49,238 research outputs found
Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets
The energy balance of a partially molten rocky planet can be expressed as a
non-linear diffusion equation using mixing length theory to quantify heat
transport by both convection and mixing of the melt and solid phases. In this
formulation the effective or eddy diffusivity depends on the entropy gradient,
, as well as entropy. First we present a simplified
model with semi-analytical solutions, highlighting the large dynamic range of
, around 12 orders of magnitude, for physically-relevant
parameters. It also elucidates the thermal structure of a magma ocean during
the earliest stage of crystal formation. This motivates the development of a
simple, stable numerical scheme able to capture the large dynamic range of
and provide a flexible and robust method for
time-integrating the energy equation.
We then consider a full model including energy fluxes associated with
convection, mixing, gravitational separation, and conduction that all depend on
the thermophysical properties of the melt and solid phases. This model is
discretised and evolved by applying the finite volume method (FVM), allowing
for extended precision calculations and using as the
solution variable. The FVM is well-suited to this problem since it is naturally
energy conserving, flexible, and intuitive to incorporate arbitrary non-linear
fluxes that rely on lookup data. Special attention is given to the numerically
challenging scenario in which crystals first form in the centre of a magma
ocean.
Our computational framework is immediately applicable to modelling high melt
fraction phenomena in Earth and planetary science research. Furthermore, it
provides a template for solving similar non-linear diffusion equations arising
in other disciplines, particularly for non-linear functional forms of the
diffusion coefficient
Nonlocality is transitive
We show a transitivity property of nonlocal correlations: There exist
tripartite nonsignaling correlations of which the bipartite marginals between A
and B as well as B and C are nonlocal and any tripartite nonsignaling system
between A, B, and C consistent with them must be such that the bipartite
marginal between A and C is also nonlocal. This property represents a step
towards ruling out certain alternative models for the explanation of quantum
correlations such as hidden communication at finite speed. Whereas it is not
possible to rule out this model experimentally, it is the goal of our approach
to demonstrate this explanation to be logically inconsistent: either the
communication cannot remain hidden, or its speed has to be infinite. The
existence of a three-party system that is pairwise nonlocal is of independent
interest in the light of the monogamy property of nonlocality.Comment: 4 pages, 2 figures, v2: published versio
Self streamlining wind tunnel: Low speed testing and transonic test section design
Comprehensive aerodynamic data on an airfoil section were obtained through a wide range of angles of attack, both stalled and unstalled. Data were gathered using a self streamlining wind tunnel and were compared to results obtained on the same section in a conventional wind tunnel. The reduction of wall interference through streamline was demonstrated
Studies of self streamlining wind tunnel real and imaginary flows
Testing in the low speed flexible walled tunnel in an effort to explain the reasons for data discrepancies at high angles of attack are presented. Automated transonic test sections were developed. The flexible walled tunnel was used in a new operating mode to a generated curved flow around the airfoil, allowing the extraction of purely rotary derivatives. Some straight wall, low speed pressure data, for wall and model, which is used for checking interference correction methods were reported. Computer software which includes an old streamlining algorithm and a prediction algorithm was examined
Supercurrent through grain boundaries in the presence of strong correlations
Strong correlations are known to severely reduce the mobility of charge
carriers near half-filling and thus have an important influence on the current
carrying properties of grain boundaries in the high- cuprates. In this
work we present an extension of the Gutzwiller projection approach to treat
electronic correlations below as well as above half-filling consistently. We
apply this method to investigate the critical current through grain boundaries
with a wide range of misalignment angles for electron- and hole-doped systems.
For the latter excellent agreement with experimental data is found. We further
provide a detailed comparison to an analogous weak-coupling evaluation.Comment: 4 pages, 3 figure
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