The finite element method with Lagrangian multipliers

Summary The Dirichlet problem for second order differential equations is chosen as a model problem to show how the finite element method may be implemented to avoid difficulty in fulfilling essential (stable) boundary conditions. The implementation is based on the application of Lagrangian multiplier. The rate of convergence is proved.This paper was supported by the Atomic Energy Commission under Contract No. AEC AT (40-1) 3443/4.     

Detection and characterization of structural changes in the hard-disk fluid under freezing and melting conditions

The fluid of two-dimensional hard disks is investigated over a range of densities by Monte Carlo simulations in order to detect and characterize structural changes which take place when the condition of freezing and melting is approached. A novel method is proposed based on the use of the Voronoi tessellation and a certain shape factor which turns out to be a clear indicator of the presence of different underlying substructures (domains). Close to the freezing condition the probability distribution of the shape factor develops a second distinct maximum corresponding to a predominant presence of near-regular hexagons, whereas the original peak, having its origin primarily in pentagons and distorted hexagons, diminishes and disappears at melting density.     

Ozone monitoring in a Mediterranean forest using diffusive and continuous sampling

Ambient ozone was measured in a forest in Castelporziano (Italy) characterised by the prevailing presence of Holm-oak trees (Quercus ilex L.) from June to November 2003. Two methods for measuring ozone were used: long-term monitoring using diffusive samplers at three heights within the canopy, and continuous monitoring at two heights using the UV method. Results for one week mean ozone levels above and below the canopy from the diffusive samplers were compared to those obtained using the automatic analyser at the same levels. A good correlation between the two sampling techniques was found. Continuous monitoring showed a daily cycle with a midday maximum and a nocturnal minimum. While the forest floor consistently had the lowest ozone concentration, there were no differences during most daytime hours. The midday maximum is clearly due to downward mixing with O₃-rich air from above. The night-time ozone decay within the canopy is the result of dry deposition of O₃ and most likely due to reaction with biogenically produced NO. AOT40 within and above the canopy mostly exceeded the critical levels.     

Left Cotorsion Rings

It is proved that if R is an associative ring that is cotorsionas a left module over itself, and J is the Jacobson radicalof R, then the quotient ring R/J is a left self-injective vonNeumann regular ring and idempotents lift modulo J. In particular,if R is indecomposable, then it is a local ring. 2000 MathematicsSubject Classification 16D50, 16D90, 16L30.     

Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems

Summary. A domain with possibly non-Lipschitz boundary is defined as a limit of monotonically expanding or shrinking domains with Lipschitz boundary. A uniquely solvable Dirichlet boundary value problem (DBVP) is defined on each of the Lipschitz domains and the limit of these solutions is investigated. The limit function also solves a DBVP on the limit domain but the problem can depend on the sequences of domains if the limit domain is unstable with respect to the DBVP. The core of the paper consists in estimates of the difference between the respective solutions of the DBVP on two close domains, one of which is Lipschitz and the other can be unstable. Estimates for starshaped as well as rather general domains are derived. Their numerical evaluation is possible and can be done in different ways. Received October 16, 2001 / Revised version received January 16, 2002 / Published online: April 17, 2002 RID="*" ID="*" The research was funded partially by the National Science Foundation under the grants NSF–Czech Rep. INT-9724783 and NSF DMS-9802367 RID="**" ID="**" Support for Jan Chleboun coming from the Grant Agency of the Czech Republic through grant 201/98/0528 is appreciated     

Can a finite element method perform arbitrarily badly?

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the -norm and the nodal point errors converge arbitrarily slowly. With the -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.

     

Chaos in the fractional-order Volta’s system: modeling and simulation

This paper deals with a new fractional-order chaotic system. It is based on the concept of Volta’s system, where the mathematical model of Volta’s system contains fractional-order derivatives. This system has simple structure and can display a double-scroll attractor. The behavior of the integer-order and the fractional-order Volta’s system with total order less than three which exhibits chaos is presented as well. Computer simulations are cross-verified by the numerical calculation and the Matlab/Simulink models.