Elliptic models and M-theory

We give a unified analysis of four-dimensional elliptic models with N=2 supersymmetry and a simple gauge group, and their relation to M-theory. Explicit calculations of the Seiberg-Witten curves and the resulting one-instanton prepotential are presented. The remarkable regularities that emerge are emphasized. In addition, we calculate the prepotential in the Coulomb phase of the (asymptotically-free) Sp(2N) gauge theory with N_f fundamental hypermultiplets of arbitrary mass.Comment: 52 pages, latex, one eps figure, uses psfig.tex; revised version: typos corrected and references adde

Ethene dimerization on zeolite-hosted Ni ions : reversible mobilization of the active site

The active site in ethene oligomerization catalyzed by Ni-zeolites is proposed to be a mobile Ni(II) complex, based on density functional theory-based molecular dynamics (DFT-MD) simulations corroborated by continuous-flow experiments on Ni-SSZ-24 zeolite. The results of the simulations at operating conditions show that ethene molecules reversibly mobilize the active site as they exchange with the zeolite as ligands on Ni during reaction. Microkinetic modeling was conducted on the basis of free-energy profiles derived with DFT-MD for oligomerization on these mobile [(ethene)(2)-Ni-alkyl](+) species. The model reproduces the experimentally observed high selectivity to dimerization and indicates that the mechanism is consistent with the observed second-order rate dependence on ethene pressure

A focus on focal surfaces

We make a systematic study of the focal surface of a congruence of lines in the projective space. Using differential techniques together with techniques from intersection theory, we reobtain in particular all the invariants of the focal surface (degree, class, class of its hyperplane section, sectional genus and degrees of the nodal and cuspidal curve). We study in particular the congruences of chords to a smooth curve and the congruences of bitangents or flexes to a smooth surface. We find that they possess unexpected components in their focal surface, and conjecture that they are the only ones with this property.Comment: Plain TeX, 33 pages with no figure

Linear stability and numerical analysis of dipolar vortices and topographic flows

The linear stability and numerical analysis of geophysical flow patterns is carried out on the beta-plane in a quasigeostrophic approximation. We consider initial steady state dipoles in a one-and-a-half-layer model that are capable of zonal drift in either direction. Despite previous numerical works suggesting that eastward propagating dipoles are stable, our high resolution simulations identify the spontaneous symmetry breaking of weak dipoles over time. The evolution is associated with a growing critical mode with even symmetry about the zonal axis. On carrying out a linear stability analysis, the critical modes obtained share consistency with the numerical fields. In addition, both methods of analysis show that the linear growth rate is inversely proportional to the dipole intensity. Furthermore, the partner separation becomes more pronounced after the linear growth stage, suggesting that nonlinear effects play a pivotal role in the underlying dynamics. Beyond this, the dynamics of initially tilted dipoles and dipole-rider solutions are considered, while stronger dipoles are further analysed using the method of distillation. Flows over sinusoidal bottom relief are considered in a two-layer model on the quasigeostrophic beta-plane. Fourier mode solutions are assumed for the layer-wise perturbation field in order to carry out a linear stability analysis, from which a coupled eigenproblem is derived between fluid columns for both zonal and meridional bottom irregularities. The presence of zonally oriented multiple ridges stabilises an otherwise unstable homogeneous zonal current with respect to increases in the number of ridges and ridge amplitude. Moreover, a bifurcation occurs in the unstable mode spectra and is dependent on the number of ridges. The critical eigenmodes in this case are found to be eddy chains of alternating sign, and these share remarkable resemblance with those obtained numerically. Meridionally oriented multiple ridges are also considered, but are found not to affect the maximum growth rate directly.Open Acces

Four-Dimensional N=2 Superstring Constructions and their (Non-) Perturbative Duality Connections

We investigate the connections between four-dimensional, N=2 M-theory vacua constructed as orbifolds of type II, heterotic, and type I strings. All these models have the same massless spectrum, which contains an equal number of vector multiplets and hypermultiplets, with a gauge group of the maximal rank allowed in a perturbative heterotic string construction. We find evidence for duality between two type I compactifications recently proposed and a new heterotic construction that we present here. This duality allows us to gain insight into the non-perturbative properties of these models. In particular we consider gravitational corrections to the effective action.Comment: 18 pages, LaTex, 1 figur

Load and resistance factor design of cold formed steel comparative study of design methods for cold formed steel

Allowable Stress Design is the current method used to design cold-formed steel structural members and connections. In this design approach, factors of safety are used to compute the allowable design stresses which are compared to the actual maximum stresses that will occur in the member during the life of the structure. In recent years, the Load and Resistance Factor Design (LRFD) method has been developed for the design of hot-rolled steel shapes and the design of cold-formed steel structural members. This method is based on probabilistic and statistical techniques to account for the many uncertainties involved with the actual design. The LRFD criteria use load factors which are applied to the external load and resistance factors that are applied to the internal resistance capacities of the structure. The allowable unfactored loads based on each design method for different types of structural members are compared and shown in graphical forms. For structural members with one type of loading, the dead-to-live load ratio contributes to the difference between the two allowable loads. For members with a combination of loads, crosssectional geometry, loading conditions, material strength, member length, along with dead-to-live load ratio will affect the difference between the allowable loads computed from allowable stress design and LRFD

Gravitational lensing by point masses on regular grid points

It is shown that gravitational lensing by point masses arranged in an infinitely extended regular lattice can be studied analytically using the Weierstrass functions. In particular, we draw the critical curves and the caustic networks for the lenses arranged in regular-polygonal -- square, equilateral triangle, regular hexagon -- grids. From this, the mean number of positive parity images as a function of the average optical depth is derived and compared to the case of the infinitely extended field of randomly distributed lenses. We find that the high degree of the symmetry in the lattice arrangement leads to a significant bias towards canceling of the shear caused by the neighboring lenses on a given lens position and lensing behaviour that is qualitatively distinct from the random star field. We also discuss some possible connections to more realistic lensing scenarios.Comment: to appear in Monthly Notices of RAS, including 17 figs, 1 appendix. High-res figs and F95 code used available upon reques

Free vibration analysis of plates and shells by using the Superposition Method

This thesis is devoted to investigate the capability of the Superposition Method for obtaining the transient response of plates and the natural frequencies of thin doubly curved shallow shells. The Superposition Method gives accurate results with only a few terms and has proved to be efficient for both cases. To investigate the transient response, all supports of a thin simply supported rectangular plate under self weight are suddenly removed. The resulting motion comprises a combination of the natural modes of a completely free plate. The modal superposition method is used for determining the transient response. The modes and natural frequencies of the plate are obtained using the Superposition Method and the Rayleigh-Ritz method with the ordinary and degenerated free-free beam functions. The W–W algorithm is then used to delimit the natural frequencies from the frequency equation derived in a determinantal form. There is an excellent agreement between the results from both approaches but the modes based on the Superposition Method result in more accurate values with fewer terms, and have shown faster convergence. The results from the Superposition Method may serve as benchmarks for the transient response of completely free plates. The transient response is found to be dominated by the lower modes. The centre of vibration is shifted parallel from the original xy plane by the distance of the first mode of the plate (a rigid body translation) multiplied by the first transient coefficient. In the investigation of doubly curved shells, the natural frequency parameters of thin shallow shells with three different sets of boundary conditions were obtained for several different curvature ratios and two aspect ratios. The solutions to the building blocks, which are subject to simply-supported out-of-plane conditions and shear diaphragm in-plane conditions at all four edges, are represented by series of sine and cosine functions, generated using Galerkin’s method since an exact solution is not available for the doubly curved shells. Once displacement functions for the building blocks are obtained, the prescribed boundary conditions of the actual shell under investigation are then satisfied using the Superposition Method. The rate of convergence is found to be excellent and the results agree well with published results obtained using the Ritz method and those obtained using a Finite Element package, Abaqus. The computations show that it is possible to obtain the first 12 natural frequency parameters of the shallow shells on the rectangular planform with a rapid convergence rate