Nonequilibrium Interactions Research Articles

Combined higher order finite volume and finite element scheme for double porosity and non-linear adsorption of transport problem in porous media

In this work, a dual porosity model of reactive solute transport in porous media is presented. This model consists of a nonlinear-degenerate advection–diffusion equation including equilibrium adsorption to the reaction combined with a first-order equation for the non-equilibrium adsorption interaction processes. The numerical scheme for solving this model involves a combined high order finite volume and finite element scheme for approximation of the advection–diffusion part and relaxation-regularized algorithm for nonlinearity-degeneracy. The combined finite volume-finite element scheme is based on a new formulation developed by Eymard et al. (2010) [10]. This formulation treats the advection and diffusion separately. The advection is approximated by a second-order local maximum principle preserving cell-vertex finite volume scheme that has been recently proposed whereas the diffusion is approximated by a finite element method. The result is a conservative, accurate and very flexible algorithm which allows the use of different mesh types such as unstructured meshes and is able to solve difficult problems. Robustness and accuracy of the method have been evaluated, particularly error analysis and the rate of convergence, by comparing the analytical and numerical solutions for first and second order upwind approaches. We also illustrate the performance of the discretization scheme through a variety of practical numerical examples. The discrete maximum principle has been proved.

Repulsive van der Waals Forces in Soft Matter: Why Bubbles Do Not Stick to Walls

Measurements of nonequilibrium hydrodynamic interactions between bubbles and solid surfaces in water provide direct evidence that repulsive van der Waals forces of quantum origin control the behavior of liquid films on solids in air. In addition to being the simplest and most universal 3-phase system, the deformable air-water interface greatly enhances the sensitivity of force measurements compared with rigid systems. The strength of the repulsive interaction, controlled by the choice of solid, is sufficient to prevent coalescence (sticking) on separation due to hydrodynamic interactions.

Numerical Simulations of Non-equilibrium Energy Transport in Nanostructures using Boltzmann Transport Equation

Heat transfer in nanostructures differ significantly from that in the bulk materials since the characteristic length scales associated with heat carriers, i.e., the mean free path and the wavelength, are comparable to the characteristic length of the nanostructures. Nanostructure materials hold the promise of novel phenomena, properties, and functions in the areas of thermoelectric energy conversion and micro/nano electronic devices. One of the major challenges in micro/nano electronic devices is to study the ‘hot spot’ generation by accurately modeling the carrier-optical phonon-acoustic phonon interactions. Thermoelectric properties are among the properties that may drastically change at nanoscale. During the last decade, advances have been made in increasing the efficiency of thermoelectric energy conversion using nanostructures. In this paper, the non-equilibrium interaction between carriers and phonons in semiconductor thin films is modeled using the Boltzmann transport model (BTM) for studying the t...

Different behaviour of local tunneling conductivity for deep and shallow impurities due to Coulomb interaction

Spatial distribution of local tunneling conductivity was investigated for deep and shallow impurities on semiconductor surfaces. Non-equilibrium Coulomb interaction and interference effects were taken into account and analyzed theoretically with the help of Keldysh formalism. Two models were investigated: mean field self-consistent approach for shallow impurity state and Hubbard-I model for deep impurity state. We have found that not only above the impurity but also at the distances comparable to the lattice period both effects interference between direct and resonant tunneling channels and on-site Coulomb repulsion of localized electrons strongly modifies form of tunneling conductivity measured by the scanning tunneling microscopy/spectroscopy (STM/STS).

Modeling Hole Transport in Wet and Dry DNA

We present a DFT/classical molecular dynamics model of DNA charge conductivity. The model involves a temperature-driven, hole-hopping charge transfer and includes the time-dependent nonequilibrium interaction of DNA with its molecular environment. We validate our method against a variety of hole transport experiments. The method predicts a significant hole-transfer slowdown of approximately 35% from dry to wet DNA with and without electric field bias. In addition, in agreement with experiments, it also predicts an insulating behavior of (GC)(N) oligomers for 40 < N < 1000, depending on the experimental setup.

The biomechanical integrin

The integrin lies at the center of our efforts to understand mechanotransduction in the human body. Over the past two decades, a wealth of information has yielded important insights into integrin structure and functioning in biochemical pathways; however, relatively little emphasis has been placed on mechanics. In this article, we review the current knowledge base of integrin mechanobiology by examining the role of integrins in stabilizing tissue structure, the mechanisms of integrin force transfer, the process of cell migration, and the pathology of cancer. In order to successfully address the gaps in cancer and other disease research going forward, future efforts of integrin mechanobiology must focus on examining cells in 3D environments and integrating our current understanding into computational models that predict the behavior of integrins in non-equilibrium interactions.

Phonon-Mediated Nonequilibrium Interaction between Nanoscale Devices

Interactions between mesoscopic devices induced by interface acoustic phonons propagating in the plane of a two-dimensional electron system (2DES) are investigated by phonon spectroscopy. In our experiments, ballistic electrons injected from a biased quantum point contact emit phonons and a portion of them are reabsorbed exciting electrons in a nearby degenerate 2DES. We perform energy spectroscopy on these excited electrons employing a tunable electrostatic barrier in an electrically separate and unbiased detector circuit. The transferred energy is found to be bounded by a maximum value corresponding to Fermi-level electrons excited and backscattered by absorbing interface phonons. Our results imply that phonon-mediated interaction plays an important role for the decoherence of solid-state-based quantum circuits.

Active soft glassy rheology of adherent cells

Adherent cells show a wide range of complex mechanical behavior that traditionally has been accounted for by different mechanisms and models, each of which can explain a limited subset of cell behavior. Experimental evidence suggests that nearly all aspects of mechanical cell behavior are closely associated with the cell's contractile machinery of actin and myosin filaments. We propose that the molecular details of actin–myosin interactions can be combined in a unified active soft glassy model that considers the arrangement of stress fibers at the macro-scale, and the soft-glassy non-equilibrium interaction of myosin and actin filaments at the micro-scale.

Modeling of Nonequilibrium Air Plasma Generation by Transversal Gas Discharge

The mathematical model of nonequilibrium air plasma at atmospheric pressure has been presented. Theoretical investigation of nonequilibrium plasma interaction with turbulent gas flow has been performed for the case of transversal gas discharge taking into account 3-D geometry of the conjugated problem. The calculated results have been compared with the experimental data and have shown good results. Influence of gas flow rate on the discharge characteristics has been analyzed. Differences in the calculated and measured electron temperature values observed are explained.

Nonequilibrium interactions between two quantum circuits

We briefly overview our recent results on nonequilibrium interactions between neighbouringelectrically isolated nanostructures. One of the nanostructures is represented by anexternally biased quantum point contact (drive-QPC), which is used to supply energyquanta to the second nanostructure (detector). Absorption of these nonequilibrium quantaof energy generates a dc current in the detector, or changes its differential conductance. Wepresent results for a double quantum dot, a single quantum dot or a second QPC placed inthe detector circuit. In all three cases a detection of quanta with energies up to∼1 meV is possible for bias voltages across the drive-QPC in the mV range. The results arequalitatively consistent with an energy transfer mechanism based on nonequilibriumacoustic phonons.

Multicellular Sprouting In Vitro

Cell motility and its guidance through cell-cell contacts is instrumental in vasculogenesis and in other developmental or pathological processes as well. During vasculogenesis, multicellular sprouts invade rapidly into avascular areas, eventually creating a polygonal pattern. Sprout elongation, in turn, depends on a continuous supply of endothelial cells, streaming along the sprout toward its tip. As long-term videomicroscopy of in vitro cell cultures reveal, cell lines such as C6 gliomas or 3T3 fibroblasts form multicellular linear arrangements in vitro, similar to the multicellular vasculogenic sprouts. We show evidence that close contact with elongated cells enhances and guides cell motility. To model the patterning process we augmented the widely used cellular Potts model with an inherently nonequilibrium interaction whereby surfaces of elongated cells become more preferred adhesion substrates than surfaces of well-spread, isotropic cells.

Nonequilibrium phenomena in adjacent electrically isolated nanostructures

We report on nonequilibrium interaction phenomena between adjacent but electrostatically separated nanostructures in GaAs. A current flowing in one externally biased nanostructure causes an excitation of electrons in a circuit of a second nanostructure. As a result we observe a dc current generated in the unbiased second nanostructure. The results can be qualitatively explained in terms of acoustic phonon based energy transfer between the two mutually isolated circuits.

Subsurface contaminant transport in the presence of colloids: Effect of nonlinear and nonequilibrium interactions

The effect of kinetic nonlinear sorption of contaminants in the presence of colloids is the focus of this study. Different sorption isotherms are considered where contaminant sorption and colloid deposition are assumed to be linear or nonlinear (Freundlich), and contaminant attachment to mobile and immobile colloids is assumed to follow either linear or Langmuir isotherms. Varying combinations accounting for different possibilities are used to investigate effects of different isotherms on contaminant transport. Two‐dimensional numerical simulations in homogenous media show that the effect of colloids on nonlinearly sorbing contaminant is altered from facilitation to retardation depending on the Freundlich exponent and concentration value. One finding from the study indicates that incorporating the colloid effect on contaminant transport does not necessarily represent a conservative assumption. The study shows that ignoring the fact that colloids have limited sites and describing contaminant attachment to colloids by linear isotherms may lead to inaccurate results. In addition, it is found that assuming colloids are linearly deposited on the solid matrix is a conservative assumption in the applications that focus on peak concentration arrival. However, when small contaminant concentrations are of concern (i.e., early arrival is the quantity of interest), assuming nonlinear colloidal deposition becomes the critical scenario.

Modeling heterogeneous interaction during SHS in the Ni-Al system: A phase-formation-mechanism map

Heterogeneous reaction Ni + Al → NiAl in strongly non-isothermal conditions typical of SHS has been modeled for planar geometry (unit bilayer Ni/Al film). The model used for simulation is based on the traditional quasi-equilibrium concept of the diffusion-controlled growth of a continuous solid product layer, NiAl, between molten Al and solid (or liquid) Ni-based solution. The basic idea is to analyze the competition between the growth of NiAl and its dissolution in parent phases due to variation in solubility limits with temperature. In calculations, a fragment of the equilibrium Ni-Al phase diagram is used along with real values of the interdiffusion coefficient in NiAl instead of determining the activation energy and preexponent by fitting the calculated and experimental results of the SHS wave temperature profile (as was done in other modeling works). The temperature dependence of phase densities is also accounted for. Simulation has revealed the existence of critical heating rates that correspond to the onset of the quasi-equilibrium dissolution-precipitation route with an intermediate solid NiAl film separating two liquid phases and then to non-equilibrium crystallization (when this film dissolves completely). Thus, the existence of non-equilibrium interaction mechanisms during SHS in the Ni-Al system, which were observed experimentally, is confirmed theoretically by the ex adverso method. A map of phase formation mechanisms is plotted which permits determining the reaction route in non-isothermal conditions.

Non-equilibrium partitioning tracer transport in porous media: 2-D physical modelling and imaging using a partitioning fluorescent dye

This paper describes an investigation into non-equilibrium partitioning tracer transport and interaction with non-aqueous-phase liquid (NAPL) contaminated water-saturated porous media using a two-dimensional (2-D) physical modelling methodology. A fluorescent partitioning tracer is employed within a transparent porous model which when imaged by a CCD digital camera can provide full spatial tracer concentrations and tracer breakthrough curves. Quasi one-dimensional (1-D) benchmarking tests in models packed with various combinations of clean quartz sand and NAPL are described. These modelled residual NAPL saturations, S n, of 0–15%. Results demonstrated that the fluorescent partitioning tracer was able to detect and quantify the presence of NAPL at low flow rates. At larger flow rates and/or higher NAPL saturations, the tracer increasingly underpredicted the NAPL volume as expected and this is attributed primarily to non-equilibrium partitioning. Despite little change in permeability, change in NAPL saturations from 4% to 8% resulted in significant NAPL saturation underestimates at the same flow rates implying coalescence of NAPL into wider separated but larger ganglia. A 2-D investigation of an idealised heterogeneous residual NAPL contaminated flow field indicated little permeability change in the NAPL contaminated zone and thus little flow bypassing, leading to reduced underpredictions of NAPL saturations than for equivalent quasi 1-D cases. This was attributed to increased ‘sampling’ of the NAPL by the tracer. The process is clearly visually identifiable from the experimental images. This rapid and relatively inexpensive experimental method is of value in laboratory studies of partitioning tracer behaviour in porous media; in particular, the ability to observe full field concentrations makes it valuable for the study of complex heterogeneous systems.

Statistical Mesomechanics of Solid, Linking Coupled Multiple Space and Time Scales

This review begins with the description of a new challenge in solid mechanics: multiphysics and multiscale coupling, and its current situations. By taking spallation as an example, it is illustrated that the fundamental difficulty in these multiscale nonequilibrium problems is due to the hierarchy and evolution of microstructures with various physics and rates at various length levels in solids. Then, some distinctive thoughts to pinpoint the obstacles and outcome are outlined. Section 3 highlights some paradigms of statistical averaging and new thoughts to deal with the problems involving multiple space and time scales, in particular the nonequilibrium damage evolution to macroscopic failure. In Sec. 4, several frameworks of mesomechanics linking multiple space and time scales, like dislocation theory, physical mesomechanics, Weibull theory, and stochastic theory, are briefly reviewed and the mechanisms underlying the trans-scale coupling are elucidated. Then we turn to the frameworks mainly concerning damage evolution in Sec. 5, namely, statistical microdamage mechanics and its trans-scale approximation. Based on various trans-scale frameworks, some possible mechanisms governing the trans-scale coupling are reviewed and compared in Sec. 6. Since the insight into the very catastrophic transition at failure is closely related to strong trans-scale coupling, some new concepts on nonequilibrium and strong interaction are discussed in Sec. 7. Finally, this review is concluded with a short summary and some suggestions. “This review article cites 130 references.”

Kinetic Structure Simulations of Nematic Polymers in Plane Couette Cells. II: In-Plane Structure Transitions

Nematic, or liquid crystalline, polymer (LCP) composites are composed of large aspect ratio rod-like or platelet macromolecules. This class of nanocomposites exhibits tremendous potential for high performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. Fibers made from nematic polymers have set synthetic materials performance standards for decades. The current target is to engineer multifunctional films and molded parts, for which processing flows are shear-dominated. Nematic polymer films inherit anisotropy from collective orientational distributions of the molecular constituents and develop heterogeneity on length scales that are, as yet, not well understood and thereby uncontrollable. Rigid LCPs in viscous solvents have a theoretical and computational foundation from which one can model parallel plate Couette cell experiments and explore anisotropic structure generation arising from nonequilibrium interactions between hydrodynamics, molecular short- and long-range elasticity, and confinement effects. Recent progress on the longwave limit of homogeneous nematic polymers in imposed simple shear and linear planar flows [R. G. Larson and H. Ottinger, Macromolecules, 24 (1991), pp. 6270--6282], [V. Faraoni, M. Grosso, S. Crescitelli, and P. L. Maffettone, J. Rheol., 43 (1999), pp. 829--843], [M. Grosso, R. Keunings, S. Crescitelli, and P. L. Maffettone, Phys. Rev. Lett., 86 (2001), pp. 3184--3187], [M. G. Forest, Q. Wang, and R. Zhou, Rheol. Acta, 43 (2004), pp. 17--37], [M. G. Forest, Q. Wang, and R. Zhou, Rheol. Acta, 44 (2004), pp. 80--93], [M. G. Forest, Q. Wang, R. Zhou, and E. Choate, J. Non-Newtonian Fluid Mech., 118 (2004), pp. 17--31], [M. G. Forest, R. Zhou, and Q. Wang, Phys. Rev. Lett., 93 (2004), 088301] provides resolved kinetic simulations of the molecular orientational distribution. These results characterize anisotropy and dynamic attractors of sheared bulk domains and underscore limitations of mesoscopic models for orientation of the rigid rod or platelet ensembles. In this paper, we apply our resolved kinetic structure code [R. Zhou, M. G. Forest, and Q. Wang, Multiscale Model. Simul., 3 (2005), pp. 853--870] to model onset and saturation of heterogeneity in the orientational distribution by coupling a distortional elasticity potential (with distinct elasticity constants) and anchoring conditions in a plane Couette cell. For this initial study, the flow field is imposed and the orientational distribution is confined to the shear deformation plane, which affords comparison with seminal [T. Tsuji and A. D. Rey, Phys. Rev. E (3), 62 (2000), pp. 8141--8151] as well as our own mesoscopic model simulations [H. Zhou, M. G. Forest, and Q. Wang, J. Non-Newtonian Fluid Mech., submitted], [H. Zhou and M. G. Forest, Discrete Contin. Dyn. Syst. Ser. B}, to appear].

Numerical investigation of ultrashort laser damage in semiconductors

A complete self-consistent model for transport dynamics in semiconductors caused by ultrashort-pulse laser heating is presented based on the relaxation-time approximation of the Boltzmann equation. Carrier–lattice nonequilibrium interactions are simulated to obtain the temporal and spatial evolution of the carrier density and temperature as well as the lattice temperature. It is shown that the calculated damage threshold based on the carrier density criterion agrees fairly well with the experimental data for both Si and Ge semiconductors, especially for sub-picosecond pulses. It is also found that one-photon absorption and Auger recombination are the two critical factors that influence the electron–hole carrier generation.

A rapid non-equilibrium critical precipitation assay to assess aluminium-ligand interactions

In many natural situations (e.g. environmental and biological) aqueous metal-ligand interactions occur in complex, dynamic solutions and do not adhere to true equilibrium. Nonetheless, equilibrium-based assays in simple solutions are generally used to model metal-ligand interactions of natural systems. Moreover, these are time consuming and not easily applied or understood by many applied scientists. Here, a ‘critical precipitation assay’ was used to investigate the interaction of common ligands with aluminium at pH 7.0, under non-equilibrium conditions. Results obtained were correlated with literature-derived stability constants for the aluminium-ligand interactions, while high-resolution 1H nuclear magnetic resonance spectroscopy (1H NMR) was used to confirm the nature of observed interactions. Weak interaction with aluminium was confirmed for traditional weak ligands (e.g. bicarbonate) as these were unable to compete with the hydroxide ion for aluminium at pH 7.0. Two types of interaction were seen for the ‘stronger’ ligands that could compete with hydroxy-polymerisation. Firstly, distinct aluminium:ligand stoichiometric ratios were observed for ligands such as ethylenediaminetetra-acetic acid (1:1) or 1,3,5-trideoxy-1,3,5-tris( dimethylamino)-cis-inositol (1:2). Secondly, most ligands, including citrate and maltol, did not prevent hydroxy-polymerisation but did maintain more aluminium ‘in solution’ (approximately 2.5:1 aluminium:ligand) than permitted by acceptable aluminium:ligand stoichiometric ratios, suggesting the formation of dynamic metastable hydroxy-bridged aluminium-ligand complexes. 1H NMR with aluminium and maltol or citrate, supported this idea as complex spectral patterns were observed prior to precipitation. Aluminium maintained in solution at pH 7.0 correlated, with literature-derived stability constants suggesting that non-equilibrium aluminium-ligand interactions approximate to equilibrium and that this assay could be used as a quick screening method for investigation of aluminium-ligand interactions.

NONEQUILIBRIUM EFFECTS AND MANY-PARTICLE INTERACTION IN TUNNELING SPECTROSCOPY OF IMPURITY d-ORBITAL

We report the direct observation by low temperature scanning tunneling microscopy and scanning tunneling spectroscopy of the d-orbital of a Mn p-type impurity appearing on a cleaved InAs (110) surface. STM images reveal remarkable cross-like protrusions and round depressions around isolated impurity atom on the surface at opposite polarity of tunneling bias voltage. By means of diagram technique for nonequilibrium processes we show that the crucial interplay between nonequilibrium charging effects and many-particle interaction leading to Coulomb singularities provides a consistent description of the experimental results.