Infinite Slab Geometry Research Articles

Three-dimensional spontaneous flow transition in a homeotropic active nematic

Active nematics are driven, non-equilibrium systems relevant to biological processes including tissue mechanics and morphogenesis, and to active metamaterials in general. We study the three-dimensional spontaneous flow transition of an active nematic in an infinite slab geometry using a combination of numerics and analytics. We show that it is determined by the interplay of two eigenmodes – called S- and D-mode – that are unstable at the same activity threshold and spontaneously breaks both rotational symmetry and chiral symmetry. The onset of the unstable modes is described by a non-Hermitian integro-differential operator, which we determine their exponential growth rates from using perturbation theory. The S-mode is the fastest growing. After it reaches a finite amplitude, the growth of the D-mode is anisotropic, being promoted perpendicular to the S-mode and suppressed parallel to it, forming a steady state with a full three-dimensional director field and a well-defined chirality. Lastly, we derive a model of the leading-order time evolution of the system close to the activity threshold.

Quantization in Chiral Higher Order Topological Insulators: Circular Dichroism and Local Chern Marker.

The robust quantization of observables in units of universal constants is a hallmark of topological phases. We show that chiral higher order topological insulators (HOTIs), bulk insulators with chiral hinge states, present two unusual features related to quantization. First, we show that circular dichroism is quantized to an integer or zero depending on the orientation of the sample. This probe locates the hinge states, and can be used to distinguish different types of chiral HOTIs. Second, we find that the average of the local Chern marker over a single surface, an observable related to the surface Hall conductivity known to be quantized in the infinite slab geometry, is nonuniversal for a finite surface. This is due to a nonuniversal contribution of the hinge states, previously unaccounted for, that distinguishes surfaces of chiral HOTIs from Chern insulators. Our findings are relevant to establish higher order topology in systems such as the axion insulator candidate EuIn_{2}As_{2}, and cold atomic realizations.

Depth sensitivity of frequency domain optical measurements in diffusive media.

The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain (where the source amplitude is modulated at radio-frequencies) by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry. Furthermore, solutions for the relative contrast of AC, PH and DC signals when a totally absorbing plane is placed at a fixed depth of the slab have also been obtained. The solutions have been validated by comparisons with gold standard Monte Carlo simulations. The obtained results show that the AC signal, for modulation frequencies < 200 MHz, has a depth sensitivity with similar characteristics to that of the continuous-wave (CW) domain (source modulation frequency of zero). Thus, the depth probed by such a signal can be estimated by using the formula of penetration depth for the CW domain (Sci. Rep.6, 27057 (2016)). However, the PH signal has a different behavior compared to the CW domain, showing a larger depth sensitivity at shallow depths and a less steep relative contrast as a function of depth. These results mark a clear difference in term of depth sensitivity between AC and PH signals, and highlight the complexity of the estimation of the actual depth probed in tissue spectroscopy.

Conductance fluctuations and disorder induced ν=0 quantum Hall plateau in topological insulator nanowires

Clean topological insulators exposed to a magnetic field develop Landau levels accompanied by a nonzero Hall conductivity for the infinite slab geometry. In this work we consider the case of disordered topological insulator nanowires and find, in contrast, that a zero Hall plateau emerges within a broad energy window close to the Dirac point. We numerically calculate the conductance and its distribution for a statistical ensemble of disordered nanowires, and use the conductance fluctuations to study the dependence of the insulating phase on system parameters, such as the nanowire length, disorder strength and the magnetic field.

Higher order mode analyses of power spectral density and Feynman-α method in accelerator driven system with periodically pulsed spallation neutron source

This paper deals with the theory of higher order modes in the Feynman Y function and the cross power spectral density (CPSD) in an accelerator-driven system (ADS) where pulsed spallation neutrons are injected at a constant frequency. A theoretical formula that considers the effect of higher order modes of the correlated and uncorrelated components in the Feynman Y function for an ADS is newly derived in this paper. Although the formula for the correlated and uncorrelated components of a CPSD was derived in a recent publication of the author of this paper, the verification has not been done yet. These formulae for the Feynman Y function and CPSD are applied to a subcritical multiplying system with a one-dimensional infinite slab geometry. The Feynman Y functions and CPSD calculated with the theoretical formulae are compared with the Monte Carlo simulations of these noise techniques. The theoretical formulae reproduce the Monte Carlo simulations very well, thereby substantiating the theoretical formulae derived in this paper. The correlated and uncorrelated components of the Feynman Y functions and CPSD are decomposed into the sum of the fundamental mode and other higher order modes. The higher order mode effect in the uncorrelated component is much more significant than in the correlated component.

THE ESCAPE PROBABILITIES FOR SLAB AND SPHERICAL GEOMETRIES IN PLASMA SPECTROSCOPY

In this paper, the concepts of the photon escape probability and the transmission factor are reviewed and the photon escape probabilities for infinite plane-parallel slab and spherical geometries are discussed. The photon escape probabilities using the transmission factor, for Lorentzian profile and Holtsmarkian profile, are discussed. Finally, the photon escape probabilities we calculated are compared with that calculated using before method for Lorentzian profile and Holtsmarkian profile, and some useful conclusions are drawn.

Fourier Convergence Analysis of Two-Dimensional/One-Dimensional Coupling Methods for the Three-Dimensional Neutron Diffusion Eigenvalue Problems

The purpose of this paper is to present the Fourier convergence analysis of four methods for performing two-dimensional/one-dimensional (2-D/1-D) coupling to solve neutron diffusion eigenvalue problems (EVPs). The four methods differ principally in the manner of using the interface currents or node average fluxes to perform the 2-D/1-D coupling. Method A uses net currents, method B employs partial currents, method C uses a current correction factor, and method D uses an analytic expression for the axial net currents. In a previous paper, we analyzed the convergence behavior of these methods for the 2-D/1-D coupling of the fixed source problem (FSP). In this paper, the convergence performance of these methods is analyzed for the EVP using a one-group neutron diffusion EVP in a homogeneous infinite slab geometry. Among the four methods, method A diverges for small mesh sizes as it did in the FSP, whereas the other methods are stable regardless of the mesh size. The spectral radii of methods C and D are identical while the latter had a smaller spectral radius than the former in an FSP. The spectral radii of methods C and D are smaller than that of method B in the range of practical mesh size. The spectral radii approach one for all the methods as the mesh size increases, while in the FSP the spectral radii of method B approached a finite positive value and those of the other methods approached zero. For practical applications, method C has several advantages over the other methods and is the preferred 2-D/1-D coupling method for EVPs.

Prediction of drying times for irregular shaped multi-dimensional moist solids

In this paper, we deal with development of a new analytical model for predicting drying times of irregular shaped multi-dimensional moist solids. Irregular products are approximated by representative elliptical cylinder and ellipsoid for two- and three-dimensional shapes, respectively. Using the experimental drying parameters that are available from the literature, drying times of irregular, multi-dimensional products are determined through the present models. In this regard, geometric shape factors for elliptic cylinder and ellipsoid are employed and based on the reference drying time for an infinite slab geometry. In addition, the present models are verified through comparison with experimental drying times of several food products. The accuracy of the predictions using the present models is then discussed.

The numerical solution for reaction–diffusion combustion with fuel consumption

This paper describes and studies the reaction between a gaseous oxidant and a solid porous fuel, which allows for the consumption of the fuel [J. Appl. Math. 47 (1991) 33]. Here we consider the effects of including consumption of the solid fuel of a poisoning of a solid catalyst by the ongoing reaction. We assume a single exothermic process, first-order in the concentration each of fuel and oxidant and with an Arrhenious temperature dependence of the reaction rate constant. The solid reactant has an infinite slab geometry of thickness 2 l and is surround by a reservoir of constant oxidant concentration and a fixed ambient temperature. Further, the reaction is assumed not to alter the integrity or pore structure of the solid. We solved three coupled partial differential equations which describe this problem by using the finite-difference scheme [Numerical Solution of Partial Differential Equations (Finite Difference Method), Clarendon Press, Oxford, 1978] which was first applied to a finite difference scheme by Crank [Q. J. Mech. Appl. Math. 10 (1957) 220; J. Inst. Math. Appl. 10 (1872) 19]. Using this method we can transform the partial differential equations to a system of linear algebraic equations [Int. J. Eng. Sci. 36 (5/6) (1998) 625; Appl. Math. Computat. 113 (2–3) (2000) 85]. This system is solved with the Dirichlet boundary conditions. The effects of the Frank–Kamenetskii parameter λ and the Lewis number L are examined.

Determination of drying times for regular multi-dimensional objects

Drying of multi-dimensional food products is investigated analytically. A simple method is developed for the determination of drying time of multi-dimensional products using drying parameters that are available from the literature or can be determined experimentally. In this respect, geometric shape factors for different regular multi-dimensional products are introduced. Drying time that can be calculated analyticaly for an infinite slab geometry is used to predict the drying times for other multi-dimensional products by means of the geometric shape factors. The present model is verified through comparison with experimental drying times of several food products in different shapes that are obtained from the literature. The comparison of the results obtained from the present model with the experimental data shows that the predictions are accurate within ±10% range, in general.

A computer program based on finite difference method for studying thermal initiation of explosives

The thermal decomposition of an explosive material is accompanied by generation of a certain amount of heat and, under certain conditions, can lead to the well-known phenomena of self-ignition. Therefore, it is of great importance to predict whether or not an explosive material will ignite under given conditions (specimen mass and shape, surrounding temperature, etc.). An own computer program named THERMEX, for studying thermal ignition phenomena, is discussed in this paper. The program uses the finite difference method to describe the reactive heat conduction phenomena in infinite slab, cylindrical, and spherical geometry of explosive materials. The analysis of the stability requirements of the finite difference method applied in the program is carried out. The program is tested by the comparison of calculated results with the results of calculation by other authors. Reasonable agreement was found under identical computational conditions.

Thermal diffusivity of idli batter

The thermal diffusivity (α) of idli batter was determined experimentally assuming infinite slab geometry under transient heat transfer conditions. The value α of batter determined using batch (1.38 × 10 −7 m 2 s −1) and continuous (1.1 × 10 −7 m 2 s −1) idli steaming units were compared with the value obtained using Riedel's equation (1.42 × 10 −7 m 2 s −1) and Martens equation (1.47 × 10 −7 m 2 s −1).

Characteristics of the a.c. losses in Ag-sheathed PbBi2223 tapes

A mini review of our latest results on the a.c. losses in Ag-sheathed PbBi2223 tapes is presented with the focus on self-field losses in a variety of situations and external losses with and without a d.c. transport current. Comparative measurements with the thermometric and electric methods have demonstrated the validity of the electric method despite the problem of a distribution of the loss electric field. Using these two methods the effect of a longitudinal distribution of critical current along the tape has been shown. The influence of a transverse distribution of the local J c through the core of the tape is also examined. Studies of the magnetic field dependence of the self-field losses have shown that different regions of the core have a different J c( B) dependence, in contrast to the temperature dependence where all regions of the core show a similar dependence. Measurements at higher frequencies show the importance of flux diffusion where an increased dB dt gives an increased induced critical current. At sufficiently higher frequencies (> 200 Hz) the self-field of the core is shown to induce eddy current losses within the silver sheath of the tape. For the external a.c. field case in parallel fields the losses are well described by the infinite slab geometry. For the case of the perpendicular field the losses are considerably less than those expected from either the thin ellipse or rectangle geometry. Possible mechanisms for this discrepancy include granularity of the tape or partial uncoupling of the filaments. For the combined action of an a.c. external field and a d.c. transport current our results show that the total losses cannot be obtained using only using a pick-up loop to measure the flux changes within the tape. An additional loss sustained by the d.c. current source also needs to be measured via a pair of voltage taps.

Vortex response to the ac field in anisotropic high- Tc superconductors

The ac response of anisotropic high- T c superconductors in the mixed states is theoretically analyzed. The physical picture proposed by Geshkenbein, Vinokur and Fehrenbacher together with the theory of thermally assisted flux flow is generalized to include the material anisotropy. The results show that the transition in the real part and the peak in the imaginary part of magnetic ac permeability are due to skin effect and, additionally, related to the sample dimensions. For an isotropic superconductor, the infinite slab geometry exhibits a maximum peak absorption, while a minimum dissipation peak is obtained in the case of a square rod. The peak frequency in the infinite slab is, however, the lowest as compared with other finite prisms. In the very anisotropic superconductors, the thin edges lower the dissipation peak and raise the peak frequency as well. Dependence of the irreversibility line in the mixed state on the geometric factor is therefore suggested.

Photon-measurement density functions Part I: Analytical forms

This paper addresses the problem of tomographic reconstruction of absorption and scattering parameters in the optical region from measurements of transilluminated light. Specifically, the question of the sensitivity of different measurement schemes on the boundary of an object to perturbations of the optical parameters within the object are addressed. The concept of a photon-sampling volume [Appl. Opt. 33, 448 (1994)] and a photon-hitting density [Appl. Opt. 32, 448 (1993)] is extended to a photon-measurement density function (PMDF). The PMDF is derived from the Green's function of the diffusion equation and can be expressed for measurements such as the time-varying intensity, integrated intensity, temporal moments, and phase shift, as well as for both absorption and diffusion perturbations. Closed-form solutions are given for a number of these functions in infinite space, half-space, and slab geometries. Example results are given in terms of three-dimensional images.

Power-Law Critical-State Model for Magnetization of Type-II Superconductors

The magnetization of a type-II superconductor obeying the power-law critical state model J c = KB-n is discussed for the case of an infinitely long rectangular bar placed in a parallel field. Explicit formulas are derived for all branches of the high-field hysteresis loop. Both the infinite slab and circular cylinder geometries are included as special cases. It is shown that the vertical width of the hysteresis loop has the asymptotic high-field behavior ΔM(B a) ∼J c(B a), with a prefactor given by the geometrical aspect ratio. Also, two more terms in the functional expansion of ΔM { J c} are derived. These terms are shown to vanish rapidly when the applied field exceeds the full penetration value. This allows for a new way of extracting J c(B) from magnetization data.

Time-resolved investigation of radiation trapping for the transition [formula omitted] following the generation of Sr[5s5p(3PJ)] by pulsed dye-laser excitation at elevated temperatures

We present a kinetic investigation of radiation trapping for the transition Sr[5s5p(3P1)] → Sr[5s2(1S0)] + hν at λ = 689.3 nm following the pulsed dye-laser generation of Sr[5s5p(3PJ)] at elevated temperature following excitation of ground state atomic strontium, Sr[5s2(1S0)], at the resonance wavelength. Sr[5s5p(3PJ)], 1.807 eV above the 1S0 ground state, was produced following laser photolysis to the 3P1 state in a slow flow system, kinetically equivalent to a static system, in the presence of helium buffer gas and at temperatures in the range 670–900 K. Following rapid Boltzmann equilibration within the Sr(5s5p(3P0,1,2)] spin-orbit manifold, time-resolved emission profiles at λ = 689.3 nm were recorded using signal averaging and computerised analysis techniques under a range of conditions of temperature and pressure, emission from the 3P0.2 levels being negligible, these being so-called “reservoir states”. First-order decay coefficients (κ′(3PJ)) were characterized for the emission at the resonance wavelength as well as integrated atomic fluorescence emission intensities using a sensitivity calibration of the total optical detection system. The resulting mean radiative lifetime for the transition (τc = 20.7 μs) was found to be in accord with the results of previous investigations, and the variation of the integrated atomic fluorescence emission intensities with the pressure of helium in accord with considerations of pressure broadening. Furthermore, the absolute second-order rate constant for the quenching of Sr(53PJ) by He (κQ = (2.9 ± 0.2) × 10−15cm3 atoms−1 s−1T = 840 K) was found to be in accord with the previous upper limit reported for this quantity by time-resolved emission investigations and the value reported from phase-shift techniques. The experimental curve of κ′(3PJ) versus temperature and hence Sr(51S0) density was constructed and compared with the results for radiation trapping according to the theory of (a) Milne, employing the diffusion theory of radiation for low “equivalent opacity” and infinite slab geometry of a thickness comparable with that of the laser beam and (b) Holstein, calculated as a general transport problem by solving a Boltzmann-type integro-differential equation in terms of a transmission coefficient. The results are found to be in accord with the calculations using the theory of Milne. This approach extends the previous empirical corrections that have been made for this effect with Sr(53P1). In more general terms it establishes from fundamentals the importance of radiation trapping for this transition at λ = 689.3 nm, which, whilst characterised by a relatively large mean radiative lifetime by comparison with that for a fully allowed electric-dipole atomic emission, is, nevertheless, subject to radiation trapping at the densities typically employed with time-resolved measurements following pulsed dye-laser excitation.

New critical-state model for magnetization of hard type-II superconductors

We propose a critical-state model based on the empirical fact that the critical current density Jc in high-Tc superconductors in some cases is found to decay to an essentially field independent level at large inductions B. The new critical current function, Jc(‖B‖), consists of a constant plus a field dependent term of the Kim model type. Analytical expressions for internal induction profiles and the entire shape of major magnetization loops, as well as the initial branch, are derived for the infinite slab geometry. As an illustration it is shown that the new model gives a precise overall description of a magnetization loop measured for melt processed YBa2Cu3Ox.

Critical state models for flux-pinning-induced magnetostriction in type-II superconductors

Models and calculated results are presented for the flux-pinning-induced magnetostriction in type-II superconductors. Three models are considered for the critical state; the original Bean model, the Kim model, and the exponential model in which the critical current density is assumed to depend exponentially on the flux density. The analytic expressions of the length change under the magnetic field are derived for specimens having infinite slab geometry and under the assumption that the reversible part of the total magnetization is negligibly small. The results are used for computer simulations and the hysteresis loops are calculated over a wide range of the relevant parameters. Since the pinning-induced magnetostriction reveals the pinning force directly, the hysteresis loops for each model have different features which are discussed in detail. It is also shown that the pinning force of the sample can be directly inferred from the width of the magnetostriction hysteresis loop. Finally, the experimental results on high-temperature superconductors are discussed in comparison with the calculated results.

Analysis of the frequency response method applied to non-isothermal sorption studies

A model describing non-isothermal sorption of gases within sorbent material with a monodisperse pore structure, in a batch frequency response system, subjected to small periodic volume perturbations is formulated. The model accounts for internal mass diffusion resistance, surface mass transfer resistance, external film heat transfer resistance, and heat transfer to the surrounding environment. The general model is linearised, and analytical solutions for the in-phase and out-of-phase components of the gas temperature and pressure response and the sorbent particle temperature response to a harmonic perturbation of the system volume are presented for infinite slab, infinite cylinder and spherical microparticle geometry. Finite rates of heat transfer from the gas phase to the environment and from the sorbent particle to the gas phase are shown to influence significantly the in-phase and out-of-phase components of the gas pressure response.