Inhomogeneous Systems Research Articles

Advancing Energy Materials by In Situ Atomic Scale Methods

AbstractDespite significant advancements in materials design for renewable energy devices, the fundamental understanding of the underlying processes in many materials remains limited, particularly in complex, inhomogeneous systems and interfaces. In such cases, in situ studies with high spatial and energy resolution are essential for uncovering new insights into excitation, dissipation, and conversion processes. Recent progress in in situ atomic scale methods has greatly enhanced the understanding of energy materials. Here, key advances are reviewed, including in situ, environmental and ultra‐fast transmission electron microscopy, scanning probe techniques, single‐photon‐resolved infrared spectroscopy, velocity‐resolved molecular kinetics, and in situ grazing‐incidence X‐ray spectroscopy. These techniques enable the study of energy conversion with spatial resolution from nanometers down to individual atoms, energy resolution down to meV, and single‐quantum detection. Especially they enable access to processes that involve multiple degrees of freedom, strong coupling, or spatial inhomogeneities. They have driven a qualitative leap in the fundamental understanding of energy conversion processes, opening new avenues for improving existing materials and designing novel clean and efficient energy materials in photovoltaics, friction, and surface chemistry and (photo‐)electrochemistry.

Neural Density Functional Theory of Liquid-Gas Phase Coexistence

We use supervised machine learning together with the concepts of classical density functional theory to investigate the effects of interparticle attraction on the pair structure, thermodynamics, bulk liquid-gas coexistence, and associated interfacial phenomena in many-body systems. Local learning of the one-body direct correlation functional is based on Monte Carlo simulations of inhomogeneous systems with randomized thermodynamic conditions, randomized planar shapes of the external potential, and randomized box sizes. Focusing on the prototypical Lennard-Jones system, we test predictions of the resulting neural attractive density functional across a broad spectrum of physical behavior associated with liquid-gas phase coexistence in bulk and at interfaces. We analyze the bulk radial distribution function g(r) obtained from automatic differentiation and the Ornstein-Zernike route and determine (i) the Fisher-Widom line, i.e., the crossover of the asymptotic (large distance) decay of g(r) from monotonic to oscillatory, (ii) the (Widom) line of maximal correlation length, (iii) the line of maximal isothermal compressibility, and (iv) the spinodal by calculating the poles of the structure factor in the complex plane. The bulk binodal and the density profile of the free liquid-gas interface are obtained from density functional minimization and the corresponding surface tension from functional line integration. We also show that the neural functional describes accurately the phenomena of drying at a hard wall and of capillary evaporation for a liquid confined in a slit pore. Our neural framework yields results that improve significantly upon standard mean-field treatments of interparticle attraction. Comparison with independent simulation results demonstrates a consistent picture of phase separation even when restricting the training to supercritical states only. We argue that phase coexistence and its associated signatures can be discovered as emerging phenomena via functional mappings and educated extrapolation. Published by the American Physical Society 2025

Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid

We present a study of spin-unpolarized and spin-polarized two-dimensional uniform electron liquids using variational and diffusion quantum Monte Carlo (VMC and DMC) methods with Slater-Jastrow-backflow trial wave functions. Ground-state VMC and DMC energies are obtained in the density range 1≤rs≤40. Single-particle and many-body finite-size errors are corrected using canonical-ensemble twist-averaged boundary conditions and extrapolation of twist-averaged energies to the thermodynamic limit of infinite system size. System-size-dependent errors in Slater-Jastrow-backflow DMC energies caused by partially converged VMC energy minimization calculations are discussed. We find that, for 1≤rs≤5, optimizing the backflow function at each twist lowers the twist-averaged DMC energy at finite system size. However, nonsystematic system-size-dependent effects remain in the DMC energies, which can be partially removed by extrapolation from multiple finite system sizes to infinite system size. The DMC energies in the thermodynamic limit are used to parametrize a local spin density approximation correlation functional for inhomogeneous electron systems. Our zero-temperature phase diagram shows a single transition from a paramagnetic fluid to a hexagonal Wigner crystal at rs=35(1), with no region of stability for a ferromagnetic fluid. Published by the American Physical Society 2024

Dislocation assisted coarsening of coherent precipitates: a phase field study

ABSTRACT Coarsening of precipitates in coherent systems is influenced by the elastic fields of the precipitates and the interfacial curvature. It is also known that if precipitates are connected by dislocations, coarsening is affected by the elastic fields of the dislocations and the pipe diffusivity. Although there is experimental evidence of accelerated coarsening in the presence of dislocations, these studies do not capture the effect of the elastic fields. There exist generic theoretical models that can predict the average sizes and size distributions of coarsening precipitates considering the coherency-related elastic stress fields. In this paper, we use a phase field model to study the coarsening of precipitates connected by dislocations, incorporating its elastic fields and pipe diffusivity. Specifically, we study the effects of misfit strain, elastic moduli mismatch, faster pipe mobility and the elastic fields of the dislocation on the morphology and kinetics of the coarsening precipitates. The dilatational component, associated with the edge character of the dislocations interacts with the precipitates in an elastically homogeneous system. In an elastically inhomogeneous system, the deviatoric elastic fields also interact with the precipitates influencing the morphology and kinetics of coarsening precipitates. The kinetics of coarsening is different as well, with hard precipitates coarsening faster as compared to soft precipitates, when connected by dislocations. Further, we note that the modified Gibbs–Thomson equation, which was originally derived for an isolated precipitate in an infinite matrix, is also applicable for coarsening precipitates at close proximity.

Fabricated S-scheme CoS/CeO2 heterojunction photocatalyst efficiently activates peroxymonosulfate for polyethylene terephthalate plastic degradation: Insight into radicals and electron transfer

Polyethylene terephthalate (PET) plastics are widely utilized, yet they also give rise to significant environmental contamination. In this study, a CoS/CeO2 material with an S-scheme heterojunction was constructed using CoS with CeO2 derived from MOFs and employed for the photocatalytic activation of peroxomonosulfate (PMS) for the degradation of PET. The CoS/CeO2/vis/PMS system demonstrated a degradation rate of up to 95.75 % (weight loss rate) for PET plastic. The performance of this system is much better than that of simple photocatalytic or PMS systems. Photogenerated carriers generated by heterojunctions upon illumination accelerate the fast electron cycling of Co2+/Co3+ through the S-scheme transfer pathway driven by a directional interfacial electric field. This promoted efficient mass transfer in the inhomogeneous phase system (such as SO4•−, e−) and acted as an adsorption activation site for PMS. In-situ X-ray photoelectron spectroscopy (In-situ XPS) and ESR test proved that the electron flow in the heterojunction conforms to the S-scheme mechanism. Density functional theory (DFT) calculations revealed the material of the CoS/CeO2 interface and the successful construction of the modulated electronic structure led to the accumulation of holes on CeO2 and electrons on CoS. Bader analysis on charge density distribution further demonstrated that the formation of the heterojunction decreased the adsorption energy of the PMS on the Co sites, which in turn lowered the energy barrier for the generation of SO4•−. This work would provide a novel solution to the problem of removing plastic pollutants from water, as well as new insight into the construction of S-scheme heterojunctions and the mechanism of photocatalytic PMS activation.

Painlevé Analysis and Soliton Solutions for an Inhomogeneous Heisenberg Ferromagnetic System

In this paper we investigate an inhomogeneous higher-order nonlinear Schrödinger equation generated from the deformation of an inhomogeneous Heisenberg ferromagnetic system. Considering the variable coefficients from the inhomogeneities in the ferromagnetic medium, we present the Painlevé-integrable condition. Introducing an auxiliary function, we obtain the one-, two- and N-soliton solutions via the Hirota method. Furthermore, we graphically analyze the influence of inhomogeneities on the soliton propagation and interaction. It is found that the inhomogeneities will cause an increasing-decreasing process of soliton amplitude, and the change of the propagation direction. The perturbation terms can affect the propagation region of soliton but have no influence on the soliton amplitude. We consider the interactions between/among two and three solitons with the same or different initial propagation directions, and observe that the inhomogeneities can influence the soliton amplitudes and propagation directions, while the perturbation parameter can only affect the propagation direction of the soliton. In addition, bound state of solitons and its interaction with soliton are analyzed under the given excitation condition.

Molecular anatomy of the pressure anisotropy in the interface of one and two component fluids: Local thermodynamic description of the interfacial tension.

Through the decomposition of the pressure into the kinetic and the intermolecular contributions, we show that the pressure anisotropy in the fluid interface, which is the source of the interfacial tension, comes solely from the latter contribution. The pressure anisotropy due to the intermolecular force between the fluid particles in the same or the different fluid components is approximately proportional to the multiplication of the corresponding fluid density gradients, and from the molecular dynamics simulation of the liquid-vapor and liquid-liquid interfaces, we demonstrate that the density gradient theory by van der Waals gives the leading order approximation of the free energy density in inhomogeneous systems, neglecting the Tolman length.

Compression theory for inhomogeneous systems

The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on inhomogeneous graphs. However, the lack of translational invariance presents a fundamental challenge to theoretical tools, such as the renormalization group, which were so successful in characterizing the universal physical behaviour in critical phenomena. Here we show that compression theory allows the extraction of relevant degrees of freedom in arbitrary geometries, and the development of efficient numerical tools to build an effective theory from data. We demonstrate our method by applying it to a strongly correlated system on an Ammann-Beenker quasicrystal, where it discovers an exotic critical point with broken conformal symmetry. We also apply it to an antiferromagnetic system on non-bipartite random graphs, where any periodicity is absent.

A Computational Tool for Determining the Local Dielectric Constants within Heterogenous Nanoscale Systems from Molecular Dynamics Trajectories

The dielectric properties play a significant role in shaping the characteristics and functional behavior of heterogeneous nanoscale systems. We have implemented a simple method and developed a flexible computational tool to determine the dielectric constant of various subcomponents of neutral inhomogeneous systems, based on dipole moment fluctuations measured in molecular dynamics (MD) trajectories. We first validate our computational approach by evaluating the dielectric constant (epsilon) of TIP3P waters, determined to be ~ 82. The dielectric of water molecules in a system surrounding a lipid bilayer decreases to ~ 62. Our method successfully calculates the dielectric constant of lipids as 9, with the headgroups exhibiting an epsilon value of approximately 8, and the hydrophobic tails possessing an epsilon value close to 1. These results are in good agreement with the known values reported in the literature. Finally, we have applied our method to optical nanosensor systems for which it has been hypothesized that the local dielectric constant changes are the key determinant of their optical sensing response. Namely, we examined the local dielectric constants in systems of single-walled carbon nanotubes functionalized with lipid molecules, in the presence and absence of target analytes (in this case, antimicrobial disruptor peptides). Our tool is currently designed for neutral species and systems but has a potential for being extended for use on the charged systems. It is a flexible computational tool that can be used to determine the local dielectric constants of subcomponents within neutral heterogeneous nanoscale systems studied in MD simulations, a functionality that, to the best of our knowledge, was not available among other codes and packages used by the computational chemistry community.

Exactly Solvable Inhomogeneous Fermion Systems

Abstract 15 exactly solvable inhomogeneous (spinless) fermion systems on 1D lattices are constructed explicitly based on the discrete orthogonal polynomials of the Askey scheme, e.g. Krawtchouk, Hahn, Racah, Meixner, and q-Racah polynomials. The Schrödinger and Heisenberg equations are solved explicitly, as the entire set of the eigenvalues and eigenstates are known explicitly. The ground-state two-point correlation functions are derived explicitly. The multipoint correlation functions are obtained by Wick’s theorem. 15 corresponding exactly solvable XX spin systems are also displayed. They all have nearest-neighbor interactions. The exact solvability of the Schrödinger equation means that the corresponding Fokker–Planck equation is also exactly solvable. This leads to 15 exactly solvable birth and death fermions and 15 birth and death spin models. These provide plenty of material for calculating interesting quantities, e.g. entanglement entropy, etc.

Modulating Coarse-Grained Dynamics by Perturbing Free Energy Landscapes.

We introduce an approach to describe the long-time dynamics of multiatomic molecules by modulating the free energy landscape (FEL) to capture dominant features of the energy-barrier crossing dynamics of the all-atom (AA) system. Notably, we establish that the self-diffusion coefficient of coarse-grained (CG) systems can be accurately delineated by enhancing conservative force fields with high-frequency perturbations. Using theoretical arguments, we show that these perturbations do not alter the lower-order distribution functions, thereby preserving the structure of the AA system after coarse-graining. We demonstrate the utility of this approach using molecular dynamics simulations of simple molecules in bulk with distinct dynamical characteristics with and without time scale separations as well as for inhomogeneous systems where a fluid is confined in a slit-like nanochannel. Additionally, we also apply our approach to more powerful many-body potentials optimized by using machine learning (ML).

Almost Periodic Solutions of Differential Equations with Generalized Piecewise Constant Delay

In this paper, we investigate differential equations with generalized piecewise constant delay, DEGPCD in short, and establish the existence and stability of a unique almost periodic solution that is exponentially stable. Our results are derived by utilizing the properties of the (μ1,μ2)-exponential dichotomy, Cauchy and Green matrices, a Gronwall-type inequality for DEGPCD, and the Banach fixed point theorem. We apply these findings to derive new criteria for the existence, uniqueness, and convergence dynamics of almost periodic solutions in both the linear inhomogeneous and quasilinear DEGPCD systems through the (μ1,μ2)-exponential dichotomy for difference equations. These results are novel and serve to recover, extend, and improve upon recent research.

Oxidative degradation of anionic dyes in wastewater by magnetic lignin micro-nano spheres catalyzed peroxymonosulfate

Lignin has gained significant attention in wastewater treatment due to its abundant resources and good adsorbability. In this work, magnetic lignin micro-nano spheres (Fe3O4@SiO2-LNS) was prepared using alkali lignin as the raw material, and was used as the adsorbent and catalyst to activate peroxymonosulfate (PMS) to build an inhomogeneous catalytic oxidation system (Fe3O4@SiO2-LNS/PMS). The system was then used to remove the stubborn acid blue 9 (AB9) dye in wastewater, and the effects of pH, catalyst dosage, PMS dosage of the system on the removal percentage of AB9 dye and the corresponding degradation mechanism were explored. The results showed that Fe3O4@SiO2-LNS/PMS system had good removal efficiency for AB9 in wastewater, and AB9 dye was completely oxidized and finally degraded into CO2 and H2O. The maximum removal percentage of AB9 was observed when the pH and temperature of the system were 6.0 and 313 K, and the removal percentage of AB9 achieved 100 % when the optimal dosage of Fe3O4@SiO2-LNS and PMS were 3.44 g/L and 53.15 mM, respectively. In addition, Fe3O4@SiO2-LNS had good stability and reusability. This work provides a promising approach for abatement of dyeing wastewater pollution and a new direction for high-value utilization of alkali lignin.

Modelling of filtered drag force for clustered particle-laden flows based on interface-resolved simulation data

Interface-resolved direct numerical simulations (DNS) of clustered settling suspensions in a periodic domain are performed to study the filtered drag force for clustered particle-laden flows. Our results show that, for the homogeneous system, the filtered drag is independent of the filter size, whereas for the clustered particle-laden flows, the averaged drag becomes smaller than the homogeneous drag at the filter size above 4 particle diameters. The drag reduction saturates at the filter size being comparable to the cluster size in the horizontal direction in our simulations. A new correlation is proposed to account for the mesoscale effect on the filtered drag force by using drift velocity and variance of the solid volume fraction, based on the modification of existing subgrid drag models for the inhomogeneous system. The existing models for the drift velocity and the variance of the solid volume fraction are assessed using our DNS data. A new model for the drift velocity and the variance of the solid volume fraction is proposed, based on the combination and modification of the previous models. All mesoscale models considered can predict well the filtered drag with comparable accuracy, and are superior to the homogeneous drag model for the clustered system. Our models with the same parameter values obtained from the large-scale system can also predict well the filtered drag for smaller computational domain sizes.

Global well-posedness for the 3D inhomogeneous incompressible magnetohydrodynamics system with axisymmetric data

We focus on the Cauchy problem of 3D inhomogeneous incompressible magnetohydrodynamics (MHD for short) system with axisymmetric initial data. It is shown that this MHD system has a unique global solution provided that ‖1r(1ρ0−1)‖L∞ is sufficiently small. Finally, we establish the L2 decay rate for any given globally smooth solution of the MHD system by using the Schonbek's Fourier splitting method.

Computing Quadratic Eigenvalues and Solvent by a New Minimization Method and a Split-Linearization Technique

To solve quadratic eigenvalue problems (QEPs), especially the gyroscopic systems, two methods are proposed: an iterative direct detection method (DDM) of the complex eigenvalues of the original QEP, and a split-linearization method (SLM) for finding the solvent matrix, which results to a standard linear eigenvalue problem (LEP) being solved to compute all eigenvalues by the symmetry extension. Reducing the dimension to one-half, the LEP is recast in a simpler QEP involving the square of the solvent. We set up two new merit functions which are minimized to detect the complex eigenvalues from the original QEP and a simpler QEP. For each eigen-parameter the merit function consists of the Euclidean norm of each derived eigen-equation, whose vector variable is solved from a derived inhomogeneous linear system. Then, the golden section search algorithm is employed to minimize the merit functions and locate the complex eigenvalue as a local minimal point. The results are compared with that computed by the cyclic-reduction-based solvent (CRS) method.

Families of exact similaritons with flexible modulations in N-coupled homogeneous and inhomogeneous systems

In this paper, a family of exact solutions to N-coupled nonlinear Schrödinger (N-CNLS) equations including bright and dark solitons, Akhmediev breathers, Kuznetsov-Ma breathers, and rogue waves are derived with the aid of a generic nonlinear wave assumption. As an application of the solutions, we present a scheme to realize amplitude coding in an identical waveguide system. Furthermore, by a general self-similar transformation method, exact controllable similaritons of N-coupled inhomogeneous NLS (N-CINLS) equations are constructed under relaxed compatibility conditions. Flexible modulations of similaritons are investigated in a typical inhomogeneous system. Based on the general self-similar transformation, we further study various and novel modulations of composite similariton of 2-CINLS regimes. The various similaritons presented here may be expected to find application in the control and transmission of nonlinear waves in realizable complex systems including those based on optical fibers and Bose-Einstein condensates.

Beam–plasma dynamics in finite-length, collisionless inhomogeneous systems

This study investigates the streaming instability triggered by ion motion in a plasma system that is finite in length, collisionless, and inhomogeneous. Employing numerical simulations using particle-in-cell techniques and kinetic equations, the study examines how inhomogeneity emerges from integrating a cold ion beam with a background plasma within a confined system. The findings suggest that steady ion flow can modify ion sound waves through acoustic reflections from system boundaries, leading to instability. Such phenomena are known to be a hydrodynamic effect. However, there are also signatures of the beam-driven ion sound instability where kinetic resonances play a pivotal role. The main objective is to understand the impact of a finite-length system on beam–plasma instability and to identify the wave modes supported in such configurations.

The inhomogeneous incompressible Hall-MHD system with only bounded density

The inhomogeneous incompressible Hall-MHD system with only bounded density

The rates and host galaxies of pair-instability supernovae through cosmic time: predictions from BPASS and IllustrisTNG

ABSTRACT Pair-instability supernovae (PISNe) have long been predicted to be the final fates of near-zero-metallicity very massive stars ($Z \lt Z_\odot /3$, M$_\mathrm{ZAMS} \gtrsim 140\, \text{M}_\odot$). However, no definite PISN has been observed to date, leaving theoretical modelling validation open. To investigate the observability of these explosive transients, we combine detailed stellar evolution models for PISNe formation, computed from the binary population and spectral synthesis code suite, bpass, with the star formation history of all individual computational elements in the Illustris-TNG simulation. This allows us to compute comic PISN rates and predict their host galaxy properties. Of particular importance is that IllustrisTNG galaxies do not have uniform metallicities throughout, with metal-enriched galaxies often harbouring metal-poor pockets of gas where PISN progenitors may form. Accounting for the chemical inhomogeneities within these galaxies, we find that the peak redshift of PISNe formation is $z=3.5$ instead of the value of $z=6$ when ignoring chemical inhomogeneities within galaxies. Furthermore, the rate increases by an order of magnitude from 1.9 to 29 PISN Gpc$^{-3}$ yr$^{-1}$ at $z=0$, if the chemical inhomogeneities are considered. Using state-of-the-art theoretical PISN light curves, we find an observed rate of 13.8 (1.2) visible PISNe per year for the Euclid-Deep survey, or 83 (7.3) over the 6-yr lifetime of the mission when considering chemically inhomogeneous (homogenous) systems. Interestingly, only 12 per cent of helium PISN progenitors are sufficiently massive to power a superluminous supernova event, which can potentially explain why PISN identification in time-domain surveys remains elusive and progress requires dedicated strategies.