Coarse-grained Density Research Articles

Dynamic density functional theory with inertia and background flow.

We present dynamic density functional theory (DDFT) incorporating general inhomogeneous, incompressible, time-dependent background flows and inertia, describing externally driven passive colloidal systems out of equilibrium. We start by considering the underlying nonequilibrium Langevin dynamics, including the effect of the local velocity of the surrounding liquid bath, to obtain the nonlinear, nonlocal partial differential equations governing the evolution of the (coarse-grained) density and velocity fields describing the dynamics of colloids. In addition, we show both with heuristic arguments, and by numerical solution, that our equations and solutions agree with existing DDFTs in the overdamped (high friction) limit. We provide numerical solutions that model the flow of hard spheres, in both unbounded and confined domains, and compare with previously derived DDFTs with and without the background flow.

Molecular Insights into the Wettability and Adsorption of Acid Gas-Water Mixture.

Sequestration of acid gas in geological formations is a disposal method with potential economic and environmental benefits. The process is governed by variables such as gas-water interfacial tension, wetting transition, and gas adsorption into water, among other things. However, the influence of the pressure and temperature on these parameters is poorly understood. This study investigates these parameters using coarse-grained molecular dynamics (CG-MD) simulations and density gradient theory (DGT). Simulations were carried out at 313.15 K and a pressure range of 0-15 MPa. A comparison was made against H2S-water systems to clarify the effects of adsorption on interfacial tension due to vapor-liquid-liquid equilibrium. The predicted H2S-water interfacial tension and phase densities by CG-MD and DGT matched the experimental values well. The adsorption can be quantified via the Gibbs Adsorption function Γ12, which correlated well with the three-phase transition. On the one hand, pressure increments below the three-phase transition revealed a significant adsorption of H2S. On the other hand, above the three-phase transition, the Gibbs Adsorption capacity remained constant, which indicated a saturation of H2S at the water surface due to liquid-liquid equilibrium. Finally, H2S behaves markedly differently in wetting transition, rather than the involved for CO2 to different molecular layers beneath the surface of aqueous solutions. In this respect, H2S is represented by a first-order wetting transition while CO2 presents a critical wetting. Finally, it has also been found that the preferential adsorption of H2S over the H2O interface is greater if compared to that of CO2, due to its strong interaction with water. In fact, we have also demonstrated that CO2 under triphasic conditions strongly influences the wetting of the ternary system.

Microscopic theory of a Janus motor in a non-equilibrium fluid: Surface hydrodynamics and boundary conditions.

We present a derivation from the first principles of the coupled equations of motion of an active self-diffusiophoretic Janus motor and the hydrodynamic densities of its fluid environment that are nonlinearly displaced from equilibrium. The derivation makes use of time-dependent projection operator techniques defined in terms of slowly varying coarse-grained microscopic densities of the fluid species number, total momentum, and energy. The exact equations of motion are simplified using time scale arguments, resulting in Markovian equations for the Janus motor linear and angular velocities with average forces and torques that depend on the fluid densities. For a large colloid, the fluid equations are separated into bulk and interfacial contributions, and the conditions under which the dynamics of the fluid densities can be accurately represented by bulk hydrodynamic equations subject to boundary conditions on the colloid are determined. We show how the results for boundary conditions based on continuum theory can be obtained from the molecular description and provide Green-Kubo expressions for all transport coefficients, including the diffusiophoretic coupling and the slip coefficient.

A data driven approach for cross-slip modelling in continuum dislocation dynamics

Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that is a function of the screw segment length and the stress acting on the dislocation. In continuum dislocation dynamics (CDD), the information regarding the length of the screw dislocation segment and local stress state on dislocations are lost due to the coarse-grained representation of the density. In this work, a data driven approach to characterize the lost information by analyzing the discrete dislocation configurations is proposed to enable cross-slip modeling in the CDD framework in terms of the coarse-grained dislocation density and stress fields. The analysis showed that the screw segment length follows an exponential distribution, and the stress fluctuations, defined as the difference between the stress on the dislocations and the mean field stress in CDD, follows a Lorentzian distribution. A novel approach for cross slip implementation in CDD employing the screw segment length and stress fluctuation statistics was proposed and rigorously tested by comparing the CDD cross-slip rates with discrete dislocation dynamics (DDD) rates. This approach has been applied in conjunction with three cross-slip models used in DDD simulations differing mainly in the functional form of cross slip activation energy. It was found that different cross-slip activation energy formulations yielded different cross-slip rates, yet the effect on mechanical stress-strain response and dislocation density evolution was minimal for the [001] type loading.

Monte-Carlo simulation of mass density field coupled dynamics for microstructural evolution of Fe-Cr binary alloys

The phase transformation kinetics and micro-structure evolutions of four different Fe-Cr binary alloys, i.e. Fe-Cr (12.8%), Fe-Cr (20.0%), Fe-Cr (30.0%) and Fe-Cr (40.0%) at 673 K, are investigated by using the kinetic Monte-Carlo simulation combined with spatial coarse-grained mass density field description. For all studied Fe-Cr alloys, it is found that the number density of Cr-rich precipitate undergoes a rather rapid increasing at the nucleation stage and then gradually decreases with the simulation time increasing in the coarsening stage during aging. Increasing the Cr concentration in Fe-Cr alloy can significantly reduce the duration of nucleation and the time interval between nucleation and coarsening. From the coarse-grained mass density field models of Cr-rich precipitates at different aging stages for the four Fe-Cr alloys, we discover that the Cr-rich phase shows the isolated spherical particle-like morphology for the aged Fe-Cr (12.8%) alloy, revealing the nucleation and growth (NG) mechanism. Meanwhile, the Cr-rich precipitates possess a characteristic three-dimensional interconnected microstructure, a signature of spinodal decomposition mechanism. Otherwise, the Cr-rich phase morphology in Fe-Cr (20.0%) exhibits the characteristics of both NG mechanism and SD mechanism. It is also found that the short-range order parameter of Cr atoms in Fe-Cr alloy is indeed very sensitive to the change of atomic structure at the early stage of aging or nucleation stage, which, however, is almost independent of the changing of morphology of Cr-precipitates in the later coarsening process. Finally, the phase transformation kinetics of Cr-rich precipitates during aging are analyzed by calculating the phase volume fraction, average diameter and number density, concluding that the Cr-rich phase growth kinetics in Fe-Cr (20.0%) alloy can be described by the well-known Lifshitz-Slyozov-Wagner law in the coarsening stage. However, the coarsening kinetics of Fe-Cr (12.8%), Fe-Cr (30.0%) and Fe-Cr (40.0%) alloys are not caused by the LSW mechanism.

Effective potentials in a rotating spin-orbit-coupled spin-1 spinor condensate

We theoretically study the stationary-state vortex lattice configurations of rotating spin-orbit (SO)- and coherently-coupled spin-1 Bose–Einstein condensates (BECs) trapped in quasi-two-dimensional harmonic potentials. The combined effects of rotation, SO and coherent couplings are analyzed systematically from the single-particle perspective. Through the single-particle Hamiltonian, which is exactly solvable for one-dimensional coupling, we illustrate that a boson in these rotating SO- and coherently-coupled condensates are subjected to effective toroidal, symmetric double-well, or asymmetric double-well potentials under specific coupling and rotation strengths. In the presence of mean-field interactions, using the coupled Gross–Pitaevskii formalism at moderate to high rotation frequencies, the analytically obtained effective potential minima and the numerically obtained coarse-grained density maxima position are in excellent agreement. On rapid rotation, we further find that the spin-expectation per particle of an antiferromagnetic spin-1 BEC approaches unity indicating a similarity in the response with ferromagnetic SO-coupled condensates.

Metastable states of microgel fluids with Hertzian interaction potentials

We consider here a coarse-grained model for a soft matter system in which the particles interact with the Hertzian potential uH(r)=ϵ01−r/σμ, characterized by parameters {ϵ0,σ,μ}. Using the coarse-grained one-particle density ρ(x) as an order parameter, the free energy functional typical of the classical density functional theory (DFT) is studied. The static correlations of the uniform density state, required as an input in the DFT model, is calculated using the Bridge function method for the Hertzian fluid. The free energy functional analysis obtains new minima signifying metastable states between uniform liquid and the crystal. In particular, using classical DFT methods, a metastable amorphous state characterized by a low degree of mass localization is predicted. We obtain the transformation line on the density-temperature plot showing the possible liquid–liquid transition between the uniform liquid state and the inhomogeneous liquid state. With the increase of ϵ0 for the Hertzian interaction, the model reproduces the hard-sphere results.

Coarse graining empirical densities and currents in continuous-space steady states

We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to statistical mechanics and thermodynamics on the level of individual trajectories. We focus on the important and non-trivial effect of a spatial coarse graining. Making use of a generalized time-reversal symmetry we provide deeper insight about the physical meaning of fluctuations of the coarse-grained empirical density and current, and explain why a systematic variation of the coarse-graining scale offers an efficient method to infer bounds on a system's dissipation. Moreover, we discuss emerging symmetries in the statistics of the empirical density and current, and the statistics in the central-limit regime. More broadly our work promotes the application of stochastic calculus as a powerful direct alternative to Feynman-Kac theory and path-integral methods.

Mathematical, Thermodynamical, and Experimental Necessity for Coarse Graining Empirical Densities and Currents in Continuous Space.

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically "optimal" coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.

An efficient and minimalist scheme for continuum dislocation dynamics

Continuum dislocation dynamics methods have received considerable interests for simulating dislocation microstructures at the meso-scale, serving as potential tools for bridging the gap between micro- and macro-scale models for the plastic behaviours of crystalline materials. Recently, an exact evolution equation for the “all-dislocation” density that represents dislocation quantities over both space and dislocation-character domains has been developed by one of the present authors. The “all-dislocation” representation is superior to representations based on the Nye tensor or geometrically necessary dislocations (GND), since the statistically stored dislocation (SSD) contents will be preserved. In this paper, a numerical scheme is presented to solve the dynamics of the “all-dislocation” density efficiently, with long-range elastic interaction between dislocations accounted for via Mura's formula after singularity removal. The proposed simulation scheme is demonstrated by simulation examples in the multi-scale hierarchy, from intensive microstructures of individual dislocations including Frank-Read source and Orowan looping, to extensive microstructures of coarse-grained dislocation densities in single- and multi-slip in the face-centred cubic crystal structure.

Competition in a system of Brownian particles: Encouraging achievers.

We introduce and analytically and numerically study a simple model of interagent competition, where underachievement is strongly discouraged. We consider N≫1 particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it. We show that, in the limit of N→∞, the dynamics of the coarse-grained particle density field can be described by a nonlocal hydrodynamic theory which was encountered in a study of the spatial extent of epidemics in a critical regime. The hydrodynamic theory predicts relaxation of the system toward a stationary density profile of the "swarm" of particles, which exhibits a power-law decay at large distances. An interesting feature of this relaxation is a nonstationary "halo" around the stationary solution, which continues to expand in a self-similar manner. The expansion is ultimately arrested by finite-N effects at a distance of order sqrt[N] from the origin, which gives an estimate of the average radius of the swarm. The hydrodynamic theory does not capture the behavior of the particle farthest from the origin-the current leader. We suggest a simple scenario for typical fluctuations of the leader's distance from the origin and show that the mean distance continues to grow indefinitely as sqrt[t]. Finally, we extend the inter-agent competition from n=2 to an arbitrary number n of competing Brownian particles (n≪N). Our analytical predictions are supported by Monte Carlo simulations.

Complexity calculation for an amorphous metastable solid

We use a field-theoretic model to study the partition function of a many-particle system without quenched-disorder. The model is formulated in terms of the coarse-grained density field ρ(x) used in classical density functional theory (DFT). A corresponding free energy landscape (FEL) is depicted in the function space of the continuum field. The number of local minima in the FEL is defined as the Complexity Sc. Following the standard trick of mapping into a composite system of m identical replicas, and finally taking the m→1 limit, Sc is calculated. The two-point structural correlations of the density fluctuations are needed as an input. A vital step of the present work is using the static correlations of the inhomogeneous metastable state obtained in classical DFT. The inhomogeneous state is described in terms of overlapping Gaussian density profiles centred on a set of random lattice points {Ri}. Our results for Sc(η) on extrapolation to higher packing fractions (η)tends to zero, obtaining the corresponding Kauzmann point ηK. We obtain the dependence of the ηK on the properties of the inhomogeneous structure for the structure {Ri}.

Vortex lattices in binary Bose–Einstein condensates: collective modes, quantum fluctuations, and intercomponent entanglement

We study binary Bose–Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. Within the mean-field theory, the two types of fields have been shown to give the same vortex-lattice phase diagram. We develop an improved effective field theory to study properties of collective modes and ground-state intercomponent entanglement. Here, we point out the need to introduce renormalized coupling constants for coarse-grained densities. We show that the low-energy excitation spectra for the two types of fields are related to each other by suitable rescaling with the renormalized coupling constants. By calculating the entanglement entropy, we find that for an intercomponent repulsion (attraction), the two components are more strongly entangled in the case of parallel (antiparallel) fields, in qualitative agreement with recent studies for a quantum (spin) Hall regime. We also find that the entanglement spectrum exhibits an anomalous square-root dispersion relation, which leads to a subleading logarithmic term in the entanglement entropy. All of these are confirmed by numerical calculations based on the Bogoliubov theory with the lowest-Landau-level approximation. Finally, we investigate the effects of quantum fluctuations on the phase diagrams by calculating the correction to the ground-state energy due to zero-point fluctuations in the Bogoliubov theory. We find that the boundaries between rhombic-, square-, and rectangular-lattice phases shift appreciably with a decrease in the filling factor.

Microscopic density-functional approach to nonlinear elasticity theory

Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the macroscopic phenomena of a solid crystal. As the relevant variables we specify the coarse-grained densities of the conserved quantities and a properly defined displacement field which describes the local translations, rotations, and deformations. In order to stay within the framework of the conventional density-functional theory we first and mainly consider the isothermal case and omit the effects of heat transport and warming by friction where later we extend our theory to the general case and include these effects. We proceed in two steps. First, we apply the concept of local thermodynamic equilibrium and minimize the free energy functional under the constraints that the macroscopic relevant variables are fixed. As results we obtain the local free energy density and we derive explicit formulas for the elastic constants which are exact within the framework of density-functional theory. Second, we apply the methods of nonequilibrium statistical mechanics with projection-operator techniques. We extend the projection operators in order to include the effects of coarse-graining and the displacement field. As a result we obtain the time-evolution equations for the relevant variables with three kinds of terms on the right-hand sides: reversible, dissipative, and fluctuating terms. We find explicit formulas for the transport coefficients which are exact in the limit of continuum mechanics if the projection operators are properly defined. By construction the theory allows the diffusion of particles in terms of point defects where, however, in a normal crystal this diffusion is suppressed.

Spatially heterogeneous dynamics and locally arrested density fluctuations from first principles

We present a first-principles formalism for studying dynamical heterogeneities in glass-forming liquids. Based on the non-equilibrium self-consistent generalized Langevin equation theory, we were able to describe the time-dependent local density profile during the particle interchange among small regions of the fluid. The final form of the diffusion equation contains both the contribution of the chemical potential gradient written in terms of a coarse-grained density and a collective diffusion coefficient as well as the effect of a history-dependent mobility factor. With this diffusion equation, we captured interesting phenomena in glass-forming liquids such as the cases when a strong density gradient is accompanied by a very low mobility factor attributable to the denser part: in such circumstances, the density profile falls into an arrested state even in the presence of a density gradient. On the other hand, we also show that above a certain critical temperature, which depends on the volume fraction, any density heterogeneity relaxes to a uniform state in a finite time, known as equilibration time. We further show that such equilibration time varies little with the temperature in diluted systems but can change drastically with temperature in concentrated systems.

Cr-Precipitates Growth Kinetics and Microstructure Evolution of Fe-Cr Binary Alloys from Kinetic Monte-Carlo Simulation Combined with Spatial Coarse-Grained Mass Density Field Description

Cr-Precipitates Growth Kinetics and Microstructure Evolution of Fe-Cr Binary Alloys from Kinetic Monte-Carlo Simulation Combined with Spatial Coarse-Grained Mass Density Field Description

An Efficient Radio Map Learning Scheme Based on Kernel Density Function

Training an accurate and up-to-date radio map has always been a primary concern for implementing a WiFi fingerprint-based localization system. This paper presents a novel radio map learning scheme for online learning a set of kernel density functions, which function like a traditional radio map in WiFi fingerprint-based localization systems. To be specific, each kernel density function corresponds to one specific access point (AP) and predicts the probability of having a received signal strength (RSS) measurement from this AP at any position. In the offline phase, a set of coarse-grained kernel density functions are initially established by the Multivariate Kernel Density Estimation (MKDE) through a fast site survey. In the online phase, these kernel density functions are recursively refined through Incremental-MKDE (IMKDE) using freshly crowdsourced fingerprints, which essentially fuses the historical features in the previous kernel density functions and up-to-date features in the current fingerprints. A compression technique is applied to improve the computation and storage efficiency. In addition, pedestrian dead reckoning (PDR) is leveraged to calibrate the location labels of crowdsourced fingerprints. Extensive experiments are carried out in a real scenario of nearly 1000 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m^2$</tex-math></inline-formula> for five months, and a comparison made between the IMKDE based method and several existing popular solutions confirms the superiority of the proposed IMKDE in terms of both computational complexity and localization accuracy.

EDENet: Elaborate density estimation network for crowd counting

For the CNN-based density estimation approaches in the field of crowd counting, how to generate a high-quality density map with accurate counting performance and detailed spatial description is still an open question. In this paper, to tackle the aforementioned contradiction, we propose an end-to-end trainable architecture called Elaborate Density Estimation Network for Crowd Counting (EDENet), which can gradually generate high-quality density estimation maps based on distributed supervision. Specifically, EDENet is composed of Feature Extraction Network (FEN), Feature Fusion Network (FFN), Double-Head Network (DHN) and Adaptive Density Fusion Network (ADFN). The FEN adopts VGG as the backbone network and employs Spatial Adaptive Pooling (SAP) to extract coarse-grained features. The FFN can effectively fuse contextual information and localization information for enhancing the spatial description ability of fine-grained features. In the DHN, the Density Attention Module (DAM) can provide attention masks of foreground-background, thereby urging the Density Regression Module (DRM) to focus on the pixels around the head annotations to regress density maps with different resolutions. The ADFN constructed on the basis of the adaptive weighting mechanism can directly introduce coarse-grained density representation into high-resolution density maps to strengthen the commonality and dependency among density maps. Extensive experiments on four benchmark crowd datasets (the ShanghaiTech, the UCF-QNRF, the JHU-CRWORD++ and the NWPU-Crowd) indicate that EDENet can achieve state-of-the-art recognition performance and high robustness. Not only that, the density map with the highest Peak Signal to Noise Ratio (PSNR) can be considered to be of high quality.

Multiscale Approaches for Confined Ring Polymer Solutions.

We apply a hierarchy of multiscale modeling approaches to investigate the structure of ring polymer solutions under planar confinement. In particular, we employ both monomer-resolved (MR-DFT) and a coarse-grained (CG-DFT) density functional theories for fully flexible ring polymers, with the former based on a flexible tangent hard-sphere model and the latter based on an effective soft-colloid representation, to elucidate the ring polymer organization within slits of variable width in different concentration regimes. The predicted monomer and polymer center-of-mass densities in confinement, as well as the surface tension at the solution-wall interface, are compared to explicit molecular dynamics (MD) simulations. The approaches yield quantitative (MR-DFT) or semiquantitative (CG-DFT) agreement with MD. In addition, we provide a systematic comparison between confined linear and ring polymer solutions. When compared to their linear counterparts, the rings are found to feature a higher propensity to structure in confinement that translates into a distinct shape of the depletion potentials between two walls immersed into a polymer solution. The depletion potentials that we extract from CG-DFT and MR-DFT are in semiquantitative agreement with each other. Overall, we find consistency among all approaches as regards the shapes, trends, and qualitative characteristics of density profiles and depletion potentials induced on hard walls by linear and cyclic polymers.

Persistent fluctuations of the swarm size of Brownian bees.

The "Brownian bees" model describes a system of N-independent branching Brownian particles. At each branching event the particle farthest from the origin is removed so that the number of particles remains constant at all times. Berestycki etal. [arXiv:2006.06486] proved that at N→∞ the coarse-grained spatial density of this particle system lives in a spherically symmetric domain and is described by the solution of a free boundary problem for a deterministic reaction-diffusion equation. Furthermore, they showed [arXiv:2005.09384] that, at long times, this solution approaches a unique spherically symmetric steady state with compact support: a sphere whose radius ℓ_{0} depends on the spatial dimension d. Here we study fluctuations in this system in the limit of large N due to the stochastic character of the branching Brownian motion, and we focus on persistent fluctuations of the swarm size. We evaluate the probability density P(ℓ,N,T) that the maximum distance of a particle from the origin remains smaller than a specified value ℓ<ℓ_{0} or larger than a specified value ℓ>ℓ_{0} on a time interval 0<t<T, where T is very large. We argue that P(ℓ,N,T) exhibits the large-deviation form -lnP≃NTR_{d}(ℓ). For all d's we obtain asymptotics of the rate function R_{d}(ℓ) in the regimes ℓ≪ℓ_{0},ℓ≫ℓ_{0}, and |ℓ-ℓ_{0}|≪ℓ_{0}. For d=1 the whole rate function can be calculated analytically. We obtain these results by determining the optimal (most probable) density profile of the swarm, conditioned on the specified ℓ and by arguing that this density profile is spherically symmetric with its center at the origin.