Product-type block preconditioners for electromagnetic cavity problems

In a radar detecting system, the radar cross section (RCS) of a target is an important application in electromagnetics computation. Cavity prediction is usually required in the computation process. When wavelengths of electromagnetic field are large, cavity calculation is a challenging problem. The main aim of this paper is to employ the preconditioned GMRES method to solve linear systems arising in cavity calculation of the transverse magnetic and transverse electric problems. We develop new preconditioners based on fast transforms and Toeplitz solvers. Our numerical results show that the proposed preconditioners are quite efficient and effective, especially when the wavelength is large.     

Sizing initial stockpiles in a conventional military retrograde movement

The importance of stockpiles in waging and supporting war has long been recognized by the military. However, despite this recognition, very few theoretical attempts have been undertaken to incorporate stockpile considerations in land combat models. This paper describes a multicriteria optimization model to estimate the minimum stockpile required to sustain fighting a conventional mobile delaying land battle. By studying the post-optimality analysis, valuable insights on the relationships between the key governing parameters can be established.     

Decay properties and quasi-stationary distributions for stopped Markovian bulk-arrival and bulk-service queues

We consider decay properties including the decay parameter, invariant measures and quasi-stationary distributions for a Markovian bulk-arrival and bulk-service queue which stops when the waiting line is empty. Investigating such a model is crucial for understanding the busy period and other related properties of the Markovian bulk-arrival and bulk-service queuing processes. The exact value of the decay parameter λ _C is first obtained. We show that the decay parameter can be easily expressed explicitly. The invariant measures and quasi-distributions are then revealed. We show that there exists a family of invariant measures indexed by λ∈[0,λ _C ]. We then show that under some mild conditions there exists a family of quasi-stationary distributions also indexed by λ∈[0,λ _C ]. The generating functions of these invariant measures and quasi-stationary distributions are presented. We further show that this stopped Markovian bulk-arrival and bulk-service queueing model is always λ _C -transient. Some deep properties regarding λ _C -transience are examined and revealed. The clear geometric interpretation of the decay parameter is explained. A few examples are then provided to illustrate the results obtained in this paper.     

Sound absorption of a quadratic and cubic nonlinearly vibrating curved panel absorber

This study investigated the sound absorption of a nonlinearly vibrating curved panel backed by a cavity. Very few studies on similar nonlinear structural-acoustic problems have been conducted to date, although there have been many on nonlinear plate or linear structural-acoustic problems. A curved panel is considered because the overall absorption bandwidth can be designed by appropriately adjusting the panel curvature, which is a key factor in controlling the structural resonant frequencies and absorption peaks. The theoretical formulation is developed based on the assumptions of quadratic and cubic nonlinear structural vibrations, and the linear acoustic pressure induced within the cavity. An approach based on the numerical integration method is developed to solve the nonlinear governing equation of the structural-acoustic problem. In the parametric study, the panel displacement amplitude converges with an increasing number of modes. The effects of excitation level, cavity depth, and damping factor are also examined. The quadratic and cubic nonlinearities and their effects on the sound absorption are also investigated. An experiment was conducted. The theoretical and experimental observations correspond reasonably with each other.     

Intramolecular (4+3) cycloadditions of nitrogen-tethered epoxy enosilanes for the synthesis of heteropolycycles

Furans bearing epoxy enolsilane units linked by a nitrogen heteroatom tether undergo intramolecular (4 + 3) cycloadditions to generate bis-heteroatomic polycyclic adducts having piperidine moieties in their frameworks. The cycloadducts, ultimately derived from furfural, a renewal chemical feedstock, are obtained with up to 4:1 dr and with ee retained from the epoxide.     

Radial Hetero[5]catenanes: Peripheral Isomer Sequences of the Interlocked Macrocycles

A pair of radial [5]catenanes, with either an isomeric cyclic ‐AABB‐ or ‐ABAB‐ type sequence of the interlocked β‐cyclodextrin (β‐CD) and cucurbit[6]uril (CB[6]) units, has been efficiently synthesized. Because of a marked difference in the binding strength and interlocking sequence of the peripheral macrocycles, interesting sequence‐dependent properties, characteristic of mechanically bonded macrocycles, were realized. Variable‐temperature ¹H NMR studies showed that the ‐ABAB‐ isomer has a more independent β‐CD dynamic, whereas the β‐CD motions in the ‐AABB‐ isomer are coupled. Dynamics of the pH‐insensitive β‐CD can also be further modulated upon base‐triggered mobilization of the CB[6]. These unique properties of the mechanical bond expressed in a sequence‐specific fashion and the transmission of the control on the macrocycle dynamics from one interlocked component to another, highlight the potential of similar complex hetero[n]catenanes in the design of advanced, multicomponent molecular machines.     

Nonlinear Effects on Coexistence Phenomenon in Parametric Excitation

We investigate the effect of nonlinearites on a parametrically excited ordinary differential equation whose linearization exhibits the phenomenon of coexistence. The differential equation studied governs the stability of a mode of vibration in an unforced conservative two degree of freedom system used to model thefree vibrations of a thin elastica. Using perturbation methods, we show thatat parameter values corresponding to coexistence, nonlinear terms can cause the origin to become nonlinearly unstable,even though linear stability analysis predicts the origin to be stable.We also investigate the bifurcations associated with this instability.