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All sourcesNASA NTRSDOE OSTI
NASA NTRS2007

Multiyear On-orbit Calibration and Performance of Terra MODIS Thermal Emissive Bands

Since launch in December 1999, Terra MODIS has been making continuous Earth observations for more than seven years. It has produced a broad range of land, ocean, and atmospheric science data products for improvements in studies of global climate and environmental change. Among its 36 spectral bands, there are 20 reflective solar bands (RSB) and 16 thermal emissive bands (TEB). MODIS thermal emissive bands cover the mid-wave infrared (MWIR) and long-wave infrared (LWIR) spectral regions with wavelengths from 3.7 to 14.4pm. They are calibrated on-orbit using an on-board blackbody (BB) with its temperature measured by a set of thermistors on a scan-by-scan basis. This paper will provide a brief overview of MODIS TEB calibration and characterization methodologies and illustrate on-board BB functions and TEB performance over more than seven years of on-orbit operation and calibration. Discussions will be focused on TEB detector short-term stability and noise characterization, and changes in long-term response (or system gain). Results show that Terra MODIS BB operation has been extremely stable since launch. When operated at its nominal controlled temperature of 290K, the BB temperature variation is typically less than +0.30mK on a scan-by-scan basis and there has been no time-dependent temperature drift. In addition to excellent short-term stability, most TEB detectors continue to meet or exceed their specified noise characterization requirements, thus enabling calibration accuracy and science data product quality to be maintained. Excluding the noisy detectors identified pre-launch and those that occurred post-launch, the changes in TEB responses have been less than 0.7% on an annual basis. The optical leak corrections applied to bands 32-36 have been effective and stable over the entire mission

Xiong, Xiaoxiong↗
NASA NTRS2019

The Magnetosphere Ionosphere Electron Precipitation Dynamics and Their Geospace Consequences During the 17 March 2013 Storm

During geomagnetic storms and substorms, the magnetosphere and ionosphere are strongly coupled by precipitating magnetospheric electrons from the Earth's plasma sheet and driven by both magnetospheric and ionospheric processes. Magnetospheric wave activity initiates electron precipitation, and the ionosphere and upper atmosphere further facilitate this process by enhancing the value of precipitated energy uxes via connection of two magnetically conjugate regions and multiple atmospheric reections. This paper focuses on the resulting electron energy uxes and afliated heightintegrated Pedersen and Hall conductances in the auroral regions produced by multiple atmospheric reections during the 17 March 2013 geomagnetic storm and their effects on the inner magnetospheric electric eld and ring current. Our study is based on the magnetically and electrically selfconsistent Rice ConvectionModelEquilibrium of the inner magnetosphere with SuperThermal Electron Transport modied electron energy uxes that take into account the electron energy interplay between the two magnetically conjugate ionospheres. SuperThermal Electron Transportmodied energy ux in the Rice ConvectionModelEquilibrium leads to a signicant difference in the global conductance pattern, ionospheric electric eld formation, Birkeland current structure, ring current energization and its energy content, subauroral polarization drifts intensications and their spatial locations, interchange instability redistribution, and overall energy interplay on the global scale.

Khazanov, George V.↗
NASA NTRS1993

Nonlinear analysis of generalized cross-field current instability

Analysis of the generalized cross-field current instability is carried out in which cross-field drift of both the ions and electrons and their temperatures are permitted to vary in time. The unstable mode under consideration is the electromagnetic generalization of the classical modified-two-stream instability. The generalized instability is made of the modified-two-stream and ion-Weibel modes. The relative importance of the features associated with the ion-Weibel mode and those of the modified-two-stream mode is assessed. Specific applications are made to the Earth's neutral sheet prior to substorm onset and to the Earth's bow shock. The numerical solution indicates that the ion-Weibel mode dominates in the Earth's neutral sheet environment. In contrast, the situation for the bow shock is dominated by the modified-two-stream mode. Notable differences are found between the present calculation and previous results on ion-Weibel mode which restrict the analysis to only parallel propagating waves. However, in the case of Earth's bow shock for which the ion-Weibel mode plays no important role, the inclusion of the electromagnetic ion response is found to differ little from the previous results which treats ions responding only to the electrostatic component of the excited waves.

Yoon, Peter H.↗
NASA NTRS1990

Microgravity acoustic mixing for particle cloud combustors

Experimental and theoretical investigations of acoustic mixing procedures designed to uniformly distribute fuel particles in a combustion tube for application in the proposed Particle Cloud Combustion Experiment (PCCE) are described. Two acoustic mixing methods are investigated: mixing in a cylindrical tube using high frequency spinning modes generated by suitably phased, or quadrature speakers, and acoustic premixing in a sphere. Quadrature mixing leads to rapid circumferential circulation of the powder around the tube. Good mixing is observed in the circulating regions. However, because axial inhomogeneities are necessarily present in the acoustic field, this circulation does not extend throughout the tube. Simultaneous operation of the quadrature-speaker set and the axial-speaker was observed to produce considerably enhanced mixing compared to operation of the quadrature-speaker set alone. Mixing experiments using both types of speakers were free of the longitudinal powder drift observed using axial-speakers alone. Vigorous powder mixing was obtained in the sphere for many normal modes: however, in no case was the powder observed to fill the sphere entirely. Theoretical analysis indicated that mixing under steady conditions cannot fill more than a hemisphere except under very unusual conditions. Premixing in a hemisphere may be satisfactory; otherwise, complete mixing in microgravity might be possible by operating the speaker in short bursts. A general conclusion is that acoustic transients are more likely to produce good mixing than steady state conditions. The reason is that in steady conditions, flow structures like nodal planes are possible and often even unavoidable. These tend to separate the mixing region into cells across which powder cannot be transferred. In contrast, transients not only are free of such structures, they also have the characteristics, desirable for mixing, of randomness and disorder. This conclusion is corroborated by mixing experiments using axial waves.

Pla, Frederic↗
NASA NTRS2018

Numerical Studies of Hall Thruster Acceleration Region Electron Transport

Azimuthal direction 1-D and azimuthal and axial direction 2-D Particle in Cell (PIC) simulations of the Hall thruster acceleration and near-plume regions are presented. The axial extent of the 2-D computational domain is based on the ExB drift parameter, 𝑫𝑬𝒙𝑩, the number of times around the channel an electron ExB drifts before being scattered. With only high energy main beam ions, the simulations produced a broad potential profile in the acceleration region. The addition of a small amount of ionization in the acceleration domain at a rate consistent with Hall thruster parameters causes the potential profile to develop two distinct regions. In the upstream portion of the computational domain, the potential profile is very steep, typical of Hall thruster acceleration regions. In the downstream portion, the potential profile is almost flat, like potentials in Hall thruster near plume regions. This bifurcation happens naturally; there is no other change in code parameters between the two results. Without the addition of a small amount of ionization in the acceleration region, the axial electron transport is very low. With ionization, the calculated ratio of electron current to ion current is the same order of those measured in Hall thrusters. This suggests that in regions with lower energy electrons and ions, plasma waves are effective in allowing crossfield transport, and axial electric fields are small. In the acceleration region, the plasma waves are less effective at scattering the energetic electrons, and high axial electric fields are needed to produce the observed cross-field electron transport.

Ortega, Alejandro Lopez↗
NASA NTRS1998

Direction-Finding Measurements of Heliospheric 2-3 kHz Radio Emissions

Using data from the Voyager 1 plasma wave instrument, a series of direction-finding measurements is presented for the intense 1992-93 heliospheric 2- to 3-kHz radio emission event, and several weaker events extending into 1994. Direction-finding measurements can only be obtained during roll maneuvers, which are performed about once every three months. Two parameters can be determined from the roll-induced intensity modulation, the azimuthal direction of arrival (measured around the roll axis), and the modulation index (the peak-to-peak amplitude divided by the peak amplitude). Measurements were made at two frequencies, 1.78 and 3.11 kHz. No roll modulation was observed at 1.78 kHz, which is consistent with an isotropic source at this frequency. In most cases an easily measurable roll modulation was detectable at 3.11 kHz. Although the azimuth angles have considerable scatter, the directions of arrival at 3.11 kHz can be organized into three groups, each of which appears to be associated with a separate upward drifting feature in the radio emission spectrum. The first group, which is associated with the main 1992-93 event, is consistent with a source located near the nose of the heliosphere. The remaining two groups, which occur after the main 1992-93 event, have azimuth angles well away from the nose of the heliosphere. The modulation indexes vary over a large range, from 0.06 to 0.61, with no obvious trend. Although the variations in the directions of arrival and modulation indicies appear to reflect changes in the position and angular size of the source, it is also possible that they could be caused by refraction or scattering due to density structures in the solar wind.

Gurnett, Donald A.↗
NASA NTRS2008

High-Voltage, Asymmetric-Waveform Generator

The shapes of waveforms generated by commercially available analytical separation devices, such as some types of mass spectrometers and differential mobility spectrometers are, in general, inadequate and result in resolution degradation in output spectra. A waveform generator was designed that would be able to circumvent these shortcomings. It is capable of generating an asymmetric waveform, having a peak amplitude as large as 2 kV and frequency of several megahertz, which can be applied to a capacitive load. In the original intended application, the capacitive load would consist of the drift plates in a differential-mobility spectrometer. The main advantage to be gained by developing the proposed generator is that the shape of the waveform is made nearly optimum for various analytical devices requiring asymmetric-waveform such as differential-mobility spectrometers. In addition, this waveform generator could easily be adjusted to modify the waveform in accordance with changed operational requirements for differential-mobility spectrometers. The capacitive nature of the load is an important consideration in the design of the proposed waveform generator. For example, the design provision for shaping the output waveform is based partly on the principle that (1) the potential (V) on a capacitor is given by V=q/C, where C is the capacitance and q is the charge stored in the capacitor; and, hence (2) the rate of increase or decrease of the potential is similarly proportional to the charging or discharging current. The proposed waveform generator would comprise four functional blocks: a sine-wave generator, a buffer, a voltage shifter, and a high-voltage switch (see Figure 1). The sine-wave generator would include a pair of operational amplifiers in a feedback configuration, the parameters of which would be chosen to obtain a sinusoidal timing signal of the desired frequency. The buffer would introduce a slight delay (approximately equal to 20 ns) but would otherwise leave the fundamental timing signal unchanged. The buffered timing signal would be fed as input to the level shifter. The output of the level shifter would serve as a timing and control signal for the high-voltage switch, causing the switch to alternately be (1) opened, allowing the capacitive load to be charged from a high-voltage DC power supply; then (2) closed to discharge the capacitive load to ground. Hence, the output waveform would closely approximate a series of exponential charging and discharging curves (see Figure 2).

Beegle, Luther W.↗
NASA NTRS2014

Visualizing Flutter Mechanism as Traveling Wave Through Animation of Simulation Results for the Semi-Span Super-Sonic Transport Wind-Tunnel Model

It has long been recognized that frequency and phasing of structural modes in the presence of airflow play a fundamental role in the occurrence of flutter. Animation of simulation results for the long, slender Semi-Span Super-Sonic Transport (S4T) wind-tunnel model demonstrates that, for the case of mass-ballasted nacelles, the flutter mode can be described as a traveling wave propagating downstream. Such a characterization provides certain insights, such as (1) describing the means by which energy is transferred from the airflow to the structure, (2) identifying airspeed as an upper limit for speed of wave propagation, (3) providing an interpretation for a companion mode that coalesces in frequency with the flutter mode but becomes very well damped, (4) providing an explanation for bursts of response to uniform turbulence, and (5) providing an explanation for loss of low frequency (lead) phase margin with increases in dynamic pressure (at constant Mach number) for feedback systems that use sensors located upstream from active control surfaces. Results from simulation animation, simplified modeling, and wind-tunnel testing are presented for comparison. The simulation animation was generated using double time-integration in Simulink of vertical accelerometer signals distributed over wing and fuselage, along with time histories for actuated control surfaces. Crossing points for a zero-elevation reference plane were tracked along a network of lines connecting the accelerometer locations. Accelerometer signals were used in preference to modal displacement state variables in anticipation that the technique could be used to animate motion of the actual wind-tunnel model using data acquired during testing. Double integration of wind-tunnel accelerometer signals introduced severe drift even with removal of both position and rate biases such that the technique does not currently work. Using wind-tunnel data to drive a Kalman filter based upon fitting coefficients to analytical mode shapes might provide a better means to animate the wind tunnel data.

Christhilf, David M.↗
NASA NTRS2002

Magnetic Fluctuations in the Jovian Magnetosphere

The engine that drives the jovian magnetosphere is the mass added to the Io ion torus, accelerated to corotational velocities by field-aligned currents that couple the Io torus to the jovian ionosphere. The mass of the torus builds up to an amount that the magnetic forces cannot contain and the plasma, first slowly and then more rapidly, drifts outward. Numerous authors have treated this problem based first on the observations of the Pioneer 10 and 11 flybys; then on Voyager 1 and 2, and Ulysses; and finally most recently the Galileo orbiter. The initial observations revealed the now familiar magnetodisk, in which the field above and below the magnetic equator became quite radial in orientation and much less dipolar. The Galileo observations show this transformation to occur on average at 24 R(sub J) and to often be quite abrupt. These observations are consistent with outward transport of magnetized plasma that moves ever faster radially until about 50 R(sub J) on the nightside where the field lines stretch to the breaking point, reconnection occurs, and plasma and field islands are transported down the tail ultimately removing the mass from the magnetosphere that Io had deposited deep in the inner torus. The reconnection process creates empty flux tubes connected to Jupiter that are buoyant and thought to float inward and replace the flux carried out with the torus plasma. As described above, the jovian magnetosphere could very well be in a state of steady laminar circulation, but indeed it is not. The process is very unsteady and the wave levels can be very intense. The existence of these waves in turn can lead to processes that compete with the radial circulation pattern in removing plasma from the system. These waves can scatter particles so that they precipitate into the ionosphere. This process should be important in the Io torus where the atmospheric loss cone is relatively large and becomes less important as the loss cone decreases in size with radial distance. However, the Io torus is relatively quiet compared to the region outside the torus and it is not obvious without studying this scattering carefully whether the loss in the torus or out of the torus is greater and whether it can act rapidly enough to compete with the radial transport of ions to the tail in the life cycle of the mass added at Io. Closer to Io the ion cyclotron waves are most intense and possibly are associated with the losses in the Io flux tube. The waves are also diagnostic of both the Io atmospheric composition and the size and strength of the massloading process.

Russell, Christopher T.↗
NASA NTRS2009

MODIS On-Board Blackbody Function and Performance

Two MODIS instruments are currently in orbit, making continuous global observations in visible to long-wave infrared wavelengths. Compared to heritage sensors, MODIS was built with an advanced set of on-board calibrators, providing sensor radiometric, spectral, and spatial calibration and characterization during on-orbit operation. For the thermal emissive bands (TEB) with wavelengths from 3.7 m to 14.4 m, a v-grooved blackbody (BB) is used as the primary calibration source. The BB temperature is accurately measured each scan (1.47s) using a set of 12 temperature sensors traceable to NIST temperature standards. The onboard BB is nominally operated at a fixed temperature, 290K for Terra MODIS and 285K for Aqua MODIS, to compute the TEB linear calibration coefficients. Periodically, its temperature is varied from 270K (instrument ambient) to 315K in order to evaluate and update the nonlinear calibration coefficients. This paper describes MODIS on-board BB functions with emphasis on on-orbit operation and performance. It examines the BB temperature uncertainties under different operational conditions and their impact on TEB calibration and data product quality. The temperature uniformity of the BB is also evaluated using TEB detector responses at different operating temperatures. On-orbit results demonstrate excellent short-term and long-term stability for both the Terra and Aqua MODIS on-board BB. The on-orbit BB temperature uncertainty is estimated to be 10mK for Terra MODIS at 290K and 5mK for Aqua MODIS at 285K, thus meeting the TEB design specifications. In addition, there has been no measurable BB temperature drift over the entire mission of both Terra and Aqua MODIS.

Xiaoxiong, Xiong↗
NASA NTRS2006

TRMM On-Orbit Performance Re-Accessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an HI1 rocket on November 27,1997 and transitioned in August, 2001 from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with '/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees. After the boost, onboard ephemeris errors had a direct effect on the pitch pointing, being used to compute the Earth pointing reference frame. Improvements after the orbit boost have kept the the onboard ephemeris errors generally below 20 kilometers. Ephemeris errors have secondary effects on roll and yaw, especially during high beta angle when pitch effects can couple into roll and yaw. This is illustrated in figure 3. The onboard roll bias trends as measured by PR data show correlations with the Kalman filter's gyro bias error. This particularly shows up after yaw turns (every 2 to 4 weeks) as shown in Figure 3, when a slight roll bias is observed while the onboard computed gyro biases settle to new values. As for longer term trends, the PR data shows that the roll bias was influenced by Earth horizon radiance effects prior to the boost, changing values at yaw turns, and indicated a long term drift as shown in Figure 4. After the boost, the bias variations were smaller and showed some possible correlation with solar beta angle, probably due to sun sensor misalignment effects.

Bilanow, Steve↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗