Quantum Simulator for Transport Phenomena in Fluid Flows

Transport phenomena still stand as one of the most challenging problems in computational physics. By exploiting the analogies between Dirac and lattice Boltzmann equations, we develop a quantum simulator based on pseudospin-boson quantum systems, which is suitable for encoding fluid dynamics transport phenomena within a lattice kinetic formalism. It is shown that both the streaming and collision processes of lattice Boltzmann dynamics can be implemented with controlled quantum operations, using a heralded quantum protocol to encode non-unitary scattering processes. The proposed simulator is amenable to realization in controlled quantum platforms, such as ion-trap quantum computers or circuit quantum electrodynamics processors.

Using mesoscopic models to design strong and tough biomimetic polymer networks

Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or "globules", which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N in and N out, the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N out, with the higher value of N out providing a stronger material. We also find that, if N in is smaller than N out, the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials. © 2011 American Chemical Society.

Effect of chain-length dependence of interaction parameter on spinodals for polydisperse polymer blends

The chain-length dependence of the Flory-Huggins (FH) interaction parameter is introduced into the FH lattice theory for polydisperse polymer-blend systems. The spinodals are calculated for the model polymer blends with different chain lengths and distributions. It is found that all the related variables r(n), r(w), r(z), and chain-length distribution, have effects on the spinodals for polydisperse polymer blends.

Theoretical representation of shear and pressure influence on the phase separation behavior of PVME/PS mixture

In the framework of lattice fluid model, the Gibbs energy and equation of state are derived by introducing the energy (E-s) stored during flow for polymer blends under shear. From the calculation of the spinodal of poly(vinyl methyl ether) (PVME) and polystyrene (PS) mixtures, we have found the influence of E., an equation of state in pure component is inappreciable, but it is appreciable in the mixture. However, the effect of E, on phase separation behavior is extremely striking. In the calculation of spinodal for the PVME/PS system, a thin, long and banana miscibility gap generated by shear is seen beside the miscibility gap with lower critical solution temperature. Meanwhile, a binodal coalescence of upper and lower miscibility gaps is occurred. The three points of the three-phase equilibrium are forecasted. The shear rate dependence of cloud point temperature at a certain composition is discussed. The calculated results are acceptable compared with the experiment values obtained by Higgins et at. However, the maximum positive shift and the minimum negative shift of cloud point temperature guessed by Higgins are not obtained, Furthermore, the combining effects of pressure and shear on spinodal shift are predicted.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

Numerical simulations of fluid-structure interactions in single-reed mouthpieces

Most single-reed woodwind instrument models rely on a quasistationary approximation to describe the relationship between the volume flow and. the pressure difference across the reed channel. Semiempirical models based on the quasistationary approximation are very useful in explaining the fundamental characteristics of this family of instruments such as self-sustained oscillations and threshold of blowing pressure. However, they fail at explaining more complex phenomena associated with the fluid-structure interaction during dynamic flow regimes, such as the transient and steady-state behavior of the system as a function. of the mouthpiece geometry. Previous studies have discussed the accuracy of the quasistationary approximation but the amount of literature on the subject is sparse, mainly due to the difficulties involved in the measurement of dynamic flows in channels with an oscillating reed. In this paper, a numerical technique based on the lattice Boltzmann method and a finite difference scheme is proposed in order to investigate the characteristics of fully coupled fluid-structure interaction in single-reed mouthpieces with different channel configurations. Results obtained for a stationary simulation with a static reed agree very well with those predicted by the literature based on the quasistationary approximation. However, simulations carried out for a dynamic regime with dn oscillating reed show that the phenomenon associated with flow detachment and reattachment diverges considerably frorn the theoretical assumptions. Furthermore, in the case of long reed channels, the results obtained for the vena contracta factor are in significant disagreement with those predicted by theory. For short channels, the assumption of constant vena contracta was found to be valid for only 40% of the duty cycle. (c) 2007 Acoustical Society of America.

Application of a mechanobiological simulation technique to stents used clinically

Many cardiovascular diseases are characterised by the restriction of blood flow through arteries. Stents can be expanded within arteries to remove such restrictions; however, tissue in-growth into the stent can lead to restenosis. In order to predict the long-term efficacy of stenting, a mechanobiological model of the arterial tissue reaction to stress is required. In this study, a computational model of arterial tissue response to stenting is applied to three clinically relevant stent designs. We ask the question whether such a mechanobiological model can differentiate between stents used clinically, and we compare these predictions to a purely mechanical analysis. In doing so, we are testing the hypothesis that a mechanobiological model of arterial tissue response to injury could predict the long-term outcomes of stent design. Finite element analysis of the expansion of three different stent types was performed in an idealised, 3D artery. Injury was calculated in the arterial tissue using a remaining-life damage mechanics approach. The inflammatory response to this initial injury was modelled using equations governing variables which represented tissue-degrading species and growth factors. Three levels of inflammation response were modelled to account for inter-patient variability. A lattice-based model of smooth muscle cell behaviour was implemented, treating cells as discrete agents governed by local rules. The simulations predicted differences between stent designs similar to those found in vivo. It showed that the volume of neointima produced could be quantified, providing a quantitative comparison of stents. In contrast, the differences between stents based on stress alone were highly dependent on the choice of comparison criteria. These results show that the choice of stress criteria for stent comparisons is critical. This study shows that mechanobiological modelling may provide a valuable tool in stent design, allowing predictions of their long-term efficacy. The level of inflammation was shown to affect the sensitivity of the model to stent design. If this finding was verified in patients, this could suggest that high-inflammation patients may require alternative treatments to stenting.

Derivation of an Efficient Rule System Pattern Matcher

Formalizing algorithm derivations is a necessary prerequisite for developing automated algorithm design systems. This report describes a derivation of an algorithm for incrementally matching conjunctive patterns against a growing database. This algorithm, which is modeled on the Rete matcher used in the OPS5 production system, forms a basis for efficiently implementing a rule system. The highlights of this derivation are: (1) a formal specification for the rule system matching problem, (2) derivation of an algorithm for this task using a lattice-theoretic model of conjunctive and disjunctive variable substitutions, and (3) optimization of this algorithm, using finite differencing, for incrementally processing new data.

Thermodynamic aspects of ion intercalation in KhFek[Fe(CN)(6)](l)center dot mH(2)O compounds: Application to the Everit's salt/Prussian Blue transition

The K+ reversible processes for ion exchange in KhFek[Fe(CN)(6)](l)center dot mH(2)O host compounds (Prussian Blue) were thermodynamically analyzed. A thermodynamic approach was established and developed based on the consideration of a lattice-gas model where the electronic contribution to the chemical potential is neglected and the ion-host interaction is not considered. The occupation fraction of the intercalation process was calculated from the kinetic parameters obtained through ac-electrogravimetry in a previous paper. In this way, the mass potential transfer function introduces a new way to evaluate the thermodynamic aspect of intercalation. Finally, based on the thermodynamic approach, the energy used to put each K+ ion into the host material was calculated. The values were shown to be in good agreement with the values obtained through transient techniques, for example, cyclic voltammetry. As a result, this agreement between theory and experimental data validates the thermodynamic approach considered here, and for the first time, the thermodynamic aspects of insertion were considered for mixed valence materials.

Entropy Production in Nonequilibrium Systems at Stationary States

We present a stochastic approach to nonequilibrium thermodynamics based on the expression of the entropy production rate advanced by Schnakenberg for systems described by a master equation. From the microscopic Schnakenberg expression we get the macroscopic bilinear form for the entropy production rate in terms of fluxes and forces. This is performed by placing the system in contact with two reservoirs with distinct sets of thermodynamic fields and by assuming an appropriate form for the transition rate. The approach is applied to an interacting lattice gas model in contact with two heat and particle reservoirs. On a square lattice, a continuous symmetry breaking phase transition takes place such that at the nonequilibrium ordered phase a heat flow sets in even when the temperatures of the reservoirs are the same. The entropy production rate is found to have a singularity at the critical point of the linear-logarithm type.

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction w of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that w = 1/2, corresponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase (w < 1/2) from a region with spin-glass, ferromagnetic, mixed and paramagnetic phases (w > 1/2).

The development of stylolites, from small-scale heterogeneities to multi-scale roughness

Stylolites are rough paired surfaces, indicative of localized stress-induced dissolution under a non-hydrostatic state of stress, separated by a clay parting which is believed to be the residuum of the dissolved rock. These structures are the most frequent deformation pattern in monomineralic rocks and thus provide important information about low temperature deformation and mass transfer. The intriguing roughness of stylolites can be used to assess amount of volume loss and paleo-stress directions, and to infer the destabilizing processes during pressure solution. But there is little agreement on how stylolites form and why these localized pressure solution patterns develop their characteristic roughness.rnNatural bedding parallel and vertical stylolites were studied in this work to obtain a quantitative description of the stylolite roughness and understand the governing processes during their formation. Adapting scaling approaches based on fractal principles it is demonstrated that stylolites show two self affine scaling regimes with roughness exponents of 1.1 and 0.5 for small and large length scales separated by a crossover length at the millimeter scale. Analysis of stylolites from various depths proved that this crossover length is a function of the stress field during formation, as analytically predicted. For bedding parallel stylolites the crossover length is a function of the normal stress on the interface, but vertical stylolites show a clear in-plane anisotropy of the crossover length owing to the fact that the in-plane stresses (σ2 and σ3) are dissimilar. Therefore stylolite roughness contains a signature of the stress field during formation.rnTo address the origin of stylolite roughness a combined microstructural (SEM/EBSD) and numerical approach is employed. Microstructural investigations of natural stylolites in limestones reveal that heterogeneities initially present in the host rock (clay particles, quartz grains) are responsible for the formation of the distinctive stylolite roughness. A two-dimensional numerical model, i.e. a discrete linear elastic lattice spring model, is used to investigate the roughness evolving from an initially flat fluid filled interface induced by heterogeneities in the matrix. This model generates rough interfaces with the same scaling properties as natural stylolites. Furthermore two coinciding crossover phenomena in space and in time exist that separate length and timescales for which the roughening is either balanced by surface or elastic energies. The roughness and growth exponents are independent of the size, amount and the dissolution rate of the heterogeneities. This allows to conclude that the location of asperities is determined by a polimict multi-scale quenched noise, while the roughening process is governed by inherent processes i.e. the transition from a surface to an elastic energy dominated regime.rn

Simulazione di fluidi in Computer Graphics

Questa tesi si focalizza sullo studio dei modelli fisico-matematici attualmente in uso per la simulazione di fluidi al calcolatore con l’obiettivo di fornire nozioni di base e avanzate sull’utilizzo di tali metodi. La trattazione ha lo scopo di facilitare la comprensione dei principi su cui si fonda la simulazione di fluidi e rappresenta una base per la creazione di un proprio simulatore. E’ possibile studiare le caratteristiche di un fluido in movimento mediante due approcci diversi, l’approccio lagrangiano e l’approccio euleriano. Mentre l’approccio lagrangiano ha lo scopo di conoscere il valore, nel tempo, di una qualsiasi proprietà di ciascuna particella che compone il fluido, l’approccio euleriano, fissato uno o più punti del volume di spazio occupato da quest’ultimo, vuole studiare quello che accade, nel tempo, in quei punti. In particolare, questa tesi approfondisce lo studio delle equazioni di Navier-Stokes, approcciandosi al problema in maniera euleriana. La soluzione numerica del sistema di equazioni differenziali alle derivate parziali derivante dalle equazioni sopracitate, approssima la velocità del fluido, a partire dalla quale è possibile risalire a tutte le grandezze che lo caratterizzano. Attenzione viene riservata anche ad un modello facente parte dell’approccio semi-lagrangiano, il Lattice Boltzmann, considerato una via di mezzo tra i metodi puramente euleriani e quelli lagrangiani, che si basa sulla soluzione dell’equazione di Boltzmann mediante modelli di collisione di particelle. Infine, analogamente al metodo di Lattice Boltzmann, viene trattato il metodo Smoothed Particles Hydrodynamics, tipicamente lagrangiano, secondo il quale solo le proprietà delle particelle comprese dentro il raggio di una funzione kernel, centrata nella particella di interesse, influenzano il valore della particella stessa. Un resoconto pratico della teoria trattata viene dato mediante delle simulazioni realizzate tramite il software Blender 2.76b.

The behaviour of incompatible elements during hydrous melting of metasomatized peridotite at 4–6 GPa and 1000 °C–1200 °C

Trace element behavior during hydrous melting of a metasomatized garnet–peridotite was examined at pressures of 4–6 GPa and temperatures of 1000 °C–1200 °C, conditions appropriate for fluid penetrating the mantle wedge atop the subducting slab. Experiments were performed in a rocking multi-anvil apparatus using a diamond-trap setup. The compositions of the fluid and melt phases were measured using the cryogenic LA-ICP-MS technique. The water-saturated solidus of the K-lherzolite composition is located between 900 °C and 1000 °C at 4 GPa and between 1000 °C and 1100 °C at 5 and 6 GPa. The partition coefficients between fluid or melt and clinopyroxene reveal an asymmetric MREE trough with a minimum at Dy. The clinopyroxene in equilibrium with aqueous fluids is characterized by DUfluid–cpx > DThfluid–cpx while DUmelt–cpx tends to be similar to DThmelt–cpx. The partition coefficients between fluid or melt and garnet reveal very strong light to heavy REE fractionation, DLa/DLu from 95 (hydrous melt) to 1600 (aqueous fluid). The LILE are highly incompatible with partition coefficients > 50. The behavior of HFSE are decoupled, with DZr,Hf close to 1 while DNb,Ta > 10. Garnet is characterized by DUmelt/fluid–garnet < DThmelt/fluid–garnet. A comparison of our experimental partitioning results for trivalent cations as well as the results from the literature and the calculations carried out using the lattice strain model adapted to the presence of water in the bulk system indicates that H2O in the fluid or melt phase has a prominent effect on trace element partitioning. Garnet in mantle rocks in equilibrium with an aqueous fluid is characterized by significantly higher Do(3 +) for REE in the X site of the garnet compared with the partitioning values of the optimal cation in garnet in equilibrium with hydrous melts. Our data show for the first time that the change in the nature of the mobile phase (fluid vs. melt) does affect the affinities of trace elements into the garnet crystal at conditions below the second critical endpoint of the system. The same also applies for clinopyroxene, although this is less clear. Consequently, our new data allow for refinements in predictive modeling of element transfer from the slab to the mantle wedge and of possible compositions of metasomatized mantle that sources OIB magmatism.

3D Soil Images Structure Quantification using Relative Entropy

Soil voids manifest the cumulative effect of local pedogenic processes and ultimately influence soil behavior - especially as it pertains to aeration and hydrophysical properties. Because of the relatively weak attenuation of X-rays by air, compared with liquids or solids, non-disruptive CT scanning has become a very attractive tool for generating three-dimensional imagery of soil voids. One of the main steps involved in this analysis is the thresholding required to transform the original (greyscale) images into the type of binary representation (e.g., pores in white, solids in black) needed for fractal analysis or simulation with Lattice?Boltzmann models (Baveye et al., 2010). The objective of the current work is to apply an innovative approach to quantifying soil voids and pore networks in original X-ray CT imagery using Relative Entropy (Bird et al., 2006; Tarquis et al., 2008). These will be illustrated using typical imagery representing contrasting soil structures. Particular attention will be given to the need to consider the full 3D context of the CT imagery, as well as scaling issues, in the application and interpretation of this index.