Equivalent beam modeling using numerical reduction techniques

Numerical procedures that can accomplish model reductions for space trusses were developed. Three techniques are presented that can be implemented using current capabilities within NASTRAN. The proposed techniques accomplish their model reductions numerically through use of NASTRAN structural analyses and as such are termed numerical in contrast to the previously developed analytical techniques. Numerical procedures are developed that permit reductions of large truss models containing full modeling detail of the truss and its joints. Three techniques are presented that accomplish these model reductions with various levels of structural accuracy. These numerical techniques are designated as equivalent beam, truss element reduction, and post-assembly reduction methods. These techniques are discussed in detail

The Complexity of Approximately Counting Tree Homomorphisms

We study two computational problems, parameterised by a fixed tree H. #HomsTo(H) is the problem of counting homomorphisms from an input graph G to H. #WHomsTo(H) is the problem of counting weighted homomorphisms to H, given an input graph G and a weight function for each vertex v of G. Even though H is a tree, these problems turn out to be sufficiently rich to capture all of the known approximation behaviour in #P. We give a complete trichotomy for #WHomsTo(H). If H is a star then #WHomsTo(H) is in FP. If H is not a star but it does not contain a certain induced subgraph J_3 then #WHomsTo(H) is equivalent under approximation-preserving (AP) reductions to #BIS, the problem of counting independent sets in a bipartite graph. This problem is complete for the class #RHPi_1 under AP-reductions. Finally, if H contains an induced J_3 then #WHomsTo(H) is equivalent under AP-reductions to #SAT, the problem of counting satisfying assignments to a CNF Boolean formula. Thus, #WHomsTo(H) is complete for #P under AP-reductions. The results are similar for #HomsTo(H) except that a rich structure emerges if H contains an induced J_3. We show that there are trees H for which #HomsTo(H) is #SAT-equivalent (disproving a plausible conjecture of Kelk). There is an interesting connection between these homomorphism-counting problems and the problem of approximating the partition function of the ferromagnetic Potts model. In particular, we show that for a family of graphs J_q, parameterised by a positive integer q, the problem #HomsTo(H) is AP-interreducible with the problem of approximating the partition function of the q-state Potts model. It was not previously known that the Potts model had a homomorphism-counting interpretation. We use this connection to obtain some additional upper bounds for the approximation complexity of #HomsTo(J_q)

Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

A compositional minimization approach for large asynchronous design verification

pre-printThis paper presents a compositional minimization approach with efficient state space reductions for verifying non-trivial asynchronous designs. These reductions can result in a reduced model that contains the exact same set of observably equivalent behavior in the original model, therefore no false counter-examples result from the verification of the reduced model. This approach allows designs that cannot be handled monolithically or with partial-order reduction to be verified without difficulty. The experimental results show significant scale-up of the compositional minimization approach using these reductions on a number of large asynchronous designs

Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions

We study a class of nonlinear pricing models which involves the feedback effect from the dynamic hedging strategies on the price of asset introduced by Sircar and Papanicolaou. We are first to study the case of a nonlinear demand function involved in the model. Using a Lie group analysis we investigate the symmetry properties of these nonlinear diffusion equations. We provide the optimal systems of subalgebras and the complete set of non-equivalent reductions of studied PDEs to ODEs. In most cases we obtain families of exact solutions or derive particular solutions to the equations.Comment: 14 page

Civil helicopter noise assessment study Boeing-Vertol model 347

A study was conducted to forecast the noise restrictions which may be imposed on civil transport helicopters in the 1975-1985 time period. Certification and community acceptance criteria were predicted. A 50 passenger tandem rotor helicopter based on the Boeing-Vertol Model 347 was studied to determine the noise reductions required, and the means of achieving them. Some of the important study recommendations are: (1) certification limits should be equivalent to 95 EPNdb at data points located at 500 feet to each side of the touchdown/takeoff point, and 1000 feet from this point directly under the approach and departure flight path. (2) community acceptance should be measured as Equivalent Noise Level (Leq), based on dBA, with separate limits for day and night operations, and (3) in order to comply with the above guidelines, the Model 347 helicopter will require studies and tests leading to several modifications

Linear Temporal Logic and Propositional Schemata, Back and Forth (extended version)

This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one logic to the other. Some consequences about complexity are given. We report about first experiments and the consequences about possible improvements in existing implementations are analyzed.Comment: Extended version of a paper submitted at TIME 2011: contains proofs, additional examples & figures, additional comparison between classical LTL/schemata algorithms up to the provided translations, and an example of how to do model checking with schemata; 36 pages, 8 figure

Acoustic tests of duct-burning turbofan jet noise simulation

The results of a static acoustic and aerodynamic performance, model-scale test program on coannular unsuppressed and multielement fan suppressed nozzle configurations are summarized. The results of the static acoustic tests show a very beneficial interaction effect. When the measured noise levels were compared with the predicted noise levels of two independent but equivalent conical nozzle flow streams, noise reductions for the unsuppressed coannular nozzles were of the order of 10 PNdB; high levels of suppression (8 PNdB) were still maintained even when only a small amount of core stream flow was used. The multielement fan suppressed coannular nozzle tests showed 15 PNdB noise reductions and up to 18 PNdB noise reductions when a treated ejector was added. The static aerodynamic performance tests showed that the unsuppressed coannular plug nozzles obtained gross thrust coefficients of 0.972, with 1.2 to 1.7 percent lower levels for the multielement fan-suppressed coannular flow nozzles. For the first time anywhere, laser velocimeter velocity profile measurements were made on these types of nozzle configurations and with supersonic heated flow conditions. Measurements showed that a very rapid decay in the mean velocity occurs for the nozzle tested

Will Border Carbon Adjustments Work?

Abstract and PDF report are also available on the MIT Joint Program on the Science and Policy of Global Change website (http://globalchange.mit.edu/).The potential for greenhouse gas (GHG) restrictions in some nations to drive emission increases in other nations, or leakage, is a contentious issue in climate change negotiations. We evaluate the potential for border carbon adjustments (BCAs) to address leakage concerns using an economy-wide model. For 2025, we find that BCAs reduce leakage by up to two-thirds, but result in only modest reductions in global emissions and significantly reduce welfare. In contrast, BCA-equivalent leakage reductions can be achieved by very small emission charges or efficiency improvements in nations targeted by BCAs, which have negligible welfare effects. We conclude that BCAs are a costly method to reduce leakage but such policies may be effective coercion strategies. We also investigate the impact of BCAs on sectoral output and evaluate the leakage contributions of trade and changes in the price of crude oil.This study received support from the MIT Joint Program on the Science and Policy of Global Change, which is funded by a consortium of government, industry and foundation sponsors