Down Of Dynamics Research Articles

Effective detection of early warning signal with power spectrum in climate change system

The development of early warning signals (EWS) before abrupt changes can help prevent system collapse. Current EWS, such as increasing autocorrelation (AC) and variance, provide general indicators of impending tipping points by detecting the slowing down of dynamics near transitions. However, these conventional EWS often fail to distinguish between oscillatory behavior (e.g., Hopf bifurcation) and shifts to a distant attractor (e.g., Fold bifurcation). Additionally, traditional EWS are less reliable in systems affected by density-dependent noise. To address these limitations, alternative EWS based on power spectrum analysis, known as spectral EWS, have been proposed. In this study, we apply analytical approximations for EWS as systems approach different types of local bifurcations. This novel method allows us to use spectral EWS that offer enhanced sensitivity to approaching transitions and increased robustness to density-dependent noise. We demonstrate the application of spectral EWS as robust indicators across three general models with different bifurcations. Our analysis also reveals distinct signals preceding transitions in data from sea ice loss. This combined approach underscores the advantages of incorporating spectral EWS into existing methodologies, providing a more comprehensive toolkit for anticipating critical transitions in real-world systems.

Cooperatively rearranging regions change shape near the mode-coupling crossover for colloidal liquids on a sphere

The structure and dynamics of liquids on curved surfaces are often studied through the lens of frustration-based approaches to the glass transition. Competing glass transition theories, however, remain largely untested on such surfaces and moreover, studies hitherto have been entirely theoretical/numerical. Here we carry out single particle-resolved imaging of dynamics of bi-disperse colloidal liquids confined to the surface of a sphere. We find that mode-coupling theory well captures the slowing down of dynamics in the moderate to deeply supercooled regime. Strikingly, the morphology of cooperatively rearranging regions changed from string-like to compact near the mode-coupling crossover—a prediction unique to the random first-order theory of glasses. Further, we find that in the limit of strong curvature, Mermin–Wagner long-wavelength fluctuations are irrelevant and liquids on a sphere behave like three-dimensional liquids. A comparative evaluation of competing mechanisms is thus an essential step towards uncovering the true nature of the glass transition.

Lead–Oxygen Bond Length Distributions of the Relaxor Ferroelectric 0.67PbMg1/3Nb2/3O3–0.33PbTiO3 from 207Pb Nuclear Magnetic Resonance

We investigate changes in the local environment of 207Pb sites in the relaxor ferroelectric 0.67PbMg1/3Nb2/3O3–0.33PbTiO3 using variable temperature magic angle spinning nuclear magnetic resonance. We observe a Gaussian distribution of 207Pb chemical shifts with a mean chemical shift of −1469 ± 8 ppm and a standard deviation of 229 ± 8 ppm at 306 K and a mean chemical shift of −1410 ± 1 ppm and a standard deviation of 275 ± 1 ppm at 117 K. This corresponds to a decrease in the mean Pb–O bond length and a concurrent decrease in the effective coordination number from 6 to 5.8. An observed change in the asymmetry parameter from 0.4 to 0.8 for deshielded sites as well as a change in the shielding anisotropy of 300 ppm compared to 180 ppm for the more shielded resonances, indicating that the lead sites experience a more asymmetric environment at low temperature. Our observations support the unique direction model for Pb2+ ion displacements, in line with similar relaxor ferroelectric systems near room temperature. Multifield T1 relaxation behavior observed between 9.4 and 21.1 T is indicative of a slowing down of dynamics around 200 K, and appears to be determined by spin-rotation fluctuations at high temperatures and a magnetic-field-dependent relaxation pathway at low temperatures.

Mechanical relaxation and freezing in the room temperature strain glass alloy Ti50(Pd40Cr10)

The alloy Ti50(Pd40Cr10) undergoes a strain glass transition around room temperature evidenced by frequency dispersion of dynamic mechanical properties and lack of average structure change from that of the high symmetry austenite phase. However, since the strain glass transition is not a thermodynamic phase transition but a dynamic freezing process governed by the kinetics, a quantitative characterization of the slowing down of dynamics during the strain glass transition is still lacking. In the present study, the probability distribution function (PDF) of the relaxation time of the strain glass alloy is investigated spanning the whole transition temperature range (253 K–313 K). The slowing down of dynamics of the strain glass is indicated by the rapid increase of the characteristic relaxation time () upon cooling. The , as a function of temperature, shows a transition from Vogel–Fulcher relationship to an Arrhenius relationship. Such a change suggests two fundamentally different states: unfrozen strain glass state and frozen strain glass state. Furthermore, the spread of the PDF is connected to the fraction of quasi-static nanodomains, which helps the understanding of the dynamic freezing process in the strain glass.

Power law relationship between diffusion coefficients in multi-component glass forming liquids.

The slow down of dynamics in glass forming liquids as the glass transition is approached has been characterised through the Adam-Gibbs relation, which relates relaxation time scales to the configurational entropy. The Adam-Gibbs relation cannot apply simultaneously to all relaxation times scales unless they are coupled, and exhibit closely related temperature dependences. The breakdown of the Stokes-Einstein relation presents an interesting situation to the contrary, and in analysing it, it has recently been shown that the Adam-Gibbs relation applies to diffusion coefficients rather than to viscosity or structural relaxation times related to the decay of density fluctuations. However, for multi-component liquids --the typical cases considered in computer simulations, metallic glass formers, etc.-- such a statement raises the question of which diffusion coefficient is described by the Adam-Gibbs relation. All diffusion coefficients can be consistently described by the Adam-Gibbs relation if they bear a power law relationship with each other. Remarkably, we find that for a wide range of glass formers, and for a wide range of temperatures spanning the normal and the slow relaxation regimes, such a relationship holds. We briefly discuss possible rationalisations of the observed behaviour.

A characteristic energy scale in glasses.

Intrinsically generated structural disorder endows glassy materials with a broad distribution of various microscopic quantities-such as relaxation times and activation energies-without an obvious characteristic scale. At the same time, macroscopic glassy responses-such as Newtonian (linear) viscosity and nonlinear plastic deformation-are widely interpreted in terms of a characteristic energy scale, e.g., an effective temperature-dependent activation energy in Arrhenius relations. Nevertheless, despite its fundamental importance, such a characteristic energy scale has not been robustly identified. Inspired by the accumulated evidence regarding the crucial role played by disorder- and frustration-induced soft quasilocalized excitations in determining the properties and dynamics of glasses, we propose that the bulk average of the glass response to a localized force dipole defines such a characteristic energy scale. We show that this characteristic glassy energy scale features remarkable properties: (i) It increases dramatically in underlying inherent structures of equilibrium supercooled states approaching the glass transition temperature Tg, significantly surpassing the corresponding increase in the macroscopic shear modulus, dismissing the common view that structural variations in supercooled liquids upon vitrification are minute. (ii) Its variation with annealing and system size is very similar in magnitude and form to that of the energy of the softest non-phononic vibrational mode, thus establishing a nontrivial relation between a rare glassy fluctuation and a bulk average response. (iii) It exhibits striking dependence on spatial dimensionality and system size due to the long-ranged fields associated with quasilocalization, which are speculated to be related to peculiarities of the glass transition in two dimensions. In addition, we identify a truly static growing lengthscale associated with the characteristic glassy energy scale and discuss possible connections between the increase of this energy scale and the slowing down of dynamics near the glass transition temperature. Open questions and future directions are discussed.

Slow relaxation in structure-forming ferrofluids

We study the behavior of colloidal magnetic fluids at low density for various dipolar interaction strengths by performing extensive Langevin dynamics simulations with model parameters that mimic cobalt-based ferrofluids used in experiments. Our study mainly focuses on the structural and dynamical properties of dipolar fluids and the influence of structural changes on their dynamics. Drastic changes from chainlike to networklike structures in the absence of an external magnetic field are observed. This crossover plays an important role in the slowing down of dynamics that is reflected in various dynamical properties including the tracer diffusion and the viscosity and also in the structural relaxation.

Hydration dynamics of protein molecules in aqueous solution: Unity among diversity#

Dielectric dispersion and NMRD experiments have revealed that a significant fraction of water molecules in the hydration shell of various proteins do not exhibit any slowing down of dynamics. This is usually attributed to the presence of the hydrophobic residues (HBR) on the surface, although HBRs alone cannot account for the large amplitude of the fast component. Solvation dynamics experiments and also computer simulation studies, on the other hand, repeatedly observed the presence of a non-negligible slow component. Here we show, by considering three well-known proteins (lysozyme, myoglobin and adelynate kinase), that the fast component arises partly from the response of those water molecules that are hydrogen bonded with the backbone oxygen (BBO) atoms. These are structurally and energetically less stable than those with the side chain oxygen (SCO) atoms. In addition, the electrostatic interaction energy distribution (EIED) of individual water molecules (hydrogen bonded to SCO) with side chain oxygen atoms shows a surprising two peak character with the lower energy peak almost coincident with the energy distribution of water hydrogen bonded to backbone oxygen atoms (BBO). This two peak contribution appears to be quite general as we find it for lysozyme, myoglobin and adenylate kinase (ADK). The sharp peak of EIED at small energy (at less than 2 k B T) for the BBO atoms, together with the first peak of EIED of SCO and the HBRs on the protein surface, explain why a large fraction (~ 80%) of water in the protein hydration layer remains almost as mobile as bulk water. Significant slowness arises only from the hydrogen bonds that populate the second peak of EIED at larger energy (at about 4 kBT). Thus, if we consider hydrogen bond interaction alone, only 15–20% of water molecules in the protein hydration layer can exhibit slow dynamics, resulting in an average relaxation time of about 5–10 ps. The latter estimate assumes a time constant of 20–100 ps for the slow component. Interestingly, relaxation of water molecules hydrogen bonded to back bone oxygen exhibit an initial component faster than the bulk, suggesting that hydrogen bonding of these water molecules remains frustrated. This explanation of the heterogeneous and non-exponential dynamics of water in the hydration layer is quantitatively consistent with all the available experimental results, and provides unification among diverse features. This study reveals a bimodal electrostatic energy distribution of protein–water hydrogen bonds involving side chain oxygen and faster than bulk water hydrogen bond breaking dynamics of protein–water hydrogen bond involving backbone oxygen.

Roles of icosahedral and crystal-like order in the hard spheres glass transition

A link between structural ordering and slow dynamics has recently attracted much attention from the context of the origin of glassy slow dynamics. Candidates for such structural order are icosahedral, exotic amorphous and crystal-like. Each type of order is linked to a different scenario of glass transition. Here we experimentally access local structural order in polydisperse hard spheres by particle-level confocal microscopy. We identify the key structures as icosahedral and FCC-like order, both statistically associated with slow particles. However, when approaching the glass transition, the icosahedral order does not grow in size, whereas crystal-like order grows. It is the latter that governs the dynamics and is linked to dynamic heterogeneity. This questions the direct role of the local icosahedral ordering in glassy slow dynamics and suggests that the growing length scale of structural order is essential for the slowing down of dynamics and the non-local cooperativity in particle motion.

Suppression of the rate of growth of dynamic heterogeneities and its relation to the local structure in a supercooled polydisperse liquid

The relationship between the microscopic arrangement of molecules in a supercooled liquid and its slow dynamics at low temperature near glass transition is studied by molecular dynamics simulations. A Lennard-Jones liquid with polydispersity in size and mass of constituent particles is chosen as the model system. Our studies reveal that the local structure (that varies with polydispersity) plays a crucial role both in the slowing down of dynamics and in the growth of the dynamic heterogeneities, besides determining the glass forming ability of the system. Increasing polydispersity at fixed volume fraction is found to suppress the rate of growth of dynamic correlations, as detected by the growth in the peak of the nonlinear density response function, chi4(t). The growth in dynamical correlation is manifested in a stronger than usual breakdown of Stokes-Einstein relation at lower polydispersity at low temperatures and also leads to a decrease in the fragility of the system with polydispersity. We show that the suppression of the rate of growth of the dynamic heterogeneity can be attributed to the loss of structural correlations (as measured by the structure factor and the local bond orientational order) with polydispersity. While a critical polydispersity is required to avoid crystallization, we find that a further increase in polydispersity lowers the glass forming ability.

What does the potential energy landscape tell us about the dynamics of supercooled liquids and glasses?

For a model glass former we demonstrate via computer simulations how macroscopic dynamic quantities can be inferred from a potential energy landscape (PEL) analysis. The essential step is to consider whole superstructures of many PEL minima, called metabasins, rather than single minima. We show that two types of metabasins exist: some allowing for quasifree motion on the PEL (liquidlike), and the others acting as traps (solidlike). The activated, multistep escapes from the latter metabasins are found to dictate the slowing down of dynamics upon cooling over a much broader temperature range than is currently assumed.

Phase space geometry and slow dynamics

We describe a non-Arrhenius mechanism for the slowing down of dynamics that is inherent to the high dimensionality of the phase space. We show that such a mechanism is at work both in a family of mean-field spin-glass models without any domain structure and in the case of ferromagnetic domain growth. The marginality of spin-glass dynamics, as well as the existence of a `quasi-equilibrium regime' can be understood within this scenario. We discuss the question of ergodicity in an out-of equilibrium situation.