Inhomogeneous Model Research Articles

Thermal-density-functional-theory approach to quantum thermodynamics

Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent advances in experimental techniques for controlling and preparing these systems have increased interest in this area, as they have the potential to drive the development of quantum technologies. In this study, we present a density-functional-theory approach to extract detailed information about the statistics of work and the irreversible entropy associated with quantum quenches at finite temperature. Specifically, we demonstrate that these quantities can be expressed as functionals of thermal and out-of-equilibrium densities, which may serve as fundamental variables for understanding finite-temperature many-body processes. We, then, apply our method to the case of the inhomogeneous Hubbard model, showing that our density-functional-theory-based approach can be usefully employed to unveil the distinctive roles of interaction and external potential on the thermodynamic properties of such a system. Published by the American Physical Society 2024

Eshelby's inhomogeneity model within Mindlin's first strain gradient elasticity theory and its applications in composite materials

Eshelby's inhomogeneity problem is solved within the second form of Mindlin's first strain gradient elasticity theory for the prediction of the effective elastic properties of composites. Considering Green's function technique, an integral equation is established for an ellipsoidal inhomogeneity embedded in a homogeneous elastic medium and subjected to non-uniform boundary conditions. Within isotropic elasticity, the mean strain inside a spherical inhomogeneity is detailed to provide analytical results. In addition to the elastic properties of the inhomogeneity and the matrix, the strain localization depends on five gradient elastic constants, introduced by the first strain gradient elasticity theory. The effective bulk and shear moduli of a two-phase composite are predicted through Mori-Tanaka's scheme. The strain localization and the effective elastic moduli are then expressed within some simplified gradient elasticity theories. To test the relevance of the developed model, its predictions are compared with those of some investigations and the effective elastic properties are analyzed for a metal matrix composite. Finally, some comparisons with experimental data are performed to estimate the characteristic length scale parameters and gradient elastic constants of local phases.

Characteristics of Supercritical CO2 Non-Mixed Phase Replacement in Intraformational Inhomogeneous Low-Permeability Reservoirs

Under the influence of the sedimentation process, the phenomenon of intraformational non-homogeneity is widely observed in low-permeability reservoirs. In the development process of water and gas replacement (WAG), the transport law of water and gas and the distribution of residual oil are seriously affected by the non-homogeneity of reservoir properties. In this paper, a study on two types of reservoirs with certain lengths and thicknesses is carried out, and a reasonable development method is proposed according to the characteristics of each reservoir. Firstly, through indoor physical simulation experiments combined with low-field nuclear magnetic resonance scanning (NMR), this study investigates the influence of injection rate and core length on the double-layer low-permeability inhomogeneous core replacement and pore throat mobilization characteristics. Then, a two-layer inhomogeneous low-permeability microscopic model is designed to investigate the model’s replacement and pore throat mobilization characteristics under the combined influence of rhythmites, gravity, the injection rate, etc. Finally, based on the results of the core replacement and numerical simulation, a more reasonable development method is proposed for each type of reservoir. The results show that for inhomogeneous cores of a certain length, the WAG process can significantly increase the injection pressure and effectively seal the high-permeability layer through the Jamin effect to improve the degree of recovery. Moreover, for positive and reverse rhythm reservoirs of a certain thickness, the injection rate can be reduced according to the physical properties of the reservoir, and the gravity overburden phenomenon of the gas is used to achieve the effective development of the upper layers. The effect of the development of a positive rhythm reservoir therefore improved significantly. These findings provide data support for improving the development effectiveness of CO2 in low-permeability inhomogeneous reservoirs and emphasize the importance of the influence of multiple factors, such as injection flow rate, gravity, and rhythm, in CO2 replacement.

Impact of inhomogeneous diffusion on secondary cosmic ray and antiproton local spectra

Recent γ-ray and neutrino observations seem to favor the consideration of non-uniform diffusion of cosmic rays (CRs) throughout the Galaxy.In this study, we investigate the consequences of spatially-dependent inhomogeneous propagation of CRs on the fluxes of secondary CRs and antiprotons detected at Earth. A comparison is made among different scenarios in search of potential features that may guide us toward favoring one over another in the near future. We also examine both the influence of inhomogeneous propagation in the production of secondary CRs from interactions with the gas, and the effects of this scenario on the local fluxes of antiprotons and light antinuclei produced as final products of dark matter annihilation. Our results indicate that the consideration of an inhomogeneous diffusion model could improve the compatibility of the predicted local antiproton flux with that of B, Be and Li, assuming only secondary origin of these particles. In addition, our model predicts a slightly harder local antiproton spectrum, making it more compatible with the high energy measurements of AMS-02.Finally, no significant changes are expected in the predicted local flux of antiprotons and antinuclei produced from dark matter among the different considered propagation scenarios.

McVittie–Plummer Spacetime: Plummer Sphere Immersed in the FLRW Universe

The McVittie–Plummer spacetime is a spherically symmetric inhomogeneous cosmological model that represents a spherical star system embedded in a standard Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model. We study the main physical properties of this gravitational field. Regarding the interplay between the physics of the local system and the expanding background, we employ the Misner–Sharp mass–energy function to show that there is a relatively weak time-dependent general relativistic coupling between the astrophysical system and the background FLRW cosmological model. The coupling term is proportional to the inverse of the scale factor and decreases as the Universe expands.

Elucidating Antibiotic Permeation through the Escherichia coli Outer Membrane: Insights from Molecular Dynamics.

Antibiotic resistance represents a critical public health threat, with an increasing number of Gram-negative pathogens demonstrating resistance to a broad range of clinical drugs. A primary challenge in enhancing antibiotic efficacy is overcoming the robust barrier presented by the bacterial outer membrane. Our research addresses a longstanding question: What is the rate of antibiotic permeation across the outer membrane (OM) of Gram-negative bacteria? Utilizing molecular dynamics (MD) simulations, we assess the passive permeability profiles of four commercially available antibiotics─gentamicin, novobiocin, rifampicin, and tetracycline across an asymmetric atomistic model of the Escherichia coli (E. coli) OM, employing the inhomogeneous solubility-diffusion model. Our examination of the interactions between these drugs and their environmental context during OM permeation reveals that extended hydrogen bond formation and drug-cation interactions significantly hinder the energetics of passive permeation, notably affecting novobiocin. Our MD simulations corroborate well with experimental data and reveal new implications of solvation on drug permeability, overall advancing the possible use of computational prediction of membrane permeability in future antibiotic discovery.

Smooth Gowdy-symmetric generalised Taub–NUT solutions with polynomial initial data

Abstract We consider smooth Gowdy-symmetric generalised Taub–NUT solutions, a class of inhomogeneous cosmological models with spatial three-sphere topology. They are characterised by existence of a smooth past Cauchy horizon and, with the exception of certain singular cases, they also develop a regular future Cauchy horizon. Several examples of exact solutions were previously constructed, where the initial data (in form of the initial Ernst potentials) are polynomials of low degree. Here, we generalise to polynomial initial data of arbitrary degree. Utilising methods from soliton theory, we obtain a simple algorithm that allows us to construct the resulting Ernst potential with purely algebraic calculations. We also derive an explicit formula in terms of determinants, and we illustrate the method with two examples.

Microwave scattering properties of ice crystal particles during the melting process.

Ice crystal particles play an important role in the study of cloud resolution, climate models, and radiative forcing. During the melting process, significant changes occur in the microphysical properties of ice crystal particles, such as the ice phase state, morphology, and mixing state. This process further affects the scattering and radiation characteristics properties of ice crystal particles. In this study, we constructed a non-spherical and inhomogeneous particle model based on the melting process of ice crystal particles. The scattering properties of melting ice crystal particles under four selected microwave frequency bands (92 GHz, 220 GHz, 280 GHz, and 340 GHz) are investigated by using discrete dipole approximation (DDA) method. The influence of ice crystal content (ICC) and particle aspect ratio on the scattering properties of ice crystal particles under thin coating and medium coating conditions are emphasized. The results show that the melting process significantly affects the scattering properties of melting ice crystal particles in a frequency dependent manner. Additionally, even slight melting of ice crystal particles leads to drastic changes in their scattering properties. Furthermore, we found that the morphology of ice crystal nuclei has a significant impact on their scattering characteristics even at medium levels of melting degree. In summary, this study confirms that it is essential to consider morphology and inhomogeneous characteristics during the melting process for microwave detection of ice crystal particles. This research may have significant implications for studies related to detection and inversion techniques for ice crystal particles.

Bridging electronic and classical density-functional theory using universal machine-learned functional approximations.

The accuracy of density-functional theory (DFT) calculations is ultimately determined by the quality of the underlying approximate functionals, namely the exchange-correlation functional in electronic DFT and the excess functional in the classical DFT formalism of fluids. For both electrons and fluids, the exact functional is highly nonlocal, yet most calculations employ approximate functionals that are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations show promise in advancing applications of both electronic and classical DFTs, but so far these two distinct research areas have implemented disparate approaches with limited generality. Here, we formulate a universal ML framework and training protocol to learn nonlocal functionals that combine features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this new approach for several 1D and quasi-1D problems and demonstrate that functionals with exactly the same hyperparameters achieve excellent accuracy for a diverse set of systems, including the hard-rod fluid, the inhomogeneous Ising model, the exact exchange energy of electrons, the electron kinetic energy for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to approximate exact 3D functionals spanning electronic and classical DFTs.

More than one landslide per road kilometer – surveying and modeling mass movements along the Rishikesh–Joshimath (NH-7) highway, Uttarakhand, India

Abstract. The rapidly expanding Himalayan road network connects rural mountainous regions. However, the fragility of the landscape and poor road construction practices lead to frequent mass movements alongside roads. In this study, we investigate fully or partially road-blocking landslides along National Highway (NH-7) in Uttarakhand, India, between Rishikesh and Joshimath. Based on an inventory of >300 landslides along the ∼250 km long corridor following exceptionally high rainfall during September and October 2022, we identify the main controls on the spatial occurrence of mass-movement events. Our analysis and modeling approach conceptualizes landslides as a network-attached spatial point pattern. We evaluate different gridded rainfall products and infer the controls on landslide occurrence using Bayesian analysis of an inhomogeneous Poisson process model. Our results reveal that slope, rainfall amounts, lithology and road widening are the main controls on landslide occurrence. The individual effects of aggregated lithozones are consistent with previous assessments of landslide susceptibilities of rock types in the Himalayas. Our model spatially predicts landslide occurrences and can be adapted to other rainfall scenarios, thus having potential applications for efficiently allocating efforts for road maintenance. To this end, our results highlight the vulnerability of the Himalayan road network to landslides. Climate change and increasing exposure along this pilgrimage route will likely exacerbate landslide risk along the NH-7 in the future.

Model for random atmospheric inhomogeneities in engine noise auralization

Modelling the impact of atmospheric turbulence is not often encountered in aircraft noise auralizations despite its relevance to human-ear perception. As sound waves propagating through turbulent media undergo modulations, observable in phase and amplitude fluctuations, the plausibility of aircraft noise auralizations is increased by taking this effect into account. This paper presents an extension of a method first developed by Rietdijk et al., for modelling these fluctuations for spherical sound waves travelling through randomly inhomogeneous media. The extensions of the method presented in this paper are: (1) Height-dependent von Kármán spectra are implemented to model slanted or vertical sound propagation. (2) An overlap-add-method is introduced to model a moving sound source when height-dependent changes of turbulence characteristics are considered. (3) Easier to measure input parameters for the (meteorological) conditions are implemented, like e.g. the day time or relative humidity. The method is integrated into a global framework dedicated to engine noise simulation, propagation and auralization, developed and validated by the German Aerospace Center (DLR). A good match with measured functions of phase and amplitude fluctuations are observed, as well as realistic reproduction of spectrograms, time signals and the psychoacoustic fluctuation strength of the auralizations with respect to real flyovers.

Inhomogeneity effects on earthquake fault events.

We present a detailed analysis of the dynamical behavior of an inhomogeneous Burridge-Knopoff model, a simplified mechanical model of an earthquake. Regardless of the size of seismic faults, a soil element rarely has a continuous appearance. Instead, their surfaces have complex structures. Thus, the model we suggest keeps the full Newtonian dynamics with inertial effects of the original model, while incorporating the inhomogeneities of seismic fault surfaces in stick-slip friction force that depends on the local structure of the contact surfaces as shown in recent experiments. The numerical results of the proposed model show that the cluster size and the moment distributions of earthquake events are in agreement with the Gutenberg-Richter law without introducing any relaxation mechanism. The exponent of the power-law size distribution we obtain falls within a realistic range of value without fine tuning any parameter. On the other hand, we show that the size distribution of both localized and delocalized events obeys a power law in contrast to the homogeneous case. Thus, no crossover behavior between small and large events occurs.

Minisuperspace description for inhomogeneous cosmological models and the role of the Lie symmetries

We explore the application of Lie symmetries to simplify the gravitational field equations of inhomogeneous cosmology. By employing these symmetries, we demonstrate the construction of a point-like Lagrangian and establish the existence of a minisuperspace description. Finally we show how the Lie symmetries can be applied to construct new solutions for the Wheeler-DeWitt equation.

Inhomogeneous Fluid Transport Modeling in Dual-Scale Porous Media Considering Fluid-Solid Interactions.

Dynamics of fluid transport in ultratight reservoirs such as organic-rich shales differ from those in high-permeable reservoirs due to the complex nature of fluid transport and fluid-solid interaction in nanopores. We present a multiphase multicomponent transport model for primary production and gas injection in shale, considering the dual-scale porosity and intricate fluid-solid interactions. The pore space in the shale matrix is divided into macropores and nanopores based on pore size distribution. We employ density functional theory (DFT) to account for fluid-solid interactions and to compute the inhomogeneous fluid density distribution and phase behavior within a dual-scale matrix. The calculated fluid thermodynamic properties and transmissibility values are then integrated into the multiphase multicomponent transport model grounded in Maxwell-Stefan theory to simulate primary oil production from and gas injection into organic-rich shales. Our findings highlight DFT's adeptness in detailing the complex fluid inhomogeneities within nanopores─a critical concept that a cubic equation of state does not capture. Fluids within pores are categorized into confined and bulk states, restricted by a threshold pore width of 30 nm. Different compositions of fluid mixtures are observed in macropores and nanopores: heavier hydrocarbon components preferentially accumulate in nanopores due to their strong fluid-solid interactions. We utilize the developed model to simulate hydrocarbon production from an organic-rich shale matrix as well as CO2 injection into the matrix. During primary hydrocarbon production, strong fluid-solid interactions in nanopores impede the mobility of heavy components in the near-wall region, leading to their confinement. Consequently, heavy components mostly remain within the nanopores in the shale matrix during primary hydrocarbon production. During the CO2 injection process, the injected CO2 alters fluid composition within macropores and nanopores, promoting fluid redistribution. Injected CO2 engages in competitive fluid-solid interactions against intermediate hydrocarbons, successfully displacing a considerable number of these hydrocarbons from the nanopores.

Modelling Salmonella Typhi in high-density urban Blantyre neighbourhood, Malawi, using point pattern methods

Salmonella Typhi is a human-restricted pathogen that is transmitted by the faecal–oral route and causative organism of typhoid fever. Using health facility data from 2016 to 2020, this study focuses on modelling the spatial variation in typhoid risk in Ndirande township in Blantyre. To pursue this objective, we developed a marked inhomogeneous Poisson process model that allows us to incorporate both individual-level and environmental risk factors. The results from our analysis indicate that typhoid cases are spatially clustered, with the incidence decreasing by 54% for a unit increase in the water, sanitation, and hygiene (WASH) score. Typhoid intensity was also higher in children aged below 18 years than in adults. However, our results did not show evidence of a strong temporal variation in typhoid incidence. We also discuss the inferential benefits of using point pattern models to characterise the spatial variation in typhoid risk and outline possible extensions of the proposed modelling framework.

Electromagnetic transmission of two-dimensional inhomogeneous plasma photonic crystal.

A 2D tunable plasma photonic crystal (PPC) was constructed and implemented experimentally over a frequency range of 1GHz-12GHz within the electromagnetic spectrum. The PPC was simulated using an inhomogeneous model of a plasma tube based on microwave diagnostics and numerical simulations. The simulation results were found to be in good agreement with the experimental results. The data indicates that for TM polarization, localized plasmons will be excited at various positions within the tube, which does not rely on an interface with the medium, resulting in a broad forbidden band due to plasma inhomogeneity. The bandwidth of this band is consistent with the plasma frequency range. Furthermore, a lattice resonance band is observed, which is related to the incident angle. The cutoff effect of inhomogeneous PPC for TE polarization can be predicted by averaging the plasma parameters. The structure or plasma parameters can be adjusted to tune all the bands mentioned above. These findings can be used as a reference for applications in communication and microwave devices, and could potentially be utilized as a diagnostic tool for plasma parameters.

Scaling limit of the ground state Bethe roots for the inhomogeneous XXZ spin - [formula omitted] chain

It is known that for the Heisenberg XXZ spin - 12 chain in the critical regime, the scaling limit of the vacuum Bethe roots yields an infinite set of numbers that coincide with the energy spectrum of the quantum mechanical 3D anharmonic oscillator. The discovery of this curious relation, among others, gave rise to the approach referred to as the ODE/IQFT (or ODE/IM) correspondence. Here we consider a multiparametric generalization of the Heisenberg spin chain, which is associated with the inhomogeneous six-vertex model. When quasi-periodic boundary conditions are imposed the lattice system may be explored within the Bethe Ansatz technique. We argue that for the critical spin chain, with a properly formulated scaling limit, the scaled Bethe roots for the ground state are described by second order differential equations, which are multi-parametric generalizations of the Schrödinger equation for the anharmonic oscillator.

An analytical treatment to spatially inhomogeneous population balance model

In modern liquid–liquid contact components, there is an increasing use of droplet population balance models. These components include differential and completely mixed contractors. These models aim to explain the complex hydrodynamic processes occurring in the dispersion phase. The hydrodynamics of these interacting dispersions include droplet breaking, coalescence, axial dispersion, and both entry and exit events. The resulting equations for population balance are represented as integro-partial differential equations, which rarely have analytical solutions, especially when spatial dependency is apparent. Consequently, the pursuit predominantly lies in seeking numerical solutions to resolve these complex equations. In this study, we have devised analytical solutions for inhomogeneous breakage and coagulation by employing the population balance equation (PBEs) applicable to both batch and continuous flow systems. The innovative approaches for solving PBEs in these systems leverage the Adomian decomposition method (ADM) and the homotopy analysis method (HAM). These semi-analytical methodologies effectively tackle the significant challenges related to numerical discretization and stability, which have often plagued previous solutions of the homogeneous PBEs. Our findings across all test examples demonstrate that the approximated particle size distributions utilizing these two methods converge to the analytical solutions continuously.

An amplitude-dependent nonlinear approach for vortex-induced vibration evaluation of long-span bridges with inhomogeneous cross-sections

In the design of modern long-span bridges, inhomogeneous cross sections are increasingly used to meet various requirements, posing challenges in the investigation of vortex-induced vibration (VIV). This paper introduces a nonlinear approach with a focus on amplitude dependency in VIV for inhomogeneous bridges. It presents an inhomogeneous vortex-induced force model with amplitude-dependent parameters to capture spanwise variations in aerodynamics. These parameters are identified through multiple sectional wind tunnel tests. VIV amplitudes are determined by searching for solutions under the zero-damping condition for VIV. An illustrative bridge with an inhomogeneous fairing design is employed as an engineering application. The approach is rigorously validated with experimental data and applied to assess the prototype VIV behavior of the bridge with different fairing lengths. An optimal fairing length, constituting 40% of the main girder length in the mid-span, is identified to strike a balance between VIV performance and material usage. Discussion for the prediction results provides insights into the effects of fairing length inhomogeneity on VIV. In practice, deploying fairings in the large mode shape sections of the main girder achieves VIV mitigation comparable to a full-span installation.

Stochastic occupancy modeling for spaces with irregular occupancy patterns using adaptive B-Spline-based inhomogeneous Markov Chains

This paper presents a discrete time, discrete state-space in-homogeneous Markov Chains model for stochastic occupancy modeling in spaces with irregular occupancy patterns. The goal of the model is to provide accurate predictions of occupancy numbers, enabling appropriate actions to be taken for HVAC system to maintain optimal indoor environment. The proposed Markov Chain model incorporates time in-homogeneity by coupling the time-varying model parameters using a Periodic B-Spline expansion with adaptive knots, which effectively captures patterns in occupancy activity. This method optimizes the distribution of knots based on specific occupancy characteristics observed in different types of rooms. To evaluate the effectiveness of the proposed method, six months of occupancy data collected from a meeting room are utilized. A comprehensive comparison is conducted between the proposed adaptive B-Spline method and other approaches, including the counting method and uniform B-Spline method. The comparison considers both model accuracy and complexity, using metrics such as the Akaike Information Criterion and Bayesian Information Criterion. Results indicate that the proposed model achieves more accurate predictions with fewer model parameters compared to other methods. These forecasts are particularly useful in optimizing the control of HVAC systems, where accurate predictions of future occupancy numbers are essential.