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.

System implications of large radiometric array antennas

Current radiometric earth and atmospheric sensing systems in the centimeter wavelength range generally employ a directive antenna connected through a single terminal pair to a Dicke receiver. It is shown that this approach does not lend itself to systems with greatly increased spatial resolution. Signal to noise considerations relating to antenna efficiency force the introduction of active elements at the subarray level; thus, if Dicke switching is to be used, it must be distributed throughout the system. Some possible approaches are suggested. The introduction of active elements at the subarray level is found to ease the design constraints on time delay elements, necessary for bandwidth, and on multiple beam generation, required in order to achieve sufficient integration time with high resolution

Incorporating Heterogeneity in Command Center Interactions

One of the many complexities of multinational coalition operations stems from differences in culture, military procedures, and command and control processes between the cooperating command centers. These differences can influence the interactions between decision makers of different command centers and can affect the outcome of the coalition operation. A coalition model, composed of individual models of the five-stage interacting decision maker model, was used in a virtual experiment. The subjective parameters included in the decision maker model can be any attribute that characterizes the heterogeneity of the decision makers. In this case, the parameters of power distance and uncertainty avoidance were used, two of Hofstede\u27s (1991) cultural dimensions. The accuracy and timeliness of the coalition\u27s response was used to evaluate its performance as a function of heterogeneity. Including the presence of heterogeneity in the coalition model, through the use of subjective parameters, is the first step in formalizing the process for developing adaptive coalition architectures

A Model to Evaluate the Effect of Organizational Adaptation

When an organization’s output declines due to either internal changes or changes in its external environment, it needs to adapt. In order to evaluate the effectiveness of different adaptation strategies on organizational per- formance, an organizational model composed of individual models of a five stage interacting decision maker was designed using an object oriented design approach and implemented as a Colored Petri net. The concept of entropy is used to calculate the total activity value, a surrogate for decision maker workload, based on the functional partition and the adaptation strategy being implemented. The individual decision maker’s total activity is monitored, as overloaded decision makers constrain organizational performance. A virtual experiment was conducted; organizations implementing local and global adaptation strategies were compared to a control organization with no adaptation. The level of tolerance of the organization, the workload limit based on the concept of the bounded rationality constraint, was used to determined when a decision maker was overloaded: the limiting effect of theworkload on performance. The timeliness of the organization’s responsewas used in order to evaluate organizational output as a function of adaptation strategy

Engineering calculations for communications satellite systems planning

Observed solution times were analyzed for the extended gradient and cyclic coordinate search procedures. The times used in the analysis come from computer runs made during a previously-reported experiment conducted to assess the quality of the solutions to a BSS synthesis problem found by the two search methods. The results of a second experiment with a Fixed Satellite Service (FSS) test problem are also presented. Computational results are summarized for mixed integer programming approaches for solving FSS synthesis problems. A promising heuristic algorithm is described. A synthesis model is discussed for orbital arc allotment optimization. Research plans for the near future are also presented

Engineering calculations for communications systems planning

The single entry interference problem is treated for frequency sharing between the broadcasting satellite and intersatellite services near 23 GHz. It is recommended that very long (more than 120 longitude difference) intersatellite hops be relegated to the unshared portion of the band. When this is done, it is found that suitable orbit assignments can be determined easily with the aid of a set of universal curves. An attempt to develop synthesis procedures for optimally assigning frequencies and orbital slots for the broadcasting satellite service in region 2 was initiated. Several discrete programming and continuous optimization techniques are discussed

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

Levels of Interoperability in Coalition Systems

Systems of different command centers that are brought together in a coalition operation must have some level of interoperability in order to work together. Bares [2000] has introduced a formalism of three interoperability domains that describe the ability of the systems to define their own level of interoperability within the coalition by assessing their own and the other systems’ ability to interact on actions of the coalition. The lowest domain, interconnectivity, reflects the ability to exchange messages; this level must already have been achieved in order for the systems to participate in the coalition. The second domain, interoperability, reflects a system’s ability to identify what tasks it is able to interoperate on. The third level, intercooperability, indicates that all systems have the ability to evaluate all other systems in the coalition. By describing the interoperability domains in this manner, the domains represent increasing levels of awareness of each system’s own capabilities and those of the other systems; it represents the transition from exchanging data to exchanging knowledge. This research looks particularly at the interoperability level and the ability of systems to evaluate their own interoperability on the coalition’s actions by using Bares’ formalism of interoperability to assign actions to systems participating in the coalition

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

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