118 research outputs found
Stacking Characteristics of Composite Cardboard Boxes
This paper presents a simplified model and method for finding the deflection char acteristics of stacked cardboard boxes, provided the load-deflection characteristic of the box is known. A computer program, based on this model, allows the stability of stacked boxes to be investigated and to indicate the limits to the height of the stack and box parameters required to prevent stack toppling.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68424/2/10.1177_073168448300200302.pd
Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory
Approximate and exact nodes of fermionic wavefunctions: coordinate transformations and topologies
A study of fermion nodes for spin-polarized states of a few-electron ions and
molecules with one-particle orbitals is presented. We find exact nodes
for some cases of two electron atomic and molecular states and also the first
exact node for the three-electron atomic system in state using
appropriate coordinate maps and wavefunction symmetries. We analyze the cases
of nodes for larger number of electrons in the Hartree-Fock approximation and
for some cases we find transformations for projecting the high-dimensional node
manifolds into 3D space. The node topologies and other properties are studied
using these projections. We also propose a general coordinate transformation as
an extension of Feynman-Cohen backflow coordinates to both simplify the nodal
description and as a new variational freedom for quantum Monte Carlo trial
wavefunctions.Comment: 7 pages, 7 figure
A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem
A wide variety of articles, starting with the famous paper (Gidas, Ni and
Nirenberg in Commun. Math. Phys. 68, 209-243 (1979)) is devoted to the
uniqueness question for the semilinear elliptic boundary value problem
-{\Delta}u={\lambda}u+u^p in {\Omega}, u>0 in {\Omega}, u=0 on the boundary of
{\Omega}, where {\lambda} ranges between 0 and the first Dirichlet Laplacian
eigenvalue. So far, this question was settled in the case of {\Omega} being a
ball and, for more general domains, in the case {\lambda}=0. In (McKenna et al.
in J. Differ. Equ. 247, 2140-2162 (2009)), we proposed a computer-assisted
approach to this uniqueness question, which indeed provided a proof in the case
{\Omega}=(0,1)x(0,1), and p=2. Due to the high numerical complexity, we were
not able in (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)) to treat
higher values of p. Here, by a significant reduction of the complexity, we will
prove uniqueness for the case p=3
Generalization of the Zlámal condition for simplicial finite elements in ℝ d
The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method in 2d. In this paper we present and discuss its generalization to simplicial partitions in any space dimension
Decision-Making for Long Memory Data in Technical-Economic Design, Fractals and Decision Area Bubbles
Identification of a memory kernel in a semilinear integrodifferential parabolic problem with applications in heat conduction with memory
Coagulation equations with gelation
Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel K ij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation t c , and give an exact postgelation solution for the model K ij =( ij ω ) (ω>1/2) and K ij =a i+j ( a >1). For the model K ij = i ω + j ω ( ω <1, without gelation) initial solutions are given. It is argued that the kernel K ij ∼ ij ω with ω≃1−1/d ( d is dimensionality) effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer ( Ω =1). For all Ω the exponents, t=Ω +3/2 and σ=Ω −1/2, γ =(3/2− Ω)/(Ω − 1/2) and Β =1, characterize the size distribution, at and slightly below the gel point, under the assumption that scaling is valid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45146/1/10955_2005_Article_BF01019497.pd
Identifying Mechanical Properties of Viscoelastic Materials in Time Domain Using the Fractional Zener Model
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