Continuum Systems Research Articles

Migration patterns of phthalic acid esters from mulch plastic film in the soil-plant-atmosphere continuum system.

Plastic film mulching is an important agricultural practice, but its release of phthalic acid esters (PAEs) poses threats to soil and human health. However, the migration patterns of PAEs during the lifecycle of mulch plastic film (MPF) remain unclear. This study aims to explore the temporal patterns of release of PAEs during the MPF's lifecycle and evaluate the migration patterns of PAEs from MPF in the soil-plant-atmosphere continuum (SPAC) system through pot experiments and model simulations. The results reveal that during the mulching period, 44.90-56.71% of the PAEs released went into the atmosphere and 14.97-18.90% into the soil, while during the residual film period, 24.39-40.13% were slowly released into the soil. Elevated soil water content increased maize transpiration rates, leading to higher concentrations of PAEs in roots, stems, and fruits, but lower concentrations in leaves. In 2020, the estimated total release of PAEs from MPF in northwest China amounted to 35.42 tons. Notably, PAEs predominantly accumulated in the soil, with minimal accumulation in plant tissues. Moreover, PAEs were primarily removed through degradation. Our results elucidate the migration patterns of PAEs from MPF in the SPAC system, facilitating the evaluation of PAE pathways into the human food chain.

Harmonic flow-field representations of quantum bits and gates

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

Maximizing the toughness of polymer nanocomposites based on the radial strength of carbon nanotubes

Similarity in the mechanical properties of a matrix and an inclusion is key to designing tough nanocomposites. Matching the matrix and inclusions with similar mechanical strengths prevents stress perturbation at the interface, enabling nanocomposites to withstand higher loads as a homogeneous material. We tabulate the chirality-dependent radial buckling properties of multi-walled carbon nanotubes (MWCNTs) and present a design methodology for providing optimal strengthening properties for poly(p-phenylene terephthalamide) matrices. The structural orientation effect of the aromatic rings of polymer chains surrounding MWCNTs provides a strong support against transverse loading. The effect of the interfacial area of different materials on the toughness of the entire continuum system is characterized through a nonlinear finite element model. MWCNT buckling and polymer yielding occur simultaneously under conditions selected by the proposed methodology, thereby maximizing the reinforcing effect of the nanocomposites by creating a continuous stress field at the interface.

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

A discrete-to-continuum model for the human cornea with application to keratoconus.

We introduce a discrete mathematical model for the mechanical behaviour of a planar slice of human corneal tissue, in equilibrium under the action of physiological intraocular pressure (IOP). The model considers a regular (two-dimensional) network of structural elements mimicking a discrete number of parallel collagen lamellae connected by proteoglycan-based chemical bonds (crosslinks). Since the thickness of each collagen lamella is small compared to the overall corneal thickness, we upscale the discrete force balance into a continuum system of partial differential equations and deduce the corresponding macroscopic stress tensor and strain energy function for the micro-structured corneal tissue. We demonstrate that, for physiological values of the IOP, the predictions of the discrete model converge to those of the continuum model. We use the continuum model to simulate the progression of the degenerative disease known as keratoconus, characterized by a localized bulging of the corneal shell. We assign a spatial distribution of damage (i.e. reduction of the stiffness) to the mechanical properties of the structural elements and predict the resulting macroscopic shape of the cornea, showing that a large reduction in the element stiffness results in substantial corneal thinning and a significant increase in the curvature of both the anterior and posterior surfaces.

Elastic wave spin and unidirectional routing in thin rod systems

The unusual topology of elastic waves in continuum systems has been recently uncovered. Prominently, the spin of Rayleigh-Lamb waves has been experimentally observed and used to achieve the unidirectional wave propagation. In this work, the elastic wave spin in thin rod systems is theoretically predicted and experimentally observed, for all the three basic wave modes, i.e., the zero-order flexural, longitudinal and torsional modes. By elaborately building up the subwavelength chiral sources, the spin-momentum locking has been achieved for these three modes within broad frequency range. Interestingly and surprisingly, the spin-momentum locking occurs for flexural and longitudinal modes in both circular and non-circular thin rods; the spin-momentum locking for torsional modes only exits in non-circular thin rods, due to the warping effect in non-circular cross-section rods. Our results open up the door for elastic wave spin in thin rod systems, and provide general tips for the research on basic modes in diverse thin rods, based on either the continuum media or the artificial metamaterials in future.

Entanglement Hamiltonian for inhomogeneous free fermions

We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. In particular, we consider a lattice with a linear, as well as a continuum system with a quadratic potential. It is shown that, for both models, conformal field theory predicts a Bisognano–Wichmann form for the entanglement Hamiltonian of a half-infinite system. Furthermore, despite being nonrelativistic, this result is inherited by our models in the form of operators that commute exactly with the entanglement Hamiltonian. After appropriate rescaling, they also yield an excellent approximation of the entanglement spectra, which becomes asymptotically exact in the bulk of the trapped Fermi gas. For the gradient chain, however, the conformal result is recovered only after taking a proper continuum limit.

Long-Term Impacts on Clinical Practice Along the HIV Care Continuum: Addressing Workforce Gaps Through a Clinician Scholars Program.

The Clinician Scholars Program (CSP) was designed to expand the HIV care workforce by improving the clinical capacity of clinicians in underserved areas. This evaluation assessed program participants' long-term practice changes and system changes. The year-long program combined mentoring, training, and on-site clinical observation. Qualitative interviews (N = 46) were conducted with Scholars at least 2 years following CSP, supplemented by a 2023 survey. Multiple coders analyzed transcripts using open coding. Thematic analysis explored practice changes and efforts to move patients along the HIV care continuum. Findings indicate positive long-term impacts of CSP regarding the HIV care continuum and care system engagement. Over 90% of Scholars remained working in HIV care, with 75% maintaining or increasing patient loads and 72% making changes to their clinical practice. This training model appears to enhance care along the HIV care continuum and may be adaptable to other contexts that address complex chronic conditions.

Equilibrium in the Computing Continuum through Active Inference

Computing Continuum (CC) systems are challenged to ensure the intricate requirements of each computational tier. Given the system’s scale, the Service Level Objectives (SLOs), which are expressed as these requirements, must be disaggregated into smaller parts that can be decentralized. We present our framework for collaborative edge intelligence, enabling individual edge devices to (1) develop a causal understanding of how to enforce their SLOs and (2) transfer knowledge to speed up the onboarding of heterogeneous devices. Through collaboration, they (3) increase the scope of SLO fulfillment. We implemented the framework and evaluated a use case in which a CC system is responsible for ensuring Quality of Service (QoS) and Quality of Experience (QoE) during video streaming. Our results showed that edge devices required only ten training rounds to ensure four SLOs; furthermore, the underlying causal structures were also rationally explainable. The addition of new types of devices can be done a posteriori; the framework allowed them to reuse existing models, even though the device type had been unknown. Finally, rebalancing the load within a device cluster allowed individual edge devices to recover their SLO compliance after a network failure from 22% to 89%.

Numerical Validation of Fully Coupled Nonlinear Seismic Soil–Pile–Structure Interaction

While many researchers have broadly studied soil–structure interaction (SSI) problems to comprehend SSI effects on the overall system’s behavior, some critical numerical modeling issues have not been sufficiently investigated to achieve the most accurate results. Furthermore, most scholars have not provided detailed explanations of the validation process for their proposed numerical models. Modeling pile foundations in a three-dimensional (3D) continuum system in a fully coupled manner is often challenging for engineers who do not specialize in structural and geotechnical earthquake engineering, as it can be very time-consuming and complicated. Therefore, this work aims to validate a finite element model of seismic soil–pile–structure interaction (SPSI) problems in a continuum soil body by comparing the results of numerical models with those of a centrifuge test and computed numerical simulations available in the literature. In this regard, several newly developed elements in OpenSees (Version 3.6.0) are tested. The results of this work demonstrate a closer alignment with prior experimental research findings. It is believed that providing detailed numerical modeling and validation processes will assist researchers in better understanding crucial issues in modeling soil–pile–structure interaction problems.

StructMesh: A storage framework for serverless computing continuum

Computing continuum is becoming a solution for organizations to process and analyze data for supporting decision-making processes. In this context, serverless paradigm is arising as a solution to manage continuum computing. However, the management of data storage still represents an obstacle for integrating continuum computing and serverless paradigms into a single solution, as this has to be performed transparently to users through multiple infrastructures. This paper presents StructMesh, a storage framework for serverless continuum systems. This framework is based on a processing plane where functions are managed as patterns, and a data plane based on storage meshes that represent maps of storage resources available in a given infrastructure. The logical interconnection of storage meshes enables organizations to integrate storage resources into a single unified storage service, which creates data exchange channels for continuum processing throughout multiple infrastructures. These meshes include load-balancing and data allocation/location algorithms for transparently and automatically managing the inputs/outputs of functions throughout these channels, as well as non-functional requirement schemes for organizations to manage sensitive data. We developed a framework prototype that harmonizes processing serverless functions with storage functions for building serverless pipeline services. A case study was conducted by using these services for processing meteorological and earth observation data throughout multiple infrastructures. The evaluation revealed the efficiency of StructMesh when managing data through fog and cloud infrastructures. It also showed the feasibility of StructMesh to create and enable continuum data exchange channels for serverless pipelines.

Incorporating canopy radiation enhances the explanation of maize yield change and increases model accuracy under film mulching

Plastic film mulching (PM) has been extensively used to increase crop yields in dryland regions in China. However, the impact of differently colored PM on crop radiation utilization due to the optical properties of the underlying PM surfaces remains unclear. We conducted a two-year field experiment in northwest China to evaluate the dynamics of photosynthetically active radiation interception and absorption (fIPAR and fAPAR), as well as the radiation use efficiency for intercepted and absorbed radiation (RUEi and RUEa) during spring maize (Zea mays L.) growth periods. Two fertilization levels (high and low) and 3 PM treatments (transparent film, black film, and no film) were considered in this study. We also developed empirical regression functions to calculate canopy fAPAR, accounting for both canopy and underlying surface characteristics. Furthermore, we used canopy absorption radiation to drive the Soil-Plant-Atmosphere Continuum System (SPACSYS) model to simulate maize biomass and yield. We found that transparent film mulching (TM) exhibited higher fIPAR and fAPAR than black film mulching and no mulching (CK). TM had an increase of RUEi and RUEa by 10.6% and 9.7%, respectively, relative to CK, resulting in a 9.3–19.2% increase in maize yield and a 25.8–30.2% increase in the partial factor productivity of nitrogen. These increases were mainly attributed to the increased relative chlorophyll content, net photosynthesis rate, and extended grain-filling period under TM. We found that the modified radiation input increased the accuracy of the SPACSYS model in simulating maize biomass and yield. We underscore the importance of using TM in dryland areas to increase crop yields and advocate for incorporating canopy radiation data into crop models, especially in agricultural regions where plastic film mulching is used, to enhance the accuracy of yield simulations.

Discrete-to-continuum models of pre-stressed cytoskeletal filament networks

We introduce a mathematical model for the mechanical behaviour of the eukaryotic cell cytoskeleton. This discrete model involves a regular array of pre-stressed protein filaments that exhibit resistance to enthalpic stretching, joined at cross-links to form a network. Assuming that the inter-cross-link distance is much shorter than the length scale of the cell, we upscale the discrete force balance to form a continuum system of governing equations and deduce the corresponding macroscopic stress tensor. We use these discrete and continuum models to analyse the imposed displacement of a bead placed in the domain, characterizing the cell rheology through the force–displacement curve. We further derive an analytical approximation to the stress and strain fields in the limit of small bead radius, predicting the net force required to generate a given deformation and elucidating the dependency on the microscale properties of the filaments. We apply these models to networks of the intermediate filament vimentin and demonstrate good agreement between predictions of the discrete, continuum and analytical approaches. In particular, our model predicts that the network stiffness increases sublinearly with the filament pre-stress and scales logarithmically with the bead size.

Interpretable machine learning of SPAC system via a mechanism-assisted gaussian process group: Representation of the system mechanism by data

Traditional models of the soil-plant-atmosphere continuum (SPAC) system are physics-based and their practical application has been hindered by issues of high parameterization, prior structural bias, and costly running. In this paper, we developed a machine learning modelling method based on the Gaussian process (GP) to avoid these difficulties of traditional modelling. At the same time, shortcomings of conventional machine learning in terms of interpretability and mechanism representation were addressed. The innovative method consisted of structuring a local GP group framework and improving kernel functions used in each local GP. The resultant model was endowed with advanced capacities, including representing interplays between subprocesses within the complex SPAC system, representing nonstationary subprocess dynamics caused by crop growth stage shifts, as well as automatically interpreting key low-order input interactions and dominant input variables for each subprocess. The performance of our model was examined on synthetic SPAC system datasets that covered three different soil conditions. Results demonstrated that its interpretations regarding subprocess mechanisms were robust across different soil conditions and consistent with domain knowledge. Compared to a conventional global GP model and two deep learning models (DNN and LSTM), our model performed significantly better not only in regular prediction experiments but also in generalization experiments that required models to be transferred across different conditions. Our study suggested that it is promising to enable a machine learning model interpretable by improving its feature representation function. For machine learning modelling of complex systems like the SPAC, it may be more important to enhance the model’s mechanism representation capability than simply using deeper networks.

A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory

In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this setting, we derive a representation formula for the solution of the Dyson equation in terms of an operator version of the Casida matrix. While the Casida matrix is well-known in the physics literature, its general formulation as an (unbounded) operator in the N-body wavefunction space appears to be new. Moreover, we derive several consequences of the solution formula obtained here; in particular, we discuss the stability of the solution and characterise the maximal meromorphic extension of its Fourier transform. We then show that for adiabatic approximations satisfying a suitable compactness condition, the maximal domains of meromorphic continuation of the initial DDRF and the solution of the Dyson equation are the same. The results derived here apply to widely used adiabatic approximations such as (but not limited to) the random phase approximation and the adiabatic local density approximation. In particular, these results show that neither of these approximations can shift the ionisation threshold of the Kohn–Sham system.

Effects of grazing and climate change on aboveground standing biomass and sheep live weight changes in the desert steppe in Inner Mongolia, China

CONTEXTThe Stipa breviflora desert steppe ecosystem is fragile and sensitive to climate change and grazing disturbance. Previous studies have reported the effects of climate change and grazing on aboveground standing biomass of the plant community and sheep live weight, however, the interaction between climate change and grazing remains unclear. Process models have become ideal tools for the evaluation of the effects of grazing management practices under climate change. OBJECTIVEWe used the Soil-Plant-Atmosphere Continuum System (SPACSYS) model to investigate aboveground standing biomass and the live weight of sheep in the desert steppe of Inner Mongolia under future climate change scenarios and different grazing management. The results will be used to inform adaptive management strategies. METHODSThe grazing experiment consisted of four treatments: no grazing (0 sheep ha−1 half year−1), light stocking rate (0.91 sheep ha−1 half year−1), moderate stocking rate (1.82 sheep ha−1 half year−1), and high stocking rate (2.71 sheep ha−1 half year−1). We used observed data on soil temperature, soil volumetric water content, changes to sheep live weight, and aboveground standing biomass of plant community to provide parameterization and validation for the SPACSYS model. We then predicted aboveground standing biomass of the plant community and sheep live weight changes for different grazing management under three representative concentration pathways (RCP) scenarios (RCP 2.6, RCP 4.5, and RCP 8.5) from 2021 to 2100. RESULTS AND CONCLUSIONSModerate and high stocking rates decreased aboveground standing biomass and sheep live weight changes more than the light stocking rate. A light stocking rate can maintain higher aboveground standing biomass and sheep live weight as well as meet production requirements. Therefore, a light stocking rate is a potentially effective management approach to improve food production security and combat global climate change in the desert steppe. SIGNIFICANCEThe model can inform management strategies for grazing in the desert steppe under climate change, supporting efforts to maintain the stability of the steppe ecosystem and increase economic benefits, while also providing a theoretical basis for adaptive management in the desert steppe.

On Causality in Distributed Continuum Systems

On Causality in Distributed Continuum Systems

Minimal reaction schemes for pattern formation.

We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.

Intent-driven orchestration of serverless applications in the computing continuum

Following the emergence of Internet of Things (IoT) and edge computing technologies and the development of distributed applications with strict Quality of Service (QoS) requirements, a transition is underway from centralized computing models to distributed computing continuum systems. The latter provide abstractions of the available resources, while they lead to the development of orchestration mechanisms with increased distributed intelligence and autonomy characteristics. These characteristics make the computing continuum suitable for managing serverless computing applications, considering their loose coupling with the resources and the need for reactiveness and efficiency to serve dynamic workloads in the edge and cloud part of the infrastructure. This paper presents an intent-based approach for the orchestration of a function chain over an edge and cloud infrastructure. We propose a Reinforcement Learning (RL) based autoscaling method that incorporates a reward function that aims to provide optimal utilization of resources and timely autoscaling of the functions, taking advantage of methods for workload prediction. Based on a high-level intent, the proposed optimization problem dictates the scheduling of the functions, minimizing the communication overhead and transformation cost while also considering the energy efficiency of the infrastructure. The proposed solution is evaluated with other state-of-the-art techniques for autoscaling and scheduling of serverless functions in a small edge infrastructure. Our solution provides 1.52% QoS violations with a slight increase in the deployed resources, while also significantly reducing the total cost and power consumption for the deployment of the function chain.

Active control of an electromagnetically induced transparency analogue in a coupled dual bound states in the continuum system integrated with graphene.

Electronically induced transparency (EIT) is a coherent optical phenomenon that induces interference within atoms, allowing certain specific frequencies of light to pass through atomic media without being absorbed. However, EIT systems face challenges related to narrow transparency windows and precise control of slow light. We propose an interference structure based on a coupled dual bound states in the continuum (BIC) system to emulate the EIT-like effect. By integrating quasi-BIC (bright mode) with BIC (dark mode), our design successfully achieves an EIT-like effect in a narrow bright mode with a full width at half maximum (FWHM) of less than 1 nm. Its notable features are the bright mode's wide tunability achieved through structural parameter adjustment and a significant group delay of up to 14.43 ps. Additionally, integrating graphene into the BIC structure introduced a form of active tunability akin to the EIT-like effect. We numerically calculate the coupling structure, and its intrinsic mechanism is analyzed. Analysis based on coupled-mode theory confirms that this active modulation primarily stems from changes in the BIC structure's loss. Due to its special frequency selectivity and insensitivity to the polarization of the light source, this narrow-band EIT-like structure is particularly suitable for high-precision optical sensing and spectroscopy. The significant group delay of this structure enhances the interaction between light and matter, improving the accuracy and efficiency of optical signal control and data transmission, opening up new avenues for slow light applications and making significant progress in the development of active tunable optical switches and modulators.