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Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid‐fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and flame propagation. The directional solidification of semi‐conductor crystals by the Bridgman—Stockbarger method^1,2 is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt—solid interface. In this work, a Chebyshev pseudospectral collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, a finite‐difference preconditioned conjugate minimum residual method and a Picard type iterative scheme.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

The purpose of this paper is to investigate the diffusion behaviors of different atoms at the Cu/Cu3Sn interface and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy.

The diffusion behaviors of different atoms at the Cu/Cu3Sn interface are analyzed, and the vacancy formation energy, diffusion energy barrier and vacancy diffusion activation energy are obtained using molecular dynamics simulation. The nudged elastic band method is used to evaluate diffusion energy barrier for Cu/Cu3Sn system.

It is found that the vacancies in the Cu/Cu3Sn interface promote the interfacial diffusion, and the formation energy of Cu vacancy in the Cu crystal is larger than that in Cu3Sn crystal. In addition, the formation energies of Cu1 vacancy and Cu2 vacancy are close to each other in Cu3Sn crystal, and they are all less than the formation energy of Sn vacancy. Furthermore, the vacancy diffusion barrier and vacancy diffusion activation energy of the Cu/Cu3Sn interface are calculated, and the results show that the vacancy diffusion activation energy of Sn was higher than that of Cu. Finally, by comparison of diffusion activation energies of different diffusion mechanisms, Cu→Cu1vac is the most possible migration path at all temperatures.

It is concluded that the vacancies in Cu/Cu3Sn interface promote interfacial diffusion, and the activation energy of vacancy diffusion in most diffusion mechanisms decreases with the increase of temperature.

An interferogram is produced by modulating the difference between the extraordinary refractive index and the ordinary refractive index for photoelastic crystals in photoelastic-modulated Fourier transform spectrometers (PEM-FTs). Due to the influence of the refractive index dispersion characteristics on the maximum optical path difference of the interferogram, it is necessary to study wavelength calibration methods.

A wavelength calibration method for PEM-FTs was proposed based on the modulation principle of the photoelastic-modulated interferometer and the relationship between the maximum optical path difference and the refractive index difference. A 632.8 nm narrow-pulse laser was used as a reference source to measure the maximum optical path difference () of the interferogram, and the parameter was used to calculate the discrete frequency points in the frequency domain. To account for the influence of refractive index dispersion on the maximum optical path difference, the refractive index curve for the photoelastic crystal was used to adjust the discrete frequency coordinates.

The error in the reconstructed spectral frequency coordinates clearly decreased. The maximum relative error was 2.5%. A good solar absorption spectrum was obtained with a PEM-FT experimental platform and the wavelength calibration method.

The interferogram is produced by adjusting the difference between extraordinary refractive index and ordinary refractive index for the photoelastic crystal in the PEM-FTs. Given the wavelength dependence on the refractive indices, in view of the modulation principle of the photoelastic modulated interferometer, the relationship between the maximum optical path difference and the refractive index difference, the variation law of the refractive index of the photoelastic crystal and the process of spectral reconstruction is presented in this paper.

A simple approach is developed for modelling the distribution of dopant in crystals grown by the Czochralski technique. Allowance is made for the temperature dependence of the diffusivity and for the diffusion of dopant behind the moving boundary. It is found that the effect can make a significant difference to the final dopant distribution. The diffusion process is modelled using a discrete method, previously developed for situations in which the boundary is static.

Commonly known as ecstasy, MDMA has been central to the British acid house, rave and dance club scene over the last 20 years. Figures from the annual national British Crime Survey suggest that ecstasy use has declined since 2001. This apparent decline is considered here alongside the concurrent emergence of a ‘new’ form of ecstasy ‐ MDMA powder or crystal ‐ and the extent to which this can be seen as a successful rebranding of MDMA as a ‘premium’ product in the wake of user disenchantment with cheap and easily available but poor quality pills. These changes have occurred within a policy context, which in the last decade has increasingly prioritised the drugs‐crime relationship through coercive treatment of problem drug users within criminal justice‐based interventions, alongside a focus on binge drinking and alcohol‐related harm. This has resulted in a significant reduction in the information, support and treatment available to ecstasy users since the height of dance drug harm reduction service provision pioneered by the Safer Dancing model in the mid‐1990s.

The design of temperature‐compensated quartz crystal oscillators (TCXOs) in thick film hybrid technology is described. TCXOs controlled by varicap diodes are usually realised with discrete NTC thermistors and resistors. Data obtained by precision measurements of voltages on varicap diodes for the same oscillator frequencies over the operating temperature range are used for calculating values of the NTC thermistors and resistors. In most cases these values cannot be found in the Renard scale, with the result that manipulation or ‘juggling’ of values is necessary. The realisation of temperature‐compensating circuits in thick film technology has certain advantages, such as miniaturisation, better characteristics at high frequencies and in particular the possibility to trim thick film resistors and NTC thermistors to values calculated for each oscillator. The method of realisation of TCXOs in thick film hybrid technology was developed and verified on prototypes. The compensation curves were obtained by measuring compensation voltages for each oscillator over the operating temperature range from — 20°C to 70°C. From these data the values of resistors and NTC thermistors were calculated. A computer program was used to minimise frequency instability error as a function of six parameters (resistance). The frequency stability (Δf/f) of TCXOs obtained was better than ±2 ppm.

This work presents a topology optimization methodology for designing microarchitectures of phononic crystals. The objective is to get microstructures having, as a consequence of wave propagation phenomena in these media, bandgaps between two specified bands. An additional target is to enlarge the range of frequencies of these bandgaps.

The resulting optimization problem is solved employing an augmented Lagrangian technique based on the proximal point methods. The main primal variable of the Lagrangian function is the characteristic function determining the spatial geometrical arrangement of different phases within the unit cell of the phononic crystal. This characteristic function is defined in terms of a level-set function. Descent directions of the Lagrangian function are evaluated by using the topological derivatives of the eigenvalues obtained through the dispersion relation of the phononic crystal.

The description of the optimization algorithm is emphasized, and its intrinsic properties to attain adequate phononic crystal topologies are discussed. Particular attention is addressed to validate the analytical expressions of the topological derivative. Application examples for several cases are presented, and the numerical performance of the optimization algorithm for attaining the corresponding solutions is discussed.

The original contribution results in the description and numerical assessment of a topology optimization algorithm using the joint concepts of the level-set function and topological derivative to design phononic crystals.

The aim of this research is to study the role and formation of hydration products particularly crystalline portlandite Ca(OH)2 in MWCNT-reinforced concrete at 28 days. Concrete is the largest manufactured building material in world in which cement, sand aggregates and water cement ratio plays governing role. Water–Cement ratio decides it strength, usage, serviceability and durability. As strength of concrete depends on formation of crystalline hydrates; therefore, water–cement ratio can alter formation of hydrates also. Unfortunately, concrete is the most brittle material and to overcome brittleness of conventional concrete is tailored with some fibers. Till now, multiwalled carbon nano tubes are the most tensile and strongest materials discovered. Addition of multiwalled carbon nano tubes changes basic properties of conventional concrete. Therefore, it is important to evaluate formation of crystalline hydrates in multiwalled carbon nano tube–reinforced concrete by micro structure analysis.

Till now, multiwalled carbon nano tube–reinforced concrete has not been analyzed at micro structure level. To accomplish the objective, four concrete mixes with 0.45, 0.48, 0.50 and 0.55 water–cement ratio having 0.5 and 1% multiwalled carbon nano tubes incorporated by weight of cement, respectively. For hardening property analysis, compressive strength was obtained by crushing cubes; flexural strength was obtained by three-point loading; and split tensile strength was obtained by splitting cylindrical specimens. For analyzing role and formation of crystalline portlandite Ca(OH)2 hydrates, X-ray diffraction test was conducted on 75-µ dust of each mix. Scanning electron microscopy analysis was performed on fractured samples of crushed cubes of multiwalled carbon nano tube–reinforced concrete samples to check aggloremation.

It was observed multiwalled carbon nano tubes successfully enhanced compressive strength, flexural strength and split tensile strength by 8.89, 5.33 and 28.90%, respectively, in comparison to reference concrete at 0.45 water–cement ratio and 0.5% multiwalled carbon nano tubes by weight of cement. When its content was increased from 0.5 to 1% by weight of cement compressive strength, flexural strength and split tensile strength diminished by 2.04, 0.32 and 1.18%, respectively, at 0.45 water–cement ratio. With the increment of water–cement ratio, overall strength decreased in all mixes, but in multiwalled carbon nano tube–reinforced concrete mixes, strength was more than reference mixes. In reference, concrete at 0.45 water–cement ratio crystalline portlandite Ca(OH)2 crystals are of nano metre size, but in carbon nano tube–reinforced concrete mix having 0.45 water–cement ratio and 0.5% multiwalled carbon nano tubes by weight of cement, its size is much smaller than reference mix, thereby enhancing mechanical strength. In reference, concrete at 0.55 water–cement ratio size of crystalline portladite Ca(OH)2 crystals is large, but with incorporation of multiwalled carbon nano tubes, their size reduced, thereby enhancing mechanical strength of carbon nano tube–reinforced concrete having 0.55 water–cement ratio and 0.5 and 1% multiwalled carbon nano tubes by weight of cement, respectively. Also at 1% multiwalled carbon nano tubes by weight of cement, agglomeration and reduction in formation of crystalline portlandite Ca(OH)2 crystals were observed. Multiwalled carbon nano tubes effectively refine pores and restrict propagation of micro cracks and act as nucleation sites for Calcium-Silicate-Hydrate phase. Geometry of crystalline axis of fracture for portlandite Ca(OH)2 crystals is altered with incorporation of multiwalled carbon nano tubes. Crystalline portlandite Ca(OH)2 crystals and bridging effect of multiwalled carbon nano tubes is governing factor for enhancing strength of multiwalled carbon nano tube reinforced concrete.

Multiwalled carbon nano tube–reinforced concrete can be used to make strain sensing concrete.

Change in geometry and size of axis of fracture of crystalline portladite Ca(OH)2 crystals with incorporation of multiwalled carbon nano tubes.

The purpose of this paper is to propose a modal method to calculate the band gaps of one-dimensional (1D) phononic crystals.

The phononic crystals have modes with exponential form envelope in the band gaps, however, outside the band gaps the modes are of amplitude modulation periodic form. Thus the start and end frequencies of band gaps can be determined from the existence conditions of periodic modes. So, the band gaps calculation of 1D phononic crystal is transformed into the existence discussion of periodic solution of mode shapes equation. The results are verified by finite element harmonic response analysis.

At the start and end frequencies of the band gap, the mode equation have solution with period of lattice constant.

Compared with the traditional theoretical methods, the proposed modal method has a clearer principle and easier calculation.