99,972 research outputs found
Rigorous Multiple-Precision Evaluation of D-Finite Functions in SageMath
We present a new open source implementation in the SageMath computer algebra
system of algorithms for the numerical solution of linear ODEs with polynomial
coefficients. Our code supports regular singular connection problems and
provides rigorous error bounds
Crystal nucleation mechanism in melts of short polymer chains under quiescent conditions and under shear flow
We present a molecular dynamics simulation study of crystal nucleation from
undercooled melts of n-alkanes, and we identify the molecular mechanism of
homogeneous crystal nucleation under quiescent conditions and under shear flow.
We compare results for n-eicosane(C20) and n-pentacontahectane(C150), i.e. one
system below the entanglement length and one above. Under quiescent conditions,
we observe that entanglement does not have an effect on the nucleation
mechanism. For both chain lengths, the chains first align and then straighten
locally. Then the local density increases and finally positional ordering sets
in. At low shear rates the nucleation mechanism is the same as under quiescent
conditions, while at high shear rates the chains align and straighten at the
same time. We report on the effects of shear rate and temperature on the
nucleation rates and estimate the critical shear rates, beyond which the
nucleation rates increase with the shear rate. We show that the viscosity of
the system is not affected by the crystalline nuclei.Comment: 9 page
Non-classical computing: feasible versus infeasible
Physics sets certain limits on what is and is not computable. These limits are very far from having been reached by current technologies. Whilst proposals for hypercomputation are almost certainly infeasible, there are a number of non classical approaches that do hold considerable promise. There are a range of possible architectures that could be implemented on silicon that are distinctly different from the von Neumann model. Beyond this, quantum simulators, which are the quantum equivalent of analogue computers, may be constructable in the near future
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