Nonlocal Absorption Research Articles

Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms

Liouville type theorems for a quasilinear elliptic differential inequality with weighted nonlocal source and gradient absorption terms

Blow-up Phenomena for a Reaction-diffusion Equation with Nonlocal Gradient Terms

In this paper, we investigate blow-up phenomena of the solution to a reaction-diffusion equation with nonlocal gradient absorption terms under Robin boundary condition on a bounded star-shaped region. Based on the method of auxiliary function and the technique of modified differential inequality, we establish some conditions on the nonlinearities for which the solution exists globally or blows up at finite time, when the sign of the constant $\sigma$ is either positive or negative. Moreover, upper and lower bounds for a blow-up time are derived under appropriate measure in higher dimensional spaces.

Design and Simulation of Nonlocal Perfect Absorption Thin Film

Design and Simulation of Nonlocal Perfect Absorption Thin Film

Modelling laser-fluid coupling and cavitation in laser lithotripsy

The absorption of laser by fluid and the resulting vapor bubbles plays a significant role in laser lithotripsy and many other industrial applications. In this talk, we present a coupled photo-thermal-mechanical model of laser interaction in compressible multiphase fluid flows. The model couples the three-dimensional compressible Navier–Stokes equation with a nonlocal laser absorption equation. The computational framework is an extension of the recently developed FIVER (“a Finite Volume method with Exact multi-material Riemann solver”) framework, which features the use of level set and embedded boundary methods for tracking material (fluid–fluid and fluid–solid) interfaces, and the solution of local, one-dimensional multi-material Riemann problems for enforcing interface conditions. We will start with a brief review of the key model equations and numerical algorithms adopted by FIVER, as well as recent efforts on verification and validation. Next, physical models of laser absorption and laser-induced heating will be presented. Numerical models and methods for simulating phase change and tracking the vapor–liquid interface will be introduced and assessed. The performance of this computational framework will be demonstrated using several simplified model problems and a numerical experiment of cavitation in Holmium:YAG laser lithotripsy.

Blow-Up Phenomenon for a Reaction–Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms

Blow-Up Phenomenon for a Reaction–Diffusion Equation with Weighted Nonlocal Gradient Absorption Terms

The onset of uninhibited heat conduction and non-local absorption in flux-limited laser-plasma ablation

We study the developing temperature profile in planar laser-ablation in the limit of a completely ionized low-Z plasma. The problem is analyzed both analytically and numerically, assuming complete laser absorption by near-critical absorption and inverse bremsstrahlung absorption, and heat conduction by flux-limited diffusion. We show through dimensional analysis that the temperature in the resulting corona and conduction zones is characterized by scaling relations expressed through three dimensional parameters and depends on two dimensionless parameters. Our results form a phase diagram for the behaviors of the maximal temperature as a function of time at different phases of the flow. The phase boundaries curve describes the transition times as a function of the flux limiter. We show that for low values of the flux-limiter the flow behavior is highly dependent on local details of the laser absorption at the critical surface. Measured experimentally, the identified transition times between the different phases can be used to infer the characteristic value of the flux-limiter.

Interactions of diffusion and nonlocal delay give rise to vegetation patterns in semi-arid environments

Vegetation pattern is caused by local instability in phase space, which can reflect the distribution characteristics of vegetation in the studied space. In semi-arid environment, the vegetation roots will not only absorb the water resources near themselves, but also absorb the water resources in the whole study area, that is to say, the absorption of water resources by vegetation roots is a nonlocal process. Meanwhile, the feedback mechanism of soil-water diffusion plays an important role in the process of water absorption by vegetation roots. However, it is not clear that how the feedback mechanism of nonlocal water absorption by vegetation roots and soil-water diffusion affects vegetation pattern. In this paper, we construct a positive feedback vegetation-water model with nonlocal delay. The instability of Turing pattern is analyzed by analytical method, and the conditions of stable pattern occurrence are obtained. At the same time, we use multi-scale analysis method to obtain the amplitude equation of vegetation-water system. We found that the non-local water absorption intensity of vegetation roots and the feedback of soil-water diffusion can cause the phase change of vegetation pattern. The change of nonlocal water absorption intensity will produce mixed vegetation pattern structure. The enhancement of soil-water diffusion feedback intensity will change the vegetation pattern structure: low density cold spot patterns → mixed patterns → high density hot spot patterns. The isolation between vegetation patches will be increased as that nonlocal water absorption intensity is enhanced or the feedback intensity of soil-water diffusion is increased. We also revealed that increasing the feedback intensity of soil water diffusion or nonlocal strength within a certain range is helpful to increase the vegetation density, while excessive feedback intensity or nonlocal strength will induce land desertification.

Stagnation-point heating of Fire II with a non-Boltzmann radiation model

The present work analyzes the stagnation-point radiative heating in the Fire II flight experiment by devising a collisional-radiative model with non-local absorption. In the stagnation-line flow-field calculations, a viscous shock layer method with a thermochemical nonequilibrium model is utilized. In the radiation calculations, a line-by-line method with the non-Boltzmann electronic populations is employed by adopting the quasi-steady state approach of the electronic master equation calculations. In constructing the electronic master equation, the best set of the electron and heavy-particle impact excitation rates is proposed to achieve better agreement with the measured radiative heating flight data. In the flow-radiation coupling procedure, the effect of the non-local absorption is modeled by devising an iterative process between the quasi-steady state electronic master equation and the radiative transfer equation calculations. Escape factors of the strongest atomic lines and the diatomic nitrogen vacuum ultraviolet systems with the non-local absorption effect are also proposed to more efficiently consider the non-local nature of the radiative transition. When compared with the experimental data from the Fire II trajectories, it is found that the present collisional-radiative model with the non-local absorption improves the ability to predict non-Boltzmann radiative heating.

Nonlocal Coherent Perfect Absorption.

Coherent absorption that occurs at two spatially separated, macroscopic lossy beam splitters is described. A superposition mode of any phase can be chosen as the absorbed or transparent mode. For a nonclassical two-photon NOON-state input, a superposition of two photons entering via one of two separate input modes, a single photon can survive the pair of beam splitters with certainty, implying nonlocal absorption of a single photon, which can be detected via the interference in the two-photon survival probability.

Bounds for the blow-up time of a porous medium equation with weighted nonlocal source and inner absorption terms

We investigate the blow-up phenomena for a porous medium equation with weighted nonlocal source and inner absorption terms subject to null Dirichlet boundary condition. Based on a modified differential inequality technique, we establish some sufficient conditions to guarantee the existence of non-global solutions to the model and also derive the upper bounds for the blow-up time. Moreover, the lower bounds for the blow-up time are obtained under some appropriate measure in the whole-dimensional space (Ngeq1).

Studies on spatial nonlocal optical absorption properties in AlGaAs/GaAs three-step quantum well

To investigate the nonlocal linear intersubband optical absorption properties in AlGaAs/GaAs three-step quantum well (3SQW) nanostructures for a p-polarized states, we deduced the expression of the optical absorption coefficient in the two-level 3SQW system by using Green’s function method and the nonlocal relation between electron and photoelectric field. For the given 3SQW nanostructure, we performed numerical calculations of the optical absorption spectra for different parameters such as angles of incidence, the well width, and the height of the step barrier potential. The numerical results show that spatial nonlocal linear optical response of electrons to light field can induce the radiation shift. It is also demonstrated that the radiation shift and optical absorbance can be controlled by the structure of the 3SQW. These results may bring about a helpful impact in designing nanomaterials with multifarious nonlocality and observing the spatial nonlocal effects in experiment.

A quasilinear parabolic problem with a source term and a nonlocal absorption

We investigate a quasi-linear parabolicproblem with nonlocal absorption, for which the comparison principle is not always available. Thesufficient conditions are established via energy method to guaranteesolution to blow up or not, and the long time behavior is alsocharacterized for global solutions.

Current-dependent potential for nonlocal absorption in quantum hydrodynamic theory

The quantum hydrodynamic theory is a promising method for describing microscopic details of macroscopic systems. The hydrodynamic equation can be directly obtained from a single particle Kohn-Sham equation that includes the contribution of an external vector potential. This derivation allows to straightforwardly incorporate in the hydrodynamic equation an exchange-correlation viscoelastic term, so that broadening of collective excitation can be taken into account, as well as a correction to the plasmon dispersion. The result is an accurate self-consistent and computationally efficient hydrodynamic description of the free electron gas. A very accurate agreement with full quantum calculations is shown.

Magnetization and ferromagnetic resonance in a Fe/Gd multilayer: experiment and modelling

Static and dynamic magnetic properties of a [Fe(35 Å)/Gd(50 Å)]12 superlattice are investigated experimentally in the temperature range 5–295 K using SQUID magnetometery and the ferromagnetic resonance (FMR) technique at frequencies 7–38 GHz. The obtained magnetization curves and FMR spectra are analysed theoretically using numerical simulation on the basis of the effective field model. At every given temperature, both static and resonance experimental data can be approximated well within the proposed model. However, a considerable temperature dependence of the effective field parameter in gadolinium layers has to be taken into account to achieve reasonable agreement with the experimental data in the entire temperature range studied. To describe the peculiarities of experimental FMR spectra, a non-local diffusion-type absorption term in Landau–Lifshitz equations is considered in addition to the Gilbert damping term. Possible reasons for the observed effects are discussed.

Extinction for the super diffusion equation with a nonlocal absorption and a gradient source

In this article, the authors establish the conditions for the extinction of solutions in finite time of the super diffusion equation u t = Δ u m + λ | ∇ u | q − a ∫ Ω u p d x , m < − 1 , in a bounded domain Ω ⊂ R N with N > 2 . It is shown that if 2 3 − m ≤ q < m m − 1 , p < 1 + m , for sufficiently small initial data u 0 , the weak solution u ( x , t ) vanishes in finite time.

Blow-up analysis for a reaction–diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux

A blow-up analysis for a nonlinear divergence form reaction–diffusion equation with weighted nonlocal inner absorption terms is considered under nonlinear boundary flux in a bounded star-shaped region. Based on the auxiliary function method and the modified differential inequality technique, we establish conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for the blow-up time are derived under appropriate measure in higher dimensional spaces. Three examples are presented to illustrate applications of our main results.

Nonlocal effects on intersubband optical absorption in square quantum wells

Based on the microscopic nonlocal optical response theory, the influence from the width and depth of the potential well on the nonlocal effects and optical absorption spectra of the square quantum well is investigated in detail. The numerical results show that the radiative shift of the spectrum line, which stems from the nonlocality of optical responses, is dependent closely on the width and depth of the potential well. It is also demonstrated that the width and depth of the quantum well have important influence on the optical absorbance from the intersubband transitions. The theoretical work may be important for the growth of the nonlocal nano-materials and the potential application in optoelectronics.

Plasmon-induced resonance energy transfer for solar energy conversion

In Forster resonance energy transfer (FRET), energy non-radiatively transfers from a blue-shifted emitter to a red-shifted absorber by dipole–dipole coupling. This study shows that plasmonics enables the opposite transfer direction, transferring the plasmonic energy towards the short-wavelength direction to induce charge separation in a semiconductor. Plasmon-induced resonance energy transfer (PIRET) differs from FRET because of the lack of a Stoke's shift, non-local absorption effects and a strong dependence on the plasmon's dephasing rate and dipole moment. PIRET non-radiatively transfers energy through an insulating spacer layer, which prevents interfacial charge recombination losses and dephasing of the plasmon from hot-electron transfer. The distance dependence of dipole–dipole coupling is mapped out for a range of detuning across the plasmon resonance. PIRET can efficiently harvest visible and near-infrared sunlight with energy below the semiconductor band edge to help overcome the constraints of band-edge energetics for single semiconductors in photoelectrochemical cells, photocatalysts and photovoltaics. Plasmon-induced resonance energy transfer is revealed and explored for solar energy harvesting from visible and near-infrared light.

Critical extinction exponents for polytropic filtration equations with nonlocal source and absorption

In this article, by applying the super-solution and sub-solution methods, instead of energy estimate methods, the authors investigate the critical extinction exponents for a polytropic filtration equation with a nonlocal source and an absorption term, and give a classification of the exponents and coefficients for the solutions to vanish in finite time or not, which improve one of our results (Applicable Analysis, 92(2013), 636–650) and the results of Zheng et al (Math. Meth. Appl. Sci., 36(2013), 730–743).

Simulation of nanostructure-based and ultra-thin film solar cell devices beyond the classical picture

An optoelectronic device simulation framework valid for arbitrary spatial variation of electronic potentials and optical modes, and for transport regimes ranging from ballistic to diffusive, is used to study the nonlocal photon absorption, photocurrent generation and carrier extraction in ultra-thin film, and nanostructure-based solar cell devices at the radiative limit. Among the effects that are revealed by the microscopic approach and which are inaccessible to macroscopic models is the impact of structure, doping- or bias-induced nanoscale potential variations on the local photogeneration rate and the photocarrier transport regime.