Short-time Behavior Research Articles

Efficient lattice Boltzmann algorithm for Brownian suspensions

A lattice Boltzmann (LB)-based hybrid method is developed to simulate suspensions of Brownian particles. The method uses conventional LB discretization (without fluid- level fluctuations) for suspending fluid, and treats Brownian particles as point masses with a stochastic thermal noise. LB equations are used to compute the velocity perturbations induced by the particle motion. It is shown that this method correctly reproduces the short-time and long-time diffusive behaviour of a Brownian particle. Unlike the earlier hybrid methods that use thermal fluctuations in the fluid, this method correctly reproduces the temperature of the particle and does not require an empirical rescaling of the bare friction coefficient to obtain the correct diffusive behaviour. It is observed that the present method is at least twice as fast as the earlier method. This method is best suited for flows of polymers and Brownian suspensions in microfluidic devices.

Ten Years of Monitoring 3C 273 with XMM–Newton

We present ten years optical/UV/X-ray observations of 3C 273 performed using XMM–Newton between 2000 and 2009. The short-time scale variability behaviour of the soft and hard X-ray light curves may suggest different origins of the soft/hard X-ray emissions. We fit well the 0.2–10 keV X-ray spectrum with a hard power-law component plus a soft Comptonization component. The lack of Γ − F correlation of the hard power-law component and the weakness of iron Kα lines may support dominance of the jet component. The soft X-ray excess correlates much better with ultraviolet than with the hard power-law component, strongly suggesting that soft excess emission originates from inverse Comptonization of UV photons.

Surrogate for Debye–Waller Factors from Dynamic Stokes Shifts

We show that the short-time behavior of time-resolved fluorescence Stokes shifts (TRSS) are similar to that of the intermediate scattering function obtained from neutron scattering at q near the peak in the static structure factor for glycerol. This allows us to extract a Debye-Waller (DW) factor analog from TRSS data at times as short as 1 ps in a relatively simple way. Using the time-domain relaxation data obtained by this method we show that DW factors evaluated at times ≥ 40 ps can be directly influenced by α relaxation and thus should be used with caution when evaluating relationships between fast and slow dynamics in glassforming systems.

Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-order PDEs

Asymptotic large- and short-time behavior of solutions of the linear disper- sion equation ut = uxxx in R×R+, and its (2k+1)th-order extensions are studied. Such a refined scattering is based on a Hermitian spectral theory for a pair {B,B ∗ } of non self-adjoint rescaled operators B=D 3+ 1 yDy+ 1 I, and the adjoint oneB ∗ =D 3 y− 1 yDy,

Phase transition in saturated porous media: Pore-fluid segregation in consolidation

Consider the consolidation process typical of soils; this phenomenon is expected not to exhibit a unique state of equilibrium, depending on external loading and constitutive parameters. Beyond the standard solution also, pore-fluid segregation can arise. Pore-fluid segregation has been recognized as a phenomenon typical of the short time behavior of a saturated porous slab or a saturated porous sphere, during consolidation. In both circumstances, the Biot three-dimensional model provides time increasing values of the water pressure (and fluid mass density) at the center of the slab (or of the sphere), at early times, if the Lamé constant μ of the skeleton is different from zero. This localized pore-fluid segregation is known in the literature as the Mandel–Cryer effect. In this paper, a nonlinear poromechanical model is formulated. The model is able to describe the occurrence of two states of equilibrium and the switching from one to the other by considering a kind of phase transition. Extending the classical Biot theory, a more than quadratic strain energy potential is postulated, depending on the strain of the porous material and the variation of the fluid mass density (measured with respect to the skeleton reference volume). When the consolidating pressure is strong enough, the existence of two distinct minima is proven.

Investigation of the effect of a variety of pulse errors on spin I = 1 quadrupolar alignment echo spectroscopy

We report on an analysis of a well known three-pulse sequence for generating and detecting spin I = 1 quadrupolar order when various pulse errors are taken into account. In the situation of a single quadrupolar frequency, such as the case found in a single crystal, we studied the potential leakage of single and/or double quantum coherence when a pulse flip error, finite pulse width effect, RF transient or a resonance offset is present. Our analysis demonstrates that the four-step phase cycling scheme studied is robust in suppressing unwanted double and single quantum coherence as well as Zeeman order that arise from the experimental artifacts, allowing for an unbiased measurement of the quadrupolar alignment relaxation time, T 1 Q . This work also reports on distortions in quadrupolar alignment echo spectra in the presence of experimental artifacts in the situation of a powdered sample, by simulation. Using our simulation tool, it is demonstrated that the spectral distortions associated with the pulse artifacts may be minimized, to some extent, by optimally choosing the time between the first two pulses. We highlight experimental results acquired on perdeuterated hexamethylbenzene and polyethylene that demonstrate the efficacy of the phase cycling scheme for suppressing unwanted quantum coherence when measuring T 1 Q . It is suggested that one employ two separate pulse sequences when measuring T 1 Q to properly analyze the short time behavior of quadrupolar alignment relaxation data.

Source-type solutions of heat equations with convection in several variables space

In this paper we study the source-type solution for the heat equation with convection: \(u_t = \Delta u + \vec b \cdot \nabla u^n\) for (x, t) ∈ ST = ℝN × (0, T] and u(x, 0) = δ(x) for x ∈ ℝN, where δ(x) denotes Dirac measure in ℝN, N ⩾ 2, n ⩾ 0 and \(\vec b = \left( {b_1 , \ldots ,b_N } \right) \in \mathbb{R}^N\) is a vector. It is shown that there exists a critical number \(p_c = \frac{{N + 2}} {N}\) such that the source-type solution to the above problem exists and is unique if 0 ⩽ n pc. Moreover, the asymptotic behavior of the solution near the origin is studied. It is shown that when \(0 < N < \frac{{N + 1}} {N}\) the convection is too weak and the short time behavior of the source-type solution near the origin is the same as that for the heat equation without convection.

Investigation of the short-time high-current behavior of vias manufactured in hybrid thick-film technology

In this contribution, the short-time high-current behavior of electrical interconnects (through-metalized vias) manufactured in thick-film technology is investigated. Such vias are reliable devices for small currents, but their behavior when high currents are applied for short times has not been fully understood. Therefore, in a four-wire-setup, short-time high-current pulses were applied to single vias and the resulting transient voltage drops were measured. Furthermore, an FEM-model was developed to simulate this voltage drops as well as the time-dependent temperature distributions inside of the vias. Input parameters were material properties and sample geometries. The good agreement between the measured and the simulated time-dependent voltage drops validated the model. The resulting temperature distributions are an appropriate engineering tool for the further development of vias with respect to reliability and high ampacity.

Thermal resistance and capacity models for borehole heat exchangers

The detailed design and energy analysis of ground source heat pump systems requires the ability to predict the short-term behavior of borehole heat exchangers (BHE). The application of fully discretized models leads to extensive computation times and a substantial effort in terms of pre-processing work. On the contrary, analytical models offer simple, parameter input-based modeling and short computation times, but they usually disregard the transient effects of heat and mass transport in the borehole and hence are not suitable for the prediction of the short-time behavior. In order to combine the advantages of both types of models, the authors developed two-dimensional thermal resistance and capacity models for different types of BHE. These models take the capacity of the grouting material with one capacity per tube into account and, therefore, the range of validity is extended to shorter times. The correct consideration of all thermal resistances between the fluid in the pipes, the grout capacities and the borehole wall is important because of the significant influence on the validity of the models. With the developed models, the modeling work and the computation time can be significantly reduced compared with fully discretized computations while precise results are still achieved. The validation of the suggested models against fully discretized FEM models shows a very good agreement. Copyright © 2010 John Wiley & Sons, Ltd.

Martensitic stainless steel AISI 420—mechanical properties, creep and fracture toughness

In this paper some experimental results and analyses regarding the behavior of AISI 420 martensitic stainless steel under different environmental conditions are presented. That way, mechanical properties like ultimate tensile strength and 0.2 percent offset yield strength at lowered and elevated temperatures as well as short-time creep behavior for selected stress levels at selected elevated temperatures of mentioned material are shown. The temperature effect on mentioned mechanical properties is also presented. Fracture toughness was calculated on the basis of Charpy impact energy. Experimentally obtained results can be of importance for structure designers.

Spin-squeezing and Dicke-state preparation by heterodyne measurement

We investigate the quantum non-demolition (QND) measurement of an atomic population based on a heterodyne detection and show that the induced back-action allows to prepare both spin-squeezed and Dicke states. We use a wavevector formalism to describe the stochastic process of the measurement and the associated atomic evolution. Analytical formulas of the atomic distribution momenta are derived in the weak coupling regime both for short and long time behavior, and they are in good agreement with those obtained by a Monte-Carlo simulation. The experimental implementation of the proposed heterodyne detection scheme is discussed. The role played in the squeezing process by the spontaneous emission is considered.

Hopping and microscopic dynamics of ultrasoft particles in cluster crystals

We have investigated the slow dynamics of ultrasoft particles in crystalline cluster phases, where point particles interact through the generalized exponential potential u(r) = e exp[−(r/σ)n], focusing on the cluster fcc phase of this model with n = 4. In an effort to elucidate how the mechanisms of mass transport depend on the microscopic dynamics and in order to mimic a realistic scenario in a related experiment we have performed molecular dynamics, Brownian dynamics, and Monte Carlo simulations. In molecular dynamics simulations the diffusion of particles proceeds through long-range jumps, guided by strong correlations in the momentum direction. In Monte Carlo and Brownian dynamics simulations jump events are short-ranged, reflecting the purely configurational nature of the dynamics. In contrast to what was found in models of glass-forming liquids, the effect of Newtonian and stochastic microscopic dynamics on the long-time relaxation cannot be accounted for by a temperature-independent rescaling of the time units. From the obvious qualitative discrepancies in the short time behavior between the three simulation methods and the non-trivial difference in jump length distributions, long time relaxation, and dynamic heterogeneity, we learn that a more complex modeling of the dynamics in realistic systems of ultrasoft colloids is required.

Stain etching of silicon with V2O5

AbstractFormation of porous silicon by etching of silicon with vanadium pentoxide dissolved in HF(aq) has been studied with infrared spectroscopy and electron microscopy. The rate of film growth depends strongly on the V2O5 concentration. Addition of ethanol greatly decreases the etch rate and changes the pore morphology from a mixture of {100} + {110} planes to predominantly {100} planes. A plot of thickness vs. etch time in aqueous solutions evolves from a quadratic to a linear dependence. A model is developed in which the surface area depends linearly on film thickness and the thickness exhibits the measured functional form with respect to time. In this model pores with a uniform diameter nucleate randomly, initially grow rapidly before slowing to grow at a constant rate. The pore density increases linearly with time then saturates causing the transition to the linear growth rate phase. This model simultaneously fits both the short time and long time behaviour of the thickness and surface area. Pore formation does not involve an oxide intermediate. Films emit brilliant visible photoluminescence, and are highly uniform both in structure and photoluminescence. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Theory of Absorbance Transients of an Optically Transparent Rough Electrode

Theory for the potentiostatic absorbance transient for a species generated at the rough electrode/electrolyte interface is developed. Absorbance transients are strongly affected by electrode geometries, particularly the effect of electrode roughness which is the least understood area, is dealt here. A general operator structure between concentration, surface absorbance density, absorbance transients and arbitrary roughness profile of electrode is emphasized. The statistically averaged absorbance transients is obtained by ensemble averaging over all possible surface roughness configurations. An elegant mathematical formula between the average spectroelectrochemical absorbance transient and surface structure factor or power spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the absorbance on an approximately self-affine (or realistic) fractal and nonfractal electrode. Our results are also applicable to chronocoulometric response as its directly related to chronoabsorptometric response. Limiting behavior in short time, is attributed to the electrode roughness factor and surface curvatures. Limiting behavior in long time is like a smooth electrode response but the transition region is attributed to the mean square width of roughness. In the intermediate time, the absorbance has anomalous power law behavior which is attributed to the diffusion length weighted spatial frequency features of roughness and becomes almost time independent for large roughness electrodes. Finally, this theory provides a quantitative description of the role of roughness on potential step transmission chronoabsorptometry and chronocoulometric measurements, therefore opening up the way to explore and understand various anomalies in their response.

The displacement correlation tensor: Microstructure, ensemble anisotropy and curving fibers

Experiments with multiple diffusion wave vectors are known to carry more information than what is available from standard diffusion experiments. Here we consider a special case of this class of pulse sequences, the double wave vector diffusion experiment, and use the cumulant expansion of the signal to introduce the displacement correlation tensor. We discuss its physical interpretation and properties, noting in particular that its short time behavior allows determination of the surface to volume ratio of the pore space. We present a general expression for the displacement correlation tensor, and provide explicit expressions for a few model geometries. We then show that the scatter matrix characterizing the orientation distribution of an ensemble of cylinders is simply related to the displacement correlation tensor. This result is generalized to ensembles of pores with arbitrary shapes allowing a precise formulation of the influence of microstructural and ensemble anisotropy on the double wave vector diffusion signal in the Gaussian phase approximation. Finally, as a new application of the double wave vector diffusion signal, we analyze its behavior in a curving fiber, and suggest that the displacement correlation tensor may be used to estimate sub-voxel fiber curvature and deflection angle. The theoretical results are corroborated by computer simulations.

Short-time Oxidation Behavior of Low-carbon, Low-silicon Steel in Air at 850–1,180 °C—III: Mixed Linear-and-Parabolic to Parabolic Transition Determined Using Local Mass-Transport Theories

Under certain assumptions, Levich derived an equation for calculating gas-phase mass transport rate. This equation is commonly used to calculate the linear oxidation rate constant when the oxidation kinetics is controlled by gas phase transport and has been used in this study to calculate oxidation kinetics of steel at 850–1,180 °C in flowing air. In theory, at the early stage, two kinetics components, one linear and another parabolic, simultaneously operate at different locations of the sample, contributing to the overall kinetics and therefore, the oxidation kinetics should show an initial mixed linear-and-parabolic pattern, followed by a purely parabolic stage. However, the actual gas flow pattern in a laboratory tube furnace does not meet the requirements for deriving the Levich’s equation and as a result, significant discrepancies are found between the calculated and experimental results. To resolve the discrepancy, experimental conditions should be modified to meet the gas flow conditions required for deriving the Levich’s equation. Alternatively, a more appropriate equation under the current gas flow conditions in a laboratory tube furnace should be derived.

Thermoacoustic-wave equations for gas in a channel and a tube subject to temperature gradient

This paper develops a general theory for linear propagation of acoustic waves in a gas enclosed in a two-dimensional channel and in a circular tube subject to temperature gradient axially and extending infinitely. A ‘narrow-tube approximation’ is employed by assuming that a typical axial length is much longer than a span length, but no restriction on a thickness of thermoviscous diffusion layer is made. For each case, basic equations in this approximation are reduced to a spatially one-dimensional equation in terms of an excess pressure by making use of a method of Fourier transform. This equation, called a thermoacoustic-wave equation, is given in the form of an integro-differential equation due to memory by thermoviscous effects. Approximations of the equations for a short-time and a long-time behaviour from an initial state are discussed based on the Deborah number and the Reynolds number. It is shown that the short-time behaviour is well approximated by the equation derived previously by the boundary-layer theory, while the long-time behaviour is described by new diffusion equations. It is revealed that if the diffusion layer is thicker than the span length, the thermoviscous effects give rise to not only diffusion but also wave propagation by combined action with temperature gradient, and that negative diffusion may occur if the gradient is steep.

Integrating random matrix theory predictions with short-time dynamical effects in chaotic systems

We discuss a modification to random matrix theory eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian; instead it requires only knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard random matrix theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave-function autocorrelations and cross correlations, and show that significant improvement in accuracy is obtained for simple chaotic systems where comparison can be made with brute-force diagonalization. The accuracy of the method persists even when the short-time dynamics of the system or ensemble is known only in a classical approximation. Further improvement in the rate of convergence is obtained when the method is combined with the correlation function bootstrapping approach introduced previously.

Direct verification of the lubrication force on a sphere travelling through a viscous film upon approach to a solid wall

Experiments were performed to observe the motion of a solid sphere approaching a solid wall through a thin layer of a viscous liquid. We focus mainly on cases where the ratio of the film thickness, δ, to the sphere diameter, D, is in the range 0.03 &lt; δ/D &lt; 0.09 and the Stokes number, St, a measure of the sphere inertia to viscous forces, is below a critical level Stc so that the spheres do not rebound and escape from the liquid layer. This provides us with the scope to verify the force acting on the sphere, derived from lubrication theory. Using high-speed video imaging we show, for the first time, that the equations of motion based on the lubrication approximation correctly describe the deceleration of the sphere when St &lt; Stc. Furthermore, we show that the penetration depth at which the sphere motion is first arrested by the viscous force, which decreases with increasing Stokes number, matches well with theoretical predictions. An example for a shear-thinning liquid is also presented, showing that this simple set-up may be used to deduce the short-time dynamical behaviour of non-Newtonian liquids.

Theory of Generalized Cottrellian Current at Rough Electrode with Solution Resistance Effects

A theory for effect of uncompensated solution resistance on Nernstian (reversible) charge transfer at an arbitrary rough electrode is developed. The significant deviation from the Cottrellian behavior is explained, as arising from the resistivity of the solution and geometric irregularity of the interface. Results are obtained for various electrode roughness models, viz., (i) deterministic surface profile, (ii) roughness as random surface profile with known statistical properties, and (iii) random functions with limited self-affine fractal properties. Expressions for concentration, current density, and total current transients have a systematic operator structure in Fourier transformed (deterministic) surface profile function. For a randomly rough electrode, the statistically averaged response is obtained by ensemble averaging over all possible surface configurations. An elegant mathematical formula between the average electrochemical current transient and surface structure factor of roughness is obtained. Realistic fractal roughness is characterized as self-affine scaling property over limited length scales. Limiting behavior in short time, is attributed to resistive effects of the electrolyte, roughness factor and surface curvatures. In the intermediate time, the anomalous power law behavior is attributed to the diffusion length weighted spatial frequency features of roughness. Our results help with the quantitative understanding of generalized Cottrellian response of moderately supported electrolytic solution at rough electrode/electrolyte interface.