12,053 research outputs found
Optimum matchings in weighted bipartite graphs
Given an integer weighted bipartite graph we consider the problems of finding all the edges that occur in
some minimum weight matching of maximum cardinality and enumerating all the
minimum weight perfect matchings. Moreover, we construct a subgraph of
which depends on an -optimal solution of the dual linear program
associated to the assignment problem on that allows us to reduced
this problems to their unweighed variants on . For instance, when
has a perfect matching and we have an -optimal solution of the dual
linear program associated to the assignment problem on , we solve the
problem of finding all the edges that occur in some minimum weight perfect
matching in linear time on the number of edges. Therefore, starting from
scratch we get an algorithm that solves this problem in time
, where , , and .Comment: 11 page
Thermal evolution and lifetime of intrinsic magnetic fields of Super Earths in habitable zones
We have numerically studied the thermal evolution of various-mass terrestrial
planets in habitable zones, focusing on duration of dynamo activity to generate
their intrinsic magnetic fields, which may be one of key factors in
habitability on the planets. In particular, we are concerned with super-Earths,
observations of which are rapidly developing. We calculated evolution of
temperature distributions in planetary interior, using Vinet equations of
state, Arrhenius-type formula for mantle viscosity, and the astrophysical
mixing length theory for convective heat transfer modified for mantle
convection. After calibrating the model with terrestrial planets in the Solar
system, we apply it for 0.1-- rocky planets with surface
temperature of 300~\mbox{K} (in habitable zones) and the Earth-like
compositions. With the criterion for heat flux at the CMB (core-mantle
boundary), the lifetime of the magnetic fields is evaluated from the calculated
thermal evolution. We found that the lifetime slowly increases with the
planetary mass () independent of initial temperature gap at the
core-mantle boundary () but beyond a critical value
() it abruptly declines by the mantle viscosity
enhancement due to the pressure effect. We derived as a function of
and a rheological parameter (activation volume, ).
Thus, the magnetic field lifetime of super-Earths with
sensitively depends on , which reflects planetary
accretion, and , which has uncertainty at very high pressure. More
advanced high-pressure experiments and first-principle simulation as well as
planetary accretion simulation are needed to discuss habitability of
super-Earths.Comment: 19pages, 15 figures, accepted for publication in Ap
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