Dimensional Slab Research Articles

Fast Bayesian inference for inverse heat conduction problem using polynomial chaos and Karhunen–Loeve expansions

We present a fast Bayesian inference framework for solving inverse heat conduction problems (IHCP) for the estimation of boundary heat flux. The framework leverages the polynomial chaos expansions (PCEs) for generating computationally efficient and statistically equivalent surrogate model of the computationally expensive forward model and dimensionality reduction based on Karhunen–Loeve (K–L) expansion. We demonstrate the potential of this approach using three model problems to estimate heat flux in inverse heat conduction models. We represent the heat flux using K–L expansion to reduce the high dimensionality of the heat flux and compute the posterior probability distribution of the heat flux using the temperature measurements. The first inverse problem involves the estimation of time–varying heat flux in a one–dimensional slab using transient temperature measurements. The second problem involves the estimation of the unknown time–dependent heat flux of the disc in a realistic axisymmetric disc brake system. The third problem involves the estimation of the surface heat flux on a sounding rocket having a realistic three–dimensional geometry of the rocket module used in actual flight tests. We further obtain the inverse solution by computing the expectation of the distribution and demonstrate that this approach becomes orders of magnitude more efficient when we use the PCE surrogate model instead of the direct forward model for comparable accuracy. The numerical results show that this framework overcomes the drawback of high computational cost of Markov chain Monte Carlo (MCMC) without compromising on solution accuracy. The combination of PC–based surrogate modeling and K–L based dimensionality reduction leads to over 2000–fold speed up of numerical solution of IHCP.

Repulsive to attractive fluctuation-induced forces in disordered Landau-Ginzburg model

Critical fluctuations of some order parameter describing a fluid generates long-range forces between boundaries. Here, we discuss fluctuation-induced forces associated to a disordered Landau-Ginzburg model defined in a $d$-dimensional slab geometry $\mathbb R^{d-1}\times[0,L]$. In the model the strength of the disordered field is defined by a non-thermal control parameter. We study a nearly critical scenario, using the distributional zeta-function method, where the quenched free energy is written as a series of the moments of the partition function. In the Gaussian approximation, we show that, for each moment of the partition function, and for some specific strength of the disorder, the non-thermal fluctuations, associated to an order parameter-like quantity, becomes long-ranged. We demonstrate that the sign of the fluctuation induced force between boundaries, depend in a non-trivial way on the strength of the aforementioned non-thermal control parameter.

Fractional order triple-phase-lag thermoelasticity in the context of two-temperature theory

A new mathematical model is designed through reconstructing the triple-phase-lag model proposed by Roy Choudhuri, where the integer ordered derivatives concerning the time variable are replaced by the Caputo time-fractional derivative of order δ∈(0,1]. Moreover, the three-phase-lag heat conduction equation is derived in the context of two-temperature theories to examine the joint effect of thermodynamical and conductive temperatures. The proposed formulation is applied to the finite dimensional solid slab, whose boundaries are subject to the thermal loading and free from mechanical forces. The integral transform technique is applied to converting the original boundary value problem into an eigenvalue problem. Analytical solutions of the unknown thermal parameters are obtained in the Laplace domain. Time-domain solutions of the analytical results are achieved numerically through the Gaver–Stehfest algorithm. The results are examined graphically for the fixed phase-lag variations admitting various existing thermoelasticity theories.

Fatigue Behavior of Roller-Compacted Concrete Pavement Based on Full-Scale Fatigue Test

Abstract Roller-Compacted Concrete (RCC) has been used widely for construction of pavements. The strength of RCC Pavement (RCCP) can be obtained from not only hydration of binder but also the aggregate interlock resulting from roller compaction. For this reason, RCCP normally achieves strengths greater than conventional concrete pavement with similar cement content. Even though RCCP can provide good structural performance, it has been difficult to verify its long-term performance through actual field construction. Therefore, this study evaluated the fatigue behavior using 1 by 1-m dimensional RCC slab specimens obtained in the field in order to take into consideration field variability. A set of numerical analyses indicated that the failure modes of the specimens for a given loading condition appeared to be four-directional bottom-up cracks. A fatigue equation was developed based on the relationship between the stress level and the number of load repetitions.

Decay and Vanishing of some D-Solutions of the Navier–Stokes Equations

An old problem since Leray \cite{Le:1} asks whether homogeneous D solutions of the 3 dimensional Navier-Stokes equation in $\mathbb{R}^3$ or some noncompact domains are 0. In this paper, we give a positive solution to the problem in two special cases: (1) when the solution is axially symmetric and periodic in the vertical variable; (2) full 3 dimensional slab case $\mathbb{R}^2 \times [0, 1]$ with Dirichlet boundary condition. Other partial results are also presented. The paper is self contained comparing with the first part \cite{CPZ:1} although the general idea is related.

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

This paper establishes a general proof of bulk-hinge correspondence in inversion-symmetric insulators. By continuously introducing a cut to a three dimensional second order topological insulator, the resulting spectral flow reflects parities of the bulk eigenstates, necessarily leading to band inversions through this cutting procedure. As a result, it is shown that a two dimensional slab of a three dimensional second-order topological insulator is always a two-dimensional Chern insulator.

Biosilica slab photonic crystals as an alternative to cleanroom nanofabrication?

Photonics, the manipulation of light at nanoscale, is a key enabling technology with impact in health and energy applications, among others. In most cases photonics still relies on materials and fabrication methods inherited from other disciplines, usually requiring expensive, time-consuming and environmentally-unfriendly processes. Recent experiments demonstrated that advanced photonic materials, as complex as those known as 2.5 dimensional slab photonic crystals, also occur naturally in diatoms. These microscopic algae precipitate silicic acid from water to produce silicon dioxide membranes, relying on intracellular biomineralization mechanisms. Addressing some important aspects for the potential industrial utilization of these structures, we here propose that optical materials produced by the diatoms could serve as cost-effective and environmentally friendly alternatives to cleanroom nanofabrication. We demonstrate that photonic materials grown by the diatom species Coscinodiscus granii can be separated based on its hydrokinetic characteristics. We further show that the photonic membranes present low defect rates of ca. 1/100 unit cells and that variation in pore diameter, as observed between individual membranes, can affect the photonic properties at large, but only marginally at low refractive index contrast. Finally, we list algal culture collections operating worldwide, thus providing a global network for live diatoms and diatom materials. We discuss the feasibility and bottlenecks related to scaled-up growth for direct utilization of photonic materials from diatoms.

Use of Kobayashi potential method and Lorentz–Drude model to study scattering from a PEC strip buried below a lossy dispersive NID dielectric-magnetic slab

Kobayashi potential method is applied to investigate the scattering behavior of a perfect electric conducting (PEC) strip buried below a lossy dispersive non-integer dimensional (NID) dielectric-magnetic slab. Dispersion characteristics are introduced through the Lorentz–Drude model. Due to dispersive nature of the medium occupying the slab, it operates as epsilon negative (ENG), double negative (DNG), mu negative (MNG), or double positive (DPS) material depending upon the operating frequency. Scattered fields have been obtained when the slab behaves as ENG/MNG/DNG or DPS. Efforts have also been made to highlight the impact of NID parameter and dispersion characteristics of the material of the slab. It has been observed that increase/decrease in the thickness of the slab decreases/increases the scattered field from the strip below the slab. Moreover, it also decreases as size of the obstacle increases. It has been noted that the effect of real part of constitutive parameters on scattering pattern is opposite to that of imaginary part of constitutive parameters for ENG, MNG and DPS slab while for DNG slab the trend remains same.

Radiations from line source buried beneath a non-integer dimensional planar dielectric slab

Radiation due to an electric line source placed under a planar dielectric slab of non-integer dimensional space is determined. It has been assumed that the non-integer dimensional dielectric slab is sandwiched between two integer dimensional dielectric mediums. Radiated fields are written in terms of unknown spectrums of propagating waves. The unknown spectrum functions are determined using the boundary conditions. Special cases have also been discussed to verify the derived results. Radiation pattern is given for different parameters related to the geometry.

Propagation of transverse electric mode in a non-integer dimensional dielectric slab waveguide

In this paper, solution for the transverse electric (TEz) mode propagating in a non-integer dimensional (NID) dielectric slab waveguide has been derived. For region occupied by the slab, the medium is assumed to be NID along the direction normal to interfaces of the slab. Transcendental equations yield solution in form of non-integer order Hankel functions. The order of the Hankel functions depends on parameter describing the dimension of the NID space. Graphical results has been used to depict that the behavior of modes changes substantially with respect to NID parameter. It also affects the value of propagation constant, attenuation constant and cutoff frequency. The classical result is reproduced taking NID parameter equal to two. It is observed that the value of propagation constant for TM modes is higher than the value of propagation constant for TE modes. Moreover, the value of attenuation constant for TE modes is higher than the value of attenuation constant for TM modes.

Analysis of reflection and transmission from a planar NID-dispersive slab

Behavior of transmitted and reflected power from a planar non-integer dimensional lossless dispersive slab, placed in free space, is explored for uniform electromagnetic plane wave excitation. Dispersion has been incorporated through the Lorentz-Drude model. As the frequency of excitation increases, the dispersive slab respectively behaves as epsilon positive, double negative, mu negative, double positive meta-material. Effects of variation of angle of incidence, width of the slab and frequency of excitation on behavior of the powers have been noted taking different values of the parameter modeling non-integer dimensional space.

Scattering from a cylindrical obstacle deeply buried beneath a planar non-integer dimensional dielectric slab using Kobayashi potential method

Mathematical formulation for the far-zone field scattered by a cylindrical obstacle deeply buried beneath a planar dielectric slab has been presented. Method known as Kobayashi potential method has been employed for this purpose and transverse electric uniform plane wave has been used as a source of excitation. It has been assumed that dimension of space within slab is non-integer in the direction normal to planar interfaces of the slab. Moreover, it has also been assumed that distance of each interface of the slab from obstacle is very large as compared to size of the obstacle. Due to this assumption scattered field after reflection from the slab has no interaction with the obstacle and the situation has been called deeply buried. Field pattern has also been obtained and compared with the published work.

Propagation of transverse magnetic mode in a non-integer dimensional dielectric slab waveguide

In present paper, solutions for the transverse magnetic modes propagating in a non-integer dimensional (NID) dielectric slab waveguide have been derived. Medium within the slab is NID in direction normal to the dielectric interfaces of the slab. Transcendental equations in terms of non-integer order Hankel functions have been derived. The order of non-integer order Hankel functions depends on parameter describing dimension of the NID space. Using graphical treatment, it has been shown that behavior of propagating mode changes substantially when value of the parameter describing dimension of the NID space changes. It has also been noted that NID parameter significantly effects the value of propagation constant, attenuation constant and cutoff frequency. The classical results have also been recovered when dimension of the NID slab has been taken equal to the dimension of the medium surrounding the slab.

Thermal radiation heat transfer in participating media by finite volume discretization using collimated beam incidence

The main objective of this paper is to study the heat transfer rate of thermal radiation in participating media. For that, a generated collimated beam has been passed through a two dimensional slab model of flint glass with a refractive index 2. Both Polar and azimuthal angle have been varied to generate such a beam. The Temperature of the slab and Snells law has been validated by Radiation Transfer Equation (RTE) in OpenFOAM (Open Field Operation and Manipulation), a CFD software which is the major computational tool used in Industry and research applications where the source code is modified in which radiation heat transfer equation is added to the case and different radiation heat transfer models are utilized. This work concentrates on the numerical strategies involving both transparent and participating media. Since Radiation Transfer Equation (RTE) is difficult to solve, the purpose of this paper is to use existing solver buoyantSimlpeFoam to solve radiation model in the participating media by compiling the source code to obtain the heat transfer rate inside the slab by varying the Intensity of radiation. The Finite Volume Method (FVM) is applied to solve the Radiation Transfer Equation (RTE) governing the above said physical phenomena.

An evidence of period doubling bifurcation in a dc driven semiconductor-gas discharge plasma

We present an experimental study of nonlinearity observed in a dc driven semiconductor-gas discharge system. The plasma glow is generated using planar electrodes in a vacuum chamber filled with nitrogen gas at partial atmospheric pressure. The discharge behaves oscillatory in time, showing single and sometimes multiple periodicities in plasma current and voltage measurements. Harmonic frequency generations and period doubling cascade are investigated experimentally by varying the applied voltage. To identify the stability condition, numerical simulations are conducted using COMSOL® Multiphysics software. The discharge is modeled as a one dimensional plasma slab. Numerical results are in good agreement with the experimental measurements.

Exact solution of the neutron transport equation in spherical geometry

Abstract Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using PN approximation which is widely used in neutron transport theory.

Simulation of Isotropic Acoustic Metamaterials

The model use to study electromagnetic metamaterials in transverse electric mode was modified to study the pressure distribution in an acoustic metamaterial in a two dimensional geometry. An electromagnetic wave of 30 GHz in transverse magnetic mode at normal incidence propagating through a two dimensional isotropic semi infinite double negative metamaterial slab of 640×830 cells embedded in free space with low loss damping frequency 108s-1 was studied by finite difference time dependent method with Yee’s algorithm with an explicit leapfrog scheme. The multiple cycle m-n-m pulses generating beams were used as sources. The simulations for refractive indices n=-1 and n=-16 at different time steps are presented. For n=-1, the sub-wavelength imaging is apparent, diverging the waves from source into two sources, one inside and the other outside the slab. The reverse propagation is much more significant for showing that the group velocity is much larger inside the metamaterial by the closely packed wave front, making the continuation of the wave pattern much more significant through the metamaterial into the normal space.

Simulation of Isotropic Acoustic Metamaterials

The model use to study electromagnetic metamaterials in transverse electric mode was modified to study the pressure distribution in an acoustic metamaterial in a two dimensional geometry. An electromagnetic wave of 30 GHz in transverse magnetic mode at normal incidence propagating through a two dimensional isotropic semi infinite double negative metamaterial slab of 640×830 cells embedded in free space with low loss damping frequency 108s-1was studied by finite difference time dependent method with Yee’s algorithm with an explicit leapfrog scheme. The multiple cyclem-n-mpulses generating beams were used as sources. The simulations for refractive indices n=-1 and n=-16 at different time steps are presented. For n=-1, the sub-wavelength imaging is apparent, diverging the waves from source into two sources, one inside and the other outside the slab. The reverse propagation is much more significant for showing that the group velocity is much larger inside the metamaterial by the closely packed wave front, making the continuation of the wave pattern much more significant through the metamaterial into the normal space.

Controlling a three dimensional electron slab of graded AlxGa1−xN

Polarization induced degenerate n-type doping with electron concentrations up to ∼1020 cm−3 is achieved in graded AlxGa1−xN layers (x: 0% → 37%) grown on unintentionally doped and on n-doped GaN:Si buffer/reservoir layers by metal organic vapor phase epitaxy. High resolution x-ray diffraction, transmission electron microscopy, and electron dispersive x-ray spectroscopy confirm the gradient in the composition of the AlxGa1−xN layers, while Hall effect studies reveal the formation of a three dimensional electron slab, whose conductivity can be adjusted through the GaN(:Si) buffer/reservoir.

Transient Radiation Coupled With Conduction Heat Transfer in a One Dimensional Slab

The present research work views over a solution of radiative transport problem along with conduction in one perspective piece and in the existence of participating media. The radiative transfer equations are developed for anisotropically scattering, absorbing, emitting medium and the equation is being discretized using finite volume method. Heat flux and the incident radiation effects have been computed at three different time step. Transient radiation along with transient conduction is solved and the radiative effect has been measured using radiative transfer equation while the conduction term has been measured using conduction equation.