Mathematical Methods of Physics

Mathews, Jon; Walker, R. L.; Davidon, William C.

doi:10.1119/1.1971408

Cited by 71 publications

(60 citation statements)

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“…It is natural to suppose that it is these harmonics that are responsible for the comparatively large responses at frequencies Ω that are large compared with Ω m , which are evident in Figs 1–3. It is particularly interesting that this response cuts off for driving frequencies ω that are large compared with 2Ω, rather than Ω, a fact that would suggest that one is observing the effects of a broad 2:1 resonance similar to that arising in the standard Matthieu equation (see, e.g., Matthews & Walker 1964).…”

Section: Parametric Resonance and Transient Chaosmentioning

confidence: 99%

Transient chaos and resonant phase mixing in violent relaxation

Kandrup

Vass

Sideris

2003

Monthly Notices of the Royal Astronomical Society

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This paper explores how orbits in a galactic potential can be impacted by large amplitude time-dependences of the form that one might associate with galaxy or halo formation or strong encounters between pairs of galaxies. A period of time-dependence with a strong, possibly damped, oscillatory component can give rise to large amounts of transient chaos, and it is argued that chaotic phase mixing associated with this transient chaos could play a major role in accounting for the speed and efficiency of violent relaxation. Analysis of simple toy models involving time-dependent perturbations of an integrable Plummer potential indicates that this chaos results from a broad, possibly generic, resonance between the frequencies of the orbits and harmonics thereof and the frequencies of the time-dependent perturbation. Numerical computations of orbits in potentials exhibiting damped oscillations suggest that, within a period of 10 dynamical times t_D or so, one could achieve simultaneously both `near-complete' chaotic phase mixing and a nearly time-independent, integrable end state.Comment: 11 pages and 12 figures: an extended version of the original manuscript, containing a modified title, one new figure, and approximately one page of additional text, to appear in Monthly Notices of the Royal Astronomical Societ

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Section: Parametric Resonance and Transient Chaosmentioning

confidence: 99%

Transient chaos and resonant phase mixing in violent relaxation

Kandrup

Vass

Sideris

2003

Monthly Notices of the Royal Astronomical Society

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“…In contrast, the usual Itô and corresponding Stratonovich discretizations are defined such that the path integral reduces to the Fokker-Planck equation in the weak-noise limit. The term R/6 in the Feynman Lagrangian includes a contribution of R/12 from the WKBJ approximation 54 (named after Wentzel, Kramers, Brillouin, and Jefferys) to the same order of (∆t) 3/2 .…”

Section: Algebraic Complexity Yields Simple Intuitive Resultsmentioning

confidence: 99%

Statistical Mechanics of Combat and Extensions

Ingber

1993

Toward a Science of Command, Control, and Communications

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Lester Ingber I. Introduction: C 2 in Training and Computer Models A. Necessity of Comparing Computer Models to Exercise Data This project addresses the utility of establishing a mathematical approach to compare exercise data to large scale computer models whose underlying microscopic interactions among men and machines are driven by the natural laws of physics. In this study, the focus is to compare the Janus(T) wargame to National Training Center (NTC) data, since both systems then take into account human interactions. It also should be noted that "large scale" here refers to battalion level. (Army systems scale by factors of 3−5, from company to battalion to brigade to division to corps to army.) If these battalion level computer models can be favorably compared, and if consistency can be achieved between the hierarchy of large scale battalion level, larger scale corps level, and largest scale theater level computer models, then these higher echelon computer models also can be favorably compared. This could only enhance the value of training on these higher echelon computer models. 1 The requirement of depending more and more on combat computer models (including simulations and wargames) has been brought into sharper focus because of many circumstances, e.g.: (1) the nonexistence of ample data from previous wars and training operations, (2) the rapidly shortening time scale on which tactical decisions must be made, (3) the rapidly increasing scale at which men and machines are to be deployed, (4) the increasing awareness of new scenarios that are fundamentally different from historical experiences, (5) and the rapidly increasing expense of conducting training exercises. Furthermore, such computer models could be used to augment training. We now spend several million dollars to cycle each battalion through NTC. The training of these commanders could be greatly enhanced if inexpensive pre and post training wargames were provided that statistically replicate their training missions. Even, or rather especially, for the development of such training aids, proper analysis and modeling is required to quantitatively demonstrate that the computer models are good statistical representations of the training mission. However, the level of acceptance of computer models in major military battle-management and procurement decisions appears to be similar to the level of acceptance of computer simulations in physics in the 1960s. In physics, prior to the 1960s, theory and experiment formed a close bond to serve to understand nature. In the 1960s, academicians were fascinated with evolving computer technology, but very few people seriously accepted results from computer simulations as being on a par with good theory and good experiment. Now, of course, the situation is quite different. The requirement of understanding truly complex systems has placed computer simulation, together with theory and experiment, as an equal leg of a tripod of techniques used to investigate physical nature. The requirements necessary to bring combat c...

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“…Sensitivity [10] [11] or survey speed [12] , for example, could be chosen. Lagrange multipliers [13] can be used to determine the optimal design parameters of a telescope. Similarly, if the design parameters are stacked to form a column vector p which is N p dimensional, we can use it to define an arbitrary function to find the figure of merit as F (p).Assuming that C max is the maximum cost, we can formulate C(p) which represents the cost function as shown in (1)…”

Section: Lagrange Multipliermentioning

confidence: 99%

“…Again, assuming a fixed number of antennas, we proceed to optimize with respect to N s and B assuming a linear cost function, we obtain (13).…”

Section: Case Ii: Antenna Number Per Station Is Constantmentioning

confidence: 99%

Exploring Design Optimisation Techniques of a Radio Telescope Using Fixed Costing Constraints

Iyer,

Prabhu,

Gupta

et al. 2023

J. Phys.: Conf. Ser.

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Cost optimization is a common problem encountered in the design of telescopes. This paper comprehensively discusses various radio telescope designs worldwide, focusing on their design and utilities. It contextualizes the Pulsar data challenge and subsequently discusses and develops a mathematical model for designing radio telescopes. The model assumes a fixed-cost budget. This paper expands current ideas of modeling the system using figure-of-merit equations and optimizing them based on a fixed budget to obtain optimal and affordable radio telescope designs.

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Mathematical Methods of Physics

Cited by 71 publications

References 0 publications

Transient chaos and resonant phase mixing in violent relaxation

Transient chaos and resonant phase mixing in violent relaxation

Statistical Mechanics of Combat and Extensions

Exploring Design Optimisation Techniques of a Radio Telescope Using Fixed Costing Constraints

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