Green Function Research Articles

Green covalent surface functionalization of carbon nanofillers and hybridization to improve the thermal and electrical properties of RTV SR nanocomposites

Green covalent surface functionalization of carbon nanofillers and hybridization to improve the thermal and electrical properties of RTV SR nanocomposites

Improvement of Seismic Noise Cross-correlation Function by Phase-velocity Probability Density Selection

TThe noise cross-correlation function (NCF) derived from continuous seismic records approximates the Green's Function (GF) of the far-field surface wave, which is crucial for S-wave velocity tomography. A critical step is stacking short-term NCFs over extended periods to improve the signal-to-noise ratio (S/N) and enhance the imaging quality of seismic data. However, incoherent noise significantly affects the accuracy of NCF calculations. Moreover, strong directional sources in the wavefield pose a challenge to conventional linear or phase-weighted stacking (PWS), often leading to overestimates of surface-wave phase velocity due to unresolved azimuthal effects. Selecting stationary phase zone (SPZ) data and correcting surface wave propagation paths based on source orientation requires a 2D array setup, which imposes stringent layout constraints. To address these challenges, we propose a novel data selection workflow for a 1D linear array based on the probability density distribution of surface-wave phase velocity. Firstly, we divide the noise data into different frequency bands and calculate the probability density curve of the phase velocity distribution for each frequency band. Then, based on the differences in phase velocities between SPZ data, directional source data, and incoherent noise, we select the probability density segments of SPZ data in each frequency band for stacking, effectively reducing the impact of incoherent noise and strong directional sources. The typical synthetic data and distributed acoustic sensing (DAS) field data examples demonstrate that the proposed workflow significantly improves the S/N in NCF and increases the useful bandwidth of the surface- waves dispersion curve, which furnishes reliable dispersion curve and waveform data, thereby facilitating subsequent S-wave velocity tomography.

The spin-wave energy spectrum and transition temperature of the two-dimensional VSe2-like: a retarded Green’s function method study

Based on the recent discovery of intrinsic magnetism in monolayer films VSe2, we have constructed a two-dimensional (2D) Heisenberg model incorporating the 1Tand 2Hstructures. These configurations consist of three layers: the upper and lower surface layers and a middle layer. Using the retarded Green's function method, we investigate the spin-wave energy spectrum, spin-wave density of states, and transition temperature of the system. It is found that in the 2Hstructure, the spin-wave energy spectrum of the system exhibits three direct energy gaps, with one branch being independent of the wave vector. Further analysis shows that at this constant energy, a particular surface state emerges in the 2Hstructure. In contrast, the spin-wave energy spectrum in the 1Tstructure features only two energy gaps-one direct energy gap1 and one indirect energy gap3-without forming a unique surface state. Single-ion anisotropy and interlayer interactions between the upper and lower surface layers influence the energy gaps in the spin-wave energy spectrum and the system's transition temperature. This theoretical work sheds light on forming particular surface states in monolayer 2Hstructure magnetic materials. It provides crucial theoretical support for designing and fabricating next-generation low-dimensional magnetic random-access memory.

Molecular conductance calculations of single-molecule junctions using projection-based density functional embedding.

Single-Molecule Junctions (SMJs) are key platforms for the exploration of electron transport at the molecular scale. In this study, we present a method that employs different exchange-correlation density functionals for the molecule and the lead domains in an SMJ, enabling the selection of the optimal one for each part. This is accomplished using a formally exact projection-based density-functional theory (DFT-in-DFT) embedding technique combined with the non-equilibrium Green's function method to predict zero-bias conductance. The effectiveness of this approach is illustrated through transport calculations on SMJs with benzene-1,4-diamine and its tetramethylated and tetrafluorinated variants, using the CAM-B3LYP range-separated hybrid functional for the embedded molecule and the Perdew-Burke-Ernzerhof (PBE) functional for the electrodes. The findings indicate a substantial improvement in the accuracy of the predicted zero-bias conductance compared to traditional modeling using the PBE functional across the entire system. The causes for the noted improvement are demonstrated through the examination of alterations in the energy levels of the embedded molecule, along with variations in the electrode-molecule interactions.

Computational simulation of graphene/h-BN nanopores for single-molecule herbicide sensing.

The growing world population and climate change are key drivers for the increasing pursuit of more efficient and environmentally-safe food production. In this scenario, the large scale use of herbicides demands the development new technologies to control
and monitor the application of these compounds, due to their several environmental and health-related problems. Motivated by all these issues, in this work, a hybrid graphene/boron nitride nanopore is explore to detect/identify herbicide molecules (Glyphosate, AMPA, Diuron, and 2,4-D). Solid-state nanopores based on 2D materials have been widely explored as novel generation sensors capable of single-molecule resolution. The present investigation combines the density functional theory (DFT) and non-equilibrium Green's function (NEGF) method to assess the interaction of each herbicide with the nanopore and how its interaction modulates the device's electronic
transport properties. The device's sensitivity spreads from 9.0 up to 27.0% when probed at different gate voltage values. Overall, the proposed device seems to be sensitive and selective to be considered as a promising single-molecule herbicide sensor.

Thermal Analysis of Electromagnetic Induction Heating for Cylinder-Shaped Objects.

Induction heating is one of the cleanest and most efficient methods for heating materials, utilizing electromagnetic fields induced through AC electric current. This article reports an analytical solution for transient heat transfer in a three-dimensional (3D) cylindrical object under induction heating. A simplified form of Maxwell's equations is solved to determine the heat generation inside the cylinder by calculating the current density distribution within the body. The temperature within the solid is found from the solution of the unsteady heat equation based on Green's function. Owing to multiple spatial dimensions and time, a separation of variables technique is used to find Green's function. In addition, an innovative algorithm is proposed to take care of the variable material properties in analytical treatment. The analytical solution for temperature is verified with the data obtained from experiments for identical operating conditions. The analytical solution is used to study the impact of heat transfer coefficient and input AC current frequency and amplitude during transient heat diffusion. Our analytical solution suggests that the temperature-dependent material properties significantly affect the thermal response within the solid. Unlike many other conventional heating methods, the thermal boundary condition changes with time in induction heating, which makes our solution much more challenging.

Detection and distinction of amino acids and post-translational modifications with gold nanojunctions.

Amino acids are fundamental building blocks of proteins, playing critical roles in medical diagnostics, environmental monitoring, and biomarker identification. The development of nanoscale electronic sensors capable of single-amino-acid recognition has gained significant attention due to their potential for label-free, real-time detection. In this study, we investigate the electronic transport properties of amino acids in two gold-based nanodevices with distinct architectures: a gold nanojunction and a gold-capacitor system. Using density functional theory (DFT) in combination with nonequilibrium Green's function (NEGF) calculations, we explore the sensing mechanism and conductance variations induced by different amino acids, including select phosphorylated variants. Each device was assigned a reference amino acid, F (M), for a capacitor (nanojunction) to differentiate its conductance from other molecules. Our results reveal distinct conductance that enables amino acid classification based on their electronic signatures, demonstrating that molecular discrimination is primarily governed by conductance variations as a function of the binding energy differences. The nanojunction exhibited remarkable differentiation for the amino acids S, pS, Y, and pY, rendering it especially proficient in distinguishing between structurally analogous molecules. These findings highlight the strong potential of gold-based nanodevices for precise amino acid detection, paving the way for advancements in biosensing technologies, molecular diagnostics, and biomedical applications.

Output tracking problem for a class of 3-D hyperbolic PDEs

The output tracking problem (OTP) refers to the procedure of determining an input control that ensures the system output follows a specified trajectory. In this paper, we investigate the OTP for controlled systems governed by a class of 3-D hyperbolic partial differential equations (PDEs), aiming for an exact alignment between the system output and the desired trajectory. Utilizing backstepping techniques, semigroup theory, the Hahn-Banach theorem, Laplace transforms, and Green's functions, our approach begins by establishing the OTP solution as a bounded feedback law, with Green's functions allowing the solution of a Cauchy-Euler equation. This is followed by deriving a detailed formulation for the complete state of the corresponding control problem. Finally, the approach provides an explicit formula for the OTP solution, using the desired trajectory and the solutions of specific kernel PDEs.

Green knowledge production functions with latent group structures in the presence of human capital spillovers and fiscal policies

ABSTRACT The paper analyses the green knowledge production function with human capital spillovers in the context of OECD countries by using a latent group structure methodology, to address cross-country heterogeneity, in order to enrich evidence-based policymaking. In fact, the number of groups and the group membership are often unknown features in a dataset. These ‘unknowns’ are determined using a penalized regression technique, in the presence of cross-sectional dependence and nonstationarity. Substantial heterogeneity is unveiled and classified into distinctive groups with significant macroeconomic features. Modelling the green knowledge production function with latent-group structures thus reveals heterogeneous trends over green technologies patterns, with in addition Human capital and expenditure on research and development playing an important part as drivers. In an era of radical technological change and in front of the necessity to form solid coalitions to manage international public goods, the heterogeneity of countries and groups of agents is of extreme importance to better understand economic development paths, possibly correcting technology-driven divergences by national and supranational policy actions on innovation, training, environmental domains.

Twisting nanoporous graphene on graphene: electronic decoupling and chiral currents.

Nanoporous graphene (NPG), laterally bonded carbon nanoribbons, is a promising platform for controlling coherent electron propagation in the nanoscale. However, for its successful device integration NPG should ideally be on a substrate that preserves or enhances its anisotropic transport properties. Here, using an atomistic tight-binding model combined with nonequilibrium Green's functions, we study NPG on graphene and show that their electronic coupling is modulated as a function of the interlayer twist angle. At small twist angles (θ ≲ 10°), strong hybridization leads to substantial interlayer transmission and Talbot-like interference in the current flow on both layers. Besides, injected currents exhibit chiral features due to the twist-induced mirror-symmetry-breaking. Upon increasing the twist angle, the coupling is weakened and the monolayer electronic properties are restored. Furthermore, we predict spectroscopic signatures that allow to probe the twist-dependent interlayer coupling via scanning tunneling microscopy.

Predicting nonequilibrium Green's function dynamics and photoemission spectra via nonlinear integral operator learning

Abstract Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge.
We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs.
By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ 
where $N_t$ is the number of steps taken in a simulation, thereby
making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. 
Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. 
Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

Significant negative differential resistance and current limiting effects of cyclo[14]carbon-based molecular devices with graphene electrodes

Through tip-induced dehalogenation and retro-Bergman ring-opening reaction of fully chlorinated anthanthrene (C14Cl10), the cyclo[14]carbon (C14) was prepared. Owing to its distinctive physical properties, C14 holds the potential to serve as the core unit of functional electronic devices. Herein, the density functional theory combined with the non-equilibrium Green's function technique was used to investigate the electronic transport properties of molecular devices composed of C14 molecules and graphene electrodes, systematically. We find that molecular devices composed of polyynic and cumulenic structures of C14 exhibit a significant negative differential resistance effect and effective current limiting ability at low bias voltages, respectively. Moreover, by calculating and analyzing the transmission function and projected density of states under different biases, a reasonable explanation of those effects is provided.

Convergence analysis of positive solution for Caputo–Hadamard fractional differential equation

By deriving the expression of Green function and some of its special properties and establishing appropriate substitution and appropriate cone, the existence of unique iterative positive, error estimation, and convergence rate of approximate solution are obtained for singular p-Laplacian Caputo–Hadamard fractional differential equation with infinite-point boundary conditions. Nonlinearities involve derivative terms that make our analysis difficult in the course of this research, and we deal with the difficulty of derivative terms by making appropriate substitutions. An example is given to demonstrate the validity of our main results.

First Passage Percolation, Local Uniqueness for Interlacements and Capacity of Random Walk

The study of first passage percolation (FPP) for the random interlacements model has been initiated in Andres and Prévost (Ann Appl Probab 34(2):1846–1895), where it is shown that on Zd, d≥3, the FPP distance is comparable to the graph distance with high probability. In this article, we give an asymptotically sharp lower bound on this last probability, which additionally holds on a large class of transient graphs with polynomial volume growth and polynomial decay of the Green function. When considering the interlacement set in the low-intensity regime, the previous bound is in fact valid throughout the near-critical phase. In low dimension, we also present two applications of this FPP result: sharp large deviation bounds on local uniqueness of random interlacements, and on the capacity of a random walk in a ball.

Subdiffusion Equation with Fractional Caputo Time Derivative with Respect to Another Function in Modeling Superdiffusion.

Superdiffusion is usually defined as a random walk process of a molecule, in which the time evolution of the mean-squared displacement, σ2, of the molecule is a power function of time, σ2(t)∼t2/γ, with γ∈(1,2). An equation with a Riesz-type fractional derivative of the order γ with respect to a spatial variable (a fractional superdiffusion equation) is often used to describe superdiffusion. However, this equation leads to the formula σ2(t)=κt2/γ with κ=∞, which, in practice, makes it impossible to define the parameter γ. Moreover, due to the nonlocal nature of this derivative, it is generally not possible to impose boundary conditions at a thin partially permeable membrane. We show a model of superdiffusion based on an equation in which there is a fractional Caputo time derivative with respect to another function, g; the spatial derivative is of the second order. By choosing the function in an appropriate way, we obtain the g-superdiffusion equation, in which Green's function (GF) in the long time limit approaches GF for the fractional superdiffusion equation. GF for the g-superdiffusion equation generates σ2 with finite κ. In addition, the boundary conditions at a thin membrane can be given in a similar way as for normal diffusion or subdiffusion. As an example, the filtration process generated by a partially permeable membrane in a superdiffusive medium is considered.

Modelling noise H/V spectral ratio in a laterally inhomogeneous layered medium

SUMMARY Central to the task of seismic hazard assessment is the evaluation of potential amplifications due to site effects. The horizontal-to-vertical spectral ratio (HVSR) of ambient seismic noise (ASN) is a widespread measurement to assess the predominant soil frequency of a given site and estimate the wave velocities of the subsoil stratigraphy using inversion schemes. In practice, the inversions are currently made, assuming flat layers. In fact, HVSR measurements may show significant lateral and azimuthal changes due to the spatial variations of local geology, which can introduce uncertainties into the characterization of a site. This suggests the importance of considering detailed measurements of lateral and angular variations in layered settings. Inversion of soil properties at depth for horizontally layered media has become feasible assuming that ASN constitutes a diffuse field, that is, produced by equi-partitioned uniform illumination and/or by random sources and the ensuing multiple scattering by heterogeneities. Under the diffuse field assumption (DFA), the HVSR have been modelled by calculating the imaginary parts of the Green's function (IMGs) when source and observer coincide at the same point. In this work we use the 3-D indirect boundary element method (IBEM) to model the HVSR for each independent horizontal direction referred to here as directional-HVSR for layered media with lateral inhomogeneity. The IMGs at the source required to get HVSR have locality properties that depend on frequency and may imply significant economies in the calculation. For simple models we modelled the IMGs approximately using an adaptive meshing scheme that accounts both for the locality of the problem and the diffraction properties of waves at low and high frequencies. The obtained directional-HVSR displays variations in both frequency and azimuth. The results also show that layer interface variations can lead to ‘spots’ of higher wave excitation associated to local resonant modes. This shows the importance of HVSR in forecasting earthquake response and suggests the need for denser field measurements to study lateral and azimuthal variability. In order to show the reality of directional-HVSR, field data from Chalco, a soft soil site at the southern part of the Valley of Mexico, have been preliminarily analysed.

Single-Walled ZnSe Nanotubes for High-Performance Photodetectors: A Computational Prediction.

Low-dimensional nanomaterials show great potential for developing semiconducting materials due to their distinct electronic,optical, and mechanical properties. In this study, we constructed various one-dimensional ZnSe nanotubes and investigated their transport and photoresponse properties by using the density functional theory (DFT) and non-equilibrium Green's function (NEGF) method. Under bias regulation, one-dimensional tetragonal ZnSe nanotube curled along the diagonalcan reach a current of 111.3 μA at a bias of 4.0 eV. It is worth noting that for all considered photon energies, thephotocurrent exhibits a cosine dependence on the polarization angle, which is consistent with the photogalvanic effect. The results show that our constructed ZnSe nanotubes have potential for applications in electronic and optoelectronic devices.

On the integral upper limit in the Laplace transform formulation for evaluating the half-space Green's function over an extended reacting plane.

Th e Laplace transform formulation proposed by Di and Gilbert [J. Acoust. Soc. Am. 93, 714-720 (1993)] is an efficient and accurate method for calculating the half-space Green's function. However, the integral upper limit required in this formulation has not been examined in the context of an extended reacting reflecting plane, which is a critical parameter influencing both the accuracy and efficiency of the formulation. In this article, the Laplace transform formulation is further explored, and a novel method is proposed for identifying the integral upper limit, which is verified through numerical studies.

Evolution from the Kondo phase to the RKKY phase in the small impurity spacing regime of the two-impurity Anderson model

Abstract Understanding the quantum critical phenomena is one of the most important and challenging tasks in condensed matter physics and the two-impurity Anderson model (TIAM) is a good starting point for this exploration. To this end, we employ the algebraic equation of motion approach to calculate the TIAM and analytically obtain the explicit single-particle impurity Green function under the soft-cut-off approximation (SCA). This approach effectively incorporates the impurity spacing as an intrinsic parameter. By solving the pole equations of the Green function, we have, for the first time, qualitatively calculated the spectral weight functions of the corresponding low-energy excitations. We find that when the impurity spacing is less than one lattice distance, the dynamic Rudermann-Kittel-Kasuya-Yosida (RKKY) interaction effectively enters, resulting in a rapid increase in the spectral weights of the RKKY phase, which ultimately surpass those of the Kondo phase; while the spectral weights of the Kondo phase are strongly suppressed. From the perspective of spectral weights, we further confirm the existence of a crossover from the Kondo phase to the RKKY phase in the TIAM. Based on these results, the reasons for the phenomenon of the Kondo resonance splitting are also discussed.

Enhancing the optoelectronic properties of SnS via mixed-phase heterostructure engineering.

SnS holds great promise in optoelectronics, especially in photovoltaic devices, due to its exceptional intrinsic electronic properties and optimal optical absorption. However, its prospective applications are often limited by structural instability or oxidation, leading to internal or external defect states. This study proposes a mixed-phase SnS/h-BN heterostructure to enhance chemical and thermal stability while preserving the intrinsic optoelectronic properties of SnS. High negative binding energy and ab initio molecular dynamics simulations confirm the structural and thermal stability of the heterostructure up to 600 K. The heterostructure exhibits a type-I band alignment with an indirect density functional theory (DFT) band gap of 1.38 eV, corrected to 2.20 eV using Green's function with screened Coulomb potential (GW) calculations. The vertical intralayer electric field, resulting from non-uniformity in charge dynamics within the heterostructure, influences the SnS bound excitons, causing reduction in their binding energies. The weakly bound excitons indicate effective charge separation, charge transport augmentation, and a prolonged recombination lifetime. The interface effectively combines the excellent light-harvesting capabilities of SnS with the remarkable stability of h-BN, retaining the desirable optoelectronic properties of SnS while offering enhanced charge transport and stability.