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The 3D version of the finite element program FESTER
In this report, a detailed description of the 3-D version finite element pro-gram FESTER is given. This includes: 1. A brief introduction to the package FESTER; 2. Preparing an input data file for the 3D version of FESTER; 3. Principal stress and stress invariant analyses; 4. 2D joint element (surface contact) characterisation and its mathematical formulation; 5. Formulations of the 3D stress-strain analyses for both isotropic and anisotropic materials, plane of weakness and cracking criteria; 6. 3D brick elements, infinity elements and their corresponding shape and mapping functions; 7. Large-displacement formulations; 8. Modifications to the subroutines INVAR, JNTB, TMAT, MOD2 etc; 9. Numerical examples; and 10. Conclusions
Magnetohydrodynamic normal mode analysis of plasma with equilibrium pressure anisotropy
In this work, we generalise linear magnetohydrodynamic (MHD) stability theory
to include equilibrium pressure anisotropy in the fluid part of the analysis. A
novel 'single-adiabatic' (SA) fluid closure is presented which is complementary
to the usual 'double-adiabatic' (CGL) model and has the advantage of naturally
reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and
CGL, the SA model neglects the anisotropic perturbed pressure and thus loses
non-local fast-particle stabilisation present in the kinetic approach. Another
interesting aspect of this new approach is that the stabilising terms appear
naturally as separate viscous corrections leaving the isotropic SA closure
unchanged. After verifying the self-consistency of the SA model, we re-derive
the projected linear MHD set of equations required for stability analysis of
tokamaks in the MISHKA code. The cylindrical wave equation is derived
analytically as done previously in the spectral theory of MHD and clear
predictions are made for the modification to fast-magnetosonic and slow ion
sound speeds due to equilibrium anisotropy.Comment: 19 pages. This is an author-created, un-copyedited version of an
article submitted for publication in Plasma Physics and Controlled Fusion.
IOP Publishing Ltd is not responsible for any errors or omissions in this
version of the manuscript or any version derived from i
Numerical and Theoretical Studies of Noise Effects in the Kauffman Model
In this work we analyze the stochastic dynamics of the Kauffman model
evolving under the influence of noise. By considering the average crossing time
between two distinct trajectories, we show that different Kauffman models
exhibit a similar kind of behavior, even when the structure of their basins of
attraction is quite different. This can be considered as a robust property of
these models. We present numerical results for the full range of noise level
and obtain approximate analytic expressions for the above crossing time as a
function of the noise in the limit cases of small and large noise levels.Comment: 24 pages, 9 figures, Submitted to the Journal of Statistical Physic
Spontaneous Generation of Photons in Transmission of Quantum Fields in PT Symmetric Optical Systems
We develop a rigorous mathematically consistent description of PT symmetric
optical systems by using second quantization. We demonstrate the possibility of
significant spontaneous generation of photons in PT symmetric systems. Further
we show the emergence of Hanbury-Brown Twiss (HBT) correlations in spontaneous
generation. We show that the spontaneous generation determines decisively the
nonclassical nature of fields in PT symmetric systems. Our work can be applied
to other systems like plasmonic structure where losses are compensated by gain
mechanisms.Comment: 4 pages, 5 figure
Assume-guarantee verification for probabilistic systems
We present a compositional verification technique for systems that exhibit both probabilistic and nondeterministic behaviour. We adopt an assume- guarantee approach to verification, where both the assumptions made about system components and the guarantees that they provide are regular safety properties, represented by finite automata. Unlike previous proposals for assume-guarantee reasoning about probabilistic systems, our approach does not require that components interact in a fully synchronous fashion. In addition, the compositional verification method is efficient and fully automated, based on a reduction to the problem of multi-objective probabilistic model checking. We present asymmetric and circular assume-guarantee rules, and show how they can be adapted to form quantitative queries, yielding lower and upper bounds on the actual probabilities that a property is satisfied. Our techniques have been implemented and applied to several large case studies, including instances where conventional probabilistic verification is infeasible
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