Damage models for multi-component systems

A series system of n components is subject to a damage process. The damage to each component is cumulative and when it exceeds a certain threshold the component, and hence the device, fails. For various optimality criteria related to system lifetime and system reliability, we find the optimal allocation of resources among the components where the total resources are limited and the allocation of the resources determines the threshold level of each component. Various inventory-type applications are noted.     

On Time Discretizations for Spectral Methods

New methods are introduced for the time integration of the Fourier and Chebyshev methods of solution for dynamic differential equations. These methods are unconditionally stable, even though no matrix inversions are required. Time steps are chosen by accuracy requirements alone. For the Fourier method both leapfrog and Runge-Kutta methods are considered. For the Chebyshev method only Runge-Kutta schemes are tested. Numerical calculations are presented to verify the analytic results. Applications to the shallow water equations are presented.     

Time-optimal control for a model of bacterial growth

A time-optimal control problem is solved for Monod's model of bacterial growth in continuous culture. The solution is obtained using Green's theorem and has a simple feedback form.     

Radially isospectral annular membranes

^** Email: h.gottlieb{at}griffith.edu.au By utilizing transformations of both the radial coordinate andthe radial wave function, densities of annular membranes whichare radially isospectral to any given radial density are produced.In particular, new families of annular membrane densities arefound which are radially isospectral to a uniform membrane.Some new generalizations for completely isospectral annularmembranes (including angle-dependent densities) are also given.     

Semiempirical molecular orbital calculations of anisotropic 1H, 13C and 19F hyperfine coupling constants in hydrocarbon and fluorocarbon radicals

The anisotropic hyperfine coupling constants (AHCC) from the electron spin resonance (E.S.R.) spectra of a variety of atoms in organic radicals have been calculated by means of semiempirical molecular orbital wavefunctions in the INDO approximation. Hyperfine tensors involving ¹H, ¹³C and ¹⁹F nuclei are obtained for the ?H, ?H₃, CH₃?H₂, (CH₃)₃? hydrocarbon radicals, malonic acid radical, ?H₂F, ?F₂H, ?F₃ and CF₃?H₂ radicals. The calculated values are compared with available experimental, non-empirical and semiempirical values for these radicals. All integrals of the operator entering the electronic contributions have been evaluated over Slater type orbitals. The introduction of deorthogonalized wavefunctions gives generally better calculated results. In particular, the tensor components of the ¹⁹F AHCC are in good agreement with the experimental results without the necessity of readjusting the effective nuclear charges.     

The Uptake and Assembly of Alkanes within a Porous Nanocapsule in Water: New Information about Hydrophobic Confinement

In Nature, enzymes provide hydrophobic cavities and channels for sequestering small alkanes or long‐chain alkyl groups from water. Similarly, the porous metal oxide capsule [{Mo^VI₆O₂₁(H₂O)₆}₁₂{(Mo^V₂O₄)₃₀(L)₂₉(H₂O)₂}]^41? (L=propionate ligand) features distinct domains for sequestering differently sized alkanes (as in Nature) as well as internal dimensions suitable for multi‐alkane clustering. The ethyl tails of the 29 endohedrally coordinated ligands, L, form a spherical, hydrophobic “shell”, while their methyl end groups generate a hydrophobic cavity with a diameter of 11 Å at the center of the capsule. As such, C₇ to C₃ straight‐chain alkanes are tightly intercalated between the ethyl tails, giving assemblies containing 90 to 110 methyl and methylene units, whereas two or three ethane molecules reside in the central cavity of the capsule, where they are free to rotate rapidly, a phenomenon never before observed for the uptake of alkanes from water by molecular cages or containers.     

Correlation of Moments and Critical Phenomenon in Disassembly of Hot Nuclei

We used Monte Carlo method to generate the configurations of disassembly of hot nucleus Au* based on the Atomic Mass Table and the conservation of mass and charge number.The resulted charge distribution of fragments was then used to calculate the conditional moments.The logarithm correlation between second and third moments of experimental charge distribution is very well reproduced by theory.It seems that no connection to the critical phenomenon of concerned system exists.     

THE EFFECT OF THE FREEZE-OUT VOLUME IN THE MULTIFRAGMENTATION OF VERY HOT NUCLEAR REMNANT

In this paper a simplified method for the calculation of average Coulomb energy in statistical model of the disassembly processes of hot nuclei is proposed.The effect of freeze-out volume is studied based on the assumption of Gaussion-like distribution.It is indecated that the centre and dispersion of Gaussion-like distribution somewhat reflect the location and the renge of liquid-gas coexistence phase.     

THE EVIDENCE OF DECONFINEMENT PHASE TRANSITION OF SU(2) LATTICE GAUGE MODEL BY MONTE CARLO METHOD

In this paper,we have calculated the SU(2) lattice gauge by the Monte Carlo method.For the finite temperature problem 8³×4 lattice is used and for the zero temperature problem 8⁴ lattice.From the calculations of the energy density,heat capacity and entropy density,the results indicate that there is a deconfinement phase transition when T/Λ_L=40—50.     

DIRECT SIMULATION OF DEEP INELASTIC SCATTERING OF HEAVY-IONS (I) ONE PARAMETER DISTRIBUTION

The distributions of dynamic variables in the deep inelastic scattering (DIS) of heavy-ions are studied by a direct simulation technique based on the single-nucleon-transfer-mechanism. The relative motion of the two collision partners is described by a Lagrange equation, and the transition probability of a single nucleon during the interaction time is calculated by the statisti-cal spectroscopy method.The occurrence of the transition event and the corresponding change of the dynamic variables are both treated randomly according to the transition probability. The calculated results for the reaction of ⁴⁰Ar+⁵⁸Ni(E_L=280MeV) are compared with experimental data.