Temperature dependence of conformational properties of short polyelectrolytes from simulations at a single temperature

We use a series expansion method introduced recently by Rickman and Phillpot (Phys. Rev. Lett. 1991, 66, 349) to study the temperature dependent conformational properties of short ionized polyelectrolyte chains in ionic solutions by conducting simulations at a single temperature. The charged beads located at the sites of a cubic lattice interact through screened Coulombic interactions. It is shown that this method provides results that correlate with other Monte Carlo simulations, performed over a range of temperatures, where conformational transitions induced by thermal and screening effects occur. It is also shown that the method can be used successfully when the potential is weakly dependent on temperature. © 1994 American Chemical Society.

Structural properties and energetics of diffuse Rb-87 clusters in three-dimension

A correlated two-body basis function is used to describe the three-dimensional bosonic clusters interacting via two-body van der Waals potential. We calculate the ground state and the zero orbital angular momentum excited states for Rb-N clusters with up to N = 40. We solve the many-particle Schrodinger equation by potential harmonics expansion method, which keeps all possible two-body correlations in the calculation and determines the lowest effective many-body potential. We study energetics and structural properties for such diffuse clusters both at dimer and tuned scattering length. The motivation of the present study is to investigate the possibility of formation of N-body clusters interacting through the van der Waals interaction. We also compare the system with the well studied He, Ne, and Ar clusters. We also calculate correlation properties and observe the generalised Tjon line for large cluster. We test the validity of the shape-independent potential in the calculation of the ground state energy of such diffuse cluster. These are the first such calculations reported for Rb clusters. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730972]

Existence of solutions and asymtptotic limits of the Euler-Poisson and the quantum drift-diffusion systems

My work concerns two different systems of equations used in the mathematical modeling of semiconductors and plasmas: the Euler-Poisson system and the quantum drift-diffusion system. The first is given by the Euler equations for the conservation of mass and momentum, with a Poisson equation for the electrostatic potential. The second one takes into account the physical effects due to the smallness of the devices (quantum effects). It is a simple extension of the classical drift-diffusion model which consists of two continuity equations for the charge densities, with a Poisson equation for the electrostatic potential. Using an asymptotic expansion method, we study (in the steady-state case for a potential flow) the limit to zero of the three physical parameters which arise in the Euler-Poisson system: the electron mass, the relaxation time and the Debye length. For each limit, we prove the existence and uniqueness of profiles to the asymptotic expansion and some error estimates. For a vanishing electron mass or a vanishing relaxation time, this method gives us a new approach in the convergence of the Euler-Poisson system to the incompressible Euler equations. For a vanishing Debye length (also called quasineutral limit), we obtain a new approach in the existence of solutions when boundary layers can appear (i.e. when no compatibility condition is assumed). Moreover, using an iterative method, and a finite volume scheme or a penalized mixed finite volume scheme, we numerically show the smallness condition on the electron mass needed in the existence of solutions to the system, condition which has already been shown in the literature. In the quantum drift-diffusion model for the transient bipolar case in one-space dimension, we show, by using a time discretization and energy estimates, the existence of solutions (for a general doping profile). We also prove rigorously the quasineutral limit (for a vanishing doping profile). Finally, using a new time discretization and an algorithmic construction of entropies, we prove some regularity properties for the solutions of the equation obtained in the quasineutral limit (for a vanishing pressure). This new regularity permits us to prove the positivity of solutions to this equation for at least times large enough.

Finite-element discretization of 3D energy-transport equations for semiconductors

In this thesis a mathematical model was derived that describes the charge and energy transport in semiconductor devices like transistors. Moreover, numerical simulations of these physical processes are performed. In order to accomplish this, methods of theoretical physics, functional analysis, numerical mathematics and computer programming are applied. After an introduction to the status quo of semiconductor device simulation methods and a brief review of historical facts up to now, the attention is shifted to the construction of a model, which serves as the basis of the subsequent derivations in the thesis. Thereby the starting point is an important equation of the theory of dilute gases. From this equation the model equations are derived and specified by means of a series expansion method. This is done in a multi-stage derivation process, which is mainly taken from a scientific paper and which does not constitute the focus of this thesis. In the following phase we specify the mathematical setting and make precise the model assumptions. Thereby we make use of methods of functional analysis. Since the equations we deal with are coupled, we are concerned with a nonstandard problem. In contrary, the theory of scalar elliptic equations is established meanwhile. Subsequently, we are preoccupied with the numerical discretization of the equations. A special finite-element method is used for the discretization. This special approach has to be done in order to make the numerical results appropriate for practical application. By a series of transformations from the discrete model we derive a system of algebraic equations that are eligible for numerical evaluation. Using self-made computer programs we solve the equations to get approximate solutions. These programs are based on new and specialized iteration procedures that are developed and thoroughly tested within the frame of this research work. Due to their importance and their novel status, they are explained and demonstrated in detail. We compare these new iterations with a standard method that is complemented by a feature to fit in the current context. A further innovation is the computation of solutions in three-dimensional domains, which are still rare. Special attention is paid to applicability of the 3D simulation tools. The programs are designed to have justifiable working complexity. The simulation results of some models of contemporary semiconductor devices are shown and detailed comments on the results are given. Eventually, we make a prospect on future development and enhancements of the models and of the algorithms that we used.

Quantenchemische Behandlung von elektronischem Energietransfer

Im Rahmen dieser Dissertation wurden quantenchemische Untersuchungen zum Phänomen des elektronischen Energietransfers durchgeführt. Zum einen wurden theoretische Modelle zur Berücksichtigung temperaturabhängiger Elektron-Phonon-Kopplung in vibronischen Spektren ausgearbeitet und numerischen Tests unterzogen. Zum anderen erfolgte die Bestimmung molekularer Eigenschaften bichromophorer Systeme unter Anwendung etablierter Rechenmethoden. Im Fokus stehen das Zusammenspiel elektronischer Kopplung und statischer Unordnung sowie Energietransferzeiten und der Einfluss molekularer Brücken in Dimeren auf die Kopplung. Da sich elektronischer Energietransfer spektroskopisch nachweisen lässt, wurden temperaturabhängige Simulationen der Linienform von vibronischen Übergängen, die an ein Wärmebad ankoppeln, durchgeführt. Die erforderliche Antwortfunktion zur Bestimmung der spektralen Linienform kann aus einer Kumulantenentwicklung und alternativ aus der Multi-Level Redfieldtheorie abgeleitet werden. Statt der genäherten Schwingungsstruktur des Brownschen Oszillatormodells wurde eine explizit berechnete Zustandsdichte als Ausgangspunkt verwendet. Sowohl reine Elektron-Phonon- als auch Schwingung-Phonon-Kopplung werden für verschiedene Spektraldichten der Badmoden diskutiert. Im Zuge eines Kooperationsprojekts führten wir Untersuchungen zur elektronischen Kopplung an einer homologen Reihe von Rylendimeren mit unterschiedlichen Brückenlängen durch. Zu diesem Zweck wurden Ergebnisse aus Tieftemperatureinzelmolekülmessungen und quantenchemischen Berechnungen auf Grundlage des vibronischen Kopplungsmodells herangezogen und ausgewertet. Die untersuchten Dimere zeigen einen Übergang vom Grenzfall starker Kopplung hin zu schwacher Kopplung und die mittleren Energietransferzeiten konnten in guter Übereinstimmung mit experimentellen Messwerten berechnet werden. Da eine molekulare Brücke zwischen Donor- und Akzeptoreinheit die elektronische Kopplung modifiziert, kann sie sich störend auf experimentelle Messungen auswirken. Daher wurde untersucht, ob das interchromophore Kopplungsverhalten vorwiegend durch die Polarisierbarkeit des verbrückenden Elements oder durch bindungsvermittelte Wechselwirkungen beeinflusst wird und welche Brückentypen sich folglich für experimentelle Studien eignen. Sämtliche untersuchten Brückenelemente führten zu einer Vergrößerung der elektronischen Kopplung und die Kopplungsstärke wurde maßgeblich durch brückenvermittelte Wechselwirkungen bestimmt.

Relativistic description of 3He(e,e'p)2H

The relativistic distorted-wave impulse approximation is used to describe the 3He(e, e′ p)2H process. We describe the 3He nucleus within the adiabatic hyperspherical expansion method with realistic nucleon-nucleon interactions. The overlap between the 3He and the deuteron wave functions can be accurately computed from a three-body calculation. The nucleons are described by solutions of the Dirac equation with scalar and vector (S–V) potentials. The wave function of the outgoing proton is obtained by solving the Dirac equation with a S–V optical potential fitted to elastic proton scattering data on the residual nucleus. Within this theoretical framework, we compute the cross section of the reaction and other observables like the transverse-longitudinal asymmetry, and compare them with the available experimental data measured at JLab.

Some theoretical aspects in computational analysis of adhesive lap joints

This paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Some numerical results are presented.

An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

Analysis of the effect of transverse modes on free-space optical interconnect performance

Vertical-cavity surface-emitting lasers (VCSELs) and microlenses can be used to implement free space optical interconnects (FSOIs) which do not suffer from the bandwidth limitations inherent in metallic interconnects. A comprehensive link equation describing the effects of both optical and electrical noise is introduced. We have evaluated FSOI performance by examining the following metrics: the space-bandwidth product (SBP), describing the density of channels and aggregate bandwidth that can be achieved, and the carrier-to-noise ratio (CNR), which represents the relative strength of the carrier signal. The mode expansion method (MEM) was used to account for the primary cause of optical noise: laser beam diffraction. While the literature commonly assumes an ideal single-mode laser beam, we consider the experimentally determined multimodal structure of a VCSEL beam in our calculations. It was found that maximum achievable interconnect length and density for a given CNR was significantly reduced when the higher order transverse modes were present in Simulations. However, the Simulations demonstrate that free-space optical interconnects are still a suitable solution for the communications bottleneck, despite the adverse effects introduced by transverse modes.

N-dimensional electron in an anharmonic potential:the large-N limit

We show that the energy levels predicted by a frac(1, N)-expansion method for an N-dimensional electron in an anharmonic potential are always lower than the exact energy levels but monotonically converge toward their exact eigenstates for higher ordered corrections. The technique allows a systematic approach for quantum many body problems in a confined potential and explains the remarkable agreement of such approximate theories when compared with numerical results.

Methyl chloride purification for the silicone industry

This study experimentally investigated methyl chloride (MeCl) purification method using an inhouse designed and built volumetric adsorption/desorption rig. MeCl is an essential raw material in the manufacture of silicone however all technical grades of MeCl contain concentrations (0.2 - 1.0 % wt) of dimethyl ether (DME) which poison the process. The project industrial partner had previously exhausted numerous separation methods, which all have been deemed not suitable for various reasons. Therefore, adsorption/desorption separation was proposed in this study as a potential solution with less economic and environmental impact. Pure component adsorption/desorption was carried out for DME and MeCl on six different adsorbents namely: zeolite molecular sieves (types 4 Å and 5 Å); silica gels (35-70 mesh, amorphous precipitated, and 35-60 mesh) and granular activated carbon (type 8-12 mesh). Subsequent binary gas mixture adsorption in batch and continuous mode was carried out on both zeolites and all three silica gels following thermal pre-treatment in vacuum. The adsorbents were tested as received and after being subjected to different thermal and vacuum pre-treatment conditions. The various adsorption studies were carried out at low pressure and temperature ranges of 0.5 - 3.5 atm and 20 - 100 °C. All adsorbents were characterised using Brunauer Emmett Teller (BET), thermogravimetric analysis (TGA), scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDXA) to investigate their physical and chemical properties. The well-known helium (He) expansion method was used to determine the empty manifold and adsorption cell (AC) regions and respective void volumes for the different adsorbents. The amounts adsorbed were determined using Ideal gas laws via the differential pressure method. The heat of adsorption for the various adsorbate-adsorbent (A-S) interactions was calculated using a new calorimetric method based on direct temperature measurements inside the AC. Further adsorption analysis included use of various empirical and kinetic models to determine and understand the behaviour of the respective interactions. The gas purification behaviour was investigated using gas chromatography and mass spectroscopy (GC-MC) analysis. Binary gas mixture samples were syringed from the manifold iii and AC outlet before and after adsorption/desorption analysis through manual sample injections into the GC-MS to detect and quantify the presence of DME and ultimately observe for methyl chloride purification. Convincing gas purification behaviour was confirmed using two different GC columns, thus giving more confidence on the measurement reliability. From the single pure component adsorption of DME and MeCl on the as received zeolite 4A subjected to 1 h vacuum pre-treatment, both gases exhibited pseudo second order adsorption kinetics with DME exhibiting a rate constant nearly double that of MeCl thus suggesting a faster rate of adsorption. From the adsorption isotherm classification both DME and MeCl exhibited Type II and I adsorption isotherm classifications, respectively. The strength of bonding was confirmed by the differential heat of adsorption measurement, which was found to be 23.30 and 10.21 kJ mol-1 for DME and MeCl, respectively. The former is believed to adsorb heterogeneously through hydrogen bonding whilst MeCl adsorbs homogenously via van der Waal’s (VDW) forces. Single pure component adsorption on as received zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) resulted in similar adsorption/desorption behaviour in similar quantities (mol kg-1). The adsorption isotherms for DME and MeCl on zeolite 5A, silica gels (35-70, amorphous precipitated and 35-60) and activated carbon 8-12 exhibited Type I classifications, respectively. Experiments on zeolite 5A indicated that DME adsorbed stronger, faster and with a slightly stronger strength of interaction than MeCl but in lesser quantities. On the silica gels adsorbents, DME exhibited a slightly greater adsorption capacity whilst adsorbing at a similar rate and strength of interaction compared to MeCl. On the activated carbon adsorbent, MeCl exhibited the greater adsorption capacity at a faster rate but with similar heats of adsorption. The effect of prolonged vacuum (15 h), thermal pre-treatment (150 °C) and extended equilibrium time (15 min) were investigated for the adsorption behaviour of DME and MeCl on both zeolites 4A and 5A, respectively. Compared to adsorption on as received adsorbents subjected to 1 h vacuum the adsorption capacities for DME and MeCl were found to increase by 1.95 % and 20.37 % on zeolite 4A and by 4.52 % and 6.69 % on zeolite 5A, respectively. In addition the empirical and kinetic models and differential heats of adsorption resulted in more definitive fitting curves and trends due to the true equilibrium position of the adsorbate with the adsorbent. Batch binary mixture adsorption on thermally and vacuum pre-treated zeolite 4A demonstrated purification behaviour of all adsorbents used for MeCl streams containing DME impurities, with a concentration as low as 0.66 vol. %. The GC-MS analysis showed no DME detection for the tested concentration mixtures at the AC outlet after 15 or 30 min, whereas MeCl was detectable in measurable amounts. Similar behaviour was also observed when carrying out adsorption in continuous mode. On the other hand, similar studies on the other adsorbents did not show such favourable MeCl purification behaviour. Overall this study investigated a wide range of adsorbents (zeolites, silica gels and activated carbon) and demonstrated for the first time potential to purify MeCl streams containing DME impurities using adsorption/desorption separation under different adsorbent pre-treatment and adsorption operating conditions. The study also revealed for the first time the adsorption isotherms, empirical and kinetic models and heats of adsorption for the respective adsorbentsurface (A-S) interactions. In conclusion, this study has shown strong evidence to propose zeolite 4A for adsorptive purification of MeCl. It is believed that with a technical grade MeCl stream competitive yet simultaneous co-adsorption of DME and MeCl occurs with evidence of molecular sieiving effects whereby the larger DME molecules are unable to penetrate through the adsorbent bed whereas the smaller MeCl molecules diffuse through resulting in a purified MeCl stream at the AC outlet. Ultimately, further studies are recommended for increased adsorption capacities by considering wider operating conditions, e.g. different adsorbent thermal and vacuum pre-treatment and adsorbing at temperatures closer to the boiling point of the gases and different conditions of pressure and temperature.

An eigenfunction expansion-variational method in prediction of the transverse thermal conductivity of fiber reinforced composites considering interfacial characteristics

An eigenfunction expansion-variational method based on a unit cell is developed to deal with the steady-state heat conduction problem of doubly-periodic fiber reinforced composites with interfacial thermal contact resistance or coating. The numerical results show a rapid convergence of the present method. The present solution provides a unified first-order approximation formula of the effective thermal conductivity for different interfacial characteristics and fiber distributions. A comparison with the present high-order results, available experimental data and micromechanical estimations demonstrates that the first-order approximation formula is a good engineering closed-form formula. An engineering equivalent parameter reflecting the overall influence of the thermal conductivities of the matrix and fibers and the interfacial characteristic on the effective thermal conductivity, is found. The equivalent parameter can greatly simplify the complicated relation of the effective thermal conductivity to the internal structure of a composite. (c) 2010 Elsevier Ltd. All rights reserved.

A simple numerical method for three-dimensional analysis of simple expansion chamber mufflers of rectangular as well as circular cross-section with a stationary medium

Three-dimensional effects are a primary source of discrepancy between the measured values of automotive muffler performance and those predicted by the plane wave theory at higher frequencies. The basically exact method of (truncated) eigenfunction expansions for simple expansion chambers involves very complicated algebra, and the numerical finite element method requires large computation time and core storage. A simple numerical method is presented in this paper. It makes use of compatibility conditions for acoustic pressure and particle velocity at a number of equally spaced points in the planes of the junctions (or area discontinuities) to generate the required number of algebraic equations for evaluation of the relative amplitudes of the various modes (eigenfunctions), the total number of which is proportional to the area ratio. The method is demonstrated for evaluation of the four-pole parameters of rigid-walled, simple expansion chambers of rectangular as well as circular cross-section for the case of a stationary medium. Computed values of transmission loss are compared with those computed by means of the plane wave theory, in order to highlight the onset (cutting-on) of various higher order modes and the effect thereof on transmission loss of the muffler. These are also compared with predictions of the finite element methods (FEM) and the exact methods involving eigenfunction expansions, in order to demonstrate the accuracy of the simple method presented here.

Prediction of inter-laminar stresses in composite honeycomb sandwich panels under mechanical loading using Variational Asymptotic Method

This work focuses on the formulation of an asymptotically correct theory for symmetric composite honeycomb sandwich plate structures. In these panels, transverse stresses tremendously influence design. The conventional 2-D finite elements cannot predict the thickness-wise distributions of transverse shear or normal stresses and 3-D displacements. Unfortunately, the use of the more accurate three-dimensional finite elements is computationally prohibitive. The development of the present theory is based on the Variational Asymptotic Method (VAM). Its unique features are the identification and utilization of additional small parameters associated with the anisotropy and non-homogeneity of composite sandwich plate structures. These parameters are ratios of smallness of the thickness of both facial layers to that of the core and smallness of 3-D stiffness coefficients of the core to that of the face sheets. Finally, anisotropy in the core and face sheets is addressed by the small parameters within the 3-D stiffness matrices. Numerical results are illustrated for several sample problems. The 3-D responses recovered using VAM-based model are obtained in a much more computationally efficient manner than, and are in agreement with, those of available 3-D elasticity solutions and 3-D FE solutions of MSC NASTRAN. (c) 2012 Elsevier Ltd. All rights reserved.

Synthesis, microstructure and thermal expansion studies on Ca0 center dot 5+x/2Sr0 center dot 5+x/2Zr4P6-2x Si-2x O-24 system prepared by co-precipitation method

We report on the synthesis, microstructure and thermal expansion studies on Ca0 center dot 5 + x/2Sr0 center dot 5 + x/2Zr4P6 -aEuro parts per thousand 2x Si-2x O-24 (x = 0 center dot 00 to 1 center dot 00) system which belongs to NZP family of low thermal expansion ceramics. The ceramics synthesized by co-precipitation method at lower calcination and the sintering temperatures were in pure NZP phase up to x = 0 center dot 37. For x a parts per thousand yen 0 center dot 5, in addition to NZP phase, ZrSiO4 and Ca2P2O7 form as secondary phases after sintering. The bulk thermal expansion behaviour of the members of this system was studied from 30 to 850 A degrees C. The thermal expansion coefficient increases from a negative value to a positive value with the silicon substitution in place of phosphorous and a near zero thermal expansion was observed at x = 0 center dot 75. The amount of hysteresis between heating and cooling curves increases progressively from x = 0 center dot 00 to 0 center dot 37 and then decreases for x > 0 center dot 37. The results were analysed on the basis of formation of the silicon based glassy phase and increase in thermal expansion anisotropy with silicon substitution.