Simple Exponential Relaxation Research Articles

Nanoscale Critical Phenomena in a Complex Fluid Studied by X-Ray Photon Correlation Spectroscopy.

The advent of high-speed x-ray photon correlation spectroscopy now allows the study of critical phenomena in fluids to much smaller length scales and over a wider range of temperatures than is possible with dynamic light scattering. We present an x-ray photon correlation spectroscopy study of critical fluctuation dynamics in a complex fluid typical of those used in liquid-liquid extraction (LLE) of ions, dodecane-DMDBTDMA with extracted aqueous Ce(NO_{3})_{3}. We observe good agreement with both static and dynamic scaling without the need for significant noncritical background corrections. Critical exponents agree with 3D Ising values, and the fluctuation dynamics are described by simple exponential relaxation. The form of the dynamic master curve deviates somewhat from the Kawasaki result, with a more abrupt transition between the critical and noncritical asymptotic behavior. The concepts of critical phenomena thus provide a quantitative framework for understanding the structure and dynamics of LLE systems and a path forward to new LLE processes.

Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals.

Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation, which is characterized by the dynamic structure factor, exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.

Critical nonequilibrium relaxation in the Swendsen-Wang algorithm in the Berezinsky-Kosterlitz-Thouless and weak first-order phase transitions.

Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q=5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2≤q≤4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q=5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition.

The fractional viscoelastic response of human breast tissue cells

The mechanical response of a living cell is notoriously complicated. The complex, heterogeneous characteristics of cellular structure introduce difficulties that simple linear models of viscoelasticity cannot overcome, particularly at deep indentation depths. Herein, a nano-scale stress-relaxation analysis performed with an atomic force microscope reveals that isolated human breast cells do not exhibit simple exponential relaxation capable of being modeled by the standard linear solid (SLS) model. Therefore, this work proposes the application of the fractional Zener (FZ) model of viscoelasticity to extract mechanical parameters from the entire relaxation response, improving upon existing physical techniques to probe isolated cells. The FZ model introduces a new parameter that describes the fractional time-derivative dependence of the response. The results show an exceptional increase in conformance to the experimental data compared to that predicted by the SLS model, and the order of the fractional derivative (α) is remarkably homogeneous across the populations, with a median value of 0.48 ± 0.06 for the malignant population and 0.51 ± 0.07 for the benign. The cells’ responses exhibit power-law behavior and complexity not associated with simple relaxation (SLS, α = 1) that supports the application of a fractional model. The distributions of some of the FZ parameters also preserve the distinction between the malignant and benign sample populations seen from the linear model and previous results while including the contribution of fast-relaxation behavior. The resulting viscosity, measured by a composite relaxation time, exhibits considerably less dispersion due to residual error than the distribution generated by the linear model and therefore serves as a more powerful marker for cell differentiation.

Brownian dynamics: from glassy to trivial.

We endow a system of interacting particles with two distinct, local, Markovian, and reversible microscopic dynamics that both converge to the Boltzmann-Gibbs equilibrium of standard liquids. While the first, standard, one leads to glassy dynamics, we use field-theoretical techniques to show that the latter displays no sign of glassiness. The approximations we use, akin to the mode-coupling approximation, are famous for magnifying glassy aspects of the dynamics, supposedly through the neglect of activated events. Despite this, the modified dynamics seem to stick to standard liquid relaxation. This finding singles out as applying to a realistic system of interacting particles in low dimensions and questions the role of the dynamical rules used to explore a given static free-energy landscape. Moreover, our peculiar choice of dynamical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.

A μSR study of the ruthenium perovskites ACu3Ru4O12 with A = Ca, Pr, Nd

The metallic ruthenium perovskites ACu3Ru4O12 with A = Ca, Pr,Nd were investigated by zero field (ZF) and weak transverse field (TF) muon spin rotation/relaxation (μSR) spectroscopy. The ZF spectra for CaCu3Ru4O12 show pure static Gaussian Kubo-Toyabe relaxation arising from the interaction between the muon spin and the nuclear moments of the Cu ions. This confirms that no atomic magnetic moment exists. A sudden increase of the lattice parameter a when heating above ~150 K had previously been detected by neutron diffraction. The root mean square field at the muon site Brms was found to be 0.15 mT independent of temperature, in particular around 150 K. Also, no change of spectral parameters is seen in the weak TF data in that temperature range. Those findings imply that the structural change around 150 K takes place without noticeably shifting atomic positions. The spectra for PrCu3Ru4O12 and NdCu3Ru4O12 are dominated by the interaction with the dynamic rare earth moments. The analysis requires the use of the electron-nuclear double relaxation formalism. The electronic part shows simple exponential relaxation typical for a paramagnet. It features, with reducing the temperature a steep increase of paramagnetic relaxation rate as is characteristic for an approach to a magnetic spin freezing transition from above. That result suggests that the magnetic ground states of PrCu3Ru4O12 and NdCu3Ru4O12 are spin frozen states, although bulk magnetic data give no direct evidence in that direction.

Dynamics of Glass Relaxation at Room Temperature

The problem of glass relaxation under ambient conditions has intrigued scientists and the general public for centuries, most notably in the legend of flowing cathedral glass windows. Here we report quantitative measurement of glass relaxation at room temperature. We find that Corning® Gorilla® Glass shows measurable and reproducible relaxation at room temperature. Remarkably, this relaxation follows a stretched exponential decay rather than simple exponential relaxation, and the value of the stretching exponent (β=3/7) follows a theoretical prediction made by Phillips for homogeneous glasses.

Memory function of turbulent fluctuations in soft-mode turbulence

Modal relaxation dynamics has been observed experimentally to clarify statistical-physical properties of soft-mode turbulence, the spatiotemporal chaos observed in homeotropically aligned nematic liquid crystals. We found a dual structure, dynamical crossover associated with violation of time-reversal invariance, the corresponding time scales satisfying a dynamical scaling law. To specify the origin of the dual structure, the memory function due to nonthermal fluctuations has been defined by a projection-operator method and obtained numerically using experimental results. The results of the memory function suggest that the nonthermal fluctuations can be divided into Markov and non-Markov contributions; the latter is called the turbulent fluctuation (TF). Consequently, the relaxation dynamics is separated into three characteristic stages: bare-friction, early, and late stages. If the dissipation due to TFs dominates over that of the Markov contribution, the bare-friction stage contracts; the early and late stages then configure the dual structure. The memory effect due to TFs results in a time-reversible relaxation at the early stage, and the disappearance of the memory by turbulent mixing leads to a simple exponential relaxation at the late stage. Furthermore, the memory effect due to TFs is shown to originate from characteristic spatial coherency called the patch structure.

Spin dynamics of (Pr0.5-xCex)Ca0.5MnO3 (x = 0.05, 0.10, and 0.20) system studied by muon spin relaxation

Muon spin relaxation (μSR) measurements were performed on the (Pr0.5-xCex)Ca0.5MnO3 (x = 0.05, 0.10, and 0.20) manganite system to study the influence of Ce substitution on the spin dynamics. A long-range antiferromagnetic state at low Ce substitution levels (x = 0.05) transforms to a spin-glass state by a marginal increase in x to 0.10. The manganite with x = 0.05 shows simple exponential relaxation down to low temperatures, whereas the manganites with x = 0.10 and 0.20 show a coexistence of two distinct relaxation mechanisms below spin glass-like transition temperature (TG). The μSR data for x = 0.10 and 0.20 provide evidence for the existence of a component with a root-exponential relaxation below TG, suggesting a nondiffusive relaxation mechanism similar to that in a magnetic glass. Above TG, the relaxation follows a stretched exponential function with distributed time-scales up to ∼150 K. Although similar types of relaxation dynamics exist in these two manganites (x = 0.10 and 0.20), the temperature dependent behavior slightly differ. In the light of the present results, we construct the phase-diagram of the (Pr0.5-xCex)Ca0.5MnO3 manganite system which encompasses different structural and magnetic correlations evolving as a function of Ce substitution.

New mechanism for non-trivial intra-molecular vibrational dynamics

We investigate the time evolution process of one selected (initially prepared by optical pumping) vibrational molecular state, coupled to all other intra-molecular vibrational states of the same molecule, and also to its environment. Molecular states forming the first reservoir are characterised by a discrete dense spectrum, whereas the environment reservoir states form a continuous spectrum. Assuming the equidistant reservoir states we find the exact analytical solution of the quantum dynamic equations. System reservoirs couplings yield to spontaneous decay of the states, whereas system-reservoir exchange leads to recurrence cycles and Loschmidt echo and double resonances at the interlevel reservoir transitions. Due to these couplings the system $S$ time evolution is not reduced to a simple exponential relaxation. We predict various regimes of the system dynamics, ranging from exponential decay to irregular damped oscillations. Namely, we show that there are four possible dynamic regimes of the evolution: (i) - independent of the environment exponential decay suppressing backward transitions, (ii) Loschmidt echo regime, (iii) - incoherent dynamics with multicomponent Loschmidt echo, when the system state exchanges its energy with many states of the reservoir, (iv) - cycle mixing regime, when the long term system dynamics appear to be random. We suggest applications of our results for interpretation of femtosecond vibration spectra of large molecules and nano-systems.

Time-convolutionless master equation for mesoscopic electron-phonon systems

The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.

Fast Relaxation of Carbon Nanotubes in Polymer Composite Actuators

Silicone elastomer composites containing multiwalled carbon nanotubes have been irradiated with near-infrared light to study their mechanical actuation response. We show that the speed of the stimulated response is faster than Debye relaxation, instead following a compressed-exponential law. However, the relaxation after switching off the light source follows the simple-exponential relaxation, as does the stimulated response at very low nanotube concentration. We discuss possible models and explanations to account for the fast photomechanical response.

How the all-atom simulation and the ising-based theory reconcilewith each other on the helix-coil transition.

In this report, we addressed a somewhat basic question about how the twoextreme models, the all-atom model and the Ising-based model, can beconsistent with each other regarding the polypeptide helix-coil transition.Comparisons of several physical properties were made between the resultsof the all-atom simulations and those of the Ising-based theories. Fromthe equilibrium point of view, the two models were found to exhibit aqualitatively similar trend, which is significant considering the extremedifference in precision between the two models. On the other hand, fromthe kinetic viewpoint, there appeared a difference in relaxation behaviorbetween the two models; i.e., so-called stretched exponential relaxationwas observed in the all-atom simulation whereas the kinetic Ising modelshowed simple exponential relaxation. A plausible source of the observeddifference is briefly discussed.

Femtosecond CARS of Binary Liquid Mixtures: Dephasing via Concentration Fluctuations in the Intermediate Regime

The symmetric CH3-stretching mode ν1 of CH3I is investigated in a solution of CDCl3 in the concentration range 7−100% and temperature interval 242−374 K using time-resolved coherent anti-Stokes Raman scattering (CARS) with 250 fs pulses and magic polarization geometries. Striking deviations from simple exponential relaxation dynamics are reported for mixtures with mole fractions around 0.5. Analysis of the concentration dependence allows to distinguish the dephasing contribution of concentration fluctuations with correlation time >1 ps, indicating the intermediate case for this relaxation mechanism. The results are well described by the Knapp−Fischer model for concentration fluctuations, yielding a molecular residence time in the solvation layer of 1.1−3.2 ps in the temperature range 242−374 K in accordance with theoretical estimates.

Spin-lattice relaxation of deuterated methyl groups: Implications of the pauli principle

The high-field spin-lattice relaxation of deuterated methyl groups undergoing rotational tunneling is investigated theoretically. It is found that for systems showing a tunneling frequency comparable to accessible Larmor frequencies the relaxation to equilibrium of the Zeeman energy does not follow a simple exponential time dependence even in powdered samples due to a finite coupling to the relaxation of the tunneling system. This finding contrasts to the high-temperature behavior of reorienting methyl groups which undergo simple exponential relaxation. The nonexponentiality has its origin in the statistical coupling of the three deuteron spins due to the Pauli principle.

Chain orientation in sheared molten poly(ethylene oxide) fractions by measurement of infrared dichroism

AbstractRheo‐infrared spectroscopy was used to study the development of orientation of molten narrow molar mass fractions of poly(ethylene oxide) [molar masses between 18,000 and 120,000 g/mol] during non‐Newtonian shear flow at shear rates between 2 and 270 s−1 and temperatures between 75 and 100°C. The steady state degree of orientation [expressed as the Hermans orientation function (fss)] reached a saturation level with increasing shear rate; fss increased with increasing molar mass (M) according to fss = C1 − C2/M (C1 and C2 are coefficients; the latter depended on shear rate and temperature). The coefficient C1 (fss) for a polymer with infinite molar mass took a universal value close to 0.05 for the temperatures and shear rates used. Under large shear stresses, the relationship between stress and orientation deviated markedly from linearity. The time to establish a steady state level of orientation was proportional to M1/2. The recovery of the isotropic state after the cessation of shear could initially be described by a simple exponential relaxation law: f ∝ e, where τρ is the relaxation time. The latter showed a weak molar mass dependence according to τr ∝ M0.6 and an Arrhenius temperature dependence with an activation energy of ∼60 kJ/mol. The relaxation of the shear stress after the cessation of shear was more rapid than the recovery of the isotropic state.

Moment localisation in β-MnAl

μSR has been used to map the magnetic phase diagram of β-Mn 1− x Al x and to investigate the evolution of spin fluctuations with increasing Al concentration. There is a marked change in the spin fluctuation spectrum at x = 0.08, below which simple exponential relaxation is observed, while for higher concentrations Kohlrausch relaxation, associated with spin-glass behaviour is found. This change is accompanied by a sudden increase in the magnetic transition temperature.

Slow relaxation in interpenetrated networks

Interpenetrated networks are made by cross linking linear polymer chains of two different chemical nature. We consider the kinetics of the microphase separation that occurs when such cross linking is performed on a blend where composition fluctuations are present. We assume a simple exponential relaxation between the known initial and final states. The relaxation time however is assumed to be dependent on the spatial scale, and to diverge for large enough distances. We find that the scattered intensity in a radiation scattering experiment exhibits a minimum that varies slowly with time. This is interpreted as the very slow relaxation of the initial fluctuations that are present in the initial blend and are trapped by the cross links.

Stress relaxation function of bone and bone collagen.

Relaxation Young's and shear moduli of bovine bone and bone collagen were investigated. It was found that each relaxation process observed had two stages, which were referred to as process I and process II in order of time. Process II was described by a simple exponential decay while process I was not. The Kohlrausch-Williams-Watts (KWW) function, psi(t) = exp[-(t/tau 1)B] (0 < B < 1), was found to be suitable to describe process I. The normalized relaxation modulus, M(r)(t), was expressed by the combination of the simple exponential type relaxation function and the KWW function M(r)(t) = A1exp[-(t/tau 1)B]+A2exp[-(t/tau 2)] (0 < B < or = 1). On the basis of this equation, the relaxation mechanism in bone and bone collagen was identified. According to the model proposed for the KWW relaxation function, the stress relaxation process in bone was considered to be governed by viscoelastic properties of matrix collagen fiber. The model for the KWW relaxation function requires the disordered glassy structure of collagen fiber, which is consistent with the results of the structural investigations.

PARALLELISM ON THE INTEL 860 HYPERCUBE: ISING MAGNETS, HYDRODYNAMICAL CELLULAR AUTOMATA AND NEURAL NETWORKS

Geometric parallelization was tested on the Intel Hypercube with 32 MIMD processors of 1860 type, each with 16 Mbytes of distributed memory. We applied it to Ising models in two and three dimensions as well as to neural networks and two-dimensional hydrodynamic cellular automata. For system sizes suited to this machine, up to 60960*60960 and 1410*1410*1408 Ising spins, we found nearly hundred percent parallel efficiency in spite of the needed inter-processor communications. For small systems, the observed deviations from full efficiency were compared with the scaling concepts of Heermann and Burkitt and of Jakobs and Gerling. For Ising models, we determined the Glauber kinetic exponent z≃2.18 in two dimensions and confirmed the stretched exponential relaxation of the magnetization towards the spontaneous magnetization below Tc. For three dimensions we found z≃2.09 and simple exponential relaxation.