Hybrid discrete ordinates—spherical harmonics solution to the Boltzmann Transport Equation for phonons for non-equilibrium heat conduction

The Boltzmann Transport Equation (BTE) for phonons has found prolific use for the prediction of non-equilibrium heat conduction phenomena in semiconductor materials. This article presents a new hybrid formulation and associated numerical procedures for solution of the BTE for phonons. In this formulation, the phonon intensity is first split into two components: ballistic and diffusive. The governing equation for the ballistic component is solved using two different established methods that are appropriate for use in complex geometries, namely the discrete ordinates method (DOM), and the control angle discrete ordinates method (CADOM). The diffusive component, on the other hand, is determined by invoking the first-order spherical harmonics (or P₁) approximation, which results in a Helmholtz equation with Robin boundary conditions. Both governing equations, referred to commonly as the ballistic-diffusive equations (BDE), are solved using the unstructured finite-volume procedure. Results of the hybrid method are compared against benchmark Monte Carlo results, as well as solutions of the BTE using standalone DOM and CADOM for two two-dimensional transient heat conduction problems at various Knudsen numbers. Subsequently, the method is explored for a large-scale three-dimensional geometry in order to assess convergence and computational cost. It is found that the proposed hybrid method is accurate at all Knudsen numbers. From an efficiency standpoint, the hybrid method is found to be superior to direct solution of the BTE both for steady state as well as for unsteady non-equilibrium heat conduction calculations with the computational gains increasing with increase in problem size.     

Origin of buckling phenomenon during drying of micrometer-sized colloidal droplets

The origin of the buckling of micrometer-sized colloidal droplets during evaporation-induced self-assembly (EISA) has been elucidated using electron microscopy and small-angle neutron scattering. Doughnut-like assembled grains with varying aspect ratios are formed during EISA at different physicochemical conditions. It has been revealed that this phenomenon is better explained by an existing hypothesis based on the formation of a viscoelastic shell of nanoparticles during drying than by other existing hypotheses based on the inertial instability of the initial droplets and hydrodynamic instability due to thermocapillary forces. This conclusion was further supported by the arrest of buckling through modification of the colloidal interaction in the initial dispersion.     

Nuclear–nuclear correlation function from non-Born–Oppenheimer calculations of diatomic rovibrational states with total angular momentum equal to two (N = 2). Charge asymmetry in HD

The HD molecule in rovibrational states where the total angular momentum quantum number is equal to two (N = 2) is characterised with quantum mechanical calculations without assuming the Born–Oppenheimer (BO) approximation. Explicitly correlated all-particle Gaussian functions are used in the calculations. The convergence of the total non-BO energies of the considered states with the basis set size is analysed. The calculations of the averaged interparticle distances demonstrate the asymmetry of the electronic charge distribution. The algorithm to calculate the nuclear–nuclear correlation function for the N = 2 states is derived and implemented. Plots of this function for different rovibrational states provide a visual representation of the molecular structure.     

Determination of acidic drugs and caffeine in municipal wastewaters and receiving waters by gas chromatography-ion trap tandem mass spectrometry

Some aspects of both sample preparation and instrumental techniques for analysis of such acidic drugs as acetylsalicylic acid, ibuprofen, gemfibrozil, fenoprofen, naproxen, ketoprofen, and diclofenac, as well as caffeine in surface water and municipal wastewater have been studied and further developed. Water samples were filtered and target analytes were extracted by solid-phase extraction (SPE). Supelco LC-18 and Oasis HLB SPE cartridges were used to pre-concentrate samples for acidic drugs and caffeine, respectively. A methylation process was applied to acidic drugs prior to analysis while caffeine was analyzed directly. A method of gas chromatography-ion trap tandem mass spectrometry (IT-MS/MS) for analysis of the target acidic pharmaceuticals and caffeine is presented here in detail. Such parameters as collision-induced dissociation (CID) voltage, isolation time, excitation time, excitation storage level, and electron energy were adjusted in order to optimize the instrument analytical performance. After optimization, an instrument detection limit of 0.5-20 pg/microL with signal-to-noise (S/N) not less than 5 was achieved for all target analytes. It was shown that this method has good linearity within the range of 10-2000 pg/microL. The application of the optimized IT-MS/MS parameters conjointly with the sample preparation procedure resulted in method detection limits (MDLs) of 0.1-1.0 and 20 ng/L for the determination of acidic drugs and caffeine, respectively in such samples as surface water, effluent from municipal wastewater plants, as well as receiving waters.     

Effects of sintering on microstructure and dielectric response in YCrO<Subscript>3</Subscript> nanoceramic

Effects of sintering on pore morphology and dielectric response have been investigated. Pore structure has been probed by small angle neutron scattering (SANS). It has been observed that the size distribution becomes less polydisperse with a slight modification in the distribution as sintering temperature is increased. Dielectric response in the frequency range 0.02–1000 kHz is significantly altered by modification of pore structure because of sintering. A transition from non-Debye type to near-Debye type response has been observed as the sintering temperature is increased.      

Effect of heat treatment on pore structure in nanocrystalline NiO: A small angle neutron scattering study

Nanocrystalline nickel oxide powders were calcined at 300, 600 and 900°C and pore structure evolution was followed by small angle neutron scattering (SANS). Pore size distributions at two widely separated size ranges have been revealed. Shrinkage of larger-sized pore with reduction in polydispersity has been observed with increasing heat treatment temperature. The pore structures at various heat treatment temperatures do not scale. This has been attributed to the grain boundary diffusion leading to an asymmetric shrinkage of the pores.      

Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods

This paper discusses an efficient numerical approximation technique, called the differential quadrature method (DQM), which has been adapted to model lossy uniform and nonuniform transmission lines. The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain. Using the DQM, the frequency-domain Telegrapher's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations. DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain. Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation (AWE) applied to transmission lines, the derivation mechanisms in these two disparate methods are significantly different. Unlike AWE, which employs a complex moment-matching process to obtain rational approximation, the DQM requires no approximation of transcendental functions, thereby avoiding the process of moment generation and moment matching. Due to global sampling of points in the DQM approximation, it requires far fewer grid points in order to build accurate discrete models than other numerical methods do. The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE.     

Coupled-line circuit with adjustable input conductance

A new matching circuit was developed, for which the input conductance (real part of the input admittance) can be adjusted by simply changing the length of one open-ended stub. This circuit can be utilised for matching of microstrip devices as well as for tuning of solid-state amplifiers and oscillators (such as transistors, Impatt or Gunn diodes).     

The steady-state evaluation of small anechoic chambers

An historical survey of the techniques of measurement and assessment of anechoic chambers is given with a view to deciding the optimum method of evaluating the new anechoic chamber at Bradford University. Experimental results taken on the chamber, using the inverse distance and frequency response tests, are presented. An attempt is made to correlate the results of these tests with predicted results obtained from steady-state measurements taken, in an interference tube, on the novel type of absorber used in the chamber. In conclusion, guidelines for the design of small anechoic chambers are given.     

Dynamical scaling of the structure factor of some non-Euclidean systems

Predictions of nonlinear theories on dynamics of new phase formation have been examined for the hydration of calcium silicates with light water and heavy water. In the case of hydration with light water, reasonable agreement has been observed with dynamical scaling hypothesis with a new measure of the characteristic length. The characteristic length does not follow a power law relation with time. Hydrating mass is found to be mass fractal throughout hydration, with mass fractal dimension increasing with time. But, in the case of hydration with heavy water, no agreement has been observed with the scaling hypothesis. Hydrating mass undergoes transition from mass fractal to surface fractal and finally again to mass fractal. The qualitative features of the kinetics of hydration, as measured in small-angle scattering experiments, are strikingly different for hydration with light water and heavy water.