Linear Time Dependence Research Articles

Formulization of long-time domain switching around the coercive field from imprint measurements on ferroelectric thin films

The time interval for the completion of slow polarization reversal in ferroelectric thin films measured in the order of magnitude of 10−9–100s is broadened by more than two decades as the applied field approaches the coercive field of domain switching. The domain-switching kinetics is conjectured to change from the classical Kolmogorov–Avrami–Ishibashi (KAI) model at high fields to nucleation-limited-switching (NLS) model at low fields. However, the true voltage drop across the film from the real-time measurement of the oscilloscope remains constant at a coercive voltage Vc during polarization reversal irrespective of the applied voltage. Therefore, the above high-field assumption for KAI does not exist. From our measurements, a long-time effect of imprint can occur for any slow processes of physical phenomena, even if the imprint field is very weak. The imprinted Vc can be estimated either from the voltage shift in the curve of switched polarization versus the applied voltage or directly from the height variation in domain-switching current plateau after an imprint voltage Vimp for time timp (1μs<timp<10ms). Vc reduces continually with timp under Vimp>0 to exhibit a linear time dependence in a logarithmic scale above an initial time on the order of 1.0μs, even if under Vimp<Vc, which foretells the possibility of the initial unswitched domains with negative polarizations to switch into positive states with the prolonged imprint time under a positive voltage of Vimp. After formulation of the Vc-timp dependence under Vimp according to imprint principles, we derive the time evolution of slow polarization reversal without evoking KAI and NLS approaches once the Vc distribution is obtained for a genuine thin film. The spectrum derivation is completely comparable to experimental measurements, which suggests the common physics between imprint and long-time domain switching of ferroelectric thin films.

Dielectric relaxation studies of molecular association: complexing of methyl acrylate and butyl acrylate with phenols in the MW region

Dielectric relaxation measurements on alkyl acrylates (methyl acrylate and butyl acrylate) with phenols (p-cresol, p-chlorophenol and 2,4-dichlorophenol) have been studied at microwave frequency 9.37 GHz in dilute solution of carbon tetrachloride at 308 K. The relaxation time and activation energy have been determined using the measured dielectric data. The results show a linear dependence of relaxation time on alkyl chain length of acrylic esters and acidity of phenols and also on the nature of the solvent. Comparative study of free energy of activation for the dielectric relaxation and viscous flow suggest the fact that the process of viscous flow involves greater inference by neighbouring than does dielectric relaxation, as the latter takes place by rotation only, whereas the viscous flow involves both the rotational and translational forms of motion. The validity of the single frequency equation of Higasi et al . (Bull. Chem. Soc. Jpn, 44, 988 (1971)) for multiple relaxation time τ(1) is found to be a function of the hydrogen bonding strength of phenolic hydrogen whereas the group rotation relaxation time τ(2) is a function of the steric interaction of proton donor. The relaxation time is the maximum at 50 : 50 (molar ratio).

Interface Migration Behavior of the δ→γ Interface in Low Carbon High Manganese Steel Samples De-oxidized with Ti or Al

The effect of inclusions, generated during de-oxidation and solidification, of low carbon (0.07wt%) and high manganese (0.9wt%) steels, on the rates of migrations of the boundaries between delta-ferrite/gamma-austenite interfaces, during austenite formation was investigated. The presence of two types of de-oxidation products were investigated, namely Al 2 O 3 (1-3μm) in Al-killed steel samples, and Ti-AI-(Mg)-O (0.3-1 μm) in Ti-killed steel samples. The samples were prepared in a vacuum-induction furnace and a Confocal Scanning Laser Microscope was used to image in real time the interface movement on the surface of the samples. Austenite was found to precipitate at the triple-points of the delta-ferrite grain boundaries during cooling from 1 500 to 1 460 and 1 450°C and the growth appeared to be diffusion controlled. The migration rates of delta/gamma interfacial boundaries were higher in the Al-killed steel samples than in the Ti-killed steel samples and this is attributed to the finer oxide particle population in the latter. When the samples were cooled to 1 440°C and below sword-like precipitation was observed in all samples that grew at a higher rate than what was observed at higher temperatures and the growth appeared to have linear time dependence, and thus the process appears to not be governed by long range diffusion.

Nanosecond-range measurements of imprint effect for Pt∕IrO2∕Pb(Zr0.4Ti0.6)O3∕IrO2∕Pt thin-film capacitors

The determination of the coercive voltage from the height of domain-switching current plateau in ferroelectric thin films provides the liability to estimate the coercive-voltage shift with imprint time shortly on the order of polarization-reversal time. The voltage shift exhibits a linear time dependence in a logarithmic scale above an initial time (∼1μs), below which the voltage is nearly constant. The modeling of imprint on the basis of the interfacial charge injection at different stressing voltages strongly supports Schottky emission as a dominant mechanism, instead of Frenkel-Poole emission and Fowler-Nordheim tunneling.

Corrosion of Alloy 690 process pot by sulfate containing high level radioactive waste at feed stage

Prolonged exposure of Alloy 690 process pot to sulfate containing high level radioactive waste leads to (a) depletion of Cr from the alloy, (b) intergranular attack and (c) building up of Cr 2O 3–Ni 2O 3–Fe 2O 3 mixed oxide surface layer containing Na and Cs sulfate precipitates. Time dependence of material loss from Alloy 690 is found to follow a linear relationship of the type Δ w (material loss) = −7.05 + 0.05 t. Corrosion rate calculated for 2400 h exposure is 3.66 mpy. Cr and Ni leach rates obtained for the same sample are 1.61 g m −2 d −1 and 2.52 g m −2 d −1, respectively. Ni leach rates followed a linear time dependence relationship of the type dNL Ni/d t (leach rate) = −0.09 + 0.027 t, whereas Cr leach rates obeyed a non-linear relationship of the type dNL Cr/d t (leach rate) = 0.241 + 0.027 t − 1.33 × 10 −4 t 1/2.

Nucleation and Growth of GaN Nanowires on Si(111) Performed by Molecular Beam Epitaxy

GaN nanowires (NWs) have been grown on Si(111) substrates by plasma-assisted molecular beam epitaxy (PAMBE). The nucleation process of GaN-NWs has been investigated in terms of nucleation density and wire evolution with time for a given set of growth parameters. The wire density increases rapidly with time and then saturates. The growth period until the nucleation of new nanowires is terminated can be defined as the nucleation stage. Coalescence of closely spaced nanowires reduces the density for long deposition times. The average size of the well-nucleated NWs shows linear time dependence in the nucleation stage. High-resolution transmission electron microscopy measurements of alternating GaN and AlN layers give valuable information about the length and radial growth rates for GaN and AlN in NWs.

Limit on the Cosmological Variation ofmp/mefrom the Inversion Spectrum of Ammonia

We obtain the limit on the space-time variation of the ratio of the proton mass to the electron mass, mu=m(p)/m(e), based on comparison of quasar absorption spectra of NH3 with CO, HCO+ and HCN rotational spectra. For the inversion transition in NH3 (lambda approximately 1.25 cm(-1)) the relative frequency shift is significantly enhanced: deltaomega/omega=-4.46deltamu/mu. This enhancement allows one to increase sensitivity to the variation of mu using NH3 spectra for high redshift objects. We use published data on microwave spectra of the object B0218+357 to place the limit deltamu/mu=(0.6+/-1.9) x 10(-6) at redshift z=0.6847; this limit is several times better than the limits obtained by different methods and may be significantly improved. Assuming linear time dependence we obtain mu/mu=(-1+/-3) x 10(-16) yr(-1).

Development of ${\hbox{Nb/Al-AlN}}_{\rm x}/{\hbox{Nb}}$ SIS Tunnel Junctions for Submillimeter-Wave Mixers

Nb/Al-AlN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /Nb SIS junctions have been fabricated under various conditions of plasma nitridation. Junctions with low R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> A of ~ 10 Omega mum <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> have been fabricated in pure nitrogen plasma, although this process exhibited low reproducibility. A process with higher reproducibility was realized by adopting a two-step-ignition nitridation process in a composite plasma of N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and Ar. An exponential correlation between the nitridation time and the junction R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> A was found for the junctions with barriers formed in this new process, which suggests a linear time dependence of the barrier thickness during nitridation. SIS junctions with R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> A ~ 10 Omega mum <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> can be repeatedly produced using this process. Preliminary results from X-ray photoelectron spectroscopy (XPS) observations of the nitride barrier are also presented. While the N 1s XPS signal was apparently detected in the junctions with high R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> A, their intensity was reduced as R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> A the decreases.

Long-range effects on superdiffusive algebraic solitons in anharmonic chains

Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The position variance of the soliton shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest neighbour interactions (NNI). In contrast to the NNI case where the position variance at moderate soliton velocities has a considerable linear time-dependence (normal diffusion), the solitons with LRI are dominated by a superdiffusive mechanism where the position variance mainly depends quadratic and cubic on time. Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on a FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI). A collective variable (CV) approach in the continuum approximation of the system leads to stochastic integro-differential equations which can be reduced to Langevin-type equations for the CV position and width. We are able to derive an analytical result for the soliton diffusion which agrees well with the simulations of the discrete system. Despite of structurally similar Langevin systems for the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic $t^{1.5}$ time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of $\pi$ smaller for algebraic solitons.

Leaking billiards

Billiards are idealizations for systems where particles or waves are confined to cavities, or to other homogeneous regions. In billiard systems a point particle moves freely except for specular reflections from rigid walls. However, billiard walls are not always completely reflective and measurements inside can also open the billiard. Since boundary openings have been studied extensively in the literature, we rather model leakages inside the billiard. In particular, we investigate the classical dynamics of a leakage for a continuous family of billiard systems, that is, the stadium-lemon-billiard family. With a single parameter the geometry of the billiard can be tuned from stadium (being fully hyperbolic) over circle (integrable) to the lemon-shaped billiard (mixed chaotic). For the stadium billiard we found an algebraically decaying mean escape time with the linear size of the leakage n(esc) approximately epsilon-1 together with an exponential decay of the survival probability distribution. The finding is nearly independent of the position and size of the leakage, as long as the leakage is much smaller than the system size, and it is in good agreement with a stochastic map approximation of the dynamics. Due to the mixed phase space for lemon billiards, the mean escape time depends both on the position and geometry of the leakage. For systems where quasiregular motion dominates, we found a linear dependence of the mean escape time, n(esc) approximately 1-epsilon, which we refer to as flooding law. Our findings are helpful in understanding dynamics of leaking Hamiltonian systems.

Evaporation from a Limonene Emulsion

A publication to honor the legacy of Per Ekwall, the Finnish colloid chemist, whose research was on the forefront for several decades in the area of colloidal association structures. In the article an algebraic method was applied to obtain information about the conditions during evaporation of the volatile compounds in a system of limonene, water and Laureth 4 (a commercial tetraoxyethylene dodecyl ether). The evaporation path was calculated using published information about the phase diagram of the system and about the vapor pressures of the components at selected compositions. In the calculations intervals between steps were made proportional to the difference between the excess vapor pressure of water at the selected level of relative humidity and its full vapor pressure at zero relative humidity. This calculation method inherently gave linear time dependence of the remaining water in the emulsion because of its constant vapor pressure. The calculations also revealed the amount of limonene to be close to linearly dependent on time. The reason for this latter result was found in the features of the phase diagram; in turn caused by the limonene oil phase being a W/O microemulsion with moderate vapor pressure variation with composition.

Direct Numerical Simulation of Single-Molecule DNA by Cable Dynamics

In this paper, we present direct numerical simulation (DNS) of the transient dynamics of single-molecule DNA by modeling it as a highly flexible cable. Fully nonlinear dynamic equations are derived from the principles of conservation of momentum and angular momentum, and solved via numerical means. Compared to previous models, this cable-dynamics model enables direct physical simulation of an individual biopolymer string rather than a random-walk style statistical modeling. To validate this DNS modeling approach, the canonical DNA stretching problem is simulated. The DNS solutions are compared with published benchmark results. The DNS model is further deployed to investigate the Brownian motion of single DNA molecule, and the translocation process of a DNA molecule through a nanopore induced by the presence of an external electric field. In the latter case, our simulations have exhibited good agreement with experimental observations, including the linear dependence of the translocation time on the contour length of the molecule, the formation of “hairpins” during translocation, and back-and-forth molecule motions. 1553

A fat fractal crisis in a quasi-dissipative system

A crisis, induced by a sudden change of a fat strange set to a transit, is observed in a system, which is a two-dimensional discontinuous and noninvertible map and displays a dissipation sowing linear time dependence. It is shown analytically and numerically that, in this crisis, the characteristic scaling exponent takes a large value of 1.72; this is in agreement with the observed superlong transients.

Oxidation of hydrogenated crystalline silicon as an alternative approach for ultrathin SiO2 growth

This article is devoted to the growth of thin thermal SiO2 layers on hydrogenated Si substrates as a possibility to obtain improved properties of oxide-Si structure for contemporary MOS devices. Spectral ellipsometry and atomic force microscopy have been applied for characterization of the SiO2/Si interface and surface morphology. The results show that the oxidation kinetics obeys longer linear time dependence in thin-film regime. The smaller activation energies and higher initial oxide growth rates indicate facilitation of oxide growth in the early oxidation stage. Formation of a reactive less dense Si surface layer is suggested to be responsible for the higher kinetics rates and oxide thicknesses in the very initial stage.

Controlled Radical Polymerization of Styrene by Quinone Transfer Radical Polymerization (QTRP)

Radical polymerization of styrene falls under control when conducted at 100 °C in the presence of an ortho-quinone, e.g., phenanthrenequinone (PhQ), and a catalytic amount of cobalt(II) acetylacetonate. Criteria for a controlled chain polymerization are fulfilled at least until 50% of monomer conversion, i.e., molar mass increasing with monomer conversion, molar mass predictable from the styrene/quinone molar ratio, linear time dependence of ln([M]0/[M]), and effective resumption of styrene polymerization by preformed oligopolystyrene. A tentative mechanism is proposed for this new system designated as quinone transfer radical polymerization (QTRP).

Interlayer growth at interfaces of Ti/Al–1%Mn, Ti/Al–4·6%Mg and Ti/pure Al friction weld joints by post-weld heat treatment

The interlayer growth at interfaces of Ti/Al–1%Mn and Ti/Al–4·6%Mg weld joints was studied by postweld heat treatment. The heating temperatures ranged from 676 to 873 K (400–600°C) and maximum heating time was 360 ks (100 h). The basic mechanism of interlayer growth for pure Ti/pure Al friction weld joint was also estimated. The interlayer growth rate of Ti/Al–4·6%Mg joint was much faster than for the Ti/ Al–1%Mn joint. The interlayer mainly consisted of (Al,Si)3Ti for the Ti/Al–1%Mn joint, and Al18Mg3Ti2 for the Ti/Al–4·6%Mg joint. While the interlayer grew from Al alloy substrate to the Ti side for the Ti/Al–1%Mn joint, it grew from the Ti substrate to the Al alloy side for the Ti/Al–4·6%Mg joint. The interlayer growth stopped for several hours on heating for 36 ks (10 h). Neither linear nor parabolic time-dependence relations could be exactly fit to the interlayer growth rate for both joints. The interlayer growth of Ti/Al–1%Mn was proportional to heating time raised to approximately 0·85. The crystal direction of Al3Ti interlayer growth of the Ti/Al joint was close to 〈001〉 and 〈111〉 directions obtained by OIM method. Nucleation and nuclei growth were observed at the interface of the Ti/Al joint. The nucleation and the nuclei growth are the reason for the phenomena (time dependence) described above.

Optimal control of forced cool-down processes

The optimization of forced cooling-down processes is performed using the optimal control theory. Four objective functions are shortly presented and minimized. They include the consummated cooling fluid mass and some dissipation measures, as the entropy generation and variants of the lost available work. The minimum duration for the cooling process with minimum lost available work normally exceeds the minimum duration for the cooling processes with minimum mass of cooling fluid but the reverse is sometimes true. The minimum lost available work does not depend on the initial and final temperatures of the cooled body but just on the duration of the cooling process. The cooling strategies with linear (or slightly non-linear) time dependence of cooled body temperature are based on rather strong non-linear increase in the optimum cooling fluid mass flow rate at the end of the cooling process.

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[xs] which predicts a stronger than linear time dependence of Var[xs] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.

An Improved Model for Prediction of Retention Times of Tryptic Peptides in Ion Pair Reversed-phase HPLC: Its Application to Protein Peptide Mapping by Off-Line HPLC-MALDI MS

The proposed model is based on the measurement of the retention times of 346 tryptic peptides in the 560- to 4,000-Da mass range, derived from a mixture of 17 protein digests. These peptides were measured in HPLC-MALDI MS runs, with peptide identities confirmed by MS/MS. The model relies on summation of the retention coefficients of the individual amino acids, as in previous approaches, but additional terms are introduced that depend on the retention coefficients for amino acids at the N-terminal of the peptide. In the 17-protein mixture, optimization of two sets of coefficients, along with additional compensation for peptide length and hydrophobicity, yielded a linear dependence of retention time on hydrophobicity, with an R2 value about 0.94. The predictive capability of the model was used to distinguish peptides with close m/z values and for detailed peptide mapping of selected proteins. Its applicability was tested on columns of different sizes, from nano- to narrow-bore, and for direct sample injection, or injection via a pre-column. It can be used for accurate prediction of retention times for tryptic peptides on reversed-phase (300-A pore size) columns of different sizes with a linear water-ACN gradient and with TFA as the ion-pairing modifier.

Retention indexes for temperature-programmed gas chromatography of polychlorinated biphenyls.

A noninteger retention index was defined based on a series of PCB internal standards, namely congeners 8 (2,4'-dichlorobiphenyl), 31 (2,4',5-trichlorobiphenyl), 44 (2,2',3,5'-tetrachlorobiphenyl), 101 (2,2',4,5,5'-pentachlorobiphenyl), 138 (2,2',3,4,4',5'-hexachlorobiphenyl), 180 (2,2',3,4,4',5,5'-heptachlorobiphenyl), and 194 (2,2',3,3',4,4',5,5'-octachlorobiphenyl). These retention index markers are common congeners present in technical mixtures and most environmental samples, and they show a linear dependence of retention time on the number of chlorine atoms, in the temperature-programmed analysis. The index values are calculated with a single regression equation instead of the Van den Dool and Kratz equation. The retention indexes of all 209 PCBs on two commonly used columns (DB-XLB and DB-5), as well as on a supplementary column of DB-17 in capillary gas chromatography, were determined using this system. The reliability of the retention index is quite good, with the average 95% confidence limits for three measurements on each PCB being +/-0.1 index unit under the same chromatographic conditions and +/-0.4 index unit under different column head pressures. The effect of heating rate of the programmed runs on the retention index was also investigated. The inversion of the elution order of some congener pairs on the DB-XLB column for different temperature heating rates was observed. Our index values were compared with those of Castello and Testini.