Small Characteristic Time Research Articles

Non-monotonic dependence of fluid dissipation on fluid density in fluid-coupled nanoresonators

Recent studies on fluid-coupled nanoresonators (represented by argon-filled carbon nanotubes or CNTs) have shown nonintuitive variation of the fluid dissipation (Dflu) with fluid density (ρ*) at high-frequency oscillations. In this letter, we propose a physical mechanism that can explain such a behavior. We identify that argon atoms are in the disordered (ordered) state within the CNTs at small (large) ρ*. For low-frequency oscillations, i.e., for oscillations with large characteristic excitation time scales, the argon atoms, at both large and small ρ*, have enough time to dissipate all the energy added from the imposed oscillations. But for high-frequency oscillations, i.e., for oscillations with small characteristic excitation time scales, while the argon atoms in the disordered state (low density) can dissipate all the energy in that small time, those in the ordered state (high density) cannot dissipate all the energy (and hence stores some energy) in that time. This explains the nonmonotonic density-dependence of Dflu in argon-filled CNTs at high frequency. We also explain this nonmonotonic density-dependence of Dflu from the corresponding Deborah number (De). De represents the ratio of the fluid relaxation to the excitation time scales. The relaxation time of CNT-confined argon increases with ρ*. Therefore, for a large-frequency (or a small excitation time) oscillation, De becomes large and the fluid starts losing its fluidity and shows solidlike (“elastic”) characteristics. This viscoelastic behavior ensures a partial storage (without dissipation) of the imposed oscillation, which in turn explains the nonmonotonic variation of Dflu with ρ* for large-frequency oscillations.

Acceleration of plasma in current sheet during substorm dipolarizations in the Earth's magnetotail: Comparison of different mechanisms

This work is devoted to the investigation of particle acceleration during magnetospheric dipolarizations. A numerical model is presented taking into account the four scenarios of plasma acceleration that can be realized: (A) total dipolarization with characteristic time scales of ≈3 min; (B) single peak value of the normal magnetic component B z occurring on the time scale of less than 1 min; (C) a sequence of rapid jumps of B z interpreted as the passage of a chain of multiple dipolarization fronts (DFs); and (D) the simultaneous action of mechanism (C) followed by the consequent enhancement of electric and magnetic fluctuations with the small characteristic time scale ≤1 s. In a frame of the model, we have obtained and analyzed the energy spectra of four plasma populations: electrons e−, protons H+, helium He+, and oxygen O+ ions, accelerated by the above-mentioned processes (A)–(D). It is shown that O+ ions can be accelerated mainly due to the mechanism (A); H+ and He+ ions (and to some extent electrons) can be more effectively accelerated due to the mechanism (C) than the single dipolarization (B). It is found that high-frequency electric and magnetic fluctuations accompanying multiple DFs (D) can strongly accelerate electrons e− and really weakly influence other populations of plasma. The results of modeling demonstrated clearly the distinguishable spatial and temporal resonance character of particle acceleration processes. The maximum particle energies depending on the scale of the magnetic acceleration region and the value of the magnetic field are estimated. The shapes of energy spectra are discussed.This work is devoted to the investigation of particle acceleration during magnetospheric dipolarizations. A numerical model is presented taking into account the four scenarios of plasma acceleration that can be realized: (A) total dipolarization with characteristic time scales of ≈3 min; (B) single peak value of the normal magnetic component B z occurring on the time scale of less than 1 min; (C) a sequence of rapid jumps of B z interpreted as the passage of a chain of multiple dipolarization fronts (DFs); and (D) the simultaneous action of mechanism (C) followed by the consequent enhancement of electric and magnetic fluctuations with the small characteristic time scale ≤1 s. In a frame of the model, we have obtained and analyzed the energy spectra of four plasma populations: electrons e−, protons H+, helium He+, and oxygen O+ ions, accelerated by the above-mentioned processes (A)–(D). It is shown that O+ ions can be accelerated mainly due to the mechanism (A); H+ and He+ ions (and to some exten...

A new model for simulating heat, air and moisture transport in porous building materials

This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport and its impact on the heat and moisture transfer. The achievement of the mathematical model is detailed in the continuity of Luikov’s work. A system composed of two advection–diffusion differential equations plus one exclusively diffusion equation is derived. The main issue to take into account the transient air transfer arises in the very small characteristic time of the transfer, implying very fine discretisation. To circumvent these difficulties, the numerical model is based on the Du Fort–Frankel explicit and unconditionally stable scheme for the exclusively diffusion equation. It is combined with a two–step Runge–Kutta scheme in time with the Scharfetter–Gummel numerical scheme in space for the coupled advection–diffusion equations. At the end, the numerical model enables to relax the stability condition, and, therefore, to save important computational efforts. A validation case is considered to evaluate the efficiency of the model for a nonlinear problem. Results highlight a very accurate solution computed about 16 times faster than standard approaches. After this numerical validation, the reliability of the mathematical model is evaluated by comparing the numerical predictions to experimental observations. The latter is measured within a multi-layered wall submitted to a sudden increase of vapor pressure on the inner side and driven climate boundary conditions on the outer side. A very satisfactory agreement is noted between the numerical predictions and experimental observations indicating an overall good reliability of the proposed model.

Effect of the time-weakening friction law during the nucleation process

Based on dynamic rupture simulations on a planar fault in a homogeneous half-space, we investigated the nucleation processes using the time-weakening friction law. Both the characteristic time and the rupture speed in the nucleation asperity play an important role in determining rupture behaviors on a fault plane following the time-weakening friction law, with which rupture starts from a single point in the nucleation asperity and propagates at a given speed toward the boundary of the nucleation area. Rupture with a small characteristic time or a large rupture speed in the nucleation asperity propagates earlier from the hypocenter. Rupture following the slip-weakening friction law requires a smaller radius of nucleation patch to have similar rupture front contours of the time-weakening friction law. Even if the rupture velocity in the nucleation patch of the time-weakening friction law increases to infinity, the peak slip rate in the nucleation asperity is smaller than that of the slip-weakening law. The peak ground velocity distributions of ruptures following the two friction laws are also compared.

A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames

In this paper, the chemical response of different species to turbulent effects is investigated in the context of one-dimensional laminar non-premixed flamelets. Turbulent effects are modeled as abrupt changes in the scalar dissipation rate. One-dimensional unsteady flamelet calculations assuming unity-Lewis number for all species are performed for an ethylene/air configuration. From the time-evolution of the species mass fractions, it is found that transient effects are not substantial for radicals such as OH and H, and species such as CO,CO2 and C2H2, consistent with their small characteristic chemical time scales. The steady state flamelet assumption for these species is well justified and their mass fractions can be pre-tabulated using the steady state flamelet solutions legibly. On the other hand, aromatic species are characterized by relatively slow chemistry, and substantial transient effects are observed for these species. The evolution of their mass fractions and chemical source terms are studied through a reaction flux analysis. Specifically for Polycyclic Aromatic Hydrocarbons (PAH), the chemical production terms are found to be linearly proportional to the mass fraction of smaller aromatic species, and the chemical consumption terms are found to be linearly proportional to their own mass fractions. Based on the unsteady flamelet results, the validity of various existing flamelet-based pre-tabulation methods is examined, and a new linear relaxation model is proposed for PAH. The proposed relaxation model is validated through the unsteady flamelet formulation, and results are compared against full chemistry calculations.

Non-resonant and non-enhanced Raman Correlation Spectroscopy

We present the first non-resonant and non-enhanced Raman correlation spectroscopy experiments. They are conducted on a confocal microscope combined with a Raman spectrometer. The thermal fluctuations of the Raman intensities scattered by dispersions of polystyrene particles of sub-micrometric diameters are measured and analysed by deriving the autocorrelation functions (ACFs) of the intensities. We show that for particles of diameter down to 200 nm, RCS measurements are successfully obtained in spite of the absence of any source of amplification of the Raman signal. For particles of diameter ranging from 200 to 750 nm, the ACFs present a time-decay behaviour in accordance with the model of free Brownian particles. For particles of 1000 nm in diameter, the AFCs present a different behaviour with a much smaller characteristic time. This results from the dynamics of a single-Brownian particle trapped in the confocal volume by the optical forces of the focus spot.

On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit

We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this numerically. Interestingly, in spite of the nonlinearity of the model, the approximate solution exhibits nearly a linear profile. Finally, we extend the reduced model to the simplest PDE system for shape memory alloys that can capture oscillations and then damp out these oscillations numerically. The numerical results for both limiting cases show excellent agreement. The graphs show that the valve opens in an instant, which is realistic behavior of the free boundary.

Characterization and modeling of fast traps in thermal agglomerating germanium nanocrystal metal-oxide-semiconductor capacitor

In this paper, the germanium (Ge) nanocrystals (NCs) are synthesized by using the rapid-thermal annealing and are embedded into a three-layer (SiO2∕NCs–Ge∕SiO2) capacitor structure. The samples with∕without the postmetallization annealing (PMA) treatment are investigated to compare and study the PMA affections. The charge storage characteristics of our samples are investigated with the capacitance-voltage (C-V) hystereses. The frequency independence of hysteresis windows is found and attributed to NCs as slow traps with a large characteristic time constant. The frequency-dependent C-V and conductance-voltage (G-V) experiments are further introduced to study the interface traps and the fast traps induced by the NC formation. In order to extract the related trap characteristics from the measured C-V and G-V, we propose to utilize the equivalent circuit and single-level trap model based on Shakley-Read-Hall theory. Three associated parameters including the areal trap density, trap conductance, and semiconductor capacitances are used to confirm that the single-level trap model is truly appropriate for our samples. It is then found from the model that the areal trap density is high and approaches almost uniform distribution along the valence band and bandgap but significantly reduced and then becomes decreased from valence band to the midgap after PMA treatment. In addition, after PMA treatment, the characteristic time constant becomes smaller for one order of magnitude at the same gate bias. It is attributed to the reduction of trap density and also agrees that the interface traps are dominant and has a small characteristic time constant.

Dimensional analysis of two-phase flow including a rate-dependent capillary pressure–saturation relationship

The macroscopic modelling of two-phase flow processes in subsurface hydrosystems or industrial applications on the Darcy scale usually requires a constitutive relationship between capillary pressure and saturation, the P c( S w) relationship. Traditionally, it is assumed that a unique relation between P c and S w exists independently of the flow conditions as long as hysteretic effects can be neglected. Recently, this assumption has been questioned and alternative formulations have been suggested. For example, the extended P c( S w) relationship by Hassanizadeh and Gray [Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990;13(4):169–86] proposes that the difference between the phase pressures to the equilibrium capillary pressure is a linear function of the rate of change of saturation, thereby introducing a constant of proportionality, the coefficient τ. It is desirable to identify cases where the extended relationship needs to be considered. Consequently, a dimensional analysis is performed on the basis of the two-phase balance equations. In addition to the well-known capillary and gravitational number, the dimensional analysis yields a new dimensionless number. The dynamic number Dy quantifies the ratio of dynamic capillary to viscous forces. Relating the dynamic to the capillary as well as the gravitational number gives the new numbers DyC and DyG, respectively. For given sets of fluid and porous medium parameters, the dimensionless numbers Dy and DyC are interpreted as functions of the characteristic length and flow velocity. The simulation of an imbibition process provides insight into the interpretation of the characteristic length scale. The most promising choice for this length scale seems to be the front width. We conclude that consideration of the extended P c( S w) relationship may be important for porous media with high permeability, small entry pressure and high coefficient τ when systems with a small characteristic length (e.g. steep front) and small characteristic time scale are under investigation.

Liquid Mechanical Behavior of Mixed Monolayers of Amino and Alkyl Silanes by Atomic Force Microscopy

The adsorption of mixed terminally aminated organosilyl compounds with long-chain n-alkyltrichlorosilanes on silica substrates has been studied by FTIR and AFM to deposit and study DNA. By optimization of deposition conditions, the mixed monolayers were found to be well organized and homogeneous. The amino group was protected to obtain a reproducible grafting and then deprotected after the film formation. In addition, atomic force microscopy (AFM) studies in both dynamical modes, amplitude modulation and frequency modulation, reveal that the layer behaves as a fluid as measured by the tip-cantilever and has a smaller characteristic time than the tip-cantilever. For three amplitudes, the experimental frequency shifts have been modeled for a fluidlike layer crossed by the tip. Finally, we show that this new fluidlike monolayer is suitable for DNA deposition and AFM studies.

Wave damping as a critical phenomenon

The evolution of a monochromatic Langmuir wave in a collisionless plasma is studied using Vlasov simulations for a wide range of initial amplitudes. Three types of initial electron distributions are considered: Maxwellian, Lorentzian, and dilute warm Maxwellian plus dense cold component. It is shown that there exists a critical initial amplitude ε* that separates the damping and nondamping asymptotic regimes. Depending on the initial amplitude there are three main types of asymptotic evolution: (i) monotonic linear Landau damping below the threshold, ε≪ε*; (ii) the critical case ε≈ε*, when the field damps algebraically as E(t)∝t−3.26; (iii) at ε>ε* initial damping followed by a period of subsequent exponential growth and then irregular oscillations about a nonzero amplitude. This threshold is well described as a critical phenomenon, showing power-law dependencies on the distance from the threshold not only for field quantities, which are expected of second-order phase transitions in thermodynamics, but also for temporal ones. The critical exponent for both the initial damping and growth phases differ from those expected if the threshold is caused by O’Neil’s particle trapping in the wave potential. However, trapping affects the critical exponents well above the threshold and explains the characteristic frequency of oscillations above the threshold. It is found that for a Maxwellian plasma the threshold amplitude ε* corresponds to the condition that the trapping (bounce) frequency ωb equals the modulus of the theoretical Landau damping rate |γL|; at the threshold, qc=ωb/|γL|≈1. For Lorentzian and Maxwellian-plus-cold component plasmas this ratio is qLor≈0.84 and qCM≈0.83, respectively. The temporal and the field scalings are thus interrelated, suggesting that the inclusion of the temporal dimension is vital for critical phenomena in collisionless plasmas, in contrast to thermodynamic systems where the very small characteristic time to achieve equilibrium removes time from the scaling.

Neck dynamics at the approach stage of heavy ion collisions

Neck dynamics is investigated at the approach phase of reaction. Using realistic mass parameters and friction coefficients in the classical equations of collective motion, an oscillating behaviour of the neck is obtained. Due to the small characteristic time for neck oscillations, the addition of the neck variable to the collective variable set may be questionable for internuclear distances considered. In the liquid drop model an averaging over the fast neck variable leads to a relative motion of the nuclei that is similar to the motion in a potential obtained in the frozen density approximation. The role of the nucleon flow, which is identified to the small neck, is discussed for the case of sub-barrier fusion.

Enzyme electrodes and their application.

Starting from the state of the art, principles for improving the analytical characteristics of enzyme electrodes are discussed. Coupling of appropriate amperometric electrode processes with enzyme systems, e.g. urease or aminopeptidases, results in a simplification of operation. Optimal sample frequencies are realized on the basis of enzyme membranes, with both a small characteristic diffusion time and a high enzyme activity, applied in a well-designed sample-processing system. Coupled enzyme reactions of the sequence or competition type are successfully used for extension to new analytes, e.g. inhibitors, cofactors or alternative substrates. Cyclization of the analyte enhances the sensitivity of enzyme electrodes to the nanomolar concentration range. Enzymic anti-interference layers are a tool for improving the sensor specificity. The operational characteristics of enzyme electrodes are thus adaptable to any given analytical problem.

Statistical predictability and spectra of air temperature over the northern hemisphere

Parametric models and statistical predictability of mean annual air temperature, both at individual stations (MAAT) and zonally averaged (MZAT), are evaluated. The time series have lengths from 125 to 315 years for MAAT and 86 years (1891–1976) for MZAT. The optimal parametric models of MAAT are shown to be closely approximated by a first-order Markov sequence with a small characteristic time scale, so that their statistical predictability is minimal. Variations in MZAT should be described with more complicated models; the limits of statistical predictability amount to between 4 and 5 years. The temperature spectra are estimated, and the relatively high statistical predictability is shown to result from the concentration of spectral energy at low frequencies.