Effect Of Finite Thickness Research Articles

Quantitative measurement of cast metal relics by pulsed thermal imaging

ABSTRACT Corrosion in cast metal relics has always been a concern for the conservation and restoration of ancient culture relics. In recent years, there is an increased interest in the determination of the corrosion/rust thickness and the substrate thickness of bronze and iron cultural relics. The solution of this problem is of great significance in the evaluation of the corrosion status, rust cleaning, and the restoration and conservation of metal cultural relics. This paper presents a new method for the measurement of the rust thickness and the substrate thickness of a replica cast-iron Buddha head by one-sided pulsed thermal imaging. In this method, the rust thickness and the substrate thickness of cast-iron Buddha head were determined simultaneously by a non-linear fitting of a theoretical solution with experimental values. The finite flash duration effect and the finite substrate thickness effect on the rust thickness measurement are analysed and discussed. Besides the new method, the conventional Flash method for single-layer materials was also used to estimate the wall thickness. The measurement results show that this new method has great potential and capability in the quantitative measurement of ancient iron and bronze cultural relics.

Finite-thickness effect and spin polarization of the even-denominator fractional quantum Hall states

The spin-polarized even-denominator fractional quantum Hall (FQH) states in the second Landau level (LL), i.e. 5/2 and 7/2, may possess novel quasi-particle excitations obeying non-Abelian statistics. However, the spin polarization of the 7/2 FQH state has not been investigated experimentally and the spin polarization of the 5/2 FQH state from tilted field experiments remains controversial. Using a piezo-driven sample rotator with the lowest electron temperature down to 25 mK, we studied the energy gap of the even-denominator FQH states in the second LL by precise control of the tilted angles with a resolution less than 0.1{\deg}. We observed two different energy gap dependences on the in-plane magnetic field for 5/2, 7/2, other FQH states (7/3 and 8/3) in the second LL and reentrant integer quantum Hall (RIQH) states in the third LL. Though the transition fields vary from states, their corresponding in-plane magnetic lengths are comparable to the quantum well thickness of the sample, which may result from the influence of the finite-thickness effect. At low in-plane magnetic fields, before the conjectured finite-thickness effect starts to dominate, the energy gaps of both 5/2 and 7/2 states show a non-decreasing behavior, supporting spin-polarized ground states. Our results also suggest that the 7/3, 8/3 FQH states, and the RIQH states in the third LL are spin-polarized or partially spin-polarized.

Surface mechanics of a stretched elastomer layer bonded on a rigid substrate

Thin elastomer layers bonded on a rigid substrate can be found in diverse engineering applications, in which the elastomers are often in stressed state. Previous studies have shown abundant evidence that the prestresses in an elastomer layer can greatly influence its mechanical behaviors. In this article, we have analytically derived the surface Green's function of a stressed elastomer layer with finite thickness and bonded on a rigid substrate, which enables us and others to compute surface deformation of the elastomer layer subjected to any arbitrary surface force. By using the derived surface Green's function, we further study the indentation of a prestressed elastomer layer, as well as the deposition of a liquid droplet and adhesion of a cell on a prestressed elastomer layer. The effects of prestresses and finite thickness of the elastomer layer on those problems have been uncovered.

The ratio of shear to elastic modulus of in-plane loaded masonry

When designing unreinforced masonry buildings, the wall stiffness and, consequently, the masonry elastic and shear modulus E and G are essential parameters. Current codes provide empirical estimates of the masonry elastic modulus and a ratio between the shear and elastic modulus, G/E. This ratio, commonly taken as 0.4, is not based on scientific evidence and there appears to be no consensus concerning its value and influencing parameters, meaning that current code standards might not accurately portray the shear deformations of masonry elements. To give the choice of the G/E ratio a theoretical foundation, this paper presents closed-form expressions for the G/E ratio of running-bond masonry that capture the effects of finite joint thickness, finite wall thickness and orthotropic block properties. Based on the geometry of blocks and joints as well as their elastic parameters, a validation of the developed expression using 3D finite element analyses shows good performance. For modern masonry typologies with hollow clay bricks, a G/E ratio of 0.20–0.25 is obtained. For historical masonry typologies, such as dry stacked or mortared stone masonry, as well as solid clay brick masonry, ratios between 0.30 and 0.40 are computed.

Dynamic fields at the tip of sub-Rayleigh and supershear frictional rupture fronts

The onset of frictional motion at the interface between two distinct bodies in contact is characterized by the propagation of dynamic rupture fronts. We combine friction experiments and numerical simulations to study the properties of these frictional rupture fronts. We extend previous analysis of slow and sub-Rayleigh rupture fronts and show that strain fields and the evolution of real contact area in the tip vicinity of supershear ruptures are well described by analytical fracture-mechanics solutions. Fracture-mechanics theory further allows us to determine long sought-after interface properties, such as local fracture energy and frictional peak strength. Both properties are observed to be roughly independent of rupture speed and mode of propagation. However, our study also reveals discrepancies between measurements and analytical solutions that appear as the rupture speed approaches the longitudinal wave speed. Further comparison with dynamic simulations illustrates that, in the supershear propagation regime, transient and geometrical (finite sample thickness) effects cause smaller near-tip strain amplitudes than expected from the fracture-mechanics theory. By showing good quantitative agreement between experiments, simulations and theory over the entire range of possible rupture speeds, we demonstrate that frictional rupture fronts are classic dynamic cracks despite residual friction.

Effect of finite wall thickness on entropy generation and natural convection in a nanofluid-filled partially heated square cavity

PurposeThe purpose of this paper is to study the effects of finite wall thickness on the natural convection and entropy generation in a square cavity filled with Al2O3–water nanofluid in the presence of bottom heat source.Design/methodology/approachThe moving isothermal heater was placed on the bottom solid wall. The vertical walls (left and right walls) were fully maintained at low temperatures. The rest of the bottom solid wall along with the top horizontal wall was kept adiabatic. The boundaries of the domain are assumed to be impermeable; the fluid within the cavity is a water-based nanofluid having Al2O3 nanoparticles. The Boussinesq approximation is applicable. The dimensionless governing equations subject to the selected boundary conditions are solved using the finite difference method. The current proposed numerical method is proven excellent through comparisons with the existing experimental and numerical published studies.FindingsNumerical results were demonstrated graphically in several forms including streamlines, isotherms and local entropy generation, as well as the local and average Nusselt numbers. The results reveal that the thermal conductivity and thickness of the solid wall are important control parameters for optimization of heat transfer and Bejan number within the partially heated square cavity.Originality/valueAccording to the past research studies mentioned above and to the best of the authors’ knowledge, the gap regarding the problem with entropy generation analysis and natural convection in partially heated square cavity has yet to be filled. Because of this, this study aims to investigate the entropy generation analysis as well as the natural convection in nanofluid-filled square cavity which was heated partially. A square cavity with an isothermal heater located on the bottom solid horizontal wall of the cavity and partly cold sidewalls are essential problems in thermal processing applications. Hence, the authors believe that this present work will be a valuable contribution in improving the thermal performance.

Spiral-arm instability – III. Fragmentation of primordial protostellar discs

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

Magneto-Rayleigh–Taylor Instability Driven by a Rotating Magnetic Field: Cylindrical Liner Configuration

We propose using a directional time-varying (rotating) driving magnetic field to suppress magneto-Rayleigh-Taylor (MRT) instability in dynamic Z-pinches. A rotational drive magnetic field is equivalent to two magnetic-field components, {\Theta} and Z, that alternate in time, referred to as an alternate Theta-Z-pinch configuration. We consider the finitely thick cylindrical liner configuration in this paper. We numerically integrate the perturbation equation to stagnation time based on the optimal background unperturbed trajectories. We assess the cumulative growth of the dominant mode selected by some mechanism at the beginning of an implosion. The maximum e-folding number at stagnation of the dominant mode of an optimized alternate Theta-Z-pinch is significantly lower than that of the standard Theta- or Z-pinch. The directional rotation of the magnetic field contributes to suppress the instabilities, independent of the finite thickness. The finite thickness effect plays a role only when the orientation of the magnetic field varies in time whereas it does not appear in the standard Theta- or Z-pinch. The rotating frequency of the magnetic field and the thickness of liner are both having a monotonic effect on suppression. Their synergistic effect can enhance the suppression on MRT instability. Because the MRT instability can be well suppressed in this way, the alternate Theta-Z-pinch configuration has potential applications in liner inertial fusion. This work is supported by the NSFC (Grant Nos. 11405167, 51407171, 11571293, 11605188, and 11605189) and the Foundation of the China Academy of Engineering Physics (No. 2015B0201023).

Maxwell eigenmode approach to the Casimir-Lifshitz torque

More than forty years ago, Barash published a calculation of the full retarded Casimir-Lifshitz torque for planar birefringent media with arbitrary degrees of anisotropy. An independent theoretical confirmation has been lacking since. We report a systematic and transparent derivation of the torque between two media with both electric and magnetic birefringence. Our approach, based on an eigenmode decomposition of Maxwell's equations, generalizes Barash's result for electrically birefringent materials, and can be generalized to a wide range of anisotropic materials and finite thickness effects.

A comparative study of lifetime reliability of planar MOSFET and FinFET due to BTI for the 16 nm CMOS technology node based on reaction-diffusion model

Intensive scaling of Integrated Circuits is a crucial factor for achieving high performance and astronomical packing density. However, this scaling is pushing planar MOSFET to its physical limitations. Nowadays, FinFET emerges as a promising alternative technology for planar MOSFET, due to their better efficiency. Nevertheless, this inevitably leads to a rising concern on the reliability of FinFET as the circuit lifetime reliability cannot be neglected due to this accelerated scaling of Integrated Circuits. This paper is considered as the first work that: 1) detects which CMOS technology, planar MOSFET or FinFET, is more robust against Bias Temperature Instability (BTI) aging degradation for the advanced nodes such as 16 nm; 2) precisely computes the effect of BTI on 16 nm FinFET using an adequate BTI Reaction Diffusion model that takes into consideration the effects of finite oxide thickness, and the influence of polysilicon; 3) investigates the efficiency in terms of power consumption and area for the predominant circuit level techniques that could be implemented to overcome the negative impact of BTI for FinFET technology. This research clearly indicates that FinFET technology is more robust against BTI aging degradation than planar MOSFET as the delay percentage for FinFET technology is lower than planar MOSFET technology by 26%.

The effects of a horizontal magnetic field on the Rayleigh–Taylor instability

The stability of a thin conductive liquid film flowing along a solid wall is an important problem that occurs in many proposed fusion device designs. In this paper we investigate the linear stability of an electrically conductive liquid film of finite thickness in the presence of a strong magnetic field. Inviscid flows of finite and infinite electric conductivity are considered. The magnetic field is found to decrease the unstable growth rate for both finite and infinite conductivity fluids but only narrows the unstable modes for infinite conductivity fluids. Our theory serves as an extension to the classical theory by Chandrasekhar (1961) [1] by considering the finite-thickness and finite-conductivity effects.

Finite-thickness effects in plasmonic films with periodic cylindrical anisotropy [Invited

Finite-thickness effects are analyzed theoretically for the plasma frequency and associated dielectric response function of plasmonic films formed by periodically aligned, infinitely thin, identical metallic cylinders. The plasma frequency of the system is shown to have the unidirectional square-root-of-momentum and quasilinear momentum spatial dispersion for the thick and ultrathin films, respectively. This spatial dispersion and the unidirectional dielectric response nonlocality associated with it can be adjusted not only by the film material composition but also by varying the film thickness, the cylinder length, the cylinder-radius-to-film-thickness ratio, and by choosing the substrates and superstrates of the film appropriately. Application of the theory developed to the finite-thickness periodically aligned carbon nanotube films is discussed.

Finite-thickness effect of the fluids on bubbles and spikes in Richtmyer–Meshkov instability for arbitrary Atwood numbers

This paper investigates the finite-thickness effect of two superimposed fluids on bubbles and spikes in Richtmyer–Meshkov instability (RMI) for arbitrary Atwood numbers by using the method of the small parameter expansion up to the second order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitude evolution of bubbles and spikes compared with those in classical RMI. Based on the thickness relationship of the two fluids, the thickness effect on bubbles and spikes for four cases is discussed. The thickness encourages (or reduces) the growth of bubbles or spikes, depending on not only Atwood number, but also the relationship of the thickness ratio of the heavy and light fluids, which is explicitly determined in this paper.

Theoretical study on finite-thickness effect on harmonics in Richtmyer-Meshkov instability for arbitrary Atwood numbers

The finite-thickness effect of two superimposed fluids on harmonics in the Richtmyer-Meshkov instability (RMI) for arbitrary Atwood numbers is investigated by using weakly nonlinear analysis up to the third order. When the thickness of the two fluids tends to be infinity, our results can reproduce the classical results where RMI happens at the interface separating two semi-infinity-thickness fluids of different densities. It is found that the thickness has a large influence on the amplitudes of the first three harmonics compared with those in classical RMI. On the one hand, the thickness effect encourages or reduces the amplitudes of the first three harmonics, and on the other hand, it changes the phases of the second and the third harmonics.

Adhesion of carbon nanotubes on elastic substrates with finite thickness

How carbon nanotubes (CNTs) interact with substrates is fundamental for understanding their physical properties. In existing theoretical and modeling studies, the substrates are considered to be rigid with semi-infinite thickness. In this work, the effects of finite substrate thickness and elasticity are analyzed theoretically and numerically for free boundary conditions. Based on the energy-variational approach, considering the interfacial van der Waals interactions and bending strain energies stored in CNTs and substrates, the governing equations and boundary conditions are derived analytically. The theoretical predictions are in reasonable agreement with the results of molecular dynamics simulations. When the substrate is sufficiently thick, the results of the present theoretical model are entirely consistent with previous models for the infinite-thickness substrate. However, for relatively thin substrates, the effect of substrate thickness is significant due to the geometric large deformation. Three stable adhesive states (initial non-adhesive, partially adhesive, and fully wrapping states) can be achieved, dependent on the substrate thickness, the number of CNT walls, and the interfacial adhesion work. The stability of adhesive configurations is explored by analyzing the energy variations corresponding to the adhesive deformation. We show that there exist several modes of energy variations, depending on the adhesion work and the substrate-CNT bending stiffness ratio, which exhibit linear and nonlinear influences, respectively. Our results could serve as guidelines to design CNT-on-substrate systems.

Effect of finite disk-thickness on swing amplification of non-axisymmetric perturbations in a sheared galactic disk

A typical galactic disk is observed to have a finite thickness. Here, we present the study of the physical effect of introduction of finite thickness on the generation of small-scale spiral arms by swing amplification in a differentially rotating galactic disk. The galactic disk is modelled first as a one-fluid system, and then as a gravitationally-coupled two-fluid (stars and gas) system where each fluid is taken as isothermal, and corotating with each other. We derived the equations governing the evolution of the non-axisymmetric perturbations in a sheared frame of reference while incorporating the effect of finite thickness of a galactic disk. We found that the finite thickness of a galactic disk has a generic trend of suppressing the growth of the non-axisymmetric perturbations via swing amplification. Moreover, even the observed range of disk-thickness values (∼300–500 pc) can lead to a complete suppression of swing amplification forQ∼ 1.7, whereas for an infinitesimally-thin disk, the corresponding critical value isQ∼ 2. For a two-fluid (stars and gas) system, the net amplification is shown to be set by the mutual interplay of the effect of interstellar gas in promoting the spiral features and the effect of finite thickness in preventing the spiral arms. The coexistence of these two opposite effects is shown to be capable of giving rise to diverse and complex dynamical behaviour.

Rectangular Waveguide Cross-Guide Couplers: Accurate Model for Full-Band Operation

In this letter, a precise model for accommodating the cross-guide couplers is proposed and validated. This includes accurate formulas for the polarizabilities of cross slots as well as the effect of finite wall thickness on the coupling level. The proposed model shows a leading performance compared with previously published models in the literature showing a maximum error of 2.5%. The experimental validation shows an excellent agreement with the simulated results.

Unified decomposition method to study Rayleigh-Taylor instability in liquids and solids.

In the previous studies of Rayleigh-Taylor instability, different methods were used to consider the effects of elasticity, viscosity, and magnetic fields. In this paper, a unified method, which was first used for fluids, is validated for different physical models, where the unstable mode is decomposed into an irrotational part and a rotational part, and the latter one includes the effects of nonconservative forces and constitutive relations. Previous results of solid and liquid with or without the effects of magnetic fields and finite thickness can be easily recovered after applying the corresponding interface boundary conditions. In addition, new approximate but analytical solutions of the growth rates for a semi-infinite solid-solid interface and solid-fluid interface are obtained with substantially improved accuracy in comparison with the previous ones.

Finite-thickness effect on speed of a counter-rotating vortex pair at high Reynolds numbers

We establish a general formula for the translational speed of a counter-rotating vortex pair, valid for thick cores, moving in an incompressible fluid with and without viscosity. We extend to higher order the method of matched asymptotic expansions developed by Ting and Tung (1965 Phys. Fluids 8 1039–51). The solution of the Euler or the Navier–Stokes equations is constructed in the form of a power series in a small parameter, the ratio of the core radius to the distance between the core centers. For a viscous vortex pair, the small parameter should be where ν is the kinematic viscosity of the fluid and Γ is the circulation of each vortex. A correction due to the effect of finite thickness of the vortices to the traveling speed makes its appearance at fifth order. A drastic simplification is achieved of expressing it solely in terms of the strength of the second-order quadrupole field associated with the elliptical deformation of the core. For a viscous vortex pair, we exploit the conservation law for the hydrodynamic impulse to derive the growth of the distance between the vortices, which is cubic in time.

Predictive Design and Experimental Realization of InAs/GaAs Superlattices with Tailored Thermal Conductivity

We demonstrate an ab-initio predictive approach to computing the thermal conductivity ($\kappa$) of InAs/GaAs superlattices (SLs) of varying period, thickness, and composition. Our new experimental results illustrate how this method can yield good agreement with experiment when realistic composition profiles are used as inputs for the theoretical model. Due to intrinsic limitations to the InAs thickness than can be grown, bulk-like SLs show limited sensitivity to the details of their composition profile, but the situation changes significantly when finite-thickness effects are considered. If In segregation could be minimized during the growth process, SLs with significantly higher $\kappa$ than that of the random alloy with the same composition would be obtained, with the potential to improve heat dissipation in InAs/GaAs-based devices.