366 research outputs found
RG Flow from Theory to the 2D Ising Model
We study 1+1 dimensional theory using the recently proposed method
of conformal truncation. Starting in the UV CFT of free field theory, we
construct a complete basis of states with definite conformal Casimir,
. We use these states to express the Hamiltonian of the full
interacting theory in lightcone quantization. After truncating to states with
, we numerically diagonalize the
Hamiltonian at strong coupling and study the resulting IR dynamics. We compute
non-perturbative spectral densities of several local operators, which are
equivalent to real-time, infinite-volume correlation functions. These spectral
densities, which include the Zamolodchikov -function along the full RG flow,
are calculable at any value of the coupling. Near criticality, our numerical
results reproduce correlation functions in the 2D Ising model.Comment: 31+12 page
Decoupled UMDO formulation for interdisciplinary coupling satisfaction under uncertainty
International audienceAt early design phases, taking into account uncertainty for the optimization of a multidisciplinary system is essential to establish the optimal system characteristics and performances. Uncertainty Multidisciplinary Design Optimization (UMDO) formulations have to eciently organize the dierent disciplinary analyses, the uncertainty propagation, the optimization, but also the handling of interdisciplinary couplings under uncertainty. A decoupled UMDO formulation (Individual Discipline Feasible - Polynomial Chaos Expansion) ensuring the coupling satisfaction for all the instantiations of the uncertain variables is presented in this paper. Ensuring coupling satisfaction in instantiations is essential to ensure the equivalence between the coupled and decoupled UMDO problem formulations. The proposed approach relies on the iterative construction of surrogate models based on Polynomial Chaos Expansion in order to represent at the convergence of the optimization problem, the coupling functional relations as a coupled approach under uncertainty does. The performances of the proposed formulation is assessed on an analytic test case and on the design of a new Vega launch vehicle upper stage
- …