Design of Civil Engineering Frame Structures Using a Monomial/Newton Hybrid Method

This paper presents an application of a monomial approximation method for solving systems of nonlinear equations to the design of civil engineering frame structures. This is accomplished by solving a set of equations representing the state known as fully-stressed design, where each member of the structure is stressed to the maximum safe allowable level under at least one of the loading conditions acting on it. The monomial approximation method is based on the process of condensation, which has its origin in geometric programming theory. A monomial/Newton hybrid method is presented which permits some of the design variables to be free in sign, while others are strictly positive. This hybrid method is well suited to the structural design application since some variables are naturally positive and others are naturally free. The proposed method is compared to the most commonly used fully-stressed design method in practice. The hybrid method is shown to find solutions that the conventional method cannot find, while doing so with less computational effort. The impact of this approach on the activity of structural design is discussed.     

On the use of Laplace's equation for global predictions of internuclear separation and dissociation energy

Properties of target species can be estimated by various means including interpolations in periodic charts. Interpolation is equivalent to numerical solution of the Laplace equation. A test of this equivalence, within some confidence level, for any N-atomic molecule surrounded by 4N nearest neighbors: the sum of the second differences of the data in all directions must be zero. Since very few molecules have 4N neighbors with known data, the test becomes: the sum of the averages of the second differences must be zero. The validity of these tests is explored. For radii of main-group atoms, and for internuclear separations of their diatomic combinations, the averages are different from zero and the sums of the averages are zero to within one if second-nearest neighbors are used. Dissociation potentials pass the tests but with larger scatter. Predictions for dissociation potentials, using iterative interpolation within boundaries on which there are known data, are reviewed.     

INITIAL-BOUNDARY VALUE PROBLEM FOR THE UNSATURATED LANDAU-LIFSHITZ SYSTEM

51. IntroductionLet fi C Re (n = 1,2) be a bounded smooth domain. Consider the following nonhomogeneous initial-boundary value problem for the unsaturated Landau-Lifshitz systems offerromagnetic spin chain with Gilbert damping constant afl > 0,where adZ is the exchange constallt, u = (u', u', u'), "o(x) is smooth and satisfies the unsaturated condition, i.e., Ilo(~)I gi constant, and in IVuol' < co, "o(x)IOn = op(x). DenoteW(x) = luo(x)I. We assume 0 < m = mane < M ~ mpxW. Throughout t…     

Production systems with interruptions, arbitrary topology and finite buffers

We consider a production system with finite buffers and arbitrary topology where service time is subject to interruptions in one of three ways, viz. machine breakdown, machine vacations or Npolicy. We develop a unified approximation (analytical) methodology to calculate the throughput of the system using queueing networks together with decomposition, isolation and expansion techniques. The methodology is rigorously tested covering a large experimental region. Orthogonal arrays are used to design the experiments in order to keep the number of experiments manageable. The results obtained using the approximation methodology are compared to the simulation results. The ttests carried out to investigate the differences between the two results show that they are statistically insignificant. Finally, we test the methodology by applying it to several arbitrary topology networks. The results show that the performance of the approximation methodology is consistent, robust and produces excellent results in a variety of experimental conditions.     

Tactical Decompositions of Steiner Systems and Orbits of Projective Groups

Block's lemma states that the numbers m of point-classes and n of block-classes in a tactical decomposition of a 2-(v, k, ) design with b blocks satisfy m n m + b – v. We present a strengthening of the upper bound for the case of Steiner systems (2-designs with = 1), together with results concerning the structure of the block-classes in both extreme cases. Applying the results to the Steiner systems of points and lines of projective space PG(N, q), we obtain a complete classification of the groups inducing decompositions satisfying the upper bound; answering the analog of a question raised by Cameron and Liebler (P.J. Cameron and R.A. Liebler, Lin. Alg. Appl. 46 (1982), 91–102) (and still open).     

Accurate Solution to Overdetermined Linear Equations with Errors Using L1 Norm Minimization

It has been known for many years that a robust solution to an overdetermined system of linear equations Ax b is obtained by minimizing the L1 norm of the residual error. A correct solution x to the linear system can often be obtained in this way, in spite of large errors (outliers) in some elements of the (m × n) matrix A and the data vector b. This is in contrast to a least squares solution, where even one large error will typically cause a large error in x. In this paper we give necessary and sufficient conditions that the correct solution is obtained when there are some errors in A and b. Based on the sufficient condition, it is shown that if k rows of [A b] contain large errors, the correct solution is guaranteed if (m – n)/n 2k/, where > 0, is a lower bound of singular values related to A. Since m typically represents the number of measurements, this inequality shows how many data points are needed to guarantee a correct solution in the presence of large errors in some of the data. This inequality is, in fact, an upper bound, and computational results are presented, which show that the correct solution will be obtained, with high probability, for much smaller values of m – n.     

Macroscopic Determinism in Noninteracting Systems Using Large Deviation Theory

We consider a general system of n noninteracting identical particles which evolve under a given dynamical law and whose initial microstates are a priori independent. The time evolution of the n-particle average of a bounded function on the particle microstates is then examined in the large-n limit. Using the theory of large deviations, we show that if the initial macroscopic average is constrained to be near a given value, y, then the macroscopic average at time t converges in probability as n to a value _t(y) given explicitly in terms of a canonical expectation. Some general features of the graph of _t(y) versus t are examined, particularly in regard to continuity, symmetry, and convergence.     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.     

One-Dimensional Lattice Dynamics of the Diffusion-Limited Reaction A+A→A+S: Transient Behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A+AA+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynamics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.