The 0-1 quadratic knapsack problem (QKP) in wind farm layout optimization models possible turbine locations as nodes, and power loss due to wake effects between pairs of turbines as edges in a complete graph. The goal is to select up to a certain number of turbine locations such that the sum of selected node and edge coefficients is maximized. Finding the optimal solution to the QKP is difficult in general, but it is possible to obtain a tight upper bound on the QKP's optimal value which facilitates the use of heuristics to solve QKPs by giving a good estimate of the optimality gap of any feasible solution. This article applies an upper bound method that is especially well-suited to QKPs in wind farm layout optimization due to certain features of the formulation that reduce the computational complexity of calculating the upper bound. The usefulness of the upper bound was demonstrated by assessing the performance of the greedy algorithm for solving QKPs in wind farm layout optimization. The results show that the greedy algorithm produces good solutions within 4% of the optimal value for small to medium sized problems considered in this article.
The present study proposes a mathematical model utilizing the internal state variable concept for predicting the upper bounds of the reduced axial and shear stiffnesses in cross-ply laminates with matrix cracks. The displacement components at the matrix crack surfaces are explicitly expressed in terms of the observable axial and shear strains and the undamaged material properties. The reduced axial and shear stiffnesses are predicted for glass/epoxy and graphite/epoxy laminates. Comparison of the model with other theoretical and experimental studies is also presented to confirm direct applicability of the model to angle-ply laminates with matrix cracks subjected to general in-plane loading.
Stereographic Suite 2 0 Crack 11
Geophysical inverse problems of the type encountered in electromagnetic techniques are highly non-unique. As a result, any single inverted model, though feasible, is at best inconclusive and at worst misleading. In this paper, we use modified inversion methods to establish bounds on electrical conductivity within a model of the earth. Our method consists of two steps, each making use of the 1-norm in model regularization. Both 1-norm minimization problems are framed without approximation as non-negative least-squares (NNLS) problems. First, we must identify a parsimonious set of regions within the model for which upper and lower bounds on average conductivity will be sought. This is accomplished by minimizing the 1-norm of spatial variation, which produces a model with a limited number of homogeneous regions; in fact, the number of homogeneous regions will never be greater than the number of data, regardless of the number of free parameters supplied. The second step establishes bounds for each of these regions with pairs of inversions. The new suite of inversions also uses a 1-norm penalty, but applied to the conductivity values themselves, rather than the spatial variation thereof. In the bounding step we use the 1-norm of our model parameters because it is proportional to average conductivity. For a lower bound on average conductivity, the 1-norm within a bounding region is minimized. For an upper bound on average conductivity, the 1-norm everywhere outside a bounding region is minimized. The latter minimization has the effect of concentrating conductance into the bounding region. Taken together, these bounds are a measure of the uncertainty in the associated region of our model. Starting with a blocky inverse solution is key in the selection of the bounding regions. Of course, there is a tradeoff between resolution and uncertainty: an increase in resolution (smaller bounding regions), results in greater uncertainty (wider bounds). Minimization of the 1-norm of
It is now recognized that prediction of radiative heating of entering space craft requires explicit treatment of the radiation field from the infrared (IR) to the vacuum ultra violet (VUV). While at low temperatures and longer wavelengths, molecular radiation is well described by bound-bound transitions, in the short wavelength, high temperature regime, bound-free transitions can play an important role. In this work we describe first principles calculations we have carried out for bound-bound and bound-free transitions in N2, O2, C2, CO, CN, NO, and N2+. Compared to bound ]bound transitions, bound-free transitions have several particularities that make them different to deal with. These include more complicated line shapes and a dependence of emission intensity on both bound state diatomic and atomic concentrations. These will be discussed in detail below. The general procedure we used was the same for all species. The first step is to generate potential energy curves, transition moments, and coupling matrix elements by carrying out ab initio electronic structure calculations. These calculations are expensive, and thus approximations need to be made in order to make the calculations tractable. The only practical method we have to carry out these calculations is the internally contracted multi-reference configuration interaction (icMRCI) method as implemented in the program suite Molpro. This is a widely used method for these kinds of calculations, and is capable of generating very accurate results. With this method, we must first of choose which electrons to correlate, the one-electron basis to use, and then how to generate the molecular orbitals.
High-temperature slow-crack-growth behaviour of hot-pressed silicon carbide was determined using both constant-stress-rate ("dynamic fatigue") and constant-stress ("static fatigue") testing in flexure at 1300 C in air. Slow crack growth was found to be a governing mechanism associated with failure of the material. Four estimation methods such as the individual data, the Weibull median, the arithmetic mean and the median deviation methods were used to determine the slow crack growth parameters. The four estimation methods were in good agreement for the constant-stress-rate testing with a small variation in the slow-crack-growth parameter, n, ranging from 28 to 36. By contrast, the variation in n between the four estimation methods was significant in the constant-stress testing with a somewhat wide range of n= 16 to 32.
We introduce a new function, the apparent elastic modulus strain-rate spectrum, E_app ( \\dotɛ ), for the derivation of lumped parameter constants for Generalized Maxwell (GM) linear viscoelastic models from stress-strain data obtained at various compressive strain rates ( \\dotɛ). The E_app ( \\dotɛ ) function was derived using the tangent modulus function obtained from the GM model stress-strain response to a constant \\dotɛ input. Material viscoelastic parameters can be rapidly derived by fitting experimental E_app data obtained at different strain rates to the E_app ( \\dotɛ ) function. This single-curve fitting returns similar viscoelastic constants as the original epsilon dot method based on a multi-curve global fitting procedure with shared parameters. Its low computational cost permits quick and robust identification of viscoelastic constants even when a large number of strain rates or replicates per strain rate are considered. This method is particularly suited for the analysis of bulk compression and nano-indentation data of soft (bio)materials.
A two-dimensional, numerical analysis of slow crack growth (SCG) was performed for brittle materials with finite thickness subjected to constant stress-rate ("dynamic fatigue") loading in flexure. The numerical solution showed that the conventional, simple, one-dimensional analytical solution can be used with a maximum error of about 5% in determining the SCG parameters of a brittle material with the conditions of a normalized thickness (a ratio of specimen thickness to initial crack size) T > 3.3 and of a SCG parameter n > 10. The change in crack shape from semicircular to elliptical configurations was significant particularly at both low stress rate and low T, attributed to predominant difference in stress intensity factor along the crack front. The numerical solution of SCG parameters was supported within the experimental range by the data obtained from constant stress-rate flexural testing for soda-lime glass microslides at ambient temperature.
We report absolute rate-constant measurements for the reactions of nine C(6)-C(9) alkanes with OH in 8-10 torr of nitrogen from 230 to 379 K in the Harvard University High-Pressure Flow System. Hydroxyl concentrations were measured using laser-induced fluorescence, and alkane concentrations were measured using Fourier transform infrared Spectroscopy. Ethane's reactivity was simultaneously measured as a test of experimental performance. Results were fit to a modified Arrhenius equation based on transition state theory (ignoring tunneling), k(T) = Be(-E(a)/T)/(T(1 - e(- 1.44nu(1)/T))(2)(1 - e(- 1.44nu(2)/T)), with nu(1) and nu(2) bending frequencies, set to 280 and 500 cm(-1). Results were as follows for B (10(-9) K cm(3) s(-1)), E(a) (K), and k(298) (10(-12) cm(3) s(-1)): cyclohexane, 3.24 +/- 0.14, 332 +/- 12, 7.13; cyclo-octane, 3.47 +/- 0.30, 149 +/- 26, 14.1; 2-methylhexane, 1.45 +/- 0.08, 110 +/- 15, 6.72; 3-methylhexane, 1.50 +/- 0.08, 128 +/- 16, 6.54; methylcyclopentane, 1.65 +/- 0.07, 109 +/- 13, 7.65; methylcyclohexane, 1.86 +/- 0.09, 83 +/- 14, 9.43; methylcycloheptane, 3.45 +/- 0.45, 142 +/- 36, 14.4; n-propylcyclohexane, 2.83 +/- 0.14, 112 +/- 15, 13.0; isopropylcyclohexane, 1.79 +/- 0.11, -44 +/- 34, 13.9. Uncertainties are one sigma results from linear regression fits and are likely underestimated. Room temperature rate coefficients of reaction are accurate to within 10% at two sigma. A comprehensive fit to 17 separate studies including the present work for cyclohexane gives good agreement with the present results: terms as above, 3.09 +/- 0.12, 326 +/- 12, 6.96. Five of these compounds are routinely measured in urban air within a suite of atmospheric nonmethane hydrocarbons and reach parts per billion levels. The remaining four are C8-C9 cycloalkanes with low anthropogenic emissions. Because of their high, specific reactivity with OH, their concentration decays may be used as an indirect measurement of [OH] in the atmosphere or laboratory. This data 2ff7e9595c
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