3,896 research outputs found
Solving the Optimal Mistuning Problem by Symmetry: A General Framework for Extending Flutter Boundaries in Turbomachines via Mistuning
A general framework is presented for analyzing and optimizing stability increases due to mistuning. The framework given is model independent and is based primarily on symmetry arguments. Difficult practical issues are transformed to tractable mathematical questions. It is shown that mistuning analysis reduces to a block circular matrix eigenvalue/vector problem which can be solved efficiently even for large problems. Similarly, the optimization becomes a standard linear constraint quadratic programming problem and can be solved numerically. Since the methods given are model independent, they can be applied to various models and allow the researcher to easily conclude which models accurately capture mistuning, and which do not. A simple quasi-steady model for flutter in a cascade is used to illustrate and validate results in this paper
Compressed Sensing Performance Analysis via Replica Method using Bayesian framework
Compressive sensing (CS) is a new methodology to capture signals at lower
rate than the Nyquist sampling rate when the signals are sparse or sparse in
some domain. The performance of CS estimators is analyzed in this paper using
tools from statistical mechanics, especially called replica method. This method
has been used to analyze communication systems like Code Division Multiple
Access (CDMA) and multiple input multi- ple output (MIMO) systems with large
size. Replica analysis, now days rigorously proved, is an efficient tool to
analyze large systems in general. Specifically, we analyze the performance of
some of the estimators used in CS like LASSO (the Least Absolute Shrinkage and
Selection Operator) estimator and Zero-Norm regularizing estimator as a special
case of maximum a posteriori (MAP) estimator by using Bayesian framework to
connect the CS estimators and replica method. We use both replica symmetric
(RS) ansatz and one-step replica symmetry breaking (1RSB) ansatz, clamming the
latter is efficient when the problem is not convex. This work is more
analytical in its form. It is deferred for next step to focus on the numerical
results.Comment: The analytical work and results were presented at the 2012 IEEE
European School of Information Theory in Antalya, Turkey between the 16th and
the 20th of Apri
Abelian and non-abelian symmetries in infinite projected entangled pair states
We explore in detail the implementation of arbitrary abelian and non-abelian
symmetries in the setting of infinite projected entangled pair states on the
two-dimensional square lattice. We observe a large computational speed-up;
easily allowing bond dimensions in the square lattice Heisenberg model
at computational effort comparable to calculations at without
symmetries. We also find that implementing an unbroken symmetry does not
negatively affect the representative power of the state and leads to identical
or improved ground-state energies. Finally, we point out how to use symmetry
implementations to detect spontaneous symmetry breaking.Comment: 18 pages, submitted to SciPost Physic
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