Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

Space use by foragers consuming renewable resources

Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ?x(t) ^q ? for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.     

Laser-induced temporal and wavelength resolved spectroscopy of the 2Σ−-2Π and 2Δ-2Π systems of CH and CD isolated in rare gas matrices

The relaxation dynamics of matrix isolated CH and CD have been studied using laser-induced time and wavelength resolved spectroscopy. Vibrationally relaxed B(0′-0″) fluorescence occurs following laser excitation both above and below the gas phase dissociation limit. The vibrational relaxation rate in the B state of CH is found to be 4.6 × 10⁶ sec^?1 while the corresponding rate in CD is 5.7 × 10⁵ sec^?1. The primary accepting mode in the relaxation process is consistent with rotation.     

Electron paramagnetic resonance and relaxation of amorphous silicon below 1 K

Amorphous silicon, generated within crystalline Si by ²⁸Si⁺ ion implantation, exhibits an electron spin relaxation rate which varies with temperature as T^2.37 between 0.3 and 4.2 K. These results exclude the current model of a phonon-limited, direct relaxation mechanism in a-Si. A relaxation process, consistent with the known temperature variation, is outlined. EPR signal strengths, relative to a known paramagnet at temperatures near 1.2 and 0.4 K, put limits on an antiferromagnetic Curie-Weiss temperature of 0?θ?0.06 K.     

Multivariate pressure effects on an electron hopping process in ferroelectric KTa<Subscript>1−x</Subscript>Nb<Subscript>x</Subscript>O<Subscript>3</Subscript>

The effect induced by the presence of a polaron related relaxation process on the dielectric properties of a ferroelectric KTa_1?x Nb _x O₃ (KTN) crystal was investigated (10^-2?10⁶ Hz, at 300?375 K) using broadband dielectric spectroscopy. Characterization of the process using just the standard frequency domain dielectric parameters can nonetheless provide penetrating insight into its nature and origins. The three parameters, namely: relaxation time (τ), Cole-Cole loss broadening (α), and dielectric strength (Δ?) provide each one in its own way, much useful and often overlooked information. The Activation Energy along with the Meyer-Neldel dependance, both extracted from τ serve to illuminate the dynamic properties. At the same time, α and especially the combined α(lnτ) relationship, expose the fractal structure of the underlying landscape. Finally, the static parameter Δ?, enables quantification of the dipolar correlations. Hydrostatic pressure (up to 7.5 kbar) was applied to gently perturb the system and observe the outcome on all of the various parameters. This additional degree of freedom allows for a much more comprehensive exploration of the phase space behavior of the system.     

A new relaxation effect in gold-doped lead

Internal friction studies on gold-doped lead are reported which yield a relaxation time of τ = 10^-14.9exp 0.437 eV/kT. The defect producing the relaxation process appears to have 〈100〉 symmetry and a relatively large elastic-dipole strength. Since this activation energy is equal to that measured in diffusion it is suggested that the two processes are identical, presumably from a dumb-bell configuration.     

Study of the paraelectric behavior of OH− ions in alkali halides with optical and caloric methods II.: Dynamics of the dipole alignment

The relaxation behavior of OH^? dipole centers in ten alkali halides was studied with electro-optical and electro-caloric methods as a function of applied field, temperature and host lattice system. The reorientation kinetics of the 〈100〉 oriented OH^? dipoles can be fitted successfully to a phonon-assisted (90°) orientational tunneling model. Below 5°K the observed time dependence of the optical dichroism and the T^?1 dependence of the relaxation time gives clear evidence for the predominance of one-phonon processes, while above 5°K the T^?4 dependence indicates multi-phonon processes. It could be demonstrated that in the one-phonon region of the dipole relaxation a population inversion among the dipole levels (with subsequent phonon emission) can be achieved after a fast reversal of the field polarity. An attempt is made to discuss the observed strong variation of the relaxation time (12 orders of magnitude) with the host lattice in terms of a tunneling matrix element renormalized due to the anisotropic lattice distortion around the defect.     

Observation of magnetic field dependent ultrasonic relaxation time in p-InSb

Ultrasonic attenuation and sound velocity measurements are presented for p-InSb (≈ 10¹⁴cm^?3) at low temperatures in high magnetic fields. A magnetic field dependent relaxation time is observed, which is interpreted as being due to a relaxation process via holes in the valence band.     

Phase transition and ferroelastic property studied by using the Cs nuclear magnetic resonance in a CsHSO4 single crystal

The ¹³³Cs spin-lattice relaxation time in a CsHSO₄ single crystal was measured in the temperature range from 300 to 450 K. The changes in the ¹³³Cs spin-lattice relaxation rate near T_c1 (=333 K) and T_c2 (=415 K) correspond to phase transitions in the crystal. The small change in the spin-lattice relaxation time across the phase transition from II to III is due to the fact that during the phase transition, the crystal lattice does not change very much; thus, this transition is a second-order phase transition. The abrupt change of T₁ around T_c2 (II-I phase transition) is due to a structural phase transition from the monoclinic to the tetragonal phase; this transition is a first-order transition. The temperature dependences of the relaxation rates in phases I, II, and III are indicative of a single-phonon process and can be represented by T₁⁻¹=A+BT. In addition, from the stress-strain hysteresis loop and the ¹³³Cs nuclear magnetic resonance, we know that the CsHSO₄ crystal has ferroelastic characteristics in phases II and III.     

Frequency-dependent spin-lattice relaxation study of transport processes in superionic conductors

The sensitivity of the¹⁹F spin-lattice relaxation dispersion, T₁,(ω), to motional disorder in crystalline superionic conductors of the type La_1?xSr_xF_3?x (x = 0; 0.03) is shown. T₁ times are measured in the frequency range from 90 kHz to 370 MHz using standard techniques in combination with field-cycling. The relaxation dispersion shows qualitative differences from the standard Bloembergen-Purcell-Pound behavior. At low frequencies a relaxation model using a distribution of correlation times for diffusing ions is found to be consistent with the experimental results. At frequencies higher than 50 MHz another process of the Debye type which is not induced by ionic hopping dominates the relaxation.     

Anomalously slow relaxation of a nonwetting liquid in the disordered confinement of a nanoporous medium

The time evolution of the water–disordered nanoporous medium Libersorb 23 (L23) system has been studied after complete filling at elevated pressure followed by full release of overpressure. It is established that relaxation of the L23 rapidly flows out during the overpressure relief time, following the variation in pressure. At a temperature below that of the dispersion transition (T < T _d = 284 K), e.g., at T = 277 K, the degree of filling θ decreases from 1 to 0.8 within 10 s. The degree of filling varies with time according to the power law θ ~ t ^–α with the exponent α < 0.1 over a period of t ~ 10⁵ s. This process corresponds to slow relaxation of a metastable state of a nonwetting liquid in a porous medium. At times t > 10⁵ s, the metastable state exhibits decay, manifested as the transition to a power dependence of θ(t) with a larger exponent. The relaxation of the metastable state of nonwetting liquid in a disordered porous medium is described in the mean field approximation as a continuous sequence of metastable states with a barrier decreasing upon a decrease in the degree of filling. Using this approach, it is possible to qualitatively explain the observed relaxation process and crossover transition to the stage described by θ(t) with a larger exponent.     

Response of lysozyme internal dynamics to hydration probed by13C and1H solid-state NMR relaxation

We have studied the hydration dependence of the internal protein dynamics of hen egg white lysozyme by naturally abundant¹³C and¹H nuclear magnetic resonance (NMR) relaxation. NMR relaxation timesT ₁, off-resonanceT _1p and proton-decoupled on-resonanceT _1p (only for carbon expriments) were measured in the temperature range from 0 to 50°C. The spectral resolution in carbon cross-polarization magic angle spinning spectrum allows to treat methine, methylene and methyl carbons separately, while proton experiments provide only one integral signal from all protons at a time. The relaxation times were quantitatively analyzed by the well-established correlation function formalism and model-free approach. The whole set of the data could be adequately described by a model assuming three types of motion having correlation times around 10^?4, 10^?9 and 10^?12 s. The slowest process originated from correlated conformational transitions between different energy minima, the intermediate process could be identified as librations within one energy minimum, and the fastest one is a fast rotation of methyl protons the symmetry axis of methyl groups. A comparison of the dynamic behavior of lysozyme and polylysine obtained from a previous study (A. Krushelnitsky, D. Faizullin, D. Reichert, Biopolymers 73, 1–15, 2004) reveals that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine reveal a considerable enhancement of the internal mobility, however, in different ways. The side chains of polylysine are more mobile than those of lysozyme, whereas for the backbone a reversed picture is observed. This difference correlates with structural features of lysozyme and polylysine discussed in detail. Due to the presence of a fast spin diffusion, the analysis of proton relaxation data is a more difficult task. However, our data demonstrate that the correlation functions of motion obtained from carbon and proton experiments are substantially different. We explained this by the fact that these two types of NMR relaxation experiments probe the motion of different internuclear vectors. The comparison of the proton data with our previous results on proton relaxation timesT ₁ measured over a wide temperature range indicates that at low temperatures lysozyme undergoes structural rearrangements affecting the amplitudes and/or activation energies of motions.     

Complex capacitance in the representation of modulus of the lithium niobate crystals

The lithium niobate (LiNbO₃ or LN) single crystal is grown in-house. The ac small-signal electrical characterization is conducted over a temperature range 35≤T≤150 °C as a function of measurement frequency (10≤f≤10⁶ Hz). Meaningful observation is noted only in a narrow temperature range 59≤T≤73 °C. These electrical data when analyzed via complex plane formalisms revealed single semicircular relaxation both in the complex capacitance (C^?) and in the modulus (M^?) planes. The physical meaning of this kind of observation is obtained on identifying the relaxation type, and then incorporating respective equivalent circuit model. The simplistic non-blocking nature of the equivalent circuit model obtained via M^?-plane is established as the lumped relaxation is identified in the C^?-plane. The feature of the eventual equivalent circuit model allows non-blocking aspect for the LN crystal attributing to the presence of the operative dc conduction process. Identification of this leakage dc conduction via C^?-plane is portrayed in the M^?-plane where the blocking nature is removed. The interacting interpretation between these two complex planes is successfully presented.     

Anisotropic relaxation time T′2 of solid 3He

This paper investigates an anisotropy of the adiabatic relaxation time T ₂′ for single crystalline bcc ³He. No difference in the calculation of T ₁(0) was revealed between the nearest-neighbor anti-ferromagnetic Heisenberg model and the multiple exchange model. However, we may distinguish these two models by the anisotropy of the adiabatic relaxation time T ₂′. The results presented in this paper are compared with experimental observations.     

H and K spin-lattice relaxation, ionic motion and Raman processes in the proton conducting KHSeO4 single crystal

The spin-lattice relaxation rates of ¹H and ³⁹K nuclei in KHSeO₄ crystals were studied in the temperature range 160-400 K. The spin-lattice relaxation recovery of ¹H nucleus in this crystal can be represented with a single exponential function, and the relaxation T₁⁻¹ curve of ¹H can be represented with the Bloembergen-Purcell-Pound (BPP) function. The relaxation process of ³⁹K with dominant quadrupole relaxation can be described by a linear combination of two exponential functions. T₁⁻¹ for the ³⁹K nucleus was found to have a very strong temperature dependence, T₁⁻¹=βT⁷. Rapid variations in relaxation rates are associated with critical fluctuations in the electronic spin system. The T⁷ temperature dependence of the Raman relaxation rate is shown here to be due to phonon-magnon coupling.     

Consideration of slice profiles in inversion recovery Look–Locker relaxation parameter mapping

Purpose

To include the flip angle distribution caused by the slice profile into the model used for describing the relaxation curves observed in inversion recovery Look–Locker FLASH T₁ mapping for a more accurate determination of the relaxation parameters.

Materials and methods

For each inversion time, the flip angle dependent signal of the mono-exponential relaxation model is integrated across the slice profile. The resulting Consideration of Slice Profiles (CSP) relaxation curves are compared to the mono-exponential signal model in numerical simulations as well as in phantom and in-vivo experiments.

Results

All measured relaxation curves showed systematic deviations from a mono-exponential curve increasing with flip angle and T₁ but decreasing with repetition time. Additionally, the accuracy of T₁ was found to be largely dependent on the temporal coverage of the relaxation curve. All these systematic errors were largely reduced by the CSP model.

Conclusion

The proposed CSP model represents a useful extension of the conventionally used mono-exponential relaxation model. Despite inherent model inaccuracies, the mono-exponential model was found to be sufficient for many T₁ mapping situations. However, if only a poor temporal coverage of the relaxation process is achievable or a very precise modeling of the relaxation course is needed as in model-based techniques, the mono-exponential model leads to systematic errors and the CSP model should be used instead.     

Influence of moving dislocations on the nuclear spin-lattice relaxation time in the rotating frame

Dislocation motion at various velocities in Na²³Cl single crystals was studied using the spin-locking technique. The resulting spin-lattice relaxation time in the rotating frame, T_1?, is strongly dependent on the plastic deformation rate ?e, but not on the plastic strain ?. The experimental results are in accord with a theoretical expression for T_1? based on the relaxation model of Rowland and Fradin for atomic diffusion.     

The optical conductivity of free carriers in GaAs

The optical conductivity of free electrons in polar semiconducting compounds has recently been calculated by use of a generalized Boltzmann equation derived from the equation of motion of the quantum density matrix. This reduces to the quasi-classical Boltzmann transport equation in the low frequency limit: the optical conductivity thus obtained spans a spectral range from around 30cm^?1 to 1.2 × 10⁴cm^?1 in GaAs. In this paper, the optical conductivity is calculated for GaAs as a function of carrier concentration in terms of a frequency dependent relaxation time which reduces to the usual relaxation time in the limit of low frequencies and an elastic scattering mechanism. The low frequency limit of the relaxation time is used to estimate the mobility as a function of carrier concentration. The frequency dependent relaxation time is given for GaAs at 298 K over the spectral region from 45 cm^?1 to 2.3 × 10³cm^?1 for carrier concentrations from 3.4 × 10¹⁵cm^?3 to 8.7 × 10¹⁸cm^?3.     

Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T_s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝x^d_f, where d_f is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time T_s shows a self-affine fractal with roughness exponent α=1−d_f.