Effect Of Finite Thickness Research Articles

Modeling interface-controlled phase transformation kinetics in thin films

The Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation is widely used to describe phase transformation kinetics. This description, however, is not valid in finite size domains, in particular, thin films. A new computational model incorporating the level-set method is employed to study phase evolution in thin film systems. For both homogeneous (bulk) and heterogeneous (surface) nucleation, nucleation density and film thickness were systematically adjusted to study finite-thickness effects on the Avrami exponent during the transformation process. Only site-saturated nucleation with isotropic interface-kinetics controlled growth is considered in this paper. We show that the observed Avrami exponent is not constant throughout the phase transformation process in thin films with a value that is not consistent with the dimensionality of the transformation. Finite-thickness effects are shown to result in reduced time-dependent Avrami exponents when bulk nucleation is present, but not necessarily when surface nucleation is present.

Nanomechanical and topographical imaging of living cells by atomic force microscopy with colloidal probes.

Atomic Force Microscopy (AFM) has a great potential as a tool to characterize mechanical and morphological properties of living cells; these properties have been shown to correlate with cells' fate and patho-physiological state in view of the development of novel early-diagnostic strategies. Although several reports have described experimental and technical approaches for the characterization of cellular elasticity by means of AFM, a robust and commonly accepted methodology is still lacking. Here, we show that micrometric spherical probes (also known as colloidal probes) are well suited for performing a combined topographic and mechanical analysis of living cells, with spatial resolution suitable for a complete and accurate mapping of cell morphological and elastic properties, and superior reliability and accuracy in the mechanical measurements with respect to conventional and widely used sharp AFM tips. We address a number of issues concerning the nanomechanical analysis, including the applicability of contact mechanical models and the impact of a constrained contact geometry on the measured Young's modulus (the finite-thickness effect). We have tested our protocol by imaging living PC12 and MDA-MB-231 cells, in order to demonstrate the importance of the correction of the finite-thickness effect and the change in Young's modulus induced by the action of a cytoskeleton-targeting drug.

A penetration model for metallic targets based on experimental data

The database for depth of penetration by projectiles into semi-infinite targets is quite extensive. The objective is to use the experimental semi-infinite penetration data to predict finite-thickness target effects. Similitude considerations are used to represent penetration response as a function of a normalized impact velocity, which is the ratio of the penetration pressure to the target strength. Then, a least-squares regression analysis methodology was applied to the normalized experimental data to provide an analytic expression for the normalized depth of penetration as a function of the normalized impact velocity over a very large velocity range, typically a few hundred meters per second to over 3500 m/s. We use the analytic expression, along with some simplifying assumptions, to estimate ballistic limit thickness T50 and/or the ballistic limit velocity V50. If a target is overmatched, i.e., perforated by the projectile, an estimate is also made for the projectile residual velocity and residual length. The experimental data on which the regression fit is based consists of L/D 10 projectiles, so a procedure is also developed to account for different projectile aspect ratios. A series of examples are provided to demonstrate the utility and accuracy of the approach.

Weakly nonlinear Rayleigh-Taylor instability of a finite-thickness fluid layer

A weakly nonlinear (WN) model has been developed for the Rayleigh-Taylor instability of a finite-thickness incompressible fluid layer (slab). We derive the coupling evolution equations for perturbations on the (upper) “linearly stable” and (lower) “linearly unstable” interfaces of the slab. Expressions of temporal evolutions of the amplitudes of the perturbation first three harmonics on the upper and lower interfaces are obtained. The classical feedthrough (interface coupling) solution obtained by Taylor [Proc. R. Soc. London A 201, 192 (1950)] is readily recovered by the first-order results. Our third-order model can depict the WN perturbation growth and the saturation of linear (exponential) growth of the perturbation fundamental mode on both interfaces. The dependence of the WN perturbation growth and the slab distortion on the normalized layer thickness (kd) is analytically investigated via the third-order solutions. Comparison is made with Jacobs-Catton's formula [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988)] of the position of the “linearly unstable” interface. Using a reduced formula, the saturation amplitude of linear growth of the perturbation fundamental mode is studied. It is found that the finite-thickness effects play a dominant role in the WN evolution of the slab, especially when kd < 1. Thus, it should be included in applications where the interface coupling effects are important, such as inertial confinement fusion implosions and supernova explosions.

Turbulent transport in premixed flames approaching extinction

The turbulent transport in premixed flames approaching extinction has been characterised in terms of statistical properties using an opposed jet burner featuring fractal grid generated turbulence. The burner was used in a symmetric twin flame configuration featuring pre-vaporised cyclopentane and JP-10 (exo-tetrahydrodicyclopentadiene) at equivalence ratios of 0.75 and 0.85. The choice of fuels follows from the practical importance of JP-10 as an aviation fuel with cyclic C5 compounds appearing as breakdown products. The bulk velocity was set to 3.0m/s resulting in a turbulent Reynolds number of 120. The obtained data includes conditional velocity statistics, flame curvature information and scalar fluxes. The conversion between conventionally and Favre averaged statistics follows the Bray–Moss–Libby theory and the assumption that finite reaction interface thickness effects can be neglected. The impact of deviations from the latter on statistics is explored and results suggest that the effect is modest for interface thicknesses less than 20% of the turbulent flame brush. The experimental data obtained is sufficient to enable terms up to and including triple correlations to be evaluated in closed form. The work also clearly illustrates the rapid transition from non-gradient to gradient turbulent transport as the extinction limit is approached.

The Effects of Yield Stress and Casing Thickness on Blast Impulse and Fragment Velocity

AbstractA previous paper by the author [1] showed how his equation [2], based on the model first proposed by Gurney [3] for the blast impulse from cased munitions, can be modified to allow for the yield stress of the casing metal. This paper [1] also provided validation for this further equation from available experimental data. Further issues regarding the many smaller but significant interactions between the fracturing casing and the expanding gases need to be investigated before it can be said that a complete theory of blast impulse and fragment initial velocity is in place. In this paper, an approximate evaluation will be made of the potential effect and significance of kinetic energy losses, due to dissipation by means of casing strain energy dissipation. As expected, these losses are found to be most significant for thick, low density, high yield stress casings. The effect of finite casing thickness, also not previously considered, has been found to be small.

A novel asymptotic expansion homogenization analysis for 3-D composite with relieved periodicity in the thickness direction

Abstract A new asymptotic expansion homogenization analysis is proposed to analyze 3-D composite in which thermomechanical and finite thickness effects are considered. Finite thickness effect is captured by relieving periodic boundary condition at the top and bottom of unit-cell surfaces. The mathematical treatment yields that only 2-D periodicity (i.e. in in-plane directions) is taken into account. A unit-cell representing the whole thickness of 3-D composite is built to facilitate the present method. The equivalent in-plane thermomechanical properties of 3-D orthogonal interlock composites are calculated by present method, and the results are compared with those obtained by standard homogenization method (with 3-D periodicity). Young’s modulus and Poisson’s ratio obtained by present method are also compared with experiments whereby a good agreement is particularly found for the Young’s modulus. Localization analysis is carried out to evaluate the stress responses within the unit-cell of 3-D composites for two cases: thermal and biaxial tensile loading. Standard finite element (FE) analysis is also performed to validate the stress responses obtained by localization analysis. It is found that present method results are in a good agreement with standard FE analysis. This fact emphasizes that relieving periodicity in the thickness direction is necessary to accurately simulate the real free-traction condition in 3-D composite.

Magnetic phases in NiO and MnO ultrathin films: Finite thickness and strain effects

Magnetic phases of NiO and MnO ultrathin films are established on the basis of a Hamiltonian including superexchange and dipolar interaction, disregarding the magnetocrystalline interaction because of its considerably smaller contribution in these films. The employed theoretical approach demonstrates that the finite thickness is substantially more important than the strain effect on the stabilization of the ground state configurations. An antiferromagnetic phase where ferromagnetic layers are piled up with alternating opposite in-plane orientations of the spins appears in NiO and MnO (111) ultrathin films, while a striped antiferromagnetic phase with the larger component of the magnetic moments along the growth direction is found in NiO and MnO (001) ultrathin films. These results are in qualitative agreement with available experimental results, but they disagree with the ones of a former theory, which is carefully examined.

Finite-thickness effect on crystallization kinetics in thin films and its adaptation in the Johnson–Mehl–Avrami–Kolmogorov model

The Johnson–Mehl–Avrami–Kolmogorov (JMAK) model is widely used to quantify the isothermal crystallization kinetics. The present work reports an analytical solution for the crystallization kinetics in the special case of plate-shaped samples with a finite thickness. As a result, we obtained an adapted JMAK model revealing the thickness range which influences the crystallization kinetics mode significantly. The analytical solution also provides theoretical bounds for the film thickness, where the assumption of 2D or 3D kinetics is accurate. Finally, the conclusions related to amorphous silicon and amorphous nickel-titanium thin films are reported.

Optimally focused cold atom systems obtained using density-density correlations

Resonant absorption imaging is a common technique for detecting the two-dimensional column density of ultracold atom systems. In many cases, the system's thickness along the imaging direction greatly exceeds the imaging system's depth of field, making the identification of the optimally focused configuration difficult. Here we describe a systematic technique for bringing Bose-Einstein condensates (BEC) and other cold-atom systems into an optimal focus even when the ratio of the thickness to the depth of field is large: a factor of 8 in this demonstration with a BEC. This technique relies on defocus-induced artifacts in the Fourier-transformed density-density correlation function (the power spectral density, PSD). The spatial frequency at which these artifacts first appear in the PSD is maximized on focus; the focusing process therefore both identifies and maximizes the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects.

AlGaN/GaN field effect transistors for power electronics—Effect of finite GaN layer thickness on thermal characteristics

AlGaN/GaN heterostructure field effect transistors with a 150 nm thick GaN channel within stacked AlxGa1−xN layers were investigated using Raman thermography. By fitting a thermal simulation to the measured temperatures, the thermal conductivity of the GaN channel was determined to be 60 W m−1 K−1, over 50% less than typical GaN epilayers, causing an increased peak channel temperature. This agrees with a nanoscale model. A low thermal conductivity AlGaN buffer means the GaN spreads heat; its properties are important for device thermal characteristics. When designing power devices with thin GaN layers, as well as electrical considerations, the reduced channel thermal conductivity must be considered.

Analysis of Pipe-Type Cable Impedance Formulations at Low Frequencies

This paper analyzes series impedances of screenless cables enclosed by a common conducting pipe. Established analytical formulas for pipe-type cables parameters are analyzed by taking finite pipe thickness and proximity effect into account. Analytical low-frequency approximations are developed and analyzed. The analysis shows that a classical formulation by mixing infinite and finite pipe thickness can result in incorrect inductance and even negative self-resistance at low frequency. This paper analyzes corrections to take a finite pipe thickness into account. Finite-element simulations reveal that the core-to-core proximity effect is substantial for the analyzed cable design with much lower high-frequency inductance than that obtained from analytical formulas. This paper also analyzes given proximity-effect formulations and proposes corrections based on analytical low-frequency approximations. The proposed proximity effect corrections improve resistance and inductance in common and differential mode.

Nematode locomotion in unconfined and confined fluids

The millimeter-long soil-dwelling nematode Caenorhabditis elegans propels itself by producing undulations that propagate along its body and turns by assuming highly curved shapes. According to our recent study [V. Padmanabhan et al., PLoS ONE 7, e40121 (2012)10.1371/journal.pone.0040121] all these postures can be accurately described by a piecewise-harmonic-curvature model. We combine this curvature-based description with highly accurate hydrodynamic bead models to evaluate the normalized velocity and turning angles for a worm swimming in an unconfined fluid and in a parallel-wall cell. We find that the worm moves twice as fast and navigates more effectively under a strong confinement, due to the large transverse-to-longitudinal resistance-coefficient ratio resulting from the wall-mediated far-field hydrodynamic coupling between body segments. We also note that the optimal swimming gait is similar to the gait observed for nematodes swimming in high-viscosity fluids. Our bead models allow us to determine the effects of confinement and finite thickness of the body of the nematode on its locomotion. These effects are not accounted for by the classical resistive-force and slender-body theories.

Viscous effects on the non-classical Rayleigh–Taylor instability of spherical material interfaces

The viscous and conductivity effects on the instability of a rapidly expanding material interface produced by a spherical shock tube are investigated through the employment of a high-order WENO scheme. The instability is influenced by various mechanisms, which include (a) classical Rayleigh–Taylor (RT) effects, (b) Bell–Plesset or geometry/curvature effects, (c) the effects of impulsively accelerating the interface, (d) compressibility effects, (e) finite thickness effects, and (f) viscous effects. Henceforth, the present instability studied is more appropriately referred to as non-classical RT instability to distinguish it from classical RT instability. The linear regime is examined and the development of the viscous three-dimensional perturbations is obtained by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the viscous effects on the growth of the disturbances for various conditions. The inviscid analysis does not show the existence of a maximum amplification rate. The present viscous analysis, however, shows that the growth rate increases with increasing the wave number, but there exists a peak wavenumber beyond which the growth rate decreases with increasing the wave number due to viscous effects.

Variational Monte Carlo study of spin-polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels

We compare ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half-filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consistently lower in energy except for large deviations. These results suggest that even under moderate deviations in the interaction potential (through various physical processes such as finite thickness, Landau level mixing, etc.), the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half-filled SLL (i.e. $\nu = 5/2$), consistent with recent experimental investigations.

Capillary effect on water table fluctuations in unconfined aquifers

Key Points A new governing equation of watertable dynamics was derived. A new analytical solution for watertable fluctuations was derived. The effect of finite unsaturated zone thickness was examined.

Suppression of magnetic phase separation in epitaxial SrCoOX films

Using pulsed laser deposition and a unique fast quenching method, we have prepared SrCoOx epitaxial films on SiTiO3 substrates. As electrochemical oxidation increases the oxygen content from x = 2.75 to 3.0, the films tend to favor the discrete magnetic phases seen in bulk samples for the homologous series SrCoO(3-n/8) (n = 0, 1, 2). Unlike bulk samples, 200nm thick films remain single phase throughout the oxidation cycle. 300 nm films can show two simultaneous phases during deoxidation. These results are attributed to finite thickness effects and imply the formation of ordered regions larger than approximately 300 nm.

The effects of finite metallisation thickness and conductivity in microstrip lines

PurposeThe purpose of this paper is to study and discuss the effects of the finite metallisation thickness and conductivity on the properties of microstrip lines.Design/methodology/approachEffective dielectric constant and attenuation constant of microstrip lines with finite metallization thickness and finite conductivity are analyzed by the method of lines. The experimental results are obtained by using Vector Network Analyzer and the 3680 V Universal Test Fixture of Anritsu.FindingsThe strip thickness has a great impact on the attenuation constant of the microstrip lines. The effects can be divided into three parts by the relationship between strip thickness (t) and skindepth (δ). When t<δ, the attenuation constant will decrease rapidly as the strip thickness increase. When δ < t<2δ, the attenuation constant still decrease rapidly as the strip thickness increase, but the slope of the curve will be smaller. When 2δ < t, the effects of the strip thickness will become insignificant and the attenuation constant still decrease slowly as the strip thickness increase.Originality/valueThis paper presents some useful principles about the effects of the finite metallization thickness and finite conductivity in microstrip lines. The reasons for these effects are discussed by analyzing the longitudinal electric field distribution in the strip. Finally, some experimental results are given to verify these principles.

Acceleration of Spectral Domain Approach for Generalized Multilayered Shielded Microstrip Interconnects Using Two Fast Convergent Series

A simple and versatile approach for the acceleration of the spectral domain approach for generalized shielded microstrip interconnects is presented. This approach uses asymptotic expansion for the Bessel's function and the Green's function followed by an approximation of infinite summation using two fast convergent sine cosine series. The asymptotic expansion coefficients of the Green's functions are found by a combination of analytical and numerical approaches. The infinite summation involved in the computation of the elements of the Galerkin matrix is accelerated using two fast convergent sine cosine series. The use of a few entire-domain basis functions gives very accurate results for the propagation constants for any mode in the general case of a multilayered shielded microstrip line. In addition to this, closed-form expressions are developed to choose the number of terms and some parameters to adaptively accelerate the convergence of the second type of fast convergent series for a given accuracy. This approach can be extended to handle multiple interconnects in the same layer and in different layers and also to include the effect of finite thickness and conductivity.

Influence of wall thickness on the stability of the resistive wall mode in tokamak plasmas

The influence of finite wall thickness on the stability of the resistive wall mode (RWM) in a tokamak is determined using a simple cylindrical plasma model in which the dissipation required to stabilize the mode is provided by neoclassical parallel ion viscosity. For present-day tokamaks, which possess relatively thin walls, finite wall thickness effects are found to have relatively little influence on the RWM stability boundaries, which are almost the same as those calculated in the thin-wall limit. On the other hand, for next-step devices, which are likely to possess much thicker walls than present-day tokamaks, finite wall thickness effects are found to significantly impede the ability of plasma rotation to stabilize the RWM all the way to the perfect-wall stability limit.