoA-1 levels and disease activity, drug therapy, serology, damage, mortality and CVD events in a large British SLE cohort

An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion

We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves integrability via the inverse scattering transform (IST) method. This IST-integrable class of equations contains both the KdV equation and the CH equation as limiting cases. It arises as the compatibility condition for a second order isospectral eigenvalue problem and a first order equation for the evolution of its eigenfunctions. This integrable equation is shown to be a shallow water wave equation derived by asymptotic expansion at one order higher approximation than KdV. We compare its traveling wave solutions to KdV solitons.Comment: 4 pages, no figure

On a Camassa-Holm type equation with two dependent variables

We consider a generalization of the Camassa Holm (CH) equation with two dependent variables, called CH2, introduced by Liu and Zhang. We briefly provide an alternative derivation of it based on the theory of Hamiltonian structures on (the dual of) a Lie Algebra. The Lie Algebra here involved is the same algebra underlying the NLS hierarchy. We study the structural properties of the CH2 hierarchy within the bihamiltonian theory of integrable PDEs, and provide its Lax representation. Then we explicitly discuss how to construct classes of solutions, both of peakon and of algebro-geometrical type. We finally sketch the construction of a class of singular solutions, defined by setting to zero one of the two dependent variables.Comment: 22 pages, 2 figures. A few typos correcte