Relaxation Modes Research Articles

Excitation of the Secondary Modes by the Broad Spectrum Sound in a Liquid with Relaxation Losses

Features of nonlinear phenomena and, in particular, acoustic excitation of the entropy and relaxation modes in a liquid electrolyte with a chemical reaction are examined. The total range of frequencies of an exciter is considered, and the instantaneous dynamic equations are derived which govern perturbations in the secondary modes. The instantaneous leading-order acoustic forces of the secondary modes are evaluated. Examples of harmonic and nearly harmonic acoustic exciter are considered in detail. The difference in the nonlinear acoustic phenomena in an electrolyte and gases with relaxation mechanisms are specified and discussed.

Physical activity and sedentary behavior perceptions in overweight and obese adults: A systematic review of qualitative study.

One of the largest hazards to human health is obesity, which is intimately related to sedentarism and physical inactivity. Understanding the perspectives and attitudes of adults with overweight or obesity towards their lifestyle choices related to sedentary behavior and physical activity is essential for mitigating associated health risks. This systematic review aims to collate the extent of qualitative research on the perception of sedentary behavior and physical activity among adults with overweight and obesity. A comprehensive search of Scopus, PubMed, CINAHL, and Web of Science, databases was conducted, which yielded 2,881 articles. A total of 2591 abstracts were screened, and 45 full-text articles were examined. A total of nine qualitative studies involving adults with overweight or obesity (BMI > 25 kg/m 2) were included in this systematic review. Data extraction utilized Rayyan.qcri.org software, and studies were critically appraised using Joanna Briggs's Institute checklist for qualitative research. The included studies revealed a diverse array of themes, wherein a few perceived factors reported towards sedentary behavior were lack of awareness about the hazards, mode of relaxation, family commitment, technology use, motivation deficits, and fatigue. Barriers to physical activity encompassed social, cultural, and environmental factors. In contrast, peer support, fitness facility access, accountability, mental health awareness, well-being, and weight management facilitate physical activity involvement. Perceptions in overweight and obese adults on sedentary living and exercise are intricate and multifaceted. This review provides valuable insights that can inform clinicians and researchers in promoting regular physical activity for adults with overweight and obesity.

Intermediate scattering function for polymer molecules: An approach based on relaxation mode analysis.

The theory of polymer dynamics describes the intermediate scattering function for a polymer molecule in terms of relaxation modes defined by normal coordinates for the corresponding coarse-grained model. However, due to the difficulty of defining the normal coordinates for arbitrary polymer molecules, it is generally challenging to express the intermediate scattering function for a polymer molecule in terms of relaxation modes. To overcome this challenge, we propose a general method to calculate the intermediate scattering function for a polymer molecule on the basis of a relaxation mode analysis approach [Takano and Miyashita, J. Phys. Soc. Jpn. 64, 3688 (1995)]. In the proposed method, relaxation modes defined by eigenfunctions in a Markov process are evaluated on the basis of the simulation results for a polymer molecule and used to calculate the intermediate scattering function for that molecule. To demonstrate the effectiveness of the present method, we simulate the dynamics of a linear polymer molecule in a dilute solution and apply it to the calculation of the intermediate scattering function for the polymer molecule. The evaluation results regarding the relaxation modes reasonably describe the intermediate scattering function on the length scale of the radius of gyration of the polymer molecule. Accordingly, we examine the contributions of the pure relaxation and oscillatory relaxation processes to the entire intermediate scattering function.

Detecting Shape of Hybrid Polymer/Surfactant Micelles: Cryo-Transmission Electron Microscopy, Small-Angle Neutron Scattering and Dynamic Light Scattering Study

In-depth study of shape of hybrid micelles in the micellar solutions of anionic surfactant potassium oleate, containing hydrophobic polymer poly(4-vinylpyridine) (P4VP) was conducted via cryo-transmission electron microscopy (cryo-TEM), small-angle neutron scattering (SANS) and dynamic-light scattering of visible light (DLS). Direct visualization of the solutions with cryo-TEM evidenced the coexistence of polymer-free spherical micelles and branched rodlike hybrid micelles with mean length of 200 nm and radius of 2 nm, governed by contour length of solubilized P4VP and length of hydrophobic “tail” of potassium oleate, respectively. The formation of branches in the hybrid micelles was explained by attaching the thermodynamically unfavorable end-caps of micelles to their polymer-loaded cylindrical fragments. By SANS it was shown that the cylindrical local shape and the radius of the micelles are independent of the concentration of embedded P4VP. Relaxation processes in the solutions were investigated with DLS. Three relaxation modes were observed for hybrid micelles, similar to polymer-free wormlike micelles. Fast and medium relaxation modes were attributed to diffusion of entangled micellar chains and their segments, respectively. The slow mode was related to electrostatic repulsion between similarly charged hybrid micelles.

Spectroscopic and Thermographic Qualities of Praseodymium-Doped Oxyfluorotellurite Glasses.

The thermal stability of oxyfluorotellurite glass systems, (65-x)TeO2-20ZnF2-12PbO-3Nb2O5-xPr2O3, doped with praseodymium was examined. The different concentrations of praseodymium oxide (x = 0.5 and 2 mol%) were applied to verify the thermal, optical and luminescence properties of the materials under study. The relatively high values of the Dietzel (ΔT) and Saad-Poulain (S or H') thermal stability factors determined using a differential thermal analysis (DTA) indicate the good thermal stability of the glass matrix, which gradually improves with the content of the active dopant. The temperature dependence of optical spectra in the temperature range 300-675 K for the VIS-NIR region was investigated. The involved Pr3+ optical transition intensities and relaxation dynamic of the praseodymium luminescent level were determined. The ultrashort femtosecond pulses were utilized to examine a dynamic relaxation of the praseodymium luminescent levels. Although the measured emission of the Pr3+ active ions in the studied glass encompasses the quite broad spectral region, the observed luminescence may only be attributed to 3PJ excited states. As a result, the observed decrease in the experimental lifetime for the 3P0 level along with the increasing activator content was identified as an intensification of the Pr-Pr interplay and the associated self-quenching process. The maximum relative sensitivities (Sr) estimated over a relatively wide temperature range are ~0.46% K-1 (at 300 K) for FIR (I530/I497) and 0.20% K-1 (at 600 K) for FIR (I630/I497), which seems to confirm the possibility of using investigated glasses in optical temperature sensors.

Build-up and consolidation of an attractive network of particles in cement-based pastes

The very early age flocculation of a cement based paste, in which cement is partially substituted by a calcined clay, metakaolin, is studied. We use rheological and ultrasonic reflection to monitor the evolution of the elastic properties of the paste with time, and light scattering to follow the change of its relaxation modes at small scales. We show that, at very early ages, of the order of hundreds of seconds after the paste preparation, a network of flocculated particles establishes, which manifests by a slow down of the dynamics of the relaxation modes of the paste at small scale. Then, this network consolidates and the macroscopic elastic modulus of the paste progressively increases with time, leading eventually to the setting of the paste. These observations show that, whatever the degree of replacement of clinker by metakaolin, a connected network establishes at very early times after the paste preparation, although the kinetics of flocculation slows down with clinker replacement.

Direct computations of viscoelastic moduli of biomolecular condensates.

In vitro facsimiles of biomolecular condensates are formed by different types of intrinsically disordered proteins including prion-like low complexity domains (PLCDs). PLCD condensates are viscoelastic materials defined by time-dependent, sequence-specific complex shear moduli. Here, we show that viscoelastic moduli can be computed directly using a generalization of the Rouse model and information regarding intra- and inter-chain contacts that is extracted from equilibrium configurations of lattice-based Metropolis Monte Carlo (MMC) simulations. The key ingredient of the generalized Rouse model is the Zimm matrix that we compute from equilibrium MMC simulations. We compute two flavors of Zimm matrices, one referred to as the single-chain model that accounts only for intra-chain contacts, and the other referred to as a collective model, that accounts for inter-chain interactions. The single-chain model systematically overestimates the storage and loss moduli, whereas the collective model reproduces the measured moduli with greater fidelity. However, in the long time, low-frequency domain, a mixture of the two models proves to be most accurate. In line with the theory of Rouse, we find that a continuous distribution of relaxation times exists in condensates. The single crossover frequency between dominantly elastic versus dominantly viscous behaviors is influenced by the totality of the relaxation modes. Hence, our analysis suggests that viscoelastic fluid-like condensates are best described as generalized Maxwell fluids. Finally, we show that the complex shear moduli can be used to solve an inverse problem to obtain distributions of relaxation times that underlie the dynamics within condensates.

Linear and Nonlinear Electro-optic Response of MHPOCBC

This study investigated the linear and second-order electro-optic responses in chiral smectic liquid crystal 4-(1-methylheptyloxycarbonyl) phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). The result revealed a single Debye-type relaxation in the linear electro-optic frequency dispersion, with a relaxation frequency extending up to one hundred kHz. Conversely, the second-order electro-optic response exhibited intricate temperature-dependence, accurately depicted by a phenomenological Landau theory around the SmA–SmCa* phase transition point. Notably, in the SmCa* phase, critical slowing down of the amplitude mode occurred near the transition to the SmA phase, while at lower temperatures of the SmCa* phase, a distinct low-frequency relaxation mode emerged. Furthermore, the relaxation frequency of the antiferroelectric Goldstone mode in the SmCA* phase remained constant across the entire temperature range. These findings should significantly contribute to the understanding of dynamic behaviors in chiral smectic liquid crystals, shedding light on their complex phase transitions and electro-optic properties.

Correlations between shadow glass transition, enthalpy recovery and medium range order in a Pd40Ni40P20 bulk metallic glass

Two distinct enthalpic states were induced in a Pd40Ni40P20 bulk metallic glass through cyclic annealing at 473 K (0.81Tg) and 558 K (0.96Tg), targeting individual β or α relaxation modes, here referred to as the so-called shadow glass transition (SGT) and enthalpy recovery, respectively. Fluctuation electron microscopy (FEM) was employed to systematically investigate the medium-range order (MRO) within the amorphous structure in the post-annealed state and subsequent quenching after the SGT. Comparing the results with literature data from the same glass quenched from SCL samples, a significant increase in MRO was observed after annealing at 0.81Tg. Conversely, samples quenched directly after the SGT exhibit a reduced MRO, similar to those quenched from the supercooled liquid (SCL). These findings suggest a correlation between the SGT and a decrease in MRO within the glass, a phenomenon discussed in the context of underlying structural rearrangements associated with β relaxation, encompassing the SGT. Additionally, prolonged annealing at 0.96Tg led to glass separation in the material, with remixing observed as an endothermic transformation in the SCL. The origin of this transformation is discussed as either a potential liquid–liquid or glass–liquid transition and their connection to modifications in medium-range order.

Coupling structural, chemical composition and stress fluctuations with relaxation dynamics in metallic glasses

Understanding the atomistic mechanisms of relaxation dynamics in metallic glasses remains a longstanding challenge. Here, using microsecond time scale molecular dynamics simulations, three main relaxation stages in metallic glasses are identified. At about 0.6Tg, chemical composition plays a dominant role in the relaxation, manifested by stress accumulation and only minimal variations in structure. As Tg approaches, the confluence of structural heterogeneity and chemical composition leads to the decoupling of relaxation mechanisms. At this temperature, the relaxation results in a structure with a lower energy state and a lower level of stress. In the supercooled liquid regime, an extensive increase in the number of closed-packed icosahedral clusters is responsible for accelerated structural relaxation while their packing frustration leads to the accumulation of intrinsic residual stresses in the glass. The atomistic origin of these dynamic relaxation modes is discussed in terms of structural, chemical composition and stress variations.

On the linear viscoelastic behavior of semidilute polydisperse bubble suspensions in Newtonian media

In this work, we investigated the linear viscoelasticity of semidilute polydisperse bubble suspensions via small amplitude oscillatory shear (SAOS) tests performed in a rheo-optical setup. For all tested suspensions, the measured viscoelastic moduli (G′, G″) aligned with the theoretical predictions of the Jeffreys model for average dynamic capillary numbers (⟨Cd⟩) greater than unity. But at lower ⟨Cd⟩ values, experimental G′ values exceeded theoretical predictions. To investigate this, we considered the effects of suspension polydispersity and various SAOS measurement artifacts, including bubble rise, coalescence, and changes in suspension microstructure over time. Polydispersity could not cause the observed deviation, because the viscoelastic trends deviate from those of classic single-mode relaxation only for bimodal bubble size distributions with equal volume fractions of very small and very large bubbles; in any other case, the polydisperse suspension behaves as monodisperse with a bubble radius equal to the volume-weighted mean radius. Furthermore, bubble rise proved to play a minor role, while SAOS rheo-optical experiments revealed that bubble size and organization varied negligibly during our measurements. The G′ deviation at low ⟨Cd⟩ values was linked to bubble fluid dynamic interactions induced by the bubble spatial distribution. Image analysis showed that at low bubble volume fractions, stronger and prolonged preshearing reduces these interactions by increasing the average interbubble distance. But this effect is negligible in denser suspensions, which show similar G′ trends for any applied preshearing. Finally, a multimode Jeffreys model fitted to the experimental data showed that bubble interactions complicate the relaxation process, introducing multiple relaxation modes.

Unsupervised detection of large-scale weather patterns in the northern hemisphere via Markov State Modelling: from blockings to teleconnections

Detecting recurrent weather patterns and understanding the transitions between such regimes are key to advancing our knowledge of the low-frequency variability of the atmosphere and have important implications in terms of weather and climate-related risks. We adopt an analysis pipeline inspired by Markov State Modelling and detect in an unsupervised manner the dominant winter mid-latitude Northern Hemisphere weather patterns in the Atlantic and Pacific sectors. The daily 500 hPa geopotential height fields are first classified in about 200 microstates. The weather dynamics are then represented on the basis of these microstates and the slowest decaying modes are identified from the spectral properties of the transition probability matrix. These modes are defined on the basis of the nonlinear dynamical processes of the system and not as tentative metastable states, as often done in Markov state analysis. When focusing on a shifting longitudinal window of 60∘, we find that the longitude-dependent estimate of the longest relaxation time is smaller where stronger baroclinic activity is found. In the Atlantic and Pacific sectors slow relaxation processes are mainly related to transitions between blocked regimes and zonal flow. We also find strong evidence of a dynamical regime associated with the simultaneous Atlantic-Pacific blocking. When the analysis is performed on a broader geographical region of the Atlantic sector, we discover that the slowest relaxation modes of the system are associated with transitions between dynamical regimes that resemble teleconnection patterns like the North Atlantic Oscillation and weather regimes like the Scandinavian and Greenland blocking, yet have a much stronger dynamical foundation than classical methods based e.g. on EOF analysis. Our method clarifies that, as a result of the lack of a time-scale separation in the atmospheric variability of the mid-latitudes, there is no clear-cut way to represent the atmospheric dynamics in terms of few, well-defined modes of variability. The approach proposed here can be seamlessly applied across different regions of the globe for detecting regional modes of variability, and has a great potential for intercomparing climate models and for assessing the impact of climate change on the low-frequency variability of the atmosphere.

A sensitive Ag+-mediated magnetic relaxation and colorimetry dual-mode sensing platform

To address the relatively low sensitivity of current redox reagent-mediated magnetic relaxation sensing methods, we present a novel Ag+-mediated magnetic sensing platform that enhances the sensitivity by three orders of magnitude. The new sensing platform is based on Ag+-catalyzed oxidation of Mn2+ to KMnO4, accompanied by a distinct color change, which facilitates colorimetric detection. In the case of insufficient Ag+ ions, MnO2 is an additional oxidation product and the KMnO4/MnO2 ratio is dependent on the concentration of Ag+. When combined with a specific quantity of reducing agent, both KMnO4 and MnO2 are reduced to Mn2+ with a large relaxivity, and the concentration of Mn2+ in the resultant solution inversely correlates with the amount of KMnO4 since KMnO4 consumes more reductant during reduction. Consequently, the transverse relaxation rate of the solution exhibits a negative correlation with the Ag+ concentration. Thus, by coupling this Ag+-mediated Mn2+ to KMnO4 transformation with reactions that modulate Ag+ concentration, a dual-mode sensing platform for magnetic relaxation and colorimetry can be realized. Herein, we take H2O2 as an example to verify the detection performance of this sensing platform since H2O2 can oxidize Ag0 in Ag@Fe3O4 nanoparticles to Ag+. Experimental findings demonstrate detection limits of 10 nM and 20 nM for the magnetic relaxation and colorimetry modes, respectively, affirming the excellent sensitivity and the potential practical application of this strategy.

Structural and Computational Insights into Dynamics and Intermediate States of Orexin 2 Receptor Signaling.

Orexin 2 receptor (OX2R) is a G protein-coupled receptor (GPCR) whose activation is crucial to regulation of the sleep-wake cycle. Recently, inactive and active state structures were determined from X-ray crystallography and cryo-electron microscopy single particle analysis, and the activation mechanisms have been discussed based on these static data. GPCRs have multiscale intermediate states during activation, and insights into these dynamics and intermediate states may aid the precise control of intracellular signaling by ligands in drug discovery. Molecular dynamics (MD) simulations are used to investigate dynamics induced in response to thermal perturbations, such as structural fluctuations of main and side chains. In this study, we proposed collective motions of the TM domain during activation by performing 30 independent microsecond-scale MD simulations for various OX2R systems and applying relaxation mode analysis. The analysis results suggested that TM3 had a vertical structural movement relative to the membrane surface during activation. In addition, we extracted three characteristic amino acid residues on TM3, i.e., Q1343.32, V1423.40, and R1523.50, which exhibited large conformational fluctuations. We quantitatively evaluated the changes in their equilibrium during activation in relation to the movement of TM3. We also discuss the regulation of ligand binding recognition and intracellular signal selectivity by changes in the equilibrium of Q1343.32 and R1523.50, respectively, according to MD simulations and GPCR database. Additionally, the OX2R-Gi signaling complex is stabilized in the conformation resembling a non-canonical (NC) state, which was previously proposed as an intermediate state during activation of neurotensin 1 receptor. Insights into the dynamics and intermediate states during activation gained from this study may be useful for developing biased agonists for OX2R.

Generation of High-Lying Vibrational States in Carbon Dioxide through Coherent Ladder Climbing.

Mid-infrared laser excitation of molecules into high-lying vibrational states offers a novel route to realize controlled ground-state chemistry. Here we successfully demonstrate vibrational ladder climbing in the antisymmetric stretch of CO2 in the condensed phase by using intense down-chirped mid-infrared pulses. Spectrally resolved pump-probe measurements directly observe excited-state absorptions attributed to vibrational populations up to the v = 9 state, whose corresponding energy of 2.5 eV is 46% of the dissociation energy. By the use of global fitting analysis, important spectroscopic parameters in the high-lying vibrational states, such as transition frequencies and relaxation times, are quantitatively characterized. Remarkably, our analysis shows that 40% of the molecules are excited above the typical activation barriers in the metal-catalyzed CO2 conversions. These results not only demonstrate the promising ability of infrared excitation to produce elevated vibrational states but also represent a significant step toward accelerating CO2 conversions and other chemical processes via mode-specific vibrational excitation.

A photon source model for alpha-emitter radionuclides

Objective. A Monte Carlo virtual source model named PHID (photon from Ion decay) that generates photons emitted in the complex decay chain process of alpha-emitter radionuclides is proposed, typically for use during the simulation of SPECT image acquisition. Approach. Given an alpha-emitter radionuclide, the PHID model extracts from Geant4 databases the photon emission lines from all decaying daughters for both isometric transition and atomic relaxation processes. According to a given time range, abundances and activities in the decay chain are considered thanks to the Bateman equations, taking into account the decay rates and the initial abundances. Main results. PHID is evaluated by comparison with analog Monte Carlo simulation. It generates photons with the correct energy and temporal distribution, avoiding the costly simulation of the complete decay chain thus decreasing the computation time. The exact time gain depends on the simulation setup. As an example, it is 30× faster for simulating 1 MBq of 225Ac in water for 1 section Moreover, for 225Ac, PHID was also compared to a simplified source model with the two main photon emission lines (218 and 440 keV). PHID shows that 2 times more particles are simulated and 60% more counts are detected in the images. Significance. PHID can simulate any alpha-emitter radionuclide available in the Geant4 database. As a limitation, photons emitted from Bremsstrahlung are ignored, but they represent only 0.7% of the photons above 30 keV and are not significant for SPECT imaging. PHID is open-source, available in GATE 10, and eases the investigation of imaging photon emission from alpha emitters.

Transient crosslinking controls the condensate formation pathway within chromatin networks.

The network structure of densely packed chromatin within the nucleus of eukaryotic cells acts in concert with nonequilibrium processes. Using statistical physics simulations, we explore the control provided by transient crosslinking of the chromatin network by structural-maintenance-of-chromosome (SMC) proteins over (i) the physical properties of the chromatin network and (ii) condensate formation of embedded molecular species. We find that the density and lifetime of transient SMC crosslinks regulate structural relaxation modes and tune the sol-vs-gel state of the chromatin network, which imparts control over the kinetic pathway to condensate formation. Specifically, lower density, shorter-lived crosslinks induce sollike networks and a droplet-fusion pathway, whereas higher density, longer-lived crosslinks induce gellike networks and an Ostwald-ripening pathway.

Investigation of thermodynamical, electro-optical and dielectric properties of nematic liquid crystals dispersed with low-concentration barium titanate nanoparticles

ABSTRACT A liquid crystals nanoparticles composite was prepared by dispersing barium titanate nanoparticles (BT-NPs) into a multi-component liquid crystalline material having wide range room temperature nematic phase. The thermodynamic, optical textures, electro-optical and dielectric properties of the composite sample were studied along with pristine materials. Isotropic to nematic phase transition temperature was enhanced for nano-composites as observed from thermodynamic, optical textures and dielectric investigations. Effect of BT-NPs dispersion on various display parameters of nematic liquid crystals, namely, threshold voltage, dielectric anisotropy, DC conductivity and splay elastic constant has been explored. A relaxation mode in kHz frequency range has been observed for pure and nano-composites samples, which varies with temperature and follows Arrhenius behaviour. DC conductivity enhances approximately fivefold for BT-NPs dispersed samples. The host liquid crystalline material has nematic ordering which supports alignment of BT-NPs parallel to the nematic director which consequently improves thermal stability, dielectric and electro-optical parameters of the nano-composite system.

IR absorption band of weak H-Bonded systems: Showcasing the signature of the quantum indirect damping within the framework of a new approach using non-Hermitean Hamiltonian formalism

Herein, we investigate the effects of the irreversible action of the medium on the theoretical elucidation of the IR spectrum of weakly H-bonded systems, a prototypical model which provides a rigorous treatment of the relaxation mechanisms impacts on the IR spectral density. The attention will be focused particularly on the effect of indirect damping on the IRυS(X−H⃗) spectrum beyond the harmonic and adiabatic approximations. The ultimate objective of the present investigation is the treatment of the action of the surrounding of the intermonomer modes of H-bonded systems, which must induce a broadening of the Dirac delta peaks, the nature of which, as shown by Maréchal and Witkowski theory, is a Franck–Condon progression. The quantum treatment of the IR absorption band reveals that quantum relaxation of the intermonomer mode of H-bonded complexes could be successfully approached by a non-Hermitian Hamiltonian formalism. Motivated by development of a second method that will be able to validate the first approach, a computationally efficient algorithm was proposed for elucidating the quantum indirect relaxation using Hermitean Hamiltonians. The real eigenvalues, corresponding to different energies of the system are considered to be complex by adjunction of the imaginary parts, which reflects the action of the indirect irreversible action of the medium. These two crude approaches may pave the way for the incorporation of the mechanism of indirect relaxation in more physical and complex situations dealing, particularly, with tunnelling effects in strong H-bonded species, Fermi resonances, and Davydov coupling for cyclic H-bonds dimers beyond the harmonic and adiabatic assumptions.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C′ CSA-13C′-13Cα DD CCR rate ΓzC′/C′Cα and present a novel 3D version of the transverse ΓxyC′/C′Cα CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.