Virus-sized colloid transport in a single pore: Model development and sensitivity analysis

A mathematical model is developed to simulate the transport and deposition of virus-sized colloids in a cylindrical pore throat considering various processes such as advection, diffusion, colloid-collector surface interactions and hydrodynamic wall effects. The pore space is divided into three different regions, namely, bulk, diffusion and potential regions, based on the dominant processes acting in each of these regions. In the bulk region, colloid transport is governed by advection and diffusion whereas in the diffusion region, colloid mobility due to diffusion is retarded by hydrodynamic wall effects. Colloid-collector interaction forces dominate the transport in the potential region where colloid deposition occurs. The governing equations are non-dimensionalized and solved numerically. A sensitivity analysis indicates that the virus-sized colloid transport and deposition is significantly affected by various pore-scale parameters such as the surface potentials on colloid and collector, ionic strength of the solution, flow velocity, pore size and colloid size. The adsorbed concentration and hence, the favorability of the surface for adsorption increases with: (i) decreasing magnitude and ratio of surface potentials on colloid and collector, (ii) increasing ionic strength and (iii) increasing pore radius. The adsorbed concentration increases with increasing Pe, reaching a maximum value at Pe = 0.1 and then decreases thereafter. Also, the colloid size significantly affects particle deposition with the adsorbed concentration increasing with increasing particle radius, reaching a maximum value at a particle radius of 100 nm and then decreasing with increasing radius. System hydrodynamics is found to have a greater effect on larger particles than on smaller ones. The secondary minimum contribution to particle deposition has been found to increase as the favorability of the surface for adsorption decreases. The sensitivity of the model to a given parameter will be high if the conditions are favorable for adsorption. The results agree qualitatively with the column-scale experimental observations available in the literature. The current model forms the building block in upscaling colloid transport from pore scale to Darcy scale using Pore-Network Modeling. (C) 2014 Elsevier By. All rights reserved.

Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles (Poissonian, Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE) and Gaussian symplectic ensemble (GSE)) realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one-dimensional lattice model of interacting hard-core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin-orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.

A new microscopic insight into membrane penetration and reorganization by PETIM dendrimers

Dendrimers are highly branched polymeric nanoparticles whose structure and topology, largely, have determined their efficacy in a wide range of studies performed so far. An area of immense interest is their potential as drug and gene delivery vectors. Realizing this potential, depending on the nature of cell surface-dendrimer interactions, here we report controlled model membrane penetration and reorganization, using a model supported lipid bilayer and poly(ether imine) (PETIM) dendrimers of two generations. By systematically varying the areal density of the lipid bilayers, we provide a microscopic insight, through a combination of high resolution scattering, atomic force microscopy and atomistic molecular dynamics simulations, into the mechanism of PETIM dendrimer membrane penetration, pore formation and membrane re-organization induced by such interactions. Our work represents the first systematic observation of a regular barrel-like membrane spanning pore formation by dendrimers, tunable through lipid bilayer packing, without membrane disruption.

A Gaussian network model study suggests that structural fluctuations are higher for inactive states than active states of protein kinases

We performed Gaussian network model based normal mode analysis of 3-dimensional structures of multiple active and inactive forms of protein kinases. In 14 different kinases, a more number of residues (1095) show higher structural fluctuations in inactive states than those in active states (525), suggesting that, in general, mobility of inactive states is higher than active states. This statistically significant difference is consistent with higher crystallographic B-factors and conformational energies for inactive than active states, suggesting lower stability of inactive forms. Only a small number of inactive conformations with the DFG motif in the ``in'' state were found to have fluctuation magnitudes comparable to the active conformation. Therefore our study reports for the first time, intrinsic higher structural fluctuation for almost all inactive conformations compared to the active forms. Regions with higher fluctuations in the inactive states are often localized to the aC-helix, aG-helix and activation loop which are involved in the regulation and/or in structural transitions between active and inactive states. Further analysis of 476 kinase structures involved in interactions with another domain/protein showed that many of the regions with higher inactive-state fluctuation correspond to contact interfaces. We also performed extensive GNM analysis of (i) insulin receptor kinase bound to another protein and (ii) holo and apo forms of active and inactive conformations followed by multi-factor analysis of variance. We conclude that binding of small molecules or other domains/proteins reduce the extent of fluctuation irrespective of active or inactive forms. Finally, we show that the perceived fluctuations serve as a useful input to predict the functional state of a kinase.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

ASYMPTOTIC PRESERVING SCHEME FOR A KINETIC MODEL DESCRIBING IN COMPRESSIBLE FLUIDS

The kinetic theory of fluid turbulence modeling developed by Degond and Lemou in 7] is considered for further study, analysis and simulation. Starting with the Boltzmann like equation representation for turbulence modeling, a relaxation type collision term is introduced for isotropic turbulence. In order to describe some important turbulence phenomenology, the relaxation time incorporates a dependency on the turbulent microscopic energy and this makes difficult the construction of efficient numerical methods. To investigate this problem, we focus here on a multi-dimensional prototype model and first propose an appropriate change of frame that makes the numerical study simpler. Then, a numerical strategy to tackle the stiff relaxation source term is introduced in the spirit of Asymptotic Preserving Schemes. Numerical tests are performed in a one-dimensional framework on the basis of the developed strategy to confirm its efficiency.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Collective behavior of asperities as a model for friction and adhesion

Understanding friction and adhesion in static and sliding contact of surfaces is important in numerous physical phenomena and technological applications. Most surfaces are rough at the microscale, and thus the real area of contact is only a fraction of the nominal area. The macroscopic frictional and adhesive response is determined by the collective behavior of the population of evolving and interacting microscopic contacts. This collective behavior can be very different from the behavior of individual contacts. It is thus important to understand how the macroscopic response emerges from the microscopic one. In this thesis, we develop a theoretical and computational framework to study the collective behavior. Our philosophy is to assume a simple behavior of a single asperity and study the collective response of an ensemble. Our work bridges the existing well-developed studies of single asperities with phenomenological laws that describe macroscopic rate-and-state behavior of frictional interfaces. We find that many aspects of the macroscopic behavior are robust with respect to the microscopic response. This explains why qualitatively similar frictional features are seen for a diverse range of materials. We first show that the collective response of an ensemble of one-dimensional independent viscoelastic elements interacting through a mean field reproduces many qualitative features of static and sliding friction evolution. The resulting macroscopic behavior is different from the microscopic one: for example, even if each contact is velocity-strengthening, the macroscopic behavior can be velocity-weakening. The framework is then extended to incorporate three-dimensional rough surfaces, long- range elastic interactions between contacts, and time-dependent material behaviors such as viscoelasticity and viscoplasticity. Interestingly, the mean field behavior dominates and the elastic interactions, though important from a quantitative perspective, do not change the qualitative macroscopic response. Finally, we examine the effect of adhesion on the frictional response as well as develop a force threshold model for adhesion and mode I interfacial cracks.

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.

Geographical mobility and the labour market

This paper studies the e ect of home-owners' migration costs on migration and unemployment in an economy where workers move both for work- and nonwork- related reasons. To this end, a search model with heterogeneous locations is developed and calibrated to the U.S. economy. Consistent with the empirical evidence, the model predicts that home-owners have a lower unemployment rate than renters despite their higher migration costs. The result is due to home-owners' higher transition rate to employment and lower transition rate to unemployment.In addition, the model generates lower inequality in home-owners' local unemployment rates than in renters'. In line with this result, it is documented that, for the period 1996-2013, home-owners had less unemployment dispersion across metropolitan areas than renters.

Unified circuit model for the polysilicon TFT

This paper proposes two methods to improve the modelling of thin film transistors (TFTs). The first involves integrating Poissons equation numerically, given a density of trap states and other relevant material parameters including a constant mobility. Theresult is conductance as a numerical function of gate voltage. The second method recognizes that the data for areal conductance found by numerical integration, may easily be found by measurement without making assumptions about the density of trap states.

Vortex deformation and breaking in superconductors: a microscopic description

Vortex breaking has traditionally been studied for non-uniform critical current densities, although it may also appear due to non-uniform pinning force distributions. In this article we study the case of a high-pinning/low-pinning/high-pinning layered structure. We have developed an elastic model for describing the deformation of a vortex in these systems in the presence of a uniform transport current density J for any arbitrary orientation of the transport current and the magnetic field. If J is above a certain critical value, J(c), the vortex breaks and a finite effective resistance appears. Our model can be applied to some experimental configurations where vortex breaking naturally exists. This is the case for YBa2Cu3O7-delta (YBCO) low-angle grain boundaries and films on vicinal substrates, where the breaking is experienced by Abrikosov-Josephson vortices (AJV) and Josephson string vortices (SV), respectively. With our model, we have experimentally extracted some intrinsic parameters of the AJV and SV, such as the line tension is an element of(l) and compared it to existing predictions based on the vortex structure.

Effect of microbial activities on the mobility of copper in stabilised contaminated soil

Stabilisation, using a wide range of binders including wastes, is most effective for heavy metal soil contamination. Bioremediation techniques, including bioaugmentation to enhance soil microbial population, are most effective for organic contaminants in the soil. For mixed contaminant scenarios a combination of these two techniques is currently being investigated. An essential issue in this combined remediation system is the effect of microbial processes on the leachability of the heavy metals. This paper considers the use of zeolite and compost as binder additives combined with bioaugmentation treatments and their effect on copper leachability in a model contaminated soil. Different leaching test conditions are considered including both NRA and TCLP batch leaching tests as well as flow-through column tests. Two flow rates are applied in the flow-through tests and the two leaching tests are compared. Recommendations are given as to the effectiveness of this combined remediation technique in the immobilisation of copper. © 2005 Taylor & Francis Group.