Green Function Research Articles

Electric fields near undulating dielectric membranes.

Dielectric interfaces are crucial to the behavior of charged membranes, from graphene to synthetic and biological lipid bilayers. Understanding electrolyte behavior near these interfaces remains a challenge, especially in the case of rough dielectric surfaces. A lack of analytical solutions consigns this problem to numerical treatments. We report an analytic method for determining electrostatic potentials near curved dielectric membranes in a two-dimensional periodic "slab" geometry using a periodic summation of Green's functions. This method is amenable to simulating arbitrary groups of charges near surfaces with two-dimensional deformations. We concentrate on one-dimensional undulations. We show that increasing membrane undulation increases the asymmetry of interfacial charge distributions due to preferential ionic repulsion from troughs. In the limit of thick membranes, we recover results mimicking those for electrolytes near a single interface. Our work demonstrates that rough surfaces generate charge patterns in electrolytes of charged molecules or mixed-valence ions.

Scale-Dependent Heat Transport in Dissipative Media via Electromagnetic Fluctuations.

We develop a theory for heat transport via electromagnetic waves inside media, and use it to derive a spatially nonlocal thermal conductivity tensor, in terms of the electromagnetic Green's function and potential, for any given system. While typically negligible for optically dense bulk media, the electromagnetic component of conductivity can be significant for optically dilute media, and shows regimes of Fourier transport as well as unhindered transport. Moreover, the electromagnetic contribution is relevant even for dense media, when in the presence of interfaces, as exemplified for the in-plane conductivity of a nanosheet, which shows a variety of phenomena, including absence of a Fourier regime.

Comparison of SiGeC/SiGe/SiC–Si heterojunction based vertical nanowire FET using non equilibrium Green's function

Advancement in FET technology has forced researchers to seek alternate semiconductor devices and materials. TFETs, junctionless FETs, and nanowires are a few examples of modern FETs, whereas Si alloys, graphene, and TMDC are a few materials that have shown promising behaviour to replace Si in the future. In this work, SiGeC/SiGe/SiC–Si based vertical heterostructure nanowires have been investigated. Due to the nanoscale dimensions of the FET and to incorporate the quantum effects along with Schrodinger-Poisson equations, non-equilibrium Green's function has been used as a principle simulator. For simulation, Ge/Carbon mole concentration of 0.25 and 0.01, respectively is used. To thoroughly investigate the effect of variation in doping profile and temperature range, simulated heterojunction nanowire showed that SiGeC-based nanowire result in a better ION/IOFF ratio as compared to SiGe and SiC-based heterojunction nanowire.

A new semi-analytical model for studying the performance of deep U-shaped borehole heat exchangers

In deep geothermal exploitations, the U-shaped borehole heat exchanger (UBHE) has a longer fluid retention time and a larger contact area with the formation. In order to improve the utilization efficiency of geothermal energy, it is becoming increasingly important to accurately evaluate the performance of the deep UBHEs. In this study, the authors develop a new semi-analytical model for characterizing the heat transfer behavior of the deep UBHE geothermal system. In this developed model, the temperature change within the wellbore is numerically simulated by the finite difference method, whereas the temperature change between the formation and the wellbore is analytically simulated by the Green's-function. Besides, the non-uniform heat flux distribution along the horizontal section is considered to characterize three-dimensional heat transfer behaviors. By means of this model, the influences of developing strategies and well configurations on the outlet temperature and total thermal power are investigated. The calculation results indicate that the traditional assumption of uniform temperature along the horizontal section can induce significant errors in evaluating the performance of the UBHE geothermal systems; the horizontal section length is more conducive to improving the extraction performance in a shallower geothermal formation, and a longer horizontal section leads to a higher outlet fluid temperature, together with a larger total thermal power; a higher injection rate, as well as a lower injection fluid temperature, is more favorable for improving the total thermal power; an insulation casing with a length equaling the depth of injection point can lead to the maximum thermal power of the UBHE geothermal system.

Internal wave resonance, surges, and strong nonlinear damping differentiated in two elongated lakes with the aid of an original Green's function

AbstractWhile the analogy between the wind‐pumped internal seiche in a lake and the driven damped‐harmonic oscillator is recognized, use of a damped‐oscillator model to understand internal‐wave behavior is seldom attempted due to the irregular waveforms arising from variable winds, and to the presence of nonlinear waves like surges. Using a new variable‐frequency Green's function derived for a damped oscillator within the context of the two‐layer model of a stratified basin, we examine internal wave behaviors in Seneca and Owasco Lakes, two elongated lakes in New York state with very different lengths and depths. Our approach reproduces the measured undulations of the lowest horizonal‐mode internal‐seiche with surprising fidelity. It also yields the seiche's seasonal variation of frequency, primarily due to changes in the stratification intensity and thermocline depth. Notably, our model also estimates the seiche amplitude decay‐time, a key quantity difficult to obtain for a constantly agitated seiche. The decay time matches the computed surge‐formation time, which limits seiche lifetimes to as little as one seiche period. Surges also strongly affect the undulating internal‐wave waveforms in a manner consistent with tank experiments. Finally, we find that the internal seiche in Owasco Lake exhibits a uniquely well‐defined resonance with the diel wind pattern, and, for Seneca Lake, that surges propagate bidirectionally, augmenting an oft‐cited report of surges traveling only in one direction.

Phonon Thermal Transport in UO_{2} via Self-Consistent Perturbation Theory.

Computing thermal transport from first-principles in UO_{2} is complicated due to the challenges associated with Mott physics. Here, we use irreducible derivative approaches to compute the cubic and quartic phonon interactions in UO_{2} from first principles, and we perform enhanced thermal transport computations by evaluating the phonon Green's function via self-consistent diagrammatic perturbation theory. Our predicted phonon lifetimes at T=600  K agree well with our inelastic neutron scattering measurements across the entire Brillouin zone, and our thermal conductivity predictions agree well with previous measurements. Both the changes due to thermal expansion and self-consistent contributions are nontrivial at high temperatures, though the effects tend to cancel, and interband transitions yield a substantial contribution.

Computational investigation of high Curie temperature in a new N‐type ferromagnetic diluted magnetic semiconductors, especially iron‐doped on GaSb

AbstractDiluted magnetic semiconductors have become a research area in the past few years due to the importance of new technology, spintronics devices, and green technology to withstand rising global temperatures. Both n‐type and p‐type diluted magnetic semiconductors are used in pairs for perfect performance, especially for p‐n junction diodes, the p‐d Zener model, GMR, and TMR spintronics devices. The main challenge for some researchers is to find a ferromagnetic diluted magnetic semiconductor with a Curie temperature greater than room temperature for both n‐type and p‐type ferromagnetic diluted semiconductors, but this study has solved this problem. In the present study, the ferromagnetic properties of an n‐type gallium iron antimonide diluted semiconductor have been studied using the Hamiltonian model without applying an external magnetic field, electric field, or chemical potential. We have formulated a Hamiltonian model in the system, considering the application of the green formalism function and the transformation of Holstein–Primakaff. The Curie temperature, dispersion, number of magnons, reduced magnetization, and specific heat capacity of ferromagnetic magnons of the n‐type (Ga, Fe)Sb formula are formulated. The Curie temperature versus concentration graph is plotted, and the specific heat capacity and magnetization versus temperature graphs are plotted. In this study, a surprising situation is that the Curie temperature of n‐type diluted magnetic semiconductor is investigated above room temperature, which is 330.4 K. The ferromagnetic properties of appear up to 330.4 K, which is able to play a major role in spintronic and next‐generation green nanotechnology devices.

Velocity gradient analysis of a head-on vortex ring collision

We simulate the head-on collision between vortex rings with circulation Reynolds numbers of 4000 using an adaptive, multiresolution solver based on the lattice Green's function. The simulation fidelity is established with integral metrics representing symmetries and discretization errors. Using the velocity gradient tensor and structural features of local streamlines, we characterize the evolution of the flow with a particular focus on its transition and turbulent decay. Transition is excited by the development of the elliptic instability, which grows during the mutual interaction of the rings as they expand radially at the collision plane. The development of antiparallel secondary vortex filaments along the circumference mediates the proliferation of small-scale turbulence. During turbulent decay, the partitioning of the velocity gradients approaches an equilibrium that is dominated by shearing and agrees well with previous results for forced isotropic turbulence. We also introduce new phase spaces for the velocity gradients that reflect the interplay between shearing and rigid rotation and highlight geometric features of local streamlines. In conjunction with our other analyses, these phase spaces suggest that, while the elliptic instability is the predominant mechanism driving the initial transition, its interplay with other mechanisms, e.g. the Crow instability, becomes more important during turbulent decay. Our analysis also suggests that the geometry-based phase space may be promising for identifying the effects of the elliptic instability and other mechanisms using the structure of local streamlines. Moving forward, characterizing the organization of these mechanisms within vortices and universal features of velocity gradients may aid in modelling turbulent flows.

General model of nonradiative excitation energy migration on a spherical nanoparticle with attached chromophores

Theory of multistep excitation energy migration within the set of chemically identical chromophores distributed on the surface of a spherical nanoparticle is presented. The Green function solution to the master equation is expanded as a diagrammatic series. Topological reduction of the series leads to the expression for emission anisotropy decay. The solution obtained behaves very well over the whole time range and it remains accurate even for a high number of the attached chromophores. Emission anisotropy decay depends strongly not only on the number of fluorophores linked to the spherical nanoparticle but also on the ratio of critical radius to spherical nanoparticle radius, which may be crucial for optimal design of antenna-like fluorescent nanostructures. The results for mean squared excitation displacement are provided as well. Excellent quantitative agreement between the theoretical model and Monte–Carlo simulation results was found. The current model shows clear advantage over previously elaborated approach based on the Padé approximant.

Radical and quantum interference-enhanced thermoelectric performance of the junctions based on porphyrin dimer molecules

Manipulating the π-electron magnetism of single-molecule junctions is an effective means to improve the electronic and spin-polarized thermoelectric transport properties. Here, using the density functional theory combined with the nonequilibrium Green's function method, we demonstrate that the electronic conductance (σ) of molecular junctions (MJs) can be significantly enhanced by organic radicals due to the shifting of resonant states. Moreover, we find that the spin-dependent quantum interference (SDQI) effects can be largely influenced by organic radicals. The SDQI effects result in nearly 100% spin filtering efficiency in open-shell molecules and greatly enhance the Seebeck coefficients. As a result, the thermoelectric performances of open-shell MJs at room temperature are greatly improved through the combined effects of radicals and SDQI. In particular, the maximum ZTsp in the four radical junctions reaches up to 36.5. Our results show great potential for improving thermoelectric performance through the utilization of quantum interference and organic radical.

Analytical solution for one‐dimensional thaw consolidation model with double moving boundaries

AbstractA one‐dimensional thaw consolidation model considering the density change from pore ice to pore water is established, and the model describes a special type of moving boundary problem with double moving boundaries. An analytical solution for the model under a time‐varying external load is developed using certain form of superposition principle and the similarity type of general solution. Some known solutions in literature can be recovered as special cases of the analytical solution once the density change from pore ice to pore water is neglected. If the thawing front was to cease at certain time, consolidation of thawed soil in a fixed region is then encountered, and an analytical solution for the post‐thawing consolidation problem is developed using the Green's function method. Computational examples of the analytical solutions are presented. First, comparison between our model and classical model of Morgenstern and Nixon (MN model) is conducted, showing the error caused by neglecting the density change from pore ice to pore water. The MN model overestimates the excessive pore water pressure at locations near the soil surface, while underestimates it at locations near the thawing front; the error caused by neglecting the density change becomes more pronounced with increasing ice content of frozen soil. Second, comparison between the thaw consolidation process under an instant load and that under a corresponding exponential load is made. The difference in thaw consolidation behavior between the two situations mainly displays during the early stage, when there is obvious discrepancy between the two external loads; the degree of consolidation and thaw consolidation settlement are more sensitive to the discrepancy in external load than the excessive pore water pressure is.

Generating functional for Green's functions of fluid-loaded structures.

A key step in applying the auxiliary superfield method to complex systems is the representation of the Green's function of the system as derivatives of a generating functional. This representation is known to be valid for Hermitian systems, but this precludes the application of the method to systems with fluid loading or damping. Here, it is demonstrated that the known representation continues to be valid for fluid-loaded and damped systems. Thus, the auxiliary superfield method may be applied to such systems.

Wave interaction with multiple adjacent floating solar panels with arbitrary constraints

The problem of wave interaction with multiple adjacent floating solar panels with arbitrary types and numbers of constraints is considered. All the solar panels are assumed to be homogeneous, with the same physical properties, as well as modeled by using the Kirchhoff-Love plate theory. The motion of the fluid is described by the linear velocity potential theory. The domain decomposition method is employed to obtain the solutions. In particular, the entire fluid domain is divided into two types, the one below the free surface, and the other below elastic plates. The velocity potential in the free surface domain is expressed into a series of eigenfunctions. By contrast, the boundary integral equation and the Green function are employed to construct the velocity potential of fluid beneath the entire elastic cover, with unknowns distributed along two interfaces and jumps of physical parameters of the plates. All these unknowns are solved from the system of linear equations, which is established from the matching conditions of velocity potentials and edge conditions. This approach is confirmed with much higher computational efficiency compared with the one only involving eigenfunction expansion for the fluid beneath each plate. Extensive results and discussions are provided for the reflection and transmission coefficients of water waves, maximum deflection, and principal strain of the elastic plates; especially, the influence of different types and numbers of edge constraints are investigated in detail.

Characterization of the acoustic pressure waveforms in Rijke tubes with spatially varying heat sources and temperature distributions

In this work, we implement an asymptotic expansion technique that leverages a small perturbation parameter that arises in the context of one-dimensional tubes with open-open end point configurations and spatially varying heat sources. This approach, when paired with a spectral collocation eigensolver, enables us to produce accurate predictions of the pressure mode shapes and frequencies over a wide range of parameters. These include the temperature gain across the heat source, the heat source length and location, and the overall thermal profile. The latter is intended to reproduce different flow heating configurations that emulate Rijke tube characteristics. Specifically, this investigation begins by considering three piecewise representations of the heat source by juxtaposing constant–constant temperatures before and after a heating element whose temperature is prescribed locally using three analytical functions: linear, exponential, and power-law profiles. This is followed by a logistic distribution that can be globally applied to provide a uniformly valid, continuous, and differentiable thermal profile spanning the entire tube, including the heat source element. Our fundamental formulation relies on Green's functions and an integral formulation that enables us to extract all acoustic frequencies analytically. These are found to increase monotonically with successive elevations in the temperature gain across the heat source, retractions of the heat source, length reductions in the heat source, and smoothing of the temperature gain. Along similar lines, the pressure mode shapes are found to exhibit blunter and often linear variations for higher temperature gains, longer heat sources, and upstream displacements of the heat source toward the inlet.

On the sound field of a resilient elliptical disk in an infinite baffle.

A resilient elliptical disk has zero mass and stiffness and is driven by a uniform pressure distribution rather than uniform velocity as would be the case for a rigid disk. It can represent the diffraction of a plane wave through an elliptical aperture in an infinite rigid screen of zero thickness as well as provide an idealized model of a loudspeaker of the electrostatic or planar magnetic type. Using the Fourier (Hankel) Green's function in cylindrical coordinates, together with the monopole Kirchhoff-Helmholtz boundary integral, rigorous analytical formulas are derived for calculating the surface velocity distribution, radiation admittance, on-axis pressure, and directivity pattern of an elliptical resilient disk in an infinite baffle and these are plotted over a range of normalized frequencies. The directivity is compared with that of a resilient circular disk and asymptotic low-frequency approximations are derived for the radiation resistance, reactance, and on-axis pressure.

Effects of Andrade and Burgers rheologies on glacial isostatic adjustment modeling in Antarctica

Variations in ice mass deform the Earth and modify its gravity field, a process known as Glacial Isostatic Adjustment (GIA). GIA in Antarctica remains poorly constrained due to the cumulative effect of past and present ice-mass changes, the unknown history of the past ice-mass change, and the uncertainties on the mechanical properties of the Earth. This paper investigates the effect of using Andrade and Burgers viscoelastic rheologies, rather than the commonly used Maxwell rheology, to model GIA-induced deformation in Antarctica. The Love number and Green's function formalism are used to compute the radial surface displacements and the gravity changes induced by the past and present ice-mass changes. We consider an Earth model whose elastic properties and radial structure are averaged from the Preliminary Reference Earth Model and two viscosity profiles to account for the recently published results on the present ice-mass changes. Using the three rheological laws affects the temporal response of the Earth differently, leading to smaller discrepancies than those induced by the two viscosity structures. The differences are the largest between Maxwell and Burgers rheologies during the 100–1000 years following the beginning of the surface-mass change. Results show that using the Andrade and Burgers rheologies allows the Earth to respond on decennial to centennial time scales, up to 10 m more than Maxwell. Considering only the recent ice-mass changes, the deformation rates derived from Burgers and Andrade rheologies are several times larger than those estimated by Maxwell rheology.

Effective Descriptor for Screening Single-Molecule Conductance Switches.

The adsorption-type molecular switch exhibits bistable states with an equivalently long lifetime at the organic/inorganic interface, promising reliable switching behavior and superior assembly ability in the electronic circuits at the molecular scale. However, the number of reported adsorption-type molecular switches is currently less than 10, and exploring these molecular switches poses a formidable challenge due to the intricate interplay occurring at the interface. To address this challenge, we have developed a model enabling the identification of diverse molecular switches on metal surfaces based on easily accessible physical characteristics. These characteristics primarily include the metal valency electron concentration, the work function of metal surfaces, and the electronegativity difference of molecules. Using this model, we identified 56 new molecular switches. Employing the gradient descent algorithm and statistical linear discriminant analysis, we constructed an explicit descriptor that establishes a relationship between the interfacial structure and chemical environment and the stability of molecular switches. The model's accuracy was validated through density functional theory calculations, achieving a 90% accuracy for aromatic molecular switches. The conductive switching behaviors were further confirmed by nonequilibrium Green's function transport calculations.

A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

Influence of varying carbon oxides concentrations on the selectivity of an electrical sensor utilizing graphene nanoribbons

We have considered a graphene nano ribbon-based two probe-device working on the principle of alteration of current-voltage (I–V) characteristic, upon interactions of its channel material with the adsorbed gas molecules. The analysis of sensing parameters alongside the electron transport mechanism was carried out by using density functional theory (DFT) formulated on the Hohenberg-Kohen paradigm in conjunction with the non-equilibrium green functions (NEGF) method. Electronic transport through similar work reported earlier reveals that the combination of these two techniques coordinates extremely well and yields convincing electronic results. The nanoribbon-based sensing device was employed to evaluate its capability to detect Carbon dioxide (CO2) and Carbon monoxide (CO) molecules. Analysis of the computed result reveals significant modifications in the electronic property of the device upon adsorption of carbon dioxide and carbon monoxide entities on the channel surface. One such significant and dramatic change in the characteristic that we observed is the nature of the channel that transforms from metallic to semi-metallic. Another observed change is the signal amplification capability relative to the pristine device. The signal gets amplified on increasing number of molecular entities from one to six.The transformation in sensor performance is additionally supported by examining variations in multiple parameters, including adsorption energy, charge transfer, differential resistance, and the figure of merit, also known as the peak-to-valley ratio (PVR). The investigation unveiled that the currently designed zigzag graphene nanoribbon (ZGNR) model exhibits high sensitivity to both CO2 and CO gases. This phenomenon is substantiated by the elevated adsorption energy, increased charge transfer, elevated peak-to-valley ratio (PVR), and heightened sensor response. The substantial sensor response, registering at a magnitude of 8.3, underscores the efficacy of the current system in detecting both low and high concentrations of CO and CO2 molecules. The current study emphasizes the notion that understanding the electronic and transport behaviour of zigzag graphene nanoribbons (ZGNR) and analogous materials could offer valuable insights for addressing the threat of environmental pollution.