Towards a unification of HRT and SCOZA. Analysis of exactly solvable mean-spherical and generalized mean-spherical models

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. Earlier in this respect we have studied consistency between the internal energy and free energy routes. As a next step toward this goal we here consider consistency with the compressibility route too, but we restrict explicit evaluations to a model whose exact solution is known showing that a unification works in that case. The model in question is the mean spherical model (MSM) which we here extend to a generalized MSM (GMSM). For this case, we show that the correct solutions can be recovered from suitable boundary conditions through either of SCOZA or HRT alone as well as by the combined theory. Furthermore, the relation between the HRT-SCOZA equations and those of SCOZA and HRT becomes transparent.Comment: Minimal correction of some typos found during proof reading. Accepted for publication in Phys. Rev.

Alternative mathematical programming formulations for FSS synthesis

A variety of mathematical programming models and two solution strategies are suggested for the problem of allocating orbital positions to (synthesizing) satellites in the Fixed Satellite Service. Mixed integer programming and almost linear programming formulations are presented in detail for each of two objectives: (1) positioning satellites as closely as possible to specified desired locations, and (2) minimizing the total length of the geostationary arc allocated to the satellites whose positions are to be determined. Computational results for mixed integer and almost linear programming models, with the objective of positioning satellites as closely as possible to their desired locations, are reported for three six-administration test problems and a thirteen-administration test problem

The role of service areas in the optimization of FSS orbital and frequency assignments

A relationship is derived, on a single-entry interference basis, for the minimum allowable spacing between two satellites as a function of electrical parameters and service-area geometries. For circular beams, universal curves relate the topocentric satellite spacing angle to the service-area separation angle measured at the satellite. The corresponding geocentric spacing depends only weakly on the mean longitude of the two satellites, and this is true also for alliptical antenna beams. As a consequence, if frequency channels are preassigned, the orbital assignment synthesis of a satellite system can be formulated as a mixed-integer programming (MIP) problem or approximated by a linear programming (LP) problem, with the interference protection requirements enforced by constraints while some linear function is optimized. Possible objective-function choices are discussed and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed ideal location set. A test problem is posed consisting of six service areas, each served by one satellite, all using elliptical antenna beams and the same frequency channels. Numerical results are given for the three ideal location prescriptions for both the MIP and LP formulations. The resulting scenarios also satisfy reasonable aggregate interference protection requirements

Broadcasting satellite service synthesis using gradient and cyclic coordinate search procedures

Two search techniques are considered for solving satellite synthesis problems. Neither is likely to find a globally optimal solution. In order to determine which method performs better and what factors affect their performance, we design an experiment and solve the same problem under a variety of starting solution configuration-algorithm combinations. Since there is no randomization in the experiment, we present results of practical, rather than statistical, significance. Our implementation of a cyclic coordinate search procedure clearly finds better synthesis solutions than our implementation of a gradient search procedure does with our objective of maximizing the minimum C/I ratio computed at test points on the perimeters of the intended service areas. The length of the available orbital arc and the configuration of the starting solution are shown to affect the quality of the solutions found

Engineering calculations for communications satellite systems planning

An extended gradient search code for broadcasting satellite service (BSS) spectrum/orbit assignment synthesis is discussed. Progress is also reported on both single-entry and full synthesis computational aids for fixed satellite service (FSS) spectrum/orbit assignment purposes

Engineering calculations for communications satellite systems planning

Progress is reported on a computer code to improve the efficiency of spectrum and orbit utilization for the Broadcasting Satellite Service in the 12 GHz band for Region 2. It implements a constrained gradient search procedure using an exponential objective function based on aggregate signal to noise ratio and an extended line search in the gradient direction. The procedure is tested against a manually generated initial scenario and appears to work satisfactorily. In this test it was assumed that alternate channels use orthogonal polarizations at any one satellite location

Population control of 2s-2p transitions in hydrogen

We consider the time evolution of the occupation probabilities for the 2s-2p transition in a hydrogen atom interacting with an external field, V(t). A two-state model and a dipole approximation are used. In the case of degenerate energy levels an analytical solution of the time-dependent Shroedinger equation for the probability amplitudes exists. The form of the solution allows one to choose the ratio of the field amplitude to its frequency that leads to temporal trapping of electrons in specific states. The analytic solution is valid when the separation of the energy levels is small compared to the energy of the interacting radiation.Comment: 6 pages, 3 figure

Beable trajectories for revealing quantum control mechanisms

The dynamics induced while controlling quantum systems by optimally shaped laser pulses have often been difficult to understand in detail. A method is presented for quantifying the importance of specific sequences of quantum transitions involved in the control process. The method is based on a ``beable'' formulation of quantum mechanics due to John Bell that rigorously maps the quantum evolution onto an ensemble of stochastic trajectories over a classical state space. Detailed mechanism identification is illustrated with a model 7-level system. A general procedure is presented to extract mechanism information directly from closed-loop control experiments. Application to simulated experimental data for the model system proves robust with up to 25% noise.Comment: Latex, 20 pages, 13 figure

The concept of correlated density and its application

The correlated density appears in many physical systems ranging from dense interacting gases up to Fermi liquids which develop a coherent state at low temperatures, the superconductivity. One consequence of the correlated density is the Bernoulli potential in superconductors which compensates forces from dielectric currents. This Bernoulli potential allows to access material parameters. Though within the surface potential these contributions are largely canceled, the bulk measurements with NMR can access this potential. Recent experiments are explained and new ones suggested. The underlying quantum statistical theory in nonequilibrium is the nonlocal kinetic theory developed earlier.Comment: 14 pages, CMT30 proceeding