First principles based multiparadigm modeling of electronic structures and dynamics

Electronic structures and dynamics are the key to linking the material composition and structure to functionality and performance.

An essential issue in developing semiconductor devices for photovoltaics is to design materials with optimal band gaps and relative positioning of band levels. Approximate DFT methods have been justified to predict band gaps from KS/GKS eigenvalues, but the accuracy is decisively dependent on the choice of XC functionals. We show here for CuInSe₂ and CuGaSe₂, the parent compounds of the promising CIGS solar cells, conventional LDA and GGA obtain gaps of 0.0-0.01 and 0.02-0.24 eV (versus experimental values of 1.04 and 1.67 eV), while the historically first global hybrid functional, B3PW91, is surprisingly the best, with band gaps of 1.07 and 1.58 eV. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a MAD of only 0.09 eV, which is substantially better than all modern hybrid functionals, including B3LYP (MAD of 0.19 eV) and screened hybrid functional HSE06 (MAD of 0.18 eV).

The laboratory performance of CIGS solar cells (> 20% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use the B3PW91 hybrid functional of DFT with the AEP method that we validate to provide very accurate descriptions of both band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the CBO of perfect CuInSe₂/CdS interface is large, 0.79 eV, which would dramatically degrade performance. Moreover we show that band gap widening induced by Ga adjusts only the VBO, and we find that Cd impurities do not significantly affect the CBO. Thus we show that Cu vacancies at the interface play the key role in enabling the tunability of CBO. We predict that Na further improves the CBO through electrostatically elevating the valence levels to decrease the CBO, explaining the observed essential role of Na for high performance. Moreover we find that K leads to a dramatic decrease in the CBO to 0.05 eV, much better than Na. We suggest that the efficiency of CIGS devices might be improved substantially by tuning the ratio of Na to K, with the improved phase stability of Na balancing phase instability from K. All these defects reduce interfacial stability slightly, but not significantly.

A number of exotic structures have been formed through high pressure chemistry, but applications have been hindered by difficulties in recovering the high pressure phase to ambient conditions (i.e., one atmosphere and room temperature). Here we use dispersion-corrected DFT (PBE-ulg flavor) to predict that above 60 GPa the most stable form of N₂O (the laughing gas in its molecular form) is a 1D polymer with an all-nitrogen backbone analogous to cis-polyacetylene in which alternate N are bonded (ionic covalent) to O. The analogous trans-polymer is only 0.03-0.10 eV/molecular unit less stable. Upon relaxation to ambient conditions both polymers relax below 14 GPa to the same stable non-planar trans-polymer, accompanied by possible electronic structure transitions. The predicted phonon spectrum and dissociation kinetics validate the stability of this trans-poly-NNO at ambient conditions, which has potential applications as a new type of conducting polymer with all-nitrogen chains and as a high-energy oxidizer for rocket propulsion. This work illustrates in silico materials discovery particularly in the realm of extreme conditions.

Modeling non-adiabatic electron dynamics has been a long-standing challenge for computational chemistry and materials science, and the eFF method presents a cost-efficient alternative. However, due to the deficiency of FSG representation, eFF is limited to low-Z elements with electrons of predominant s-character. To overcome this, we introduce a formal set of ECP extensions that enable accurate description of p-block elements. The extensions consist of a model representing the core electrons with the nucleus as a single pseudo particle represented by FSG, interacting with valence electrons through ECPs. We demonstrate and validate the ECP extensions for complex bonding structures, geometries, and energetics of systems with p-block character (C, O, Al, Si) and apply them to study materials under extreme mechanical loading conditions.

Despite its success, the eFF framework has some limitations, originated from both the design of Pauli potentials and the FSG representation. To overcome these, we develop a new framework of two-level hierarchy that is a more rigorous and accurate successor to the eFF method. The fundamental level, GHA-QM, is based on a new set of Pauli potentials that renders exact QM level of accuracy for any FSG represented electron systems. To achieve this, we start with using exactly derived energy expressions for the same spin electron pair, and fitting a simple functional form, inspired by DFT, against open singlet electron pair curves (H₂ systems). Symmetric and asymmetric scaling factors are then introduced at this level to recover the QM total energies of multiple electron pair systems from the sum of local interactions. To complement the imperfect FSG representation, the AMPERE extension is implemented, and aims at embedding the interactions associated with both the cusp condition and explicit nodal structures. The whole GHA-QM+AMPERE framework is tested on H element, and the preliminary results are promising.

A molecular dynamics study of the microscopic properties of simple dense fluids

The microscopic properties of a two-dimensional model dense fluid of Lennard-Jones disks have been studied using the so-called "molecular dynamics" method. Analyses of the computer-generated simulation data in terms of "conventional" thermodynamic and distribution functions verify the physical validity of the model and the simulation technique.

The radial distribution functions g(r) computed from the simulation data exhibit several subsidiary features rather similar to those appearing in some of the g(r) functions obtained by X-ray and thermal neutron diffraction measurements on real simple liquids. In the case of the model fluid, these "anomalous" features are thought to reflect the existence of two or more alternative configurations for local ordering.

Graphical display techniques have been used extensively to provide some intuitive insight into the various microscopic phenomena occurring in the model. For example, "snapshots" of the instantaneous system configurations for different times show that the "excess" area allotted to the fluid is collected into relatively large, irregular, and surprisingly persistent "holes". Plots of the particle trajectories over intervals of 2.0 to 6.0 x 10^-12 sec indicate that the mechanism for diffusion in the dense model fluid is "cooperative" in nature, and that extensive diffusive migration is generally restricted to groups of particles in the vicinity of a hole.

A quantitative analysis of diffusion in the model fluid shows that the cooperative mechanism is not inconsistent with the statistical predictions of existing theories of singlet, or self-diffusion in liquids. The relative diffusion of proximate particles is, however, found to be retarded by short-range dynamic correlations associated with the cooperative mechanism--a result of some importance from the standpoint of bimolecular reaction kinetics in solution.

A new, semi-empirical treatment for relative diffusion in liquids is developed, and is shown to reproduce the relative diffusion phenomena observed in the model fluid quite accurately. When incorporated into the standard Smoluchowski theory of diffusion-controlled reaction kinetics, the more exact treatment of relative diffusion is found to lower the predicted rate of reaction appreciably.

Finally, an entirely new approach to an understanding of the liquid state is suggested. Our experience in dealing with the simulation data--and especially, graphical displays of the simulation data--has led us to conclude that many of the more frustrating scientific problems involving the liquid state would be simplified considerably, were it possible to describe the microscopic structures characteristic of liquids in a concise and precise manner. To this end, we propose that the development of a formal language of partially-ordered structures be investigated.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.

Desenvolvimento de um simulador numérico empregando o método Smoothed Particle Hydrodynamics para a resolução de escoamentos incompressíveis. Implementação computacional em paralelo (CUDA)

Neste trabalho, foi desenvolvido um simulador numérico baseado no método livre de malhas Smoothed Particle Hydrodynamics (SPH) para a resolução de escoamentos de fluidos newtonianos incompressíveis. Diferentemente da maioria das versões existentes deste método, o código numérico faz uso de uma técnica iterativa na determinação do campo de pressões. Este procedimento emprega a forma diferencial de uma equação de estado para um fluido compressível e a equação da continuidade a fim de que a correção da pressão seja determinada. Uma versão paralelizada do simulador numérico foi implementada usando a linguagem de programação C/C++ e a Compute Unified Device Architecture (CUDA) da NVIDIA Corporation. Foram simulados três problemas, o problema unidimensional do escoamento de Couette e os problemas bidimensionais do escoamento no interior de uma Cavidade (Shear Driven Cavity Problem) e da Quebra de Barragem (Dambreak).

Simulação de escoamentos incompressíveis empregando o método Smoothed Particle Hydrodynamics utilizando algoritmos iterativos na determinação do campo de pressões

Nesse trabalho, foi desenvolvido um simulador numérico (C/C++) para a resolução de escoamentos de fluidos newtonianos incompressíveis, baseado no método de partículas Lagrangiano, livre de malhas, Smoothed Particle Hydrodynamics (SPH). Tradicionalmente, duas estratégias são utilizadas na determinação do campo de pressões de forma a garantir-se a condição de incompressibilidade do fluido. A primeira delas é a formulação chamada Weak Compressible Smoothed Particle Hydrodynamics (WCSPH), onde uma equação de estado para um fluido quase-incompressível é utilizada na determinação do campo de pressões. A segunda, emprega o Método da Projeção e o campo de pressões é obtido mediante a resolução de uma equação de Poisson. No estudo aqui desenvolvido, propõe-se três métodos iterativos, baseados noMétodo da Projeção, para o cálculo do campo de pressões, Incompressible Smoothed Particle Hydrodynamics (ISPH). A fim de validar os métodos iterativos e o código computacional, foram simulados dois problemas unidimensionais: os escoamentos de Couette entre duas placas planas paralelas infinitas e de Poiseuille em um duto infinito e foram usadas condições de contorno do tipo periódicas e partículas fantasmas. Um problema bidimensional, o escoamento no interior de uma cavidade com a parede superior posta em movimento, também foi considerado. Na resolução deste problema foi utilizado o reposicionamento periódico de partículas e partículas fantasmas.

Uma formulação implícita para o método Smoothed Particle Hydrodynamics

Em uma grande gama de problemas físicos, governados por equações diferenciais, muitas vezes é de interesse obter-se soluções para o regime transiente e, portanto, deve-se empregar técnicas de integração temporal. Uma primeira possibilidade seria a de aplicar-se métodos explícitos, devido à sua simplicidade e eficiência computacional. Entretanto, esses métodos frequentemente são somente condicionalmente estáveis e estão sujeitos a severas restrições na escolha do passo no tempo. Para problemas advectivos, governados por equações hiperbólicas, esta restrição é conhecida como a condição de Courant-Friedrichs-Lewy (CFL). Quando temse a necessidade de obter soluções numéricas para grandes períodos de tempo, ou quando o custo computacional a cada passo é elevado, esta condição torna-se um empecilho. A fim de contornar esta restrição, métodos implícitos, que são geralmente incondicionalmente estáveis, são utilizados. Neste trabalho, foram aplicadas algumas formulações implícitas para a integração temporal no método Smoothed Particle Hydrodynamics (SPH) de modo a possibilitar o uso de maiores incrementos de tempo e uma forte estabilidade no processo de marcha temporal. Devido ao alto custo computacional exigido pela busca das partículas a cada passo no tempo, esta implementação só será viável se forem aplicados algoritmos eficientes para o tipo de estrutura matricial considerada, tais como os métodos do subespaço de Krylov. Portanto, fez-se um estudo para a escolha apropriada dos métodos que mais se adequavam a este problema, sendo os escolhidos os métodos Bi-Conjugate Gradient (BiCG), o Bi-Conjugate Gradient Stabilized (BiCGSTAB) e o Quasi-Minimal Residual (QMR). Alguns problemas testes foram utilizados a fim de validar as soluções numéricas obtidas com a versão implícita do método SPH.

Analysis of multivariate stochastic signals sampled by on-line particle analyzers: Application to the quantitative assessment of occupational exposure to NOAA in multisource industrial scenarios (MSIS)

In multisource industrial scenarios (MSIS) coexist NOAA generating activities with other productive sources of airborne particles, such as parallel processes of manufacturing or electrical and diesel machinery. A distinctive characteristic of MSIS is the spatially complex distribution of aerosol sources, as well as their potential differences in dynamics, due to the feasibility of multi-task configuration at a given time. Thus, the background signal is expected to challenge the aerosol analyzers at a probably wide range of concentrations and size distributions, depending of the multisource configuration at a given time. Monitoring and prediction by using statistical analysis of time series captured by on-line particle analyzers in industrial scenarios, have been proven to be feasible in predicting PNC evolution provided a given quality of net signals (difference between signal at source and background). However the analysis and modelling of non-consistent time series, influenced by low levels of SNR (Signal-Noise Ratio) could build a misleading basis for decision making. In this context, this work explores the use of stochastic models based on ARIMA methodology to monitor and predict exposure values (PNC). The study was carried out in a MSIS where an case study focused on the manufacture of perforated tablets of nano-TiO2 by cold pressing was performed

Estudo de fluxos numéricos para modelos magneto-hidrodinâmicos utilizando o código Flash

A teoria magneto-hidrodinâmicos permite a estruturação de modelos computacionais, designados modelos MHDs, que são uma extensão da dinâmica dos fluidos para lidar com fluidos eletricamente carregados, tais como os plasmas, em que se precisa considerar os efeitos de forças eletromagnéticas. Tais modelos são especialmente úteis quando o movimento exato de uma partícula não é de interesse, sendo que as equações descrevem as evoluções de quantidades macroscópicas. Várias formas de modelos MHD têm sido amplamente utilizadas na Física Espacial para descrever muitos tipos diferentes de fenômenos de plasma, tais como reconexão magnética e interações de ventos estelares com diferentes objetos celestiais. Neste trabalho, o objetivo é analisar o comportamento de diversos fluxos numéricos em uma discretização de volumes finitos de um modelo numérico de MHD usando um esquema de malha entrelaçada sem separação direcional considerando alguns casos testes. Para as simulações, utiliza-se o código Flash, desenvolvido pela Universidade de Chicago, por ser um código de amplo interesse nas simulações astrofísicas e de fenômenos no espaço próximo à Terra. A metodologia consiste na inclusão de um fluxo numérico, permitindo melhoria com respeito ao esquema HLL.

Imbibition dynamics of nano-particulate ink-jet drops on micro-porous media

Ink-jet printing of nano-metallic colloidal fluids on to porous media such as coated papers has become a viable method to produce conductive tracks for low-cost, disposable printed electronic devices. However, the formation of well-defined and functional tracks on an absorbing surface is controlled by the drop imbibition dynamics in addition to the well-studied post-impact drop spreading behavior. This study represents the first investigation of the real-time imbibition of ink-jet deposited nano-Cu colloid drops on to coated paper substrates. In addition, the same ink was deposited on to a non-porous polymer surface as a control substrate. By using high-speed video imaging to capture the deposition of ink-jet drops, the time-scales of drop spreading and imbibition were quantified and compared with model predictions. The influences of the coating pore size on the bulk absorption rate and nano-Cu particle distribution have also been studied.

Characterize dynamic conformational space of human CCR5 extracellular domain by molecular modeling and molecular dynamics simulation

The chemokine receptor CCR5 is the receptor for several chemokines and major coreceptor for R5 human immunodeficiency virus type-1 strains entry into cell. Three-dimensional models of CCR5 were built by using homology modeling approach and 1 ns molecular dynamics (MD) simulation, because studies of site-directed mutagenesis and chimeric receptors have indicated that the N-terminus (Nt) and extracellular loops (ECLs) of CCR5 are important for ligands binding and viral fusion and entry, special attention was focused on disulfide bond function, conformational flexibility, hydrogen bonding, electrostatic interactions, and solvent-accessible surface area of Nt and ECLs of this protein part. We found that the extracellular segments of CCR5 formed a well-packet globular domain with complex interactions occurred between them in a majority of time of MID simulation, but Nt region could protrude from this domain sometimes. The disulfide bond Cys20-Cys269 is essential in controlling specific orientation of Nt region and maintaining conformational integrity of extracellular domain. RMS comparison analysis between conformers revealed the ECL1 of CCR5 stays relative rigid, whereas the ECL2 and Nt are rather flexible. Solvent-accessible surface area calculations indicated that the charged residues within Nt and ECL2 are often exposed to solvent. Integrating these results with available experimental data, a two-step gp120-CCR5 binding mechanism was proposed. The dynamic interaction of CCR5 extracellular domain with gp120 was emphasized. (C) 2004 Elsevier B.V. All rights reserved.

Statistics and dynamics of turbulence-flame alignment in premixed combustion

The geometric alignment of turbulent strain-rate structures with premixed flames greatly influences the results of the turbulence-flame interaction. Here, the statistics and dynamics of this alignment are experimentally investigated in turbulent premixed Bunsen flames using high-repetition-rate stereoscopic particle image velocimetry. In all cases, the statistics showed that the most extensive principal strain-rate associated with the turbulence preferentially aligned such that it was more perpendicular than parallel to the flame surface normal direction. The mean turbulence-flame alignment differed between the flames, with the stronger flames (higher laminar flame speed) exhibiting stronger preferential alignment. Furthermore, the preferential alignment was greatest on the reactant side of the mean flame brush. To understand these differences, individual structures of fluid-dynamic strain-rate were tracked through time in a Lagrangian manner (i.e., by following the fluid elements). It was found that the flame surface affected the orientation of the turbulence structures, with the majority of structures rotating as they approached the flame such that their most extensive principal strain-rate was perpendicular to the flame normal. The maximum change in turbulent structure orientation was found to decrease with the strength of the structure, increase with the strength of the flame, and exhibit similar trends when the structure strength and flame strength were represented by a Karlovitz number. The mean change in orientation decreased from the unburnt to burnt side of the flame brush and appears to be influenced by the overall flame shape. © 2011 The Combustion Institute.

Forecasting high-frequency futures returns using online langevin dynamics

Forecasting the returns of assets at high frequency is the key challenge for high-frequency algorithmic trading strategies. In this paper, we propose a jump-diffusion model for asset price movements that models price and its trend and allows a momentum strategy to be developed. Conditional on jump times, we derive closed-form transition densities for this model. We show how this allows us to extract a trend from high-frequency finance data by using a Rao-Blackwellized variable rate particle filter to filter incoming price data. Our results show that even in the presence of transaction costs our algorithm can achieve a Sharpe ratio above 1 when applied across a portfolio of 75 futures contracts at high frequency. © 2011 IEEE.

Studying adsorbent dynamics on a quartz crystal resonator using its nonlinear electrical response

The quartz crystal resonator has been traditionally employed in studying surface-confined physisorbed films and particles by measuring dissipation and frequency shifts. However, theoretical interpretation of the experimental observations is often challenged due to limited understanding of physical interaction mechanisms at the interfaces involved. Here we model a physisorbed interaction between particles and gold electrode surface of a quartz crystal and demonstrate how the nonlinear modulation of the electric response of the crystal due to the nonlinear interaction forces may be used to study the dynamics of the particles. In particular, we show that the graphs of the deviation in the third Fourier harmonic response versus oscillation amplitude provide important information about the onset, progress and nature of sliding of the particles. The graphs also present a signature of the surface-particle interaction and could be used to estimate the interaction energy profile. Interestingly, the insights gained from the model help to explain some of the experimental observations with physisorbed streptavidin-coated polystyrene microbeads on quartz resonators. © 2012 Elsevier B.V. All rights reserved.

Static and dynamic errors in particle tracking microrheology.

Particle tracking techniques are often used to assess the local mechanical properties of cells and biological fluids. The extracted trajectories are exploited to compute the mean-squared displacement that characterizes the dynamics of the probe particles. Limited spatial resolution and statistical uncertainty are the limiting factors that alter the accuracy of the mean-squared displacement estimation. We precisely quantified the effect of localization errors in the determination of the mean-squared displacement by separating the sources of these errors into two separate contributions. A "static error" arises in the position measurements of immobilized particles. A "dynamic error" comes from the particle motion during the finite exposure time that is required for visualization. We calculated the propagation of these errors on the mean-squared displacement. We examined the impact of our error analysis on theoretical model fluids used in biorheology. These theoretical predictions were verified for purely viscous fluids using simulations and a multiple-particle tracking technique performed with video microscopy. We showed that the static contribution can be confidently corrected in dynamics studies by using static experiments performed at a similar noise-to-signal ratio. This groundwork allowed us to achieve higher resolution in the mean-squared displacement, and thus to increase the accuracy of microrheology studies.

Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.