A method of limit point calculation in finite element structural analysis

An approach is presented for the calculation of limit points for structures described by discrete coordinates, and whose governing equations derive from finite element concepts. The nonlinear load-displacement path of the imperfect structure is first traced by use of a direct iteration scheme and the determinant of the governing algebraic equations is calculated at each solution point. The limit point is then established by extrapolation and imposition of the condition of zero slope of the plot of load vs. determinant. Three problems are solved in illustration of the approach and in comparison with alternative procedures and test data

A finite element procedure for nonlinear prebuckling and initial postbuckling analysis

A procedure cast in a form appropriate to the finite element method is presented for geometrically nonlinear prebuckling and postbuckling structural analysis, including the identification of snap-through type of buckling. The principal features of this procedure are the use of direct iteration for solution of the nonlinear algebraic equations in the prebuckling range, an interpolation scheme for determination of the initial bifurcation point, a perturbation method in definition of the load-displacement behavior through the postbuckling regime, and extrapolation in determination of the limit point for snap-through buckling. Three numerical examples are presented in illustration of the procedure and in comparison with alternative approaches

Dust sublimation by GRBs and its implications

The prompt optical flash recently detected accompanying GRB990123 suggests that, for at least some GRBs, gamma-ray emission is accompanied by prompt optical-UV emission with luminosity L(1-7.5eV)=10^{49}(\Delta\Omega/4\pi)erg/s, where \Delta\Omega is the solid angle into which gamma-ray and optical-UV emission is beamed. Such an optical-UV flash can destroy dust in the beam by sublimation out to an appreciable distance, approximately 10 pc, and may clear the dust out of as much as 10^7(\Delta\Omega/4\pi)M_sun of molecular cloud material on an apparent time scale of 10 seconds. Detection of time dependent extinction on this time scale would therefore provide strong constraints on the GRB source environment. Dust destruction implies that existing, or future, observations of not-heavily-reddened fireballs are not inconsistent with GRBs being associated with star forming regions. In this case, however, if gamma-ray emission is highly beamed, the expanding fireball would become reddened on a 1 week time scale. If the optical depth due to dust beyond approximately 8 pc from the GRB is 0.2<\tau_V<2, most of the UV flash energy is converted to infra-red, \lambda \sim 1 micron, radiation with luminosity \sim 10^{41} erg/s extending over an apparent duration of \sim 20(1+z)(\Delta\Omega/0.01) day. Dust infra-red emission may already have been observed in GRB970228 and GRB980326, and may possibly explain their unusual late time behavior.Comment: 16 pages, including 1 figure, submitted to Ap

Quasi-Relative Interiors for Graphs of Convex Set-Valued Mappings

This paper aims at providing further studies of the notion of quasi-relative interior for convex sets introduced by Borwein and Lewis. We obtain new formulas for representing quasi-relative interiors of convex graphs of set-valued mappings and for convex epigraphs of extended-real-valued functions defined on locally convex topological vector spaces. We also show that the role, which this notion plays in infinite dimensions and the results obtained in this vein, are similar to those involving relative interior in finite-dimensional spaces.Comment: This submission replaces our previous version

Ecohydrological Modeling in Agroecosystems: Examples and Challenges

Human societies are increasingly altering the water and biogeochemical cycles to both improve ecosystem productivity and reduce risks associated with the unpredictable variability of climatic drivers. These alterations, however, often cause large negative environmental consequences, raising the question as to how societies can ensure a sustainable use of natural resources for the future. Here we discuss how ecohydrological modeling may address these broad questions with special attention to agroecosystems. The challenges related to modeling the two‐way interaction between society and environment are illustrated by means of a dynamical model in which soil and water quality supports the growth of human society but is also degraded by excessive pressure, leading to critical transitions and sustained societal growth‐collapse cycles. We then focus on the coupled dynamics of soil water and solutes (nutrients or contaminants), emphasizing the modeling challenges, presented by the strong nonlinearities in the soil and plant system and the unpredictable hydroclimatic forcing, that need to be overcome to quantitatively analyze problems of soil water sustainability in both natural and agricultural ecosystems. We discuss applications of this framework to problems of irrigation, soil salinization, and fertilization and emphasize how optimal solutions for large‐scale, long‐term planning of soil and water resources in agroecosystems under uncertainty could be provided by methods from stochastic control, informed by physically and mathematically sound descriptions of ecohydrological and biogeochemical interactions

Variational Stability and Marginal Functions via Generalized Differentiation

Robust Lipschitzian properties of set-valued mappings and marginal functions play a crucial role in many aspects of variational analysis and its applications, especially for issues related to variational stability and optimizatiou. We develop an approach to variational stability based on generalized differentiation. The principal achievements of this paper include new results on coderivative calculus for set-valued mappings and singular subdifferentials of marginal functions in infinite dimensions with their extended applications to Lipschitzian stability. In this way we derive efficient conditions ensuring the preservation of Lipschitzian and related properties for set-valued mappings under various operations, with the exact bound/modulus estimates, as well as new sufficient conditions for the Lipschitz continuity of marginal functions