A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise

A Unification of Models of Tethered Satellites

In this paper, different conservative models of tethered satellites are related mathematically, and it is established in what limit they may provide useful insight into the underlying dynamics. An infinite dimensional model is linked to a finite dimensional model, the slack-spring model, through a conjecture on the singular perturbation of tether thickness. The slack-spring model is then naturally related to a billiard model in the limit of an inextensible spring. Next, the motion of a dumbbell model, which is lowest in the hierarchy of models, is identified within the motion of the billiard model through a theorem on the existence of invariant curves by exploiting Moser's twist map theorem. Finally, numerical computations provide insight into the dynamics of the billiard model

A function-based approach to cockpit procedure aids

The objective of this research is to develop and test a cockpit procedural aid that can compose and present procedures that are appropriate for the given flight situation. The procedure would indicate the status of the aircraft engineering systems, and the environmental conditions. Prescribed procedures already exist for normal as well as for a number of non-normal and emergency situations, and can be presented to the crew using an interactive cockpit display. However, no procedures are prescribed or recommended for a host of plausible flight situations involving multiple malfunctions compounded by adverse environmental conditions. Under these circumstances, the cockpit procedural aid must review the prescribed procedures for the individual malfunction (when available), evaluate the alternatives or options, and present one or more composite procedures (prioritized or unprioritized) in response to the given situation. A top-down function-based conceptual approach towards composing and presenting cockpit procedures is being investigated. This approach is based upon the thought process that an operating crew must go through while attempting to meet the flight objectives given the current flight situation. In order to accomplish the flight objectives, certain critical functions must be maintained during each phase of the flight, using the appropriate procedures or success paths. The viability of these procedures depends upon the availability of required resources. If resources available are not sufficient to meet the requirements, alternative procedures (success paths) using the available resources must be constructed to maintain the critical functions and the corresponding objectives. If no success path exists that can satisfy the critical functions/objectives, then the next level of critical functions/objectives must be selected and the process repeated. Information is given in viewgraph form

Enhancing laser sideband cooling in one-dimensional optical lattices via the dipole interaction

We study resolved sideband laser cooling of a one-dimensional optical lattice with one atom per site, and in particular the effect of the dipole interaction between radiating atoms. For simplicity, we consider the case where only a single cooling laser is applied. We derive a master equation, and solve it in the limit of a deep lattice and weak laser driving. We find that the dipole interaction significantly changes the final temperature of the particles, increasing it for some phonon wavevectors and decreasing it for others. The total phonon energy over all modes is typically higher than in the non-interacting case, but can be made lower by the right choice of parameters

Seasonal and interannual variability of North American isoprene emissions as determined by formaldehyde column measurements from space

Formaldehyde (HCHO) columns measured from space by solar UV backscatter allow mapping of reactive hydrocarbon emissions. The principal contributor to these emissions during the growing season is the biogenic hydrocarbon isoprene, which is of great importance for driving regional and global tropospheric chemistry. We present seven years (1995-2001) of HCHO column data for North America from the Global Ozone Monitoring Experiment (GOME), and show that the general seasonal and interannual variability of these data is consistent with knowledge of isoprene emission. There are some significant regional discrepancies with the seasonal patterns predicted from current isoprene emission models, and we suggest that these may reflect flaws in the models. The interannual variability of HCHO columns observed by GOME appears to follow the interannual variability of surface temperature, as expected from current isoprene emission models

Surveyor landing radar test program review Final report

Test program evaluation and modifications for Surveyor radar altimeter and Doppler velocity sensor syste

Inadequate Translations: Spanish/English Discrepancies in the Translated Sonnets of Garcilaso de la Vega

The intimate relationship one develops with his or her native language is an experience which cannot be replicated through any amount of education. Diction, vocabulary, intonation and the connotations which accompany the many facets of language all develop along with us as we progress through life\u27s experiences. Because of this deeply ingrained personal understanding, each individual\u27s perspective towards a work of art, namely poetry, is completely unique to his or her experiences with the language in which it is written. Therefore, no amount of diligent translation can make a poem inhabit the same sentiment and effect in any language other than the one it was originally written in. This phenomenon will be explained in terms of several sonnets written by Garcilaso de la Vega. While the sonnets were originally written in Spanish, several translations into English will be explored in order to express the downfalls and limitations inherent in poetic translation

Lipschitz shadowing implies structural stability

We show that the Lipschitz shadowing property of a diffeomorphism is equivalent to structural stability. As a corollary, we show that an expansive diffeomorphism having the Lipschitz shadowing property is Anosov.Comment: 11 page