Pursuit on a Graph Using Partial Information

The optimal control of a "blind" pursuer searching for an evader moving on a road network and heading at a known speed toward a set of goal vertices is considered. To aid the "blind" pursuer, certain roads in the network have been instrumented with Unattended Ground Sensors (UGSs) that detect the evader's passage. When the pursuer arrives at an instrumented node, the UGS therein informs the pursuer if and when the evader visited the node. The pursuer's motion is not restricted to the road network. In addition, the pursuer can choose to wait/loiter for an arbitrary time at any UGS location/node. At time 0, the evader passes by an entry node on his way towards one of the exit nodes. The pursuer also arrives at this entry node after some delay and is thus informed about the presence of the intruder/evader in the network, whereupon the chase is on - the pursuer is tasked with capturing the evader. Because the pursuer is "blind", capture entails the pursuer and evader being collocated at an UGS location. If this happens, the UGS is triggered and this information is instantaneously relayed to the pursuer, thereby enabling capture. On the other hand, if the evader reaches one of the exit nodes without being captured, he is deemed to have escaped. We provide an algorithm that computes the maximum initial delay at the entry node for which capture is guaranteed. The algorithm also returns the corresponding optimal pursuit policy

The stochastic dynamics of nanoscale mechanical oscillators immersed in a viscous fluid

The stochastic response of nanoscale oscillators of arbitrary geometry immersed in a viscous fluid is studied. Using the fluctuation-dissipation theorem it is shown that deterministic calculations of the governing fluid and solid equations can be used in a straightforward manner to directly calculate the stochastic response that would be measured in experiment. We use this approach to investigate the fluid coupled motion of single and multiple cantilevers with experimentally motivated geometries.Comment: 5 pages, 5 figure

Agenda Control in the Bundestag, 1980-2002

We find strong evidence of monopoly legislative agenda control by government parties in the Bundestag. First, the government parties have near-zero roll rates, while the opposition parties are often rolled over half the time. Second, only opposition parties’ (and not government parties’) roll rates increase with the distances of each party from the floor median. Third, almost all policy moves are towards the government coalition (the only exceptions occur during periods of divided government). Fourth, roll rates for government parties sky- rocket when they fall into the opposition and roll rates for opposition parties plummet when they enter government, while policy movements go from being nearly 100 per cent rightward when there is a rightist government to 100 per cent leftward under a leftist government

Exhaust cloud rise and diffusion in the atmosphere

Analytical approach develops physical-mathematical model of rocket engine exhaust cloud rise, growth, and diffusion. Analytic derivations and resultant model apply to hot exhaust cloud study or industrial stack plumes, making work results applicable to air pollution. Model formulations apply to all exhaust cloud types and various atmospheric conditions

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’

Molecular packing and chemical association in liquid water simulated using ab initio hybrid Monte Carlo and different exchange-correlation functionals

In the free energy of hydration of a solute, the chemical contribution is given by the free energy required to expel water molecules from the coordination sphere and the packing contribution is given by the free energy required to create the solute-free coordination sphere (the observation volume) in bulk water. With the SPC/E water model as a reference, we examine the chemical and packing contributions in the free energy of water simulated using different electron density functionals. The density is fixed at a value corresponding to that for SPC/E water at a pressure of 1 bar. The chemical contribution shows that water simulated at 300 K with BLYP is somewhat more tightly bound than water simulated at 300 K with the revPBE functional or at 350 K with the BLYP and BLYP-D functionals. The packing contribution for various radii of the observation volume is studied. In the size range where the distribution of water molecules in the observation volume is expected to be Gaussian, the packing contribution is expected to scale with the volume of the observation sphere. Water simulated at 300 K with the revPBE and at 350 K with BLYP-D or BLYP conforms to this expectation, but the results suggest an earlier onset of system size effects in the BLYP 350 K and revPBE 300 K systems than that observed for either BLYP-D 350 K or SPC/E. The implication of this observation for constant pressure simulations is indicated. For water simulated at 300 K with BLYP, in the size range where Gaussian distribution of occupation is expected, we instead find non-Gaussian behavior, and the packing contribution scales with surface area of the observation volume, suggesting the presence of heterogeneities in the system

Convex hull method for the determination of vapour-liquid equilibria (VLE) phase diagrams for binary and ternary systems

Amieibibama Joseph wishes to thank Petroleum Technology Development Fund (PTDF) for their financial support which has made this research possible.Peer reviewedPostprin

Rise and growth of space vehicle engine exhaust and associated diffusion models

Space vehicle plume rise and associated diffusion models at Cape Kennedy Launch Comple

Computer Assembly of Cluster-Forming Amphiphilic Dendrimers

Recent theoretical studies have predicted a new clustering mechanism for soft matter particles that interact via a certain kind of purely repulsive, bounded potentials. At sufficiently high densities, clusters of overlapping particles are formed in the fluid, which upon further compression crystallize into cubic lattices with density-independent lattice constants. In this work we show that amphiphilic dendrimers are suitable colloids for the experimental realization of this phenomenon. Thereby, we pave the way for the synthesis of such macromolecules, which form the basis for a novel class of materials with unusual properties.Comment: 4 pages, 4 figures, 1 tabl

A statistical mechanics framework for static granular matter

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistical mechanics. This ensemble, which is based on the conservation properties of the stress tensor, is distinct from the original Edwards ensemble and applies to packings of deformable grains. We combine it with a field theoretical analysis of the packings, where the field is the Airy stress function derived from the force and torque balance conditions. In this framework, Point J characterized by a diverging stiffness of the pressure fluctuations. Separately, we present a phenomenological mean-field theory of the jamming transition, which incorporates the mean contact number as a variable. We link both approaches in the context of the marginal rigidity picture proposed by [3, 4].Comment: 21 pages, 15 figure