Compressive strength of edge-loaded corrugated board panels

Postbuckling strength of simply supported corrugated board panels subjected to edge compressive loading has been studied experimentally using a specially developed test fixture. Although the load versus out-of-plane displacement response was highly sensitive to the presence of initial imperfections in the panels, the collapse loads did not vary much, which is attributed to the stable postbuckling behavior of the plates. Thin plates collapsed at nearly twice the buckling load, while thick panels collapsed at loads below the elastic critical buckling load. Local buckling of the facing on the concave side of the buckled plate was observed at load levels close to the collapse load. The plate collapse was triggered by compressive failure of the facings that initiated at the unloaded edges. A simplified design analysis was derived based on approximate postbuckling analysis and compared with an existing design formula for corrugated board panels and boxes.     

Fixed-point algorithms for frequency estimation and structured low rank approximation

We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, i.e., frequency estimation. For the basic formulation of the fixed-point algorithm we show that it converges to the solution of a related minimization problem, namely the one obtained by replacing the original objective function with its convex envelope and keeping the structured matrix constraint unchanged.It often happens that this solution agrees with the solution to the original minimization problem, and we provide a simple criterion for when this is true. We also provide more general fixed-point algorithms that can be used to treat the problems of making weighted approximations by sums of exponentials given equally or unequally spaced sampling. We apply the method to the case of missing data, although the above mentioned convergence results do not hold in this case. However, it turns out that the method often gives perfect reconstruction (up to machine precision) in such cases. We also discuss multidimensional extensions, and illustrate how the proposed algorithms can be used to recover sums of exponentials in several variables, but when samples are available only along a curve.     

Combination of schlieren and pulsed TV holography in the study of a high-speed flame jet

This paper presents studies of the propagation of a high-speed turbulent flame jet of an air/hydrogen gas mixture. The experimental results are recorded with the schlieren and the pulsed TV holography method. These methods are compared and combined to benefit from the advantages of each of them. Abel inversion has been used to achieve three-dimensional information i.e. refractive index distributions. Evaluation, calibration and Abel inversion algorithms are described together with experimental results. The results obtained from the different techniques show remarkable similarities concerning both qualitative and quantitative aspects.     

Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem

Optimization is of vital importance when performing intensity modulated radiation therapy to treat cancer tumors. The optimization problem is typically large-scale with a nonlinear objective function and bounds on the variables, and we solve it using a quasi-Newton sequential quadratic programming method. This study investigates the effect on the optimal solution, and hence treatment outcome, when solving an approximate optimization problem of lower dimension. Through a spectral decompostion, eigenvectors and eigenvalues of an approximation to the Hessian are computed. An approximate optimization problem of reduced dimension is formulated by introducing eigenvector weights as optimization parameters, where only eigenvectors corresponding to large eigenvalues are included. The approach is evaluated on a clinical prostate case. Compared to bixel weight optimization, eigenvector weight optimization with few parameters results in faster initial decline in the objective function, but with inferior final solution. Another approach, which combines eigenvector weights and bixel weights as variables, gives lower final objective values than what bixel weight optimization does. However, this advantage comes at the expense of the pre-computational time for the spectral decomposition. A preliminary version of this paper was presented at the AAPM 46th annual meeting, held July 25–29, 2004 in Pittsburgh, PA.     

Theoretical studies of smectic C liquid crystals confined in a wedge. Stability considerations and Frederiks transitions

A general deformation of a smectic C liquid crystal is composed of five different distortions, each of which can be made independently. Here we show that to each of these distortions we can assign a simple vector operator. Use of these five basis operators enables us to write down the elastic free energy density as a quadratic form consisting of nine terms. We also discuss how the nine elastic constants defined by the elastic energy expansion must fulfil certain restrictions in terms of inequalities and a specific tilt angle dependence. Assuming the smectic layers to be incompressible, we examine how certain arrangements of the smectic layers can be stable due to an interplay between the incompressibility condition and the boundary conditions which we impose on the director. One such stable configuration is the wedge, where the smectic layers form parts of concentric cylinders with the common axis coinciding with the centre of the wedge. For such a system we discuss the different director configurations which can be achieved and their stability. We also discuss the possibility of inducing Frederiks transitions for some of these configurations and calculate the corresponding thresholds, thereby demonstrating the design of an experiment which would make it possible to measure those elastic constants which are related to the deformations of the smectic layers, constants which are normally difficult to determine experimentally.     

A Contractivity Condition for Iterated Function Systems

We prove a condition for long-term contractivity and the existence of a unique invariant measure for iterated function systems. We also give an intuitive interpretation of the condition in terms of weighted derivatives and weighted Wasserstein metrics. We use our condition in order to show some results for stochastic population models based on the logistic and Ricker maps.     

Geometric partitioning and robust ad-hoc network design

We consider bounds for the price of a European-style call option under regime switching. Stochastic semidefinite programming models are developed that incorporate a lattice generated by a finite-state Markov chain regime-switching model as a representation of scenarios (uncertainty) to compute bounds. The optimal first-stage bound value is equivalent to a Value at Risk quantity, and the optimal solution can be obtained via simple sorting. The upper (lower) bounds from the stochastic model are bounded below (above) by the corresponding deterministic bounds and are always less conservative than their robust optimization (min-max) counterparts. In addition, penalty parameters in the model allow controllability in the degree to which the regime switching dynamics are incorporated into the bounds. We demonstrate the value of the stochastic solution (bound) and computational experiments using the S&P 500 index are performed that illustrate the advantages of the stochastic programming approach over the deterministic strategy.     

Poly(methyl methacrylate-co-ethyl acrylate) latex particles with poly(ethylene glycol) grafts: structure and film formation

Water-based copolymer dispersions were prepared using methyl methacrylate (MMA), ethyl acrylate (EA) (MMA/EA = 1:2), and a series of nonionic polymerizable surfactants, i.e., "surfmers" based on poly(ethylene glycol)-(meth)acrylates. The latexes were compared with the behavior of a conventionally stabilized (nonionic nonylphenol ethoxylate, NP100 with 84 ethylene oxide units) dispersion with the same MMA-EA composition (PMMAEA). A number of techniques were employed in order to characterize structure, dynamics, and film formation properties: solution/solid-state NMR, dynamic/static light scattering (DLS/SLS), differential scanning calorimetry (DSC), tensile/shear mode dynamic mechanical thermal analysis (DMTA), and atomic force microscopy (AFM). The surfmers were found to be miscible with the MMA-EA copolymer at room temperature, with 46-85 mol % of the reacted surfmer detected at the particle surfaces, and the remaining part buried in the particle bulk. In contrast, the NP100 surfactant formed a separate interphase between the copolymer particles with no mixing detected at room temperature or at 90 degrees C. For a 4.0% dry weight concentration, NP100 phase separated and further crystallized at room temperature over a period of several months. Composition fluctuations related to a limited blockiness on a length scale above approximately 2 nm were detected for PMMAEA particles, whereas the surfmer particles were found to be homogeneous also below this limit. On a particle-particle level, the dispersions tended to form colloidal crystals unless hindered by a broadened particle size distribution or, in the case of PMMAEA, by the action of NP100. Finally, a surface roughness (Rq) master plot was constructed for data above the glass transition temperature (Tg) from Tg + 11 degrees C to Tg + 57 degrees C and compared with the complex shear modulus over 11 frequency decades. Shift factors from the 2 methods obeyed the same Williams-Landel-Ferry (WLF) temperature dependence, thus connecting the long-time surface flattening process to the rheological behavior of the copolymer.     

Simulation of methane oxidation on Pt

The authors present a generic model of CH4 oxidation on Pt with the emphasis on the role of surface-oxide formation. The latter process is treated in terms of the theory of first-order phase transitions. The corresponding Monte Carlo simulations indicate that the surface-oxide formation may result in stepwise features in the reaction kinetics. Specifically, with increasing CH4 pressure and/or decreasing O2 pressure, the model predicts a sharp transition from a low-reactive state with the surface completely covered by oxide to a high-reactive state with the surface covered by chemisorbed oxygen. In the former case, the reaction is first order in CH4 and zero order in O2. In the latter case, both reaction orders are positive. All these findings help in interpreting available experiments.     

Structural, photophysical, and nonlinear absorption properties of trans-di-arylalkynyl platinum(II) complexes with phenyl and thiophenyl groups

Optical power limiting and luminescence properties of two Pt(II) complexes with thiophenyl and phenyl groups in the ligands, trans-Pt(P(n-Bu)3)2(C[triple bond]C-Ar)2, where Ar = -C4H2S-C[triple bond]C-p-C6H4-n-C5H11 (1) and -p-C6H4-C[triple bond]C-C4H3S (2), have been investigated. The fluorescence lifetimes were found to be on the sub-nanosecond time scale, and the quantum yields were low, in accord with fast intersystem crossing from the excited singlet to triplet manifold. The phosphorescence lifetimes of 1 and 2 were shorter than that of a Pt(II) complex having two phenyl groups in the ligands. In order to elucidate the C-Pt bonding nature in the ground state, the 13C NMR chemical shift of the carbon directly bonded to Pt, the coupling constants 1JPtC, 2JPtC, and 1JPtP, and IR nuC[triple bond]C wavenumbers were obtained for 1, 2, and three other trans-diarylalkynyl Pt(II) complexes. X-ray diffraction data of 1 and 2 and density functional theory calculated geometries of models of 1, 2, and trans-Pt(P(n-Bu)3)2(C[triple bond]C-p-C6H4-C[triple bond]C-C6H5)2 (3) show that 1 preferably exists in a different conformation from that of 2 and 3. The variations in photophysical, NMR, and IR data can be rationalized by differences in geometry and pi-backbonding from Pt to the alkynyl ligand.