Optimization of air vehicles operations using mixed-integer linear programming

A scenario where multiple air vehicles are required to prosecute geographically dispersed targets is considered. Furthermore, multiple tasks are to be successively performed on each target, that is, the targets must be classified, attacked, and verified as destroyed. The optimal, for example, minimum time, performance of these tasks requires cooperation among the vehicles such that critical timing constraints are satisfied, that is, a target must be classified before it can be attacked, and an air vehicle is sent to a target area to verify its destruction only after the target has been attacked. In this paper, the optimal task assignment/scheduling problem is posed as a mixed-integer linear program (MILP). The solution of the MILP assigns all tasks to the vehicles and performs the scheduling in an optimal manner, including staged departure times. Coupled tasks involving timing and task order constraints are automatically addressed. When the air vehicles have sufficient endurance, the existence of a solution is guaranteed.     

An improved 1D fiber dry spinning mass transfer model

A method of extending one-dimensional models of fiber dry spinning to take differences between surface and average mass concentrations into account is evaluated using an idealized model problem. Based on a closed form solution of the model problem, it is concluded that the method (which involves the introduction of a separate surface concentration variable and a corresponding additional equation) works well.     

Estimating biodegradative gene numbers at a JP-5 contaminated site using PCR

Applied Biochemistry and Biotechnology - We have utilized a most-probable-number polymerase chain reaction (MPN-PCR) procedure to estimate gene numbers and biodegradative potential at a jet fuel...     

A new frequency‐uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L²(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star‐shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star‐combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second‐kind integral operator for which convergence of the Galerkin method in L²(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star‐combined operator implies frequency‐explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high‐frequency case. The proof of coercivity of the star‐combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains. © 2011 Wiley Periodicals, Inc.     

Communication: direct angle-resolved measurements of collision dynamics with electronically excited molecules: NO(A2Σ+) + Ar

We report direct doubly differential (quantum state and angle-resolved) scattering measurements involving short-lived electronically excited molecules using crossed molecular beams. In our experiment, supersonic beams of nitric oxide and argon atoms collide at 90°. In the crossing region, NO molecules are excited to the A(2)Σ(+)state by a pulsed nanosecond laser, undergo rotationally inelastic collisions with Ar atoms, and are then detected 400 ns later (approximately twice the radiative lifetime of the A(2)Σ(+)state) by 1 + 1(') multiphoton ionization via the E(2)Σ(+) state. The velocity distributions of the scattered molecules are recorded using velocity-mapped ion imaging. The resulting images provide a direct measurement of the state-to-state differential scattering cross sections. These results demonstrate that sufficient scattering events occur during the short lifetimes typical of molecular excited states (～200 ns, in this case) to allow spectroscopically detected quantum-state-resolved measurements of products of excited-state collisions.     

Quantifying Density Fluctuations in Volumes of All Shapes and Sizes Using Indirect Umbrella Sampling

Water density fluctuations are an important statistical mechanical observable and are related to many-body correlations, as well as hydrophobic hydration and interactions. Local water density fluctuations at a solid-water surface have also been proposed as a measure of its hydrophobicity. These fluctuations can be quantified by calculating the probability, P _v (N), of observing N waters in a probe volume of interest v. When v is large, calculating P _v (N) using molecular dynamics simulations is challenging, as the probability of observing very few waters is exponentially small, and the standard procedure for overcoming this problem (umbrella sampling in N) leads to undesirable impulsive forces. Patel et al. (J. Phys. Chem. B 114:1632, 2010) have recently developed an indirect umbrella sampling (INDUS) method, that samples a coarse-grained particle number to obtain P _v (N) in cuboidal volumes. Here, we present and demonstrate an extension of that approach to volumes of other basic shapes, like spheres and cylinders, as well as to collections of such volumes. We further describe the implementation of INDUS in the NPT ensemble and calculate P _v (N) distributions over a broad range of pressures. Our method may be of particular interest in characterizing the hydrophobicity of interfaces of proteins, nanotubes and related systems.     

Isospin symmetry of odd-odd mirror nuclei: identification of excited states in N=Z-2 48Mn

Excited states have been observed in the N=Z-2 odd-odd nucleus 48Mn for the first time. Through comparison with the structure of 48V, a first high-spin study of an odd-odd mirror pair has been achieved. Differences between the T=1 analogue states in this pair have been interpreted in terms of Coulomb effects, with the aid of shell-model calculations in the full pf valence space. Unlike other mirror pairs, the energy differences have been interpreted almost entirely as due to a monopole effect associated with smooth changes in radius (or deformation) as a function of angular momentum. In addition, the large energy shift between analogue negative-parity states is interpreted in terms of the electromagnetic spin-orbit interaction in nuclei.     

A physical basis for non-Newtonian power-law viscosity

Many non-Newtonian materials have viscosities proportional to a power of shear rate. Although, generally, such relationships are regarded as being empirical, it is shown that power-law behavior arises when structure change with shear rate tends to saturation and results in flow activation energy being inversely proportional to shear rate. A temperature-dependent power-law index is predicted as is observed. Viscosity measurements are presented for a 10% sodium carboxymethylcellulose solution. It was found that both activation entropy and enthalpy decreased with shear rate, the former producing a small shear thickening and the latter a dominant shear thinning contribution to flow.     

Synthesis of some 2,9-disubstituted-1,10-phenanthrolines

A series of symmetrically disubstituted compounds, with substituents linked to the ring through a carbon atom, has been prepared from 2,9-dimethyl-1,10-phenanthroline. Nmr data are also reported.