Fractal Dimensions of the Hydrodynamic Modes of Diffusion

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.Comment: 20 pages, 6 figures, submitted to Nonlinearit

The Fractality of the Hydrodynamic Modes of Diffusion

Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic modes is singular and fractal. We characterize them by their Hausdorff dimension which is given in terms of Ruelle's topological pressure. For long-wavelength modes, we derive a striking relation between the Hausdorff dimension, the diffusion coefficient, and the positive Lyapunov exponent of the system. This relation is tested numerically on two chaotic systems exhibiting diffusion, both periodic Lorentz gases, one with hard repulsive forces, the other with attractive, Yukawa forces. The agreement of the data with the theory is excellent

Simulator study of the effectiveness of an automatic control system designed to improve the high-angle-of-attack characteristics of a fighter airplane

A piloted, fixed-base simulation was conducted to study the effectiveness of some automatic control system features designed to improve the stability and control characteristics of fighter airplanes at high angles of attack. These features include an angle-of-attack limiter, a normal-acceleration limiter, an aileron-rudder interconnect, and a stability-axis yaw damper. The study was based on a current lightweight fighter prototype. The aerodynamic data used in the simulation were measured on a 0.15-scale model at low Reynolds number and low subsonic Mach number. The simulation was conducted on the Langley differential maneuvering simulator, and the evaluation involved representative combat maneuvering. Results of the investigation show the fully augmented airplane to be quite stable and maneuverable throughout the operational angle-of-attack range. The angle-of-attack/normal-acceleration limiting feature of the pitch control system is found to be a necessity to avoid angle-of-attack excursions at high angles of attack. The aileron-rudder interconnect system is shown to be very effective in making the airplane departure resistant while the stability-axis yaw damper provided improved high-angle-of-attack roll performance with a minimum of sideslip excursions

Control-system techniques for improved departure/spin resistance for fighter aircraft

Some fundamental information on control system effects on controllability of highly maneuverable aircraft at high angles of attack are summarized as well as techniques for enhancing fighter aircraft departure/spin resistance using control system design. The discussion includes: (1) a brief review of pertinent high angle of attack phenomena including aerodynamics, inertia coupling, and kinematic coupling; (2) effects of conventional stability augmentation systems at high angles of attack; (3) high angle of attack control system concepts designed to enhance departure/spin resistance; and (4) the outlook for applications of these concepts to future fighters, particularly those designs which incorporate relaxed static stability

Theory and Simulation of the diffusion of kinks on dislocations in bcc metals

Isolated kinks on thermally fluctuating (1/2) screw, edge and (1/2) edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin (FKL) model is able to reproduce the coarse grained data from MD at a fraction of the computational cost, without assuming an a priori temperature dependence beyond the fluctuation-dissipation theorem. Analytic results reveal that discreteness effects play an essential r\^ole in thermally activated dislocation glide, revealing the existence of a crucial intermediate length scale between molecular and dislocation dynamics. The model is used to investigate dislocation motion under the vanishingly small stress levels found in the evolution of dislocation microstructures in irradiated materials

Reallocation Problems in Scheduling

In traditional on-line problems, such as scheduling, requests arrive over time, demanding available resources. As each request arrives, some resources may have to be irrevocably committed to servicing that request. In many situations, however, it may be possible or even necessary to reallocate previously allocated resources in order to satisfy a new request. This reallocation has a cost. This paper shows how to service the requests while minimizing the reallocation cost. We focus on the classic problem of scheduling jobs on a multiprocessor system. Each unit-size job has a time window in which it can be executed. Jobs are dynamically added and removed from the system. We provide an algorithm that maintains a valid schedule, as long as a sufficiently feasible schedule exists. The algorithm reschedules only a total number of O(min{log^* n, log^* Delta}) jobs for each job that is inserted or deleted from the system, where n is the number of active jobs and Delta is the size of the largest window.Comment: 9 oages, 1 table; extended abstract version to appear in SPAA 201

Variations in solar wind fractionation as seen by ACE/SWICS over a solar cycle and the implications for Genesis Mission results

We use ACE/SWICS elemental composition data to compare the variations in solar wind fractionation as measured by SWICS during the last solar maximum (1999-2001), the solar minimum (2006-2009) and the period in which the Genesis spacecraft was collecting solar wind (late 2001 - early 2004). We differentiate our analysis in terms of solar wind regimes (i.e. originating from interstream or coronal hole flows, or coronal mass ejecta). Abundances are normalized to the low-FIP ion magnesium to uncover correlations that are not apparent when normalizing to high-FIP ions. We find that relative to magnesium, the other low-FIP elements are measurably fractionated, but the degree of fractionation does not vary significantly over the solar cycle. For the high-FIP ions, variation in fractionation over the solar cycle is significant: greatest for Ne/Mg and C/Mg, less so for O/Mg, and the least for He/Mg. When abundance ratios are examined as a function of solar wind speed, we find a strong correlation, with the remarkable observation that the degree of fractionation follows a mass-dependent trend. We discuss the implications for correcting the Genesis sample return results to photospheric abundances.Comment: Accepted for publication in Ap

Nitrification and oxygen consumption in northwest Atlantic deep-sea sediments

The importance of nitrification in the oxygen consumption by deep-sea sediments was investigated by modelling pore water nitrate profiles from 6 northwest Atlantic cores. Total nitrification and denitrification rates were calculated from the thickness of the nitrification layer, the nitrification rate at the sediment surface (N), the coefficient of exponential decrease of the nitrification rate (B), and the first-order rate constant for denitrification. The four unknowns were determined by best fit of the model to the nitrate profiles. The nitrate profile from the furthest offshore station indicated no denitrification, so that only N and B were determined. Nitrification rates ranged from 150 × 10−6 to 3.86 × 10−6 nmole NH4+ cm−2 s− at the 1850 m and the 5105 m stations, respectively. As the oxygen consumption by nitrification could account for 35% of the published total oxygen consumption at these stations, nitrification represented a significant aerobic reaction in these deep-sea sediments. Ammonium sources included an upward ammonium flux from deeper anaerobic strata (6%) and aerobic respiration of organic matter (56%) with the remainder presumably supplied by anaerobic respiration within the oxygenated strata (38%). Nitrogen budgets based on sediment traps indicated that nitrification and burial rates agreed within a factor of 2 of sediment trap organic nitrogen fluxes. Also, 70% of the nitrogen that was nitrified or buried was returned as nitrate to the water column

Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.