Initial Relaxation Research Articles

Initial layer and relaxation limit of non-isentropic compressible Euler equations with damping

In this paper, we study the relaxation limit of the relaxing Cauchy problem for non-isentropic compressible Euler equations with damping in multi-dimensions. We prove that the velocity of the relaxing equations converges weakly to the velocity of the relaxed equations, while other variables of the relaxing equations converge strongly to the corresponding variables of the relaxed equations. We prove that as relaxation time approaches 0, there exists an initial layer for the ill-prepared data, the convergence of the velocity is strong outside the layer; while there is no initial layer for the well-prepared data, the convergence of the velocity is strong near t=0. The strong convergence rates of all variables are also estimated.

Ultrafast Electronic Energy Transfer Beyond the Weak Coupling Limit in a Proximal but Orthogonal Molecular Dyad.

Electronic energy transfer (EET) from a donor to an acceptor is an important mechanism that controls the light harvesting efficiency in a wide variety of systems, including artificial and natural photosynthesis and contemporary photovoltaic technologies. The detailed mechanism of EET at short distances or large angles between the donor and acceptor is poorly understood. Here the influence of the orientation between the donor and acceptor on EET is explored using a molecule with two nearly perpendicular chromophores. Very fast EET with a time constant of 120 fs is observed, which is at least 40 times faster than the time predicted by Coulombic coupling calculations. Depolarization of the emission signal indicates that the transition dipole rotates through ca. 64°, indicating the near orthogonal nature of the EET event. The rate of EET is found to be similar to structural relaxation rates in the photoexcited oligothiophene donor alone, which suggests that this initial relaxation brings the dyad to a conical intersection where the excitation jumps to the acceptor.

Quasi-linear viscoelastic properties of the human medial patello-femoral ligament

The evaluation of viscoelastic properties of human medial patello-femoral ligament is fundamental to understand its physiological function and contribution as stabilizer for the selection of the methods of repair and reconstruction and for the development of scaffolds with adequate mechanical properties. In this work, 12 human specimens were tested to evaluate the time- and history-dependent non linear viscoelastic properties of human medial patello-femoral ligament using the quasi-linear viscoelastic (QLV) theory formulated by Fung et al. (1972) and modified by Abramowitch and Woo (2004). The five constant of the QLV theory, used to describe the instantaneous elastic response and the reduced relaxation function on stress relaxation experiments, were successfully evaluated. It was found that the constant A was 1.21±0.96MPa and the dimensionless constant B was 26.03±4.16. The magnitude of viscous response, the constant C, was 0.11±0.02 and the initial and late relaxation time constants τ1 and τ2 were 6.32±1.76s and 903.47±504.73s respectively. The total stress relaxation was 32.7±4.7%. To validate our results, the obtained constants were used to evaluate peak stresses from a cyclic stress relaxation test on three different specimens. The theoretically predicted values fit the experimental ones demonstrating that the QLV theory could be used to evaluate the viscoelastic properties of the human medial patello-femoral ligament.

Isothermal Crystallization of PC61BM in Thin Layers Far below the Glass Transition Temperature

An isothermal study was performed on 1.25 μm thin layers of PC61BM, a benchmark acceptor for organic photovoltaics. Using fast scanning chip calorimetry allowed for a scanning rate of 30 000 K·s–1, ensuring that all non-isothermal effects were avoided. The effect of isothermal treatments above and far below the glass transition was investigated. It was proven that PC61BM can crystallize below its glass transition, a behavior seen before for several organic glasses. Isothermal treatments as far as ca. 100 K below the glass transition lead to an initial enthalpic relaxation process around the glass transition, which over time gives rise to crystals melting around 300 °C. These observations show a remarkable similarity with the two-step nucleation mechanism documented in the literature. A standard crystallization process was observed for treatments above the glass transition. By combining chip calorimetry pretreatments with atomic force microscopy, different crystal morphologies were visualized for these two...

The effect of a broad activation energy distribution on deuteron spin–lattice relaxation

Deuteron NMR spectra and spin–lattice relaxation were studied experimentally in zeolite NaY(2.4) samples containing 100% or 200% of CD3OH or CD3OD molecules of the total coverage of Na atoms in the temperature range 20–150K. The activation energies describing the methyl and hydroxyl motions show broad distributions. The relaxation data were interpreted by improving a recent model (Stoch et al., 2013 [16]) in which the nonexponential relaxation curves are at first described by a sum of three exponentials with adjustable relaxation rates and weights. Then a broad distribution of activation energies (the mean activation energy A0 and the width σ) was assumed for each essentially different methyl and hydroxyl position. The correlation times were calculated from the Arrhenius equation (containing the pre-exponential factor τ0), individual relaxation rates computed and classified into three classes, and finally initial relaxation rates and weights for each class formed. These were compared with experimental data, motional parameters changed slightly and new improved rates and weights for each class calculated, etc. This method was improved by deriving for the deuterons of the A and E species methyl groups relaxation rates, which depend explicitly on the tunnel frequency ωt. The temperature dependence of ωt and of the low–temperature correlation time were obtained by using the solutions of the Mathieu equation for a threefold potential. These dependencies were included in the simulations and as the result sets of A0, σ and τ0 obtained, which describe the methyl and hydroxyl motions in different positions in zeolite.

An analytical solution for the effect of initial stress, rotation, magnetic field and a periodic loading in a thermo-viscoelastic medium with a spherical cavity

ABSTRACTIn this article, an analytical solution for the effect of initial stress, the rotation, and the relaxation times in a magneto-thermo-viscoelastic homogeneous medium with a spherical cavity subjected to periodic loading is presented. The distribution of displacements, temperature, and stresses in a homogeneous medium, in the context of generalized thermo-elasticity using the Green-Lindsay (GL) theory is discussed and obtained in analytical form. The results are displayed graphically to illustrate the effect of initial stress, the rotation, relaxation times, magnetic field, and viscoelasticity. Comparisons are made with the previous work in the absence of rotation and initial stress.

Activation Volume and Density of Mobile Dislocations in Plastically Deforming Zr-1pctSn-1pctNb-0.1pctFe Alloy

Stress relaxation and strain rate change tests were carried out in annealed Zr-1pctSn-1pctNb-0.1pctFe alloy at room temperature. The apparent and true activation volumes were determined and the results obtained from different techniques were compared. The stress dependence of activation volume was studied in a wide range of stresses, and an analysis was made in the light of the thermal activation theory. The results suggest that surmounting of the Peierls barrier is the rate-controlling factor in the room-temperature plasticity of the alloy. Dislocation exhaustion rate during initial stress relaxation is higher in the alloy.

Hybrid collaborative optimization based on selection strategy of initial point and adaptive relaxation

There are two problems in Collaborative optimization (CO): (1) the local optima arising from the selection of an inappropriate initial point; (2) the low efficiency and accuracy root in inappropriate relaxation factors. To solve these problems, we first develop the Latin hypercube design (LHD) to determine an initial point of optimization, and then use the non-linear programming by quadratic Lagrangian (NLPQL) to search for the global solution. The effectiveness of the initial point selection strategy is verified by three benchmark functions with some dimensions and different complexities. Then we propose the Adaptive relaxation collaborative optimization (ARCO) algorithm to solve the inconsistency between the system level and the disciplines level, and in this method, the relaxation factors are determined according to the three separated stages of CO respectively. The performance of the ARCO algorithm is compared with the standard collaborative algorithm and the constant relaxation collaborative algorithm with a typical numerical example, which indicates that the ARCO algorithm is more efficient and accurate. Finally, we propose a Hybrid collaborative optimization (HCO) approach, which integrates the selection strategy of initial point with the ARCO algorithm. The results show that HCO can achieve the global optimal solution without the initial value and it also has advantages in convergence, accuracy and robustness. Therefore, the proposed HCO approach can solve the CO problems with applications in the spindle and the speed reducer.

Relativistic Doppler reflection as a probe for the initial relaxation of a non-equilibrium electron-hole plasma in silicon

This paper reviews the status of investigations of the relativistic Doppler reflection of a broadband terahertz pulse at a counter-propagating plasma front of photo-excited charge carriers in undoped silicon. When a THz pulse with 20-THz bandwidth impinges onto a moving plasma front with a carrier density in the range of 1019 per cm3, one observes a spectral up-shift, which is, however, much less pronounced than expected from simulations assuming a Drude plasma characterized by a single carrier relaxation time τ of the order of 15-100 fs. Qualitative agreement between simulations and experiments can be achieved if τ is chosen to be less than 5 fs. In order to explore carrier relaxation in more detail, optical-pump/THz-probe experiments in the conventional co-propagation geometry were performed. If the pump-probe delay is long enough for monitoring of the equilibrium value of the scattering time, τ ranges from 200 fs at low carrier density to 20 fs in the 1019-cm-3 density range. For small (sub-picosecond) pump-probe delay, the data reveal a significantly faster scattering, which slows down during energy relaxation of the charge carriers.

A new experimental model for force enhancement: steady-state and transient observations of the Drosophila jump muscle.

The increase in steady-state force after active lengthening in skeletal muscle, termed force enhancement (FE), has been observed for nearly one century. Although demonstrated experimentally at various structural levels, the underlying mechanism(s) remain unknown. We recently showed that the Drosophila jump muscle is an ideal model for investigating mechanisms behind muscle physiological properties, because its mechanical characteristics, tested thus far, duplicate those of fast mammalian skeletal muscles, and Drosophila has the advantage that it can be more easily genetically modified. To determine if Drosophila would be appropriate to investigate FE, we performed classic FE experiments on this muscle. Steady-state FE (FESS), following active lengthening, increased by 3, 7, and 12% of maximum isometric force, with increasing stretch amplitudes of 5, 10, and 20% of optimal fiber length (FLOPT), yet was similar for stretches across increasing stretch velocities of 4, 20, and 200% FLOPT/s. These FESS characteristics of the Drosophila jump muscle closely mimic those observed previously. Jump muscles also displayed typical transient FE characteristics. The transient force relaxation following active stretch was fit with a double exponential, yielding two phases of force relaxation: a fast initial relaxation of force, followed by a slower recovery toward steady state. Our analyses identified a negative correlation between the slow relaxation rate and FESS, indicating that there is likely an active component contributing to FE, in addition to a passive component. Herein, we have established the Drosophila jump muscle as a new and genetically powerful experimental model to investigate the underlying mechanism(s) of FE.

EEG feature variations under stress situations.

The goal of this study is to identify EEG parameters and electrode positions with the highest significant values to differentiate between tasks and relax periods. Different signals were recorded as 12 subjects are doing arithmetic and memory tasks under stress condition. The test consisted of an initial and final 5-minute relax periods and three 4-minute performance phases with increased stress level. θ and α bands concentrated mainly features whose variation were significant, and F3 and P4 were the best positions to distinguish between performed tasks and arousal level.

INSPIRE: A Framework for Incremental Spatial Prefix Query Relaxation

Geo-textual data are generated in abundance. Recent studies focused on the processing of spatial keyword queries which retrieve objects that match certain keywords within a spatial region. To ensure effective retrieval, various extensions were done including the allowance of errors in keyword matching and autocompletion using prefix matching. In this paper, we propose INSPIRE, a general framework, which adopts a unifying strategy for processing different variants of spatial keyword queries. We adopt the autocompletion paradigm that generates an initial query as a prefix matching query. If there are few matching results, other variants are performed as a form of relaxation that reuses the processing done in the earlier phase. The types of relaxation allowed include spatial region expansion and exact/approximate prefix/substring matching. Moreover, since the autocompletion paradigm allows appending characters after the initial query, we look at how query processing done for the initial query and relaxation can be reused in such instances. Compared to existing works which process variants of spatial keyword query as new queries over different indexes, our approach offers a more compelling way to efficient and effective spatial keyword search. Extensive experiments substantiate our claims.

Effect of hydrostatic pressure on the kinetics of the ordering of ferroelectrics upon second-order phase transitions

The effect of hydrostatic pressure on the kinetics of the formation of electrical domains in ferroelectric materials that undergo second-order phase transitions has been considered. It has been shown using the example of triglycine sulfate ferroelectric crystals undergoing an order-disorder phase transition that the applied pressure increases the ordering temperature and thus accelerates the ordering process. It has been found that, by increasing the hydrostatic pressure applied to the sample after quenching, it is possible to obtain a single-domain state, instead of the multi-domain type of ordering. The evolution curves for the average value of the order parameter and its dispersion have been obtained by numerical integration. These curves indicate that quasi-stationary multi-domain structures of the asymmetric type can be formed at specially selected pressures. It has been established that the kinetics of the formation of electrical domains in ferroelectrics depends significantly on the initial relaxation conditions, which are determined by the technological prehistory of the quenching.

STRIPPED ELLIPTICAL GALAXIES AS PROBES OF ICM PHYSICS. I. TAILS, WAKES, AND FLOW PATTERNS IN AND AROUND STRIPPED ELLIPTICALS

Elliptical cluster galaxies are progressively stripped of their atmospheres due to their motion through the intra-cluster medium (ICM). Deep X-ray observations reveal the fine-structure of the galaxy's remnant atmosphere and its gas tail and wake. This fine-structure depends on dynamic conditions (galaxy potential, initial gas contents, orbit through the host cluster), orbital stage (early infall, pre-/post-pericenter passage), and ICM plasma properties (thermal conductivity, viscosity, magnetic field structure). We aim to disentangle dynamic and plasma effects in order to use stripped ellipticals as probes of ICM plasma properties. This first paper of a series investigates the hydrodynamics of progressive gas stripping by means of inviscid hydrodynamical simulations. We distinguish a long-lasting initial relaxation phase and a quasi-steady stripping phase. During quasi-steady stripping, the ICM flow around the remnant atmosphere resembles the flow around solid bodies, including a `deadwater' region in the near wake. Gas is stripped from the remnant atmosphere predominantly at its sides via Kelvin-Helmholtz instabilities. The downstream atmosphere is largely shielded from the ICM wind and thus shaped into a tail. Observationally, both, this `remnant tail' and the stripped gas in the wake can appear as a `tail', but only in the wake can galactic gas mix with the ambient ICM. While the qualitative results are generic, the simulations presented here are tailored to the Virgo elliptical galaxy M89 (NGC 4552) for the most direct comparison to observations. Papers II and III of this series describe the effect of viscosity and compare to Chandra and XMM-Newton observations, respectively.

INFLUENCE OF MODIFIED NATURAL RUBBER ON PROPERTIES OF NATURAL RUBBER–CARBON NANOTUBE COMPOSITES

ABSTRACT Carbon nanotube (CNT)–filled natural rubber (NR) composites were prepared by using an internal mixer and a two-roll mill. Various types of NR, including unmodified NR, epoxidized NR (ENR), and maleated NR (MNR), were used. The chemical reactions between rubber molecules and functional groups on the CNT surface were characterized by attenuated total reflection Fourier transform infrared spectroscopy. Cure characteristics, tensile properties, relaxation behavior, and electrical conductivity of the various gum rubbers and the CNT-filled rubber composites were investigated. It was found that the addition of CNTs significantly affected the composite properties. This is due not only to the excellent properties of the CNT itself but also to the physical and chemical interactions between modified rubber molecules and CNT surfaces. On comparison between the three types of NR, it was observed that the ENR-CNT composite showed the highest values of delta torque, tensile strength, and initial relaxation modulus. This confirms the homogeneous distribution of CNT particles in the ENR matrix, which in turn resulted from enhanced interactions of functional groups on CNT surfaces and epoxide groups in ENR molecules. Furthermore, electrical conductivity as a function of CNT content was examined to estimate the electrical percolation threshold value and to determine the state of dispersion of CNTs.

Relaxation dynamics and exciton energy transfer in the low-temperature phase of MEH-PPV.

Understanding the effects of aggregation on exciton relaxation and energy transfer is relevant to control photoinduced function in organic electronics and photovoltaics. Here, we explore the photoinduced dynamics in the low-temperature aggregated phase of a conjugated polymer by transient absorption and coherent electronic two-dimensional (2D) spectroscopy. Coherent 2D spectroscopy allows observing couplings among photoexcited states and discriminating band shifts from homogeneous broadening, additionally accessing the ultrafast dynamics at various excitation energies simultaneously with high spectral resolution. By combining the results of the two techniques, we differentiate between an initial exciton relaxation, which is not characterized by significant exciton mobility, and energy transport between different chromophores in the aggregate.

Temperature sensitivity and model of stress relaxation properties of cement and asphalt mortar

The stress relaxation properties of two types of cement and asphalt mortar (CA mortar) in the temperature range of −40 to 60°C and at the initial strain of 0.1% was studied by dynamic mechanical thermal spectrometer. The results show that the stress relaxation process of CA mortar can be divided into attenuation stress relaxation stage and steady stress relaxation stage. The lower the temperature is, the higher the initial stress and residual stress are. At the same temperature, the stress relaxation rate and specific stress relaxation of type I CA mortar are larger than that of type II CA mortar, while the initial stress, residual stress and stress relaxation modulus are relatively smaller. The glass transition region of type I CA mortar characterized by the isochronous stress–temperature curves is −20 to 0°C. The established model agrees well with experimental results, and φ, δ are dominated parameters affecting the stress relaxation of CA mortar. This indicates that the established model can effectively predict the time dependence and temperature sensitivity of stress relaxation of CA mortar. The results can provide reference for the calculation of temperature stress of CA mortar filling layer of ballastless slab track.

Evolution of generalized two‐dimensional magnetotail equilibria in ideal and resistive MHD

AbstractWe present results of two‐dimensional (2‐D) magnetohydrodynamic (MHD) simulations of the terrestrial magnetotail. A regional adaptation of the Lyon‐Fedder‐Mobarry global MHD model is used. As initial conditions, we employ a class of asymptotic magnetotail equilibria with and without an accumulation of magnetic flux at the tailward end (a Bz hump). The former have been recently shown by full particle simulations to be unstable to a kinetic mode with formal properties of ion tearing. Thus, our goal here is to investigate the evolution of the same equilibria in the MHD approximation and assist in the physical interpretation of the kinetic simulations. This is additionally motivated by the energy principle considerations which suggest that if the system is unstable kinetically, it may also be unstable ideally. To seek dynamical MHD regimes similar to those observed in kinetic simulations, we implement two sets of boundary conditions (velocity balanced, VB, and momentum balanced, MB), one allowing plasma flows through the boundaries and the other inhibiting such flows. The use of more reflecting MB boundary conditions results in suppression of any significant dynamics, and we see no substantial changes beyond initial equilibrium relaxation. On the other hand, VB boundary conditions allow a more efficient relaxation of initial equilibrium and absorb subsequently generated plasma flows. With these boundary conditions we find the equilibrium without a flux accumulation (i.e., with constant magnetic field component normal to the current sheet) to develop an apparently resistive mode accompanied by tailward plasma flows. At the same time, the equilibria with a Bz hump of sufficiently large amplitude develop a different, ideal, mode characterized by spontaneous generation of earthward plasma flows and an exponential growth of the corresponding electric field. This growth is qualitatively similar to the corresponding fully kinetic simulations although no explosive growth of the earthward moving Bz peak is evident in the MHD calculations, just an earthward shift of a part of the initial flux accumulation. We discuss implications of our results for the possibility of existence and impact of such equilibria in the Earth's magnetotail and in global MHD simulations.

Dynamics of elastic dumbbells sedimenting in a viscous fluid: oscillations and hydrodynamic repulsion

AbstractHydrodynamic interactions between two identical elastic dumbbells settling under gravity in a viscous fluid at low Reynolds number are investigated using the point-particle model. The evolution of a benchmark initial configuration is studied, in which the dumbbells are vertical and their centres are aligned horizontally. Rigid dumbbells and pairs of separate beads starting from the same positions tumble periodically while settling. We find that elasticity (which breaks the time-reversal symmetry of the motion) significantly affects the system dynamics. This is remarkable when taking into account that elastic forces are always much smaller than gravity. We observe oscillating motion of the elastic dumbbells, which tumble and change their length non-periodically. Independently of the value of the spring constant, a horizontal hydrodynamic repulsion appears between the dumbbells: their centres of mass move apart from each other horizontally. This motion is fast for moderate values of the spring constant $k$, and slows down when $k$ tends to zero or to infinity; in these limiting cases we recover the periodic dynamics reported in the literature. For moderate values of the spring constant, and different initial configurations, we observe the existence of a universal time-dependent solution to which the system converges after an initial relaxation phase. The tumbling time and the width of the trajectories in the centre-of-mass frame increase with time. In addition to its fundamental significance, the benchmark solution presented here is important to understanding general features of systems with a larger number of elastic particles, in regular and random configurations.

Short-time diffusion in concentrated bidisperse hard-sphere suspensions.

Diffusion in bidisperse Brownian hard-sphere suspensions is studied by Stokesian Dynamics (SD) computer simulations and a semi-analytical theoretical scheme for colloidal short-time dynamics, based on Beenakker and Mazur's method [Physica A 120, 388-410 (1983); 126, 349-370 (1984)]. Two species of hard spheres are suspended in an overdamped viscous solvent that mediates the salient hydrodynamic interactions among all particles. In a comprehensive parameter scan that covers various packing fractions and suspension compositions, we employ numerically accurate SD simulations to compute the initial diffusive relaxation of density modulations at the Brownian time scale, quantified by the partial hydrodynamic functions. A revised version of Beenakker and Mazur's δγ-scheme for monodisperse suspensions is found to exhibit surprisingly good accuracy, when simple rescaling laws are invoked in its application to mixtures. The so-modified δγ scheme predicts hydrodynamic functions in very good agreement with our SD simulation results, for all densities from the very dilute limit up to packing fractions as high as 40%.