Mobility Tensor Research Articles

A coupled phase field/diffusion model for upper and lower bainitic transformation

Bainite is a steel microstructure consisting of three phases, bainitic ferrite, austenite and carbides. It forms in two different morphologies, upper and lower bainite, where different diffusion mechanisms are dominant. The aim of this work is to simulate both transformations within a unified model. To this end, we extend an own previously published model for lower bainite with diffusion across the phase interface. As a central idea we introduce weighted Helmholtz energy functions and a weighted mobility tensor, respectively. The individual Helmholtz energy functions and mobility terms are related to the different diffusion mechanisms which are responsible for the formation of both morphologies. Two representative examples illustrate the capability of the coupled phase field/diffusion model and show the expected behaviour.

Electrokinetic Control of Viscous Fingering.

We present a theory of the interfacial stability of two immiscible electrolytes under the coupled action of pressure gradients and electric fields in a Hele-Shaw cell or porous medium. Mathematically, our theory describes a phenomenon of "vector Laplacian growth," in which the interface moves in response to the gradient of a vector-valued potential function through a generalized mobility tensor. Physically, we extend the classical Saffman-Taylor problem to electrolytes by incorporating electrokinetic (EK) phenomena. A surprising prediction is that viscous fingering can be controlled by varying the injection ratio of electric current to flow rate. Beyond a critical injection ratio, stability depends only upon the relative direction of flow and current, regardless of the viscosity ratio. Possible applications include porous materials processing, electrically enhanced oil recovery, and EK remediation of contaminated soils.

Fine-Grained Urban Event Detection and Characterization Based on Tensor Cofactorization

Understanding the irregular crowd movement and social activities caused by urban events such as city festivals and concerts can benefit event management and city planning. Although various urban data can be exploited to detect such irregularities, the crowd mobility data (e.g., bike trip records) are usually in a mixed state with several basic patterns (e.g., eating, working, and recreation), making it difficult to separate concurrent events happening in the same region. The social activity data (e.g., social network check-ins) are usually oversparse, hindering the fine-grained characterization of urban events. In this paper, we propose a tensor cofactorization-based data fusion framework for fine-grained urban event detection and characterization leveraging crowd mobility data and social activity data. First, we adopt a nonnegative tensor cofactorization approach to decompose the crowd mobility tensor into several basic patterns, with the help of the auxiliary social activity tensor. We then use a multivariate-outlier-detection-based method to identify irregularities from the decomposed basic patterns and aggregate them to detect and characterize the associated urban events. We evaluate the performance of our framework using real-world bike trip data and check-in data from New York City and Washington, DC, respectively. Results show that by fusing the two types of urban data, our method achieves fine-grained urban event detection and characterization in both cities and consistently outperforms the baselines.

Lateral diffusion induced by active proteins in a biomembrane.

We discuss the hydrodynamic collective effects due to active protein molecules that are immersed in lipid bilayer membranes and modeled as stochastic force dipoles. We specifically take into account the presence of the bulk solvent that surrounds the two-dimensional fluid membrane. Two membrane geometries are considered: the free membrane case and the confined membrane case. Using the generalized membrane mobility tensors, we estimate the active diffusion coefficient and the drift velocity as a function of the size of a diffusing object. The hydrodynamic screening lengths distinguish the two asymptotic regimes of these quantities. Furthermore, the competition between the thermal and nonthermal contributions in the total diffusion coefficient is characterized by two length scales corresponding to the two membrane geometries. These characteristic lengths describe the crossover between different asymptotic behaviors when they are larger than the hydrodynamic screening lengths.

Wavelet Monte Carlo dynamics: A new algorithm for simulating the hydrodynamics of interacting Brownian particles.

We develop a new algorithm for the Brownian dynamics of soft matter systems that evolves time by spatially correlated Monte Carlo moves. The algorithm uses vector wavelets as its basic moves and produces hydrodynamics in the low Reynolds number regime propagated according to the Oseen tensor. When small moves are removed, the correlations closely approximate the Rotne-Prager tensor, itself widely used to correct for deficiencies in Oseen. We also include plane wave moves to provide the longest range correlations, which we detail for both infinite and periodic systems. The computational cost of the algorithm scales competitively with the number of particles simulated, N, scaling as N In N in homogeneous systems and as N in dilute systems. In comparisons to established lattice Boltzmann and Brownian dynamics algorithms, the wavelet method was found to be only a factor of order 1 times more expensive than the cheaper lattice Boltzmann algorithm in marginally semi-dilute simulations, while it is significantly faster than both algorithms at large N in dilute simulations. We also validate the algorithm by checking that it reproduces the correct dynamics and equilibrium properties of simple single polymer systems, as well as verifying the effect of periodicity on the mobility tensor.

Anisotropic Conductivity Tensor Imaging of In Vivo Canine Brain Using DT-MREIT.

We present in vivo images of anisotropic electrical conductivity tensor distributions inside canine brains using diffusion tensor magnetic resonance electrical impedance tomography (DT-MREIT). The conductivity tensor is represented as a product of an ion mobility tensor and a scale factor of ion concentrations. Incorporating directional mobility information from water diffusion tensors, we developed a stable process to reconstruct anisotropic conductivity tensor images from measured magnetic flux density data using an MRI scanner. Devising a new image reconstruction algorithm, we reconstructed anisotropic conductivity tensor images of two canine brains with a pixel size of 1.25 mm. Though the reconstructed conductivity values matched well in general with those measured by using invasive probing methods, there were some discrepancies as well. The degree of white matter anisotropy was 2 to 4.5, which is smaller than previous findings of 5 to 10. The reconstructed conductivity value of the cerebrospinal fluid was about 1.3 S/m, which is smaller than previous measurements of about 1.8 S/m. Future studies of in vivo imaging experiments with disease models should follow this initial trial to validate clinical significance of DT-MREIT as a new diagnostic imaging modality. Applications in modeling and simulation studies of bioelectromagnetic phenomena including source imaging and electrical stimulation are also promising.

Separation of chiral particles in a rotating electric field

When a particle having a permanent dipole is placed in a rotating electric field in a fluid, it will migrate along the direction of the angular vector of the field. The average velocity of the particle is calculated based on a Brownian motion framework that accounts for the translation-rotation coupling. An explicit expression is given for the average velocity of the particle as a function of the hydrodynamic mobility tensors and the frequency of the field. The expression indicates that the chiral particle and its mirror-image particle move in opposite direction (which accounts for the right/left molecular separation in racemic solutions), and that the migration velocity has a peak at a certain frequency determined by the geometry of the particle. Calculations are made for a twisted ribbon particle and the relation between the migration velocity and the structure of the twisted ribbon particle is discussed.

Fluid mobility over corrugated surfaces in the Stokes regime

An exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert W-function. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model, we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.

2D Phase field modeling of sintering of silver nanoparticles

The sintering mechanism of silver nanoparticles is modeled by incorporating surface, volume and grain boundary diffusion in a phase field model. A direction-dependent tensorial mobility formulation is adopted, capturing the fact that diffusion mainly occurs along the directions tangential to the surface of the particle. A finite element framework is applied to solve the governing equations in a fully coupled implicit manner, and the developed framework is demonstrated for particle sintering of equal and unequal sizes as well as at different temperatures. The obtained results are compared with experimental observations, whereby it is shown that the developed material model adequately describes the sintering mechanism of silver nanoparticles.

Effects of Spatially Dependent Mobilities on the Kinetics of the Diffusion-Controlled Association Derived from the First-Passage-Time Approach.

Brownian dynamics (BD) simulations and the first-passage-time approach are applied to investigate diffusion-controlled association in a biologically relevant model system consisting of a fixed receptor with an elongated cavity and a capsule-like ligand that fits this cavity precisely. Before the binding at the receptor cavity, the ligand undergoes translational and rotational diffusion, either free or under the influence of electrostatic interactions with the receptor. The spatial dependence of the translational and rotational mobilities of the ligand resulting from its hydrodynamic interactions (HIs) with the receptor is accounted for in BD simulations, and an accurate numerical approach is applied for the evaluation of the spatially dependent mobility tensor of the ligand. Different magnitudes of electrostatic interactions (either attraction or repulsion) between the ligand and receptor are considered. The effective range of receptor-ligand electrostatic interactions is varied to account for their screening under different conditions of ionic strength. The effects of HIs on the kinetics of the diffusion-controlled association, evaluated for different electrostatic properties of binding partners, are thoroughly analyzed and discussed.

Non reciprocal skewed rolling of a colloidal wheel due to induced chirality.

We use a rotating magnetic field to assemble an oblate cluster of paramagnetic colloidal particles. If the field is rotating about a horizontal axis, the cluster acts as a colloidal wheel rolling across the supporting glass surface. The motion is reversible upon switching the direction of rotation. Surprisingly, the reversibility is lost if the axis of field rotation is tilted with respect to the surface. The wheel then rolls in a direction that is not perpendicular to the field rotation axis. We explain the skewed rotation with an interplay between a magnetic driving torque, magnetic anisotropy and an anisotropy in the hydrodynamic mobility tensor in the vicinity of a surface. The opposing forward and backward drive induce opposite chirality in the degrees of freedom of the mechanically achiral colloidal wheel.

Non-Markovian closure kinetics of flexible polymers with hydrodynamic interactions.

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T ∼ N(3/2)ln(N/b(2)), which differs from the case of the Rouse dynamics where T ∼ N(2). The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented.

Effects of Hydrodynamic Interactions on the Apparent 1D Mobility of a Nonspecifically Bound Protein Following a Helical Path around DNA.

We investigated effects of hydrodynamic interactions on diffusivities of proteins that undergo rotation-coupled sliding along DNA. For that, we applied numerical calculations of mobility and friction tensors to systems consisting of detailed bead-shell models of DNA and proteins of different size. Using tensors that result from these calculations along with an expression for the instantaneous energy dissipation rate due to motions of a nonspecifically bound protein that follows a helical track around DNA, we evaluated apparent one-dimensional friction and mobility coefficients for model proteins. The results that we obtained indicate that hydrodynamic interactions between DNA and proteins may substantially (even several-fold) reduce the apparent one-dimensional diffusivity of proteins, when compared with results of other theoretical analyses of the rotation-coupled sliding of proteins along DNA that neglect hydrodynamic effects. Moreover, accounting for hydrodynamic effects decreases the gap between values of diffusion coefficients of proteins on DNA measured experimentally and those estimated based on theoretical calculations and analyses applied to model systems. Altogether, the current study gives insights into the significance of hydrodynamic interactions in determination of the rate of finding target sites by DNA-binding proteins.

Stokesian simulation of two unequal spheres in a pressure-driven creeping flow through a cylinder

In this paper, a novel numerical technique is generalized for analysis of mutual flow interactions between unequal particles in cylinder-bound pressure-driven flow of highly viscous fluid. The methodology is general enough to account for any polydisperse many-sphere system confined in a circular channel. The scheme is especially useful for the geometric configurations where both interparticle and particle-wall hydrodynamic interactions are significant. In such situation, particulate dynamics is governed by strong spatial variation of mobility tensors relating motion-inducing quantities (like force and torque on the bodies along with the pressure-drop in the vessel) to motion-defining ones (like translational and rotational velocities of each sphere as well as the flow-rate). Accordingly, the mobility tensors are evaluated as spatial functions to solve two different problems. First, we compute force and torque due to incoming fluid on two particles when these are fixed at a specific position inside the flow-domain. Then, we assume both to be freely suspended, and determine their motion driven by the transporting medium. In both problems, the additional pressure-loss in the channel due to the presence of the particles is also calculated representing the increase in channel-resistivity and effective viscosity, respectively.

Toward an Accurate Modeling of Hydrodynamic Effects on the Translational and Rotational Dynamics of Biomolecules in Many-Body Systems.

Proper treatment of hydrodynamic interactions is of importance in evaluation of rigid-body mobility tensors of biomolecules in Stokes flow and in simulations of their folding and solution conformation, as well as in simulations of the translational and rotational dynamics of either flexible or rigid molecules in biological systems at low Reynolds numbers. With macromolecules conveniently modeled in calculations or in dynamic simulations as ensembles of spherical frictional elements, various approximations to hydrodynamic interactions, such as the two-body, far-field Rotne-Prager approach, are commonly used, either without concern or as a compromise between the accuracy and the numerical complexity. Strikingly, even though the analytical Rotne-Prager approach fails to describe (both in the qualitative and quantitative sense) mobilities in the simplest system consisting of two spheres, when the distance between their surfaces is of the order of their size, it is commonly applied to model hydrodynamic effects in macromolecular systems. Here, we closely investigate hydrodynamic effects in two and three-body systems, consisting of bead-shell molecular models, using either the analytical Rotne-Prager approach, or an accurate numerical scheme that correctly accounts for the many-body character of hydrodynamic interactions and their short-range behavior. We analyze mobilities, and translational and rotational velocities of bodies resulting from direct forces acting on them. We show, that with the sufficient number of frictional elements in hydrodynamic models of interacting bodies, the far-field approximation is able to provide a description of hydrodynamic effects that is in a reasonable qualitative as well as quantitative agreement with the description resulting from the application of the virtually exact numerical scheme, even for small separations between bodies.

Angle Dependence of the Orbital Magnetoresistance in Bismuth

We present an extensive study of angle-dependent transverse magnetoresistance in bismuth, with a magnetic field perpendicular to the applied electric current and rotating in three distinct crystallographic planes. The observed angular oscillations are confronted with the expectations of semi-classic transport theory for a multi-valley system with anisotropic mobility and the agreement allows us to quantify the components of the mobility tensor for both electrons and holes. A quadratic temperature dependence is resolved. As Hartman argued long ago, this indicates that inelastic resistivity in bismuth is dominated by carrier-carrier scattering. At low temperature and high magnetic field, the threefold symmetry of the lattice is suddenly lost. Specifically, a $2\pi/3$ rotation of magnetic field around the trigonal axis modifies the amplitude of the magneto-resistance below a field-dependent temperature. By following the evolution of this anomaly as a function of temperature and magnetic field, we mapped the boundary in the (field, temperature) plane separating two electronic states. In the less-symmetric state, confined to low temperature and high magnetic field, the three Dirac valleys cease to be rotationally invariant. We discuss the possible origins of this spontaneous valley polarization, including a valley-nematic scenario.

Hydrodynamics and Brownian motions of a spheroid near a rigid wall.

In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement.

Kirkwood diffusivity of long semiflexible chains in nanochannel confinement.

We compute the axial diffusivity of asymptotically long semiflexible polymers confined in square channels. Our calculations employ the Kirkwood approximation of the mobility tensor by combining computational fluid dynamics (CFD) calculations of the hydrodynamic tensor in channel confinement with pruned-enriched Rosenbluth method (PERM) simulations of a discrete wormlike chain model. Three key results emerge from our study. First, for the classic de Gennes regime, we confirm that Brochard and de Gennes' blob theory correctly predicts the scaling of the axial diffusivity, contrary to the conclusions of previous analyses. Second, for the extended de Gennes regime, we show that a modified blob theory, which has been used to incorporate the effect of local stiffness on DNA diffusion in nanoslits, explains the deviation from the prediction of classic blob theory for diffusion in nanochannels. Third, we provide a calculation similar to the modified blob theory to explain the relative insensitivity of the diffusivity to channel size for channels between the extended de Gennes regime and the Odijk regime, which is the most relevant regime for experiments and technological applications of DNA confinement in nanochannels. Our results are not only relevant to the dynamics of confined semiflexible polymers such as DNA, but also reveal interesting analogies between confinement in channels and slits.

Nanoscale protein domain motion and long-range allostery in signaling proteins—a view from neutron spin echo spectroscopy

Many cellular proteins are multi-domain proteins. Coupled domain-domain interactions in these multidomain proteins are important for the allosteric relay of signals in the cellular signaling networks. We have initiated the application of neutron spin echo spectroscopy to the study of nanoscale protein domain motions on submicrosecond time scales and on nanometer length scale. Our NSE experiments reveal the activation of protein domain motions over a long distance of over more than 100Å in a multidomain scaffolding protein NHERF1 upon binding to another protein, Ezrin. Such activation of nanoscale protein domain motions is correlated with the allosteric assembly of multi-protein complexes by NHERF1 and Ezrin. Here, we summarize the theoretical framework that we have developed, which uses simple concepts from nonequilibrium statistical mechanics to interpret the NSE data, and employs a mobility tensor to describe nanoscale protein domain motion. Extracting nanoscale protein domain motion from the NSE does not require elaborate molecular dynamics simulations, nor complex fits to rotational motion, nor elastic network models. The approach is thus more robust than multiparameter techniques that require untestable assumptions. We also demonstrate that an experimental scheme of selective deuteration of a protein subunit in a complex can highlight and amplify specific domain dynamics from the abundant global translational and rotational motions in a protein. We expect NSE to provide a unique tool to determine nanoscale protein dynamics for the understanding of protein functions, such as how signals are propagated in a protein over a long distance to a distal domain.

Thermally assisted current-driven skyrmion motion

We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding Fokker-Planck equation. The resulting Fokker-Planck equation is recognized as the one for a high-friction Brownian particle which has been studied extensively in different physical contexts. It is shown that thermal fluctuations favor the skyrmion motion allowing a finite mobility even in presence of pinning traps. We calculate explicitly the mobility tensor of skyrmions in linear response to an electric current finding that it increases with temperature.