Short-time Approximation Research Articles

A novel approach to analyzing the stability of physical fields in semiconductor materials under photothermal excitation

This work employs a new approach to study the stability heating effects caused by the thermal influence of photothermal theory. In addition, our investigation identified stability mechanisms occurring at the limits of the semiconductor (SC) medium. We have examined the interactions of photosensitive, thermic, and mechanical waves inside a medium's half-space using the theory of photo-thermoelectricity. The establishment of governing equations is achieved by utilizing one-dimensional elastic-optoelectronic deformation. Utilizing advanced mathematical techniques, such as Laplace transform with short-time approximations, we transform the foremost physical domains to the frequency domain, imposing conditions on the free surface of the elastic medium to enhance stability. Employing the homotopy perturbation method, the stability of the main physical quantities is obtained, with silicon as the chosen material. Graphical analyses and discussions elucidate the physical fields after applying the numerical Laplace inverse technique with the effect of some factors like the thermo-electric coupling parameter. Comparisons between some materials like silicon and germanium are being investigated. The stability of main physical quantities with various values of eigenvalues approaches are obtained with the dual solutions of the eigenvalues.

A Computational Study of the Electronic Energy and Charge Transfer Rates and Pathways in the Tetraphenyldibenzoperiflanthene/Fullerene Interfacial Dyad.

The electronic transition rates and pathways underlying interfacial charge separation in tetraphenyldibenzoperiflanthene:fullerene (DBP:C70) blends are investigated computationally. The analysis is based on a polarization-consistent framework employing screened range-separated hybrid functional in a polarizable continuum model to parametrize Fermi's golden rule rate theory. The model considers the possible transitions within the 25 lowest excited states of a DBP:C70 dyad that are accessible by photoexcitation. The different identified pathways contributing to charge carrier generation include electron and hole transfer and backtransfer, exciton transfer, and internal relaxation steps. The larger density of states of C70 appears to explain the previously observed larger efficiency for charge separation through hole transfer mechanism. We also analyze the validity of the high-temperature and short-time semiclassical approximations of the FGR theory, where both overestimated and underestimated Marcus theory based constants can be affected.

Mathematical significance of strain rate and temperature rate on heat conduction in thermoelastic material due to line heat source

The primary purpose of the present article is to investigate the effect of strain rate and temperature rate factors on a homogeneous, unbounded isotropic elastic medium originating due to continuous line heat source. This study is based on the modified Green-Lindsay Model (MGL) theory proposed by Yu et al. (2018). This model eliminates the discontinuous nature of the displacement field reported under the temperature-rate-dependent thermoelasticity theory (GL) established by Green and Lindsay. The present work obtains the analytical solution for the distributions of stress components, temperature and displacement through the potential function approach accompanied by the Laplace transform method. The inverse Laplace transformation is performed by using short-time approximation method to find the approximated analytical solution of the problem in space-time domain. A detailed analysis of solution is discussed for MGL model and compared to the results predicted by other existing generalized thermoelastic models. The effect of strain-rate and temperature-rate-terms is acknowledged explicitly in mathematical formulation and other significant effects are notified. However, this new model predicts the infinite speed of disturbance analogous to classical theory.

Continuous-time Markov-chain models for reaction systems: fast and slow processes

It is sometimes of interest to identify the fast and slow processes in a reaction system. We present here an approach to this problem which is based on a simple stochastic model, a continuous-time Markov chain on a small number of states. We show how it is possible to use such a stochastic model to find and plot the time-courses of concentrations, and to find simple short-time and long-time approximations to these time-courses; that is, to separate the fast and the slow processes. The most significant computation involved is the exponentiation of many small matrices, which is easily accomplished in the computing environment R.

The influence of divalent cations on the dynamic surface tension of sodium dodecylbenzenesulfonate solutions

The kinetics of surfactant adsorption at interfaces is crucial in many industrial settings. Maximum bubble pressure tensiometry allows accessing the adsorption at time scales of tens of ms to uncover the initial stages of surfactant diffusion to the interface. This method was used to investigate electrolyte solutions of sodium dodecylbenzenesulfonate (SDBS), specifically targeting how the presence of small amounts of divalent cations (Mg2+, Ca2+, Sr2+ and Ba2+) influenced the adsorption kinetics and equilibrium. The dynamic surface tensions revealed that the adsorption of SDBS was strongly influenced by the presence of divalent cations due to strong interactions with the anionic surfactant. In addition, the type (i.e. size) of cations played a role. The strong divalent cation-surfactant interactions lead to distinct lowering of surfactant diffusion coefficients, calculated using the short-time approximation solution of the Ward-Tordai equation. The diffusion coefficients were slightly and similarly lowered for all types of divalent cations when the surfactant concentration was increased up to the critical micelle concentration (CMC). Above CMC, the diffusion coefficients increased steadily depending on the divalent cation. It was speculated that this could be due to differences in structure and aggregation numbers of micelles and slower disassembly of micelles to supply monomers for adsorption. Furthermore, CMC of SDBS was reduced according to the Hofmeister series in the presence of divalent cations.

Stochastic dynamics and first passage analysis of iced transmission lines via path integration method

The mechanism of stochastic factors in wind load on iced transmission line galloping has attracted widespread attention. In this paper, the random part of wind load is simulated by Gaussian white noise, and a galloping model of the iced transmission line excited by stochastic wind is established. The path integration method based on the Gauss–Legendre formula and short-time approximation is used to solve the steady-state probability density function of the system and the evolution of the transient probability density. The resonance response of the system is considered when the fluctuating wind acts. Meanwhile, through path integration, the stability of galloping motion is evaluated based on the first passage theory. Comparing with the Monte Carlo simulation, the effectiveness of the proposed method is verified. It turns out that the large external excitation intensity and the small natural frequency are not conducive to the stability of iced transmission line galloping.

Comparing semiclassical mean-field and 1-exciton approximations in evaluating optical response under strong light-matter coupling conditions.

The rigorous quantum mechanical description of the collective interaction of many molecules with the radiation field is usually considered numerically intractable, and approximation schemes must be employed. Standard spectroscopy usually contains some levels of perturbation theory, but under strong coupling conditions, other approximations are used. A common approximation is the 1-exciton model in which processes involving weak excitations are described using a basis comprising the ground state and singly excited states of the molecule cavity-mode system. In another frequently used approximation in numerical investigations, the electromagnetic field is described classically, and the quantum molecular subsystem is treated in the mean-field Hartree approximation with its wavefunction assumed to be a product of single molecules' wavefunctions. The former disregards states that take long time to populate and is, therefore, essentially a short time approximation. The latter is not limited in this way, but by its nature, disregards some intermolecular and molecule-field correlations. In this work, we directly compare results obtained from these approximations when applied to several prototype problems involving the optical response of molecules-in-optical cavities systems. In particular, we show that our recent model investigation [J. Chem. Phys. 157, 114108 (2022)] of the interplay between the electronic strong coupling and molecular nuclear dynamics using the truncated 1-exciton approximation agrees very well with the semiclassical mean-field calculation.

Approximate time domain solution for studying infinite wedge diffraction, its parameters, and characteristics.

An approximate time domain solution is derived for spherically spreading signals incident on an infinitely long rigid wedge. The solution is a short time approximation of the corresponding exact solution. The presented solution improves the accuracy of an approximate solution derived previously by the authors. The solution is extended to cylindrically spreading and plane wave incident signals. The solutions for all three types of incidence are recast in a unified form. The main advantage of this approximate solution is that it provides insight into the mechanism of diffraction. Specifically, it is shown that the time evolution of diffraction depends on a single time parameter-the diffraction delay time. Furthermore, a generator curve is presented that generates all diffraction impulse responses for all source and receiver locations, all wedge angles, and for all types of incident radiation. Finally, it is shown that any signal (irrespective of its time waveform or its type of spreading) incident on any wedge can be analyzed as an equivalent plane wave incident on a half plane. Thus, the diffraction field of a plane wave incident on a half plane (the simplest diffraction case) encompasses all wedge problems and can be considered a prototype diffraction problem.

Moisture Photo-Thermoelasticity Diffusivity in Semiconductor Materials: A Novel Stochastic Model

A unique methodology due to the effect of stochastic heating is utilized to study the Moisture Diffusivity influence of an elastic semiconductor medium under the effect of photo-thermoelasticity theory. Accurately, random processes are applied at the boundary of the semiconductor medium. The governing equations are expressed in the one-dimensional form (1D). The boundary conditions are considered random; the additional noise is regarded as white noise. The problem is set up to investigate the interaction between moisture diffusivity, thermo-elastic waves, and plasma waves. The investigation is carried out during a photothermal transport procedure while taking moisture diffusivity into consideration. The Laplace transform is used to solve the problem. The numerical solution for field distribution is obtained using the short-time approximation while performing inverse transformations of Laplace. The Wiener process notion has been used to arrive at the solutions for the stochastic case. Silicon (Si) material is used along several sample paths in a numerical study based on stochastic simulation. Additionally, a comparison of the stochastic and deterministic field variable distributions is provided. The effects of thermoelectric, thermoelastic, and reference moisture parameters of the applied force on all physical distributions are discussed graphically.

Radial basis function neural networks solution for stationary probability density function of nonlinear stochastic systems

A radial basis function neural networks (RBF-NN) solution of the reduced Fokker–Planck-Kolmogorov (FPK) equation is proposed in this paper. The activation functions consist of normalized Gaussian probability density functions (PDFs). The use of normalized Gaussian PDFs leads to a simple constraint on the coefficients for normalization of the RBF-NN solution, which as a constraint is imposed with the help of the method of Lagrange multiplier. The relationship between the proposed RBF-NN PDF solution and the generalized cell mapping with short-time Gaussian approximation is discussed, which provides a justification for Gaussian PDFs with varying means and variances in the state space. The optimal number of neurons or activation functions, which leads to the smallest error, is investigated. Four examples are presented to show the effectiveness of the proposed solution method. The results indicate that the proposed solution method is a very efficient and accurate way to compute the stationary PDF of nonlinear stochastic systems. It is also found that the distribution of the optimal coefficients as a function of the mean of Gaussian activation functions is similar to the steady-state PDF solution. Finally, we should point out that an important advantage of the RBF-NN method over methods such as finite element and finite difference is its ability to obtain solutions of the FPK equation for multi-degree-of-freedom stochastic systems.

Transient response prediction of randomly excited vibro-impact systems via RBF neural networks

Systems exposed to random excitations may fail long before stationarity is achieved, which necessitates consideration of the transient responses of the system. On the other hand, the transient response prediction of non-smooth systems may face more obstacles than that of smooth systems. One of the foremost challenges lies in the handling of vector fields with singularities in non-smooth systems. In this work, the radial basis function neural networks (RBFNN) is utilized for the first time to analyze the transient response of randomly excited vibro-impact systems (VIS), a class of typical non-smooth systems. The solution of the system response is expressed in terms of a serious of Gaussian activation functions (GAFs) with time-dependent weights. These time-dependent weights are determined by minimizing a loss function, which involves the residual of the differential equations and constraint conditions. To avoid the singularity of the initial condition being a Dirac delta function, a strategy of short-time Gaussian approximation is presented to obtain the initial weights. Two typical VISs exposed to stochastic excitations are presented to verify the suggested scheme. Appropriate comparisons to the data obtained by digital simulation show that the method yields reliable results even for strongly nonlinear systems. With the merits of high computational accuracy and satisfactory efficiency, this approach is expected to be an effective method for solution of random vibration problems of high-dimensional complex non-smooth systems.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

A Novel Stochastic Model of the Photo-Thermoelasticity Theory of the Non-Local Excited Semiconductor Medium

A novel technique under the effect of stochastic heating due to the thermal effect of the photothermal theory is investigated. Realistically, stochastic processes are taken on the boundary of the non-local semiconductor medium. The interactions between optical, thermal, and mechanical waves in a half-space of the medium are studied according to the photo-thermoelasticity theory. The governing equations are described in one dimension (1D) according to the elastic-electronic deformation. Laplace transforms with short-time approximation are used to analyze the main physical fields in linearity form. To study the problem more realistically, some conditions are taken as random with white noise on the free surface of the elastic medium. The deterministic physical quantities are obtained with a stochastic calculus when a numerical inversion of the Laplace transform is applied. The silicon material is utilized to make the stochastic simulation. The comparisons are carried out between the distributions of deterministic and stochastic (statistically, the mean and variance) of the main physical quantities along different sample paths graphically and discussed for the non-local silicon semiconductor material.

Thermoelastic interactions on a thick granular plate with type II thermoelasticity under axisymmetric temperature distribution

This paper deals with the effects of type II thermoelasticity on wave propagation in a generalized thermoelastic granular medium. A two-dimensional thick granular plate with axisymmetric temperature distribution is considered under the generalized theory (with one relaxation time) and type II thermoelasticity. The lower and upper surfaces of the plate are assumed to be stress-free and subjected to a thermal condition. The analytical solution of the different fields like temperature, displacement, stresses, rotation, and couple stresses are obtained by the Laplace transform procedure along with the Hankel transform method. The short-time approximation and Boley’s theorem are used to analyze the fields like temperature and rotation vector in the physical domain. The numerical values are displayed graphically in the middle plane for different models, and comparison illustrates the problem. The study may be helpful in soil mechanics, geophysical-prospecting, seismology, and mining engineering.

Reply to “Comment on ‘Quasielastic lepton scattering and back-to-back nucleons in the short-time approximation’ ”

We briefly review the concept of scaling and how it occurs in quasielastic electron and neutrino scattering from nuclei, and then the particular approach to scaling in the short-time approximation. We show that, whereas two-nucleon currents do significantly enhance the transverse electromagnetic response, they do not spoil scaling, but, in fact, enhance it. We provide scaling results obtained in the short-time approximation that verify this claim. The enhanced scaling, although obtained empirically, is not ``accidental''---as claimed in [O. Benhar, Phys. Rev. C 105, 049801 (2022)]---but rather reflects quasielastic kinematics and the dominant role played by pion-exchange interactions and currents in the quasielastic regime.

Comment on “Quasielastic lepton scattering and back-to-back nucleons in the short-time approximation”

The article of Pastore et al., whereas proposing an interesting and potentially useful approach for the generalization of quantum Monte Carlo techniques to the treatment of the nuclear electromagnetic response, features an incorrect and misleading discussion of $y$ scaling. The response to interactions with transversely polarized virtual photons receives sizable contributions from nonscaling processes in which the momentum transfer is shared between two nucleons. It follows that, contrary to what is stated by the the authors, $y$ scaling in the transverse channel is accidental.

Study of Hydrogen Embrittlement in Pipelines and Nuclear Power Plants: Estimates for Durability

Due to the increasing need to further develop the world gas and oil industry and the increased public attention to clean energy sources, studying and preventing Hydrogen Induced Cracking is one of the main safety concerns in nuclear power plants, oil pipelines and platforms. In this article, the growth and incubation times for internal Hydrogen Induced Cracks (HIC) are examined. Specifically, these times are modeled in two separate phases - the first phase (I) is a long time approximation, when the crack growth is believed to be slow such that the equilibrium state for gas concentration establishes instantaneously, and the stationary diffusion problem can be solved for each moment of time. The second phase (II) is a short time approximation, when the crack growth is rapid and the concentration of atomic hydrogen is dependent on time. Closed-form solutions are obtained in both cases and are then coupled using a Padé approximation.

On the adsorption kinetics of bovine serum albumin at the air–water interface

The adsorption kinetics of bovine serum albumin (BSA) at an air–water interface was investigated by experimentally measuring and theoretically modeling the dynamic surface tension (ST) data. A pendant bubble tensiometer was utilized for two ST measurements: (i) the adsorption onto a freshly created bubble surface and (ii) the bubble expansion/compression at the latter stage. The dynamic ST data, during the early stage of BSA adsorption, were best-fitted with the short-time approximation equation (diffusion-control) and the non-asymptomatic short-time formalism [mixed-control, Moorkanikkara and Blankschtein, JCIS, 296, 442–457 (2006)]. The fitting showed that the non-asymptotic short-time formalism could well predict the dynamic ST data; thereby, implying that the adsorption of BSA onto a clean air–water interface was mixed-controlled. A new approach for estimating the maximum surface concentration (Γ∞) and the intermolecular interaction amongst the adsorbed BSA molecules (K) was trialed. The relaxation of ST during a surface expansion was best-fitted with the Langmuir/Frumkin equation of state. A reasonably good fitting between the dynamic ST data and the theoretical ST profiles indicated that this approach could be used to estimate the Γ∞ and K for BSA without requiring the equilibrium ST data.

Dynamic response and bifurcation for Rayleigh-Liénard oscillator under multiplicative colored noise

The generalized mixed Rayleigh-Liénard (R-L) oscillator with both periodic and parametric excitations subjected to multiplicative colored noise is investigated in this paper. First, the deterministic global properties are calculated by the iterative compatible cell mapping method, showing the coexistence of chaotic attractor and periodic attractor. Then, under different damping control parameters, the evolutionary processes of transient and steady-state probability density functions (PDFs) of the response under multiplicative colored noise are discussed by the generalized cell mapping based on the short-time Gaussian approximation (GCM/STGA). To solve the storage problem and improve the computational efficiency of one-step transition probability density matrix, we propose to introduce the block matrix procedure into the GCM/STGA method. The results show that the evolutionary direction of PDFs is in accordance with the shape of the unstable manifold. We also observe that it takes longer to achieve the steady state for the case with the coexistence of chaotic attractor and periodic attractor than the case with only periodic attractor. Besides, the stochastic P-bifurcation occurs with changing the intensity and the correlation time for the colored noise. The GCM/STGA scheme shows good agreement with Monte Carlo simulations, which proves the effectiveness of the proposed strategy for systems with chaotic attractor and multiplicative colored noise.

The quantum mean square displacement of thermalized CO on Cu(100) in the short time approximation.

The mean square displacement 〈(x(t) - x(0))2〉 of the position x of a CO molecule adsorbed at thermal equilibrium on a Cu(100) substrate and moving along the 〈100〉 direction is evaluated quantum mechanically. The problem is treated in the independent particle formalism via the numerical solution of the time dependent Schrödinger equation with an initial thermal wave packet. The results are discussed in relation to observables from neutron scattering or helium-3 spin-echo experiments, and their interpretation in terms of classical or quantum mechanical expressions for the mean square displacement.