A single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere

We present a single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere. It is based on the assumption that the upwelling internal radiation field is dominated by a surface with a uniform brightness temperature. It allows the calculation of the scattering source function for individual aerosol types, mixtures of aerosol types, and mixtures of gas and aerosol. The approximation can be applied in a Curtis-Godson radiative transfer code and is used for operational retrievals from Mars Climate Sounder measurements. Radiance comparisons with a multiple scattering model show good agreement in the mid- and far-infrared although the approximate model tends to underestimate the radiances in realistic conditions of the Martian atmosphere. Relative radiance differences are found to be about 2% in the lowermost atmosphere, increasing to ∼10% in the middle atmosphere of Mars. The increasing differences with altitude are mostly due to the increasing contribution to limb radiance of scattering relative to emission at the colder, higher atmospheric levels. This effect becomes smaller toward longer wavelengths at typical Martian temperatures. The relative radiance differences are expected to produce systematic errors of similar magnitude in retrieved opacity profiles.     

Transition Probability (Fidelity) and Its Relatives

Transition Probability (fidelity) for pairs of density operators can be defined as a “functor” in the hierarchy of “all” quantum systems and also within any quantum system. The Introduction of “amplitudes” for density operators allows for a more intuitive treatment of these quantities, also pointing to a natural parallel transport. The latter is governed by a remarkable gauge theory with strong relations to the Riemann-Bures metric.     

Entangled three-qubit states without concurrence and three-tangle

We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.     

Simulation of laser ablation in aluminum: the effectivity of double pulses

Lasers are becoming a more and more important tool in cutting and shaping materials. Improving precision and effectivity is an ongoing demand in science and industry. One possibility is double pulses. Here, we study laser ablation of aluminum by the two-temperature model. There the laser is modeled as a source in a continuum heat conduction equation for the electrons, whose temperature then is transferred to a molecular dynamics particle model by an electron–phonon coupling term. The melting and ablation effectivity is investigated depending on the relative intensity and the time delay between two Gaussian shaped laser pulses. It turns out that at least for aluminum the optimal pulse shapes are standard Gaussian pulses. For double pulses with delay times up to 200 ps, we find a behavior as observed in experiment: The ablation depth decreases beyond a delay of 10 ps even if one does not account for the weakening at the second pulse due to laser–plasma interaction.     

Existence and Density Theorems for Stochastic Maps on Commutative C*-algebras

This paper presents theoremes on the structure of stochastic and normalized positive linear maps over commutative C*-algebras. We show how strongly the solution of the n-tupel problem for stochastic maps relates to the fact that stochastic maps of finite rank are weakly dense within stochastic maps in case of a commutative C*-algebra. We give a new proof of the density theorem and derive (besides the solution of the n-tupel problem) results concerning the extremal maps of certain convex subsets which are weakly dense. All stated facts suggest application in Statistical Physics (algebraic approach), especially concerning questions around evolution of classical systems.     

Two incidence propositions in chain geometries

The significance of the incidence propositions (Z) and (B) for chain geometries Σ(F, A, J) is determined. In preparation the structure of kinematic and nearquadratic Jordan systems is studied.     

Many parameter Hölder perturbation of unbounded operators

If \({u \mapsto A(u)}\) is a C ^0,α -mapping, for 0 < α ≤ 1, having as values unbounded self-adjoint operators with compact resolvents and common domain of definition, parameterized by u in an (even infinite dimensional) space, then any continuous (in u) arrangement of the eigenvalues of A(u) is indeed C ^0,α in u.     

A multicriteria approach for optimizing bus schedules and school starting times

In many rural counties pupils on their way to school are a large, if not the largest group of customers for public mass transit. Hence an effective optimization of public mass transit in these regions must include the traffic caused by pupils. Besides a change in the schedules of the buses and the starting times of the trips, the school starting time may become an integral part of the planning process. We discuss the legal framework for this optimization problem in German states and counties and present a multi-objective mixed-integer linear programming formulation for the simultaneous specification of school and trip starting times. For its solution, we develop a two-stage decomposition heuristic and apply it to practical data sets from three different rural German counties.     

Optimizing source and receiver placement in multistatic sonar networks to monitor fixed targets

Multistatic sonar networks consisting of non-collocated sources and receivers are a promising development in sonar systems, but they present distinct mathematical challenges compared to the monostatic case in which each source is collocated with a receiver. This paper is the first to consider the optimal placement of both sources and receivers to monitor a given set of target locations. Prior publications have only considered optimal placement of one type of sensor, given a fixed placement of the other type. We first develop two integer linear programs capable of optimally placing both sources and receivers within a discrete set of locations. Although these models are capable of placing both sources and receivers to any degree of optimality desired by the user, their computation times may be unacceptably long for some applications. To address this issue, we then develop a two-step heuristic process, Adapt-LOC, that quickly selects positions for both sources and receivers, but with no guarantee of optimality. Based on this, we also create an iterative approach, Iter-LOC, which leads to a locally optimal placement of both sources and receivers, at the cost of larger computation times relative to Adapt-LOC. Finally, we perform computational experiments demonstrating that the newly developed algorithms constitute a powerful portfolio of tools, enabling the user to slect an appropriate level of solution quality, given the available time to perform computations. Our experiments include three real-world case studies.     

Optimally solving the alternative subgraphs assembly line balancing problem

Assembly line balancing problems (ALBP) consist of distributing the total workload for manufacturing any unit of the products to be assembled among the work stations along a manufacturing line as used in the automotive or the electronics industries. Usually, it is assumed that the production process is fixed, i.e., has been determined in a preceding planning step. However, this sequential planning approach is often suboptimal because the efficiency of the production process can not be evaluated definitely without knowing the distribution of work. Instead, both decisions should be taken simultaneously. This has led to the Alternative Subgraphs ALBP. We give an alternative representation of the problem, formulate an improved mixed-integer program and propose a solution approach based on SALOME, an effective branch-and-bound procedure for the well-known Simple ALBP. Computational experiments indicate that the proposed procedure is successful in finding optimal solutions for small- and medium-sized problem instances and rather good heuristic solutions for large-scaled instances.