Diffusion Wave Research Articles

Detecting the waves of southward culture diffusion along the eastern margin of Tibetan Plateau during the Neolithic and Bronze Age: a sarcophagus burial perspective

Detecting the waves of southward culture diffusion along the eastern margin of Tibetan Plateau during the Neolithic and Bronze Age: a sarcophagus burial perspective

Stability of planar diffusion wave for three‐dimensional bipolar Euler–Poisson system with time‐dependent over‐damping

This paper is concerned with the asymptotic behavior of the solution to the Cauchy problem for the three‐dimensional bipolar Euler–Poisson system with time‐dependent over‐damping. We prove that the Cauchy problem admits a unique global‐in‐time smooth solution that tends to the planar diffusion wave as time goes to infinity provided that the initial perturbation is sufficiently small. Moreover, we also obtain the convergence rate of the solution toward the planar diffusion wave. The proof is completed by the time‐weighted energy method.

Electroencephalography can Ubiquitously Delineate the Brain Dysfunction of Neurodegenerative Dementia by Both Visual and Automatic Analysis Methods: A Preliminary Study.

Introduction: The aim was to examine the differences in electroencephalography (EEG) findings by visual and automated quantitative analyses between Alzheimer's disease (AD) and dementia with Lewy bodies (DLB) and Parkinson's disease with dementia (PDD). Methods: EEG data of 20 patients with AD and 24 with DLB/PDD (12 DLB and 12 PDD) were retrospectively analyzed. Based on the awake EEG, the posterior dominant rhythm frequency and proportion of patients who showed intermittent focal and diffuse slow waves (IDS) were visually and automatically compared between the AD and DLB/PDD groups. Results: On visual analysis, patients with DLB/PDD showed a lower PDR frequency than patients with AD. In patients with PDR <8 Hz and occipital slow waves or patients with PDR <8 Hz and IDS, DLB/PDD was highly suspected (PPV 100%) and AD was unlikely (PPV 0%). On automatic analysis, the findings of the PDR were similar to those on visual analysis. Comparisons between visual and automatic analysis showed an overlap in the focal slow wave commonly detected by both methods in 10 of 44 patients, and concordant presence or absence of IDS in 29 of 43 patients. With respect to PDR <8 Hz and the combination of PDR <8 Hz and IDS, PPV and NPV in DLB/PDD and AD were not different between visual and automatic analysis. Conclusions: As the noninvasive, widely available clinical tool of low expense, visual analysis of EEG findings provided highly sufficient information to delineate different brain dysfunction in AD and DLB/PDD, and automatic EEG analysis could support visual analysis especially about PD.

Numerical simulation of an effective transform mechanism with convergence analysis of the fractional diffusion-wave equations

In the current study, we solve two very important mathematical models, such as the time fractional-order space-fractional telegraph and diffusion-wave equations using a reliable technique called the Adomian decomposition natural method (ADNM), which combines Adomian decomposition and natural transform. The diffusion wave equation describes the flood wave propagation, which is used in solving overland and open channel flow problems. For this reason, it is critical to fully understand and effectively solve the diffusion wave equations. Because telegraph equations are crucial for modeling and developing voltage or frequency transmission, they are widely used in physics and engineering. Furthermore, the designing process is greatly impacted by the uncertainty in the system parameters. For nonlinear ordinary differential equations based on the theorem of Banach fixed point, we provide existence and uniqueness theorem proofs. The present approach has been successfully used to explore exact solutions for time fractional-order and space fractional-order applications. The results show how effective and valuable the ADNM. This paper presents a methodology that will be used in future work to address similar nonlinear problems related to fractional calculus.

Surface treatment of metal by combined particle beam

This work is related to modeling of metal surface modification process by combined particles beam. On the basis of thermodynamics of irreversible processes, including equations of state in differential form, a nonlinear model is formulated. The model takes into account the interaction of thermal, diffusion and mechanical waves and finiteness of relaxation times of thermal and diffusion processes. For the combined particle flow such model is proposed for the first time. The numerical algorithm is based on implicit difference schemes. The study of the interaction of waves of different nature is carried out on the example of a copper target treated with nickel and gold particles. It is shown that deformations take the maximal value at the left boundary, which is directly related to the presence of impurity concentration gradients. Depending on the pulse duration, the difference between the extrema on the elastic wave becomes less significant. With increasing temperature, obviously, the diffusion process accelerates. The propagation velocities of the interacting waves are different. The character of distributions of concentrations of introduced particles directly depends on the value of parameters proportional to relaxation times.

Velocity of ultrasound diffusion in heterogeneous media and its applications

This paper investigates the velocity of ultrasonic diffusion in heterogeneous media under the conditions where the diffuse wave approximation is valid (λ≤a). The diffusion velocity is defined as the moving speed of the peak of the energy evolution curve. The peak arrival time as a function of transport distance is calculated for infinite spaces and bounded domains. The results show that the peak arrival time is independent of the domain’s geometry, i.e. the size, shape, and boundary conditions. This is confirmed by comparing the arrival times in an infinite space and a bounded domain with a geometric feature – a surface-breaking crack of varying depth. Therefore, the velocity of ultrasonic diffusion is an intrinsic property of a medium, and the formula for the infinite three-dimensional space is sufficient to calculate the arrival time–transport distance relationship, given the diffuse properties of the medium. These findings eliminate the needs for the finite element numerical simulations in the applications to determine geometric parameters such as the crack depth using diffuse ultrasound. The diffusion velocity is a function of transport distance in general, while its far-field asymptotic value is constant regardless of the dimensionality and geometry of the domain.

Passive wall thickness monitoring using acoustic emission excitation

Erosion-corrosion is a problematic damage mechanism for the oil and gas industry. To manage the risk of erosion-corrosion networks of particle impact monitoring systems have been installed on pipelines in order to detect acoustic emission from abrasive sand particles impacting the inside surface of the pipe. It would be of value if the existing network of particle impact monitoring systems were not only capable of detecting particle impact, but also sizing the remaining wall thickness. Particle impact monitoring systems are passive and are not generally equipped for excitation. This paper explores the feasibility of using passive acoustic emission transducers for wall thickness measurement, utilizing the fact that active pulse-echo measurements can be approximated by autocorrelating diffuse acoustic waves, such as those generated by particle impact. Two measurement modalities are presented: a) time-of-flight measurements and b) resonant ultrasound spectroscopy measurements. The more usual time-of-flight based measurement is limited by the fact that acoustic emission transducers typically have sensitive bandwidths limited to <1 MHz. The relatively low frequency operation limits the use to thick wall components where the component thickness ≫ ultrasonic wavelength. In thinner walled components a resonant ultrasound spectroscopy approach is required. Experimental measurements are shown that are truly passive (with no purposeful excitation at all), and semi-passive, utilizing acoustic emission from sand impact or compressed air as the excitation source. Results show very good agreement with active measurements.

Wave propagation for the isentropic compressible Navier–Stokes/Allen–Cahn system

We study the Cauchy problem for the three‐dimensional isentropic compressible Navier–Stokes/Allen–Cahn system, which models the phase transitions in two‐component patterns interacting with a compressible fluid. Under the assumption that the initial perturbation is small and decays spatially, we establish the global existence and the pointwise behavior of strong solutions to this nonconserved system. To deal with the source terms involving the phase variable, we employ the Green's function and space‐time weighted estimates. The analysis shows that the phase variable mainly contains the diffusion wave with exponential decaying amplitude over time, and consequently the density and momentum of the compressible fluid adhere to a generalized Huygens principle.

A New Perspective for Scientific Modelling: Sparse Reconstruction Based Approach for Learning Time-Space Fractional Differential Equations

Abstract This paper studies a sparse reconstruction based approach to learn time-space fractional differential equations, i.e. to identify parameter values and particularly the order of the fractional derivatives. The approach uses a generalized Taylor series expansion to generate, in every iteration, a feature matrix which is used to learn the fractional orders of both, temporal and spatial derivatives by minimizing the LASSO operator using Differential Evolution algorithm. To verify the robustness of the method, numerical results for time-space fractional diffusion equation, wave equation, and Burgers? equation at different noise levels in the data are presented. Finally, the methodology is applied to a realistic example where underlying fractional differential equation associated to published experimental data obtained from an in-vitro cell culture assay is learned.

Solidification of concentrated zero-valent iron slurry: A microrheology study using diffusing wave spectroscopy

Concentrated zero-valent iron (ZVI) slurries (CIS) are commonly encountered during the water treatment using ZVI, in the processes such as delivery, settling, and pumping of the ZVI slurry; about the CIS, knowledge about their rheology is critical to the operation of these processes, but little is known about this aspect so far. Herein, microrheology of the CIS of four different ZVI is studied using diffuse wave spectroscopy (DWS). Results show that the CIS of two iron nanoparticles solidify immediately after their separation from water (<3 h), with a fast growth of macroscopic viscosity and a rapid weakening of the fluidity; the CIS of the microscale ZVI (mZVI) is nearly pure viscous or liquid-like and solidifies slower than the nanoparticle CIS; CIS of the floc modified ZVI (mZVI(floc)) is viscoelastic and remains stable in rheology over an extended period up to four days. Such differences in CIS rheology are explained by the coarse surface of the nanoparticle aggregates, the smooth surface of mZVI particles, the intertwined floc coating of mZVI(floc) particles, and the corresponding disparity in surface friction between the particles or aggregates. The solidification of CIS is explained by the binding effect of the oxidation products of the ZVI-water reaction. This study provides information about CIS rheology and offers guidance for process operations in the water treatment using ZVI. This study also shows that the DWS technique is informative in characterizing CIS and the method may be equally applicable for studying other concentrated particle slurries in water treatment.

Green's function and pointwise space-time behaviors of the three-dimensional relativistic Boltzmann equation

The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and Huygens waves with the speed a2+b2 at low-frequency, the singular kinetic wave and the remainder term decaying exponentially in space and time. In addition, we establish the pointwise space-time estimate of the global solution to the nonlinear relativistic Boltzmann equation with non-smooth initial data based on the Green's function.

Systematic Literature Review (SLR): Explorations flood systems theory and appropriate modeling

Urban flood risk assessment conducts a comprehensive evaluation of hazard formative factors, hazard formative environment, hazard-affected bodies, and capabilities for disaster prevention and reduction in order to obtain an accurate assessment of flood risk levels. The current study aimed to conduct a systematic review of the existing literature on engagement outcomes, focusing on high-quality studies Each step of the SLR method and their results are explained in detail in the following subsections using SLR performed. Using the SLR method can help answer the objectives of this research in the form of: What type of modeling to overcome flooding This research uses the SLR method which aims to recognize, review, and evaluate Using bibliometric analysis.To achieve the goal of SLR, the variables of interest are organized based on the general characteristics of the article and the specific parameters used general information about the article includes year of publication, type of analysis (quantitative, qualitative, cartographic or mixed), type and scale of research, and the country or region where the research was conducted. The model consists of three components, including rainfall runoff, river channels, and flooding The flow in the channel was generated with a 1D diffusion wave model, and the outflow on the slope was generated with a 2D model.This article showed the basic steps that need to be followed to conduct SLR This method generates topic-specific existing knowledge, trends, and observed gaps and helps to draw relevant conclusions for policy makers and the scientific community. and the appropriate modeling is Press RRI refers to 2D grid-based fluid dynamics and is a model that combines a hydrological model and a flood model.

Systematic Literature Review (SLR): Explorations flood systems theory and appropriate modeling

Urban flood risk assessment conducts a comprehensive evaluation of hazard formative factors, hazard formative environment, hazard-affected bodies, and capabilities for disaster prevention and reduction in order to obtain an accurate assessment of flood risk levels. The current study aimed to conduct a systematic review of the existing literature on engagement outcomes, focusing on high-quality studies Each step of the SLR method and their results are explained in detail in the following subsections using SLR performed. Using the SLR method can help answer the objectives of this research in the form of: What type of modeling to overcome flooding This research uses the SLR method which aims to recognize, review, and evaluate Using bibliometric analysis.To achieve the goal of SLR, the variables of interest are organized based on the general characteristics of the article and the specific parameters used general information about the article includes year of publication, type of analysis (quantitative, qualitative, cartographic or mixed), type and scale of research, and the country or region where the research was conducted. The model consists of three components, including rainfall runoff, river channels, and flooding The flow in the channel was generated with a 1D diffusion wave model, and the outflow on the slope was generated with a 2D model.This article showed the basic steps that need to be followed to conduct SLR This method generates topic-specific existing knowledge, trends, and observed gaps and helps to draw relevant conclusions for policy makers and the scientific community. and the appropriate modeling is Press RRI refers to 2D grid-based fluid dynamics and is a model that combines a hydrological model and a flood model.

Imprinting and the evolution of evaluation: A descriptive account of social impact evaluation methodological practice

This study investigates the evolution of evaluation approaches within the charitable sector, emphasising the proliferation of options throughout waves of evaluation diffusion. We draw on imprinting theory to describe the persistence of specific practices despite the emergence of alternatives. The research aims to examine the imprinted values and practices of earlier evaluation waves on the current practice of evaluation by documenting the current methodological practice in a large sample of evaluation reports. The study illuminates the enduring impact of theory-driven evaluation, introduced in the 1980s, on current practices. However, it also reveals how this approach has evolved over subsequent evaluation waves, acquiring divergent characteristics. This imprinting is not only due to effectiveness but also due to normative pressures, which prioritise conformity with norms over practical utility. The study highlights the potential consequences of this imprinting, including management-focused evaluations and mission drift. We conclude by offering practical options to address tensions within the field and call for further research to better understand the nuances of decision-making in evaluation approaches.

Acoustic response of patchy-saturated porous media: Coupling Biot's poroelasticity equations for mono- and biphasic pore fluids.

Patchy saturation is a term used in the seismic prospecting literature to describe the state of a geological formation in which two immiscible pore fluids prevail in mesoscopic-scale clusters. If the pore fluids have contrasting compressibilities, wave-induced fluid pressure diffusion (FPD) processes may induce significant attenuation and velocity dispersion on seismic waves. Biot's monophasic poroelasticity theory is widely used to model the seismic response of rocks containing binary patches of two immiscible pore fluids. Even though effective fluid approximations may help to represent more realistic partially saturated patches using Biot's monophasic equations, the so inferred dissipation may not be representative of actual biphasic FPD phenomena. In this work, Biot's equations for mono- and biphasic fluids are combined to model FPD processes in porous media, comprising fully and partially saturated patches. An analytical solution for one-dimensional layered patchy-saturated media is presented which permits to explain some, as of yet enigmatic, experimentally observed characteristics such as increased seismic attenuation and stiffening effects occurring at low saturations. The results show that the existence of an additional diffusive wave mode within partially saturated patches may render conventional binary and effective fluid approaches incorrect and error prone.

Atomistic wave packet investigation of phonon scattering at rough surfaces

Investigating the phonon-surface scattering mechanism is essential for the evaluation of thermal transport in nanostructures. The theoretical description to quantify this mechanism remains to be developed at the atomic scale. This work presents a phonon wave packet method to study the phonon-surface scattering behavior at rough surfaces. We obtain the specularity distribution dependent on phonon polarization, wavelength, and surface roughness. The reflection of the diffuse wave packet is primarily attributed to the surface shadowing effect at a higher incident angle, surface disorder, and surface-induced localized modes. Taking the wavevector-dependent specularity data as input, the thermal conductivity of silicon nanowires is calculated based on the Boltzmann Transport Equation. Our specularity model provides an accurate evaluation for predicting thermal conductivity. This work offers an atomic-level analysis for phonon-surface interaction, which is helpful for the understanding of thermal transport in nanostructures.

Enhancing flood wave modelling of reservoir failure: a comparative study of structure-from-motion based 2D and 3D methodologies

Predicting flood wave propagation from reservoir failures is critical to practical flood hazard assessment and risk management. Flood waves are sensitive to topography, channel geometry, structures, and natural features along floodplain paths. Thus, the accuracy of flood wave modelling depends on how precisely those features are represented. This study introduces an enhancing approach to flood wave modelling by accurately representing three-dimensional objects in floodplains using the structure-from-motion (SfM). This method uses an unmanned aerial vehicle to capture topographic complexities and account for ground objects that impact flood propagation. Using the three-dimensional volume of fluid numerical approach significantly improves an enhanced representation of turbulent flow dynamics and computational efficiency, especially in handling large topography datasets. Reproductions from this enhanced three-dimensional approach were validated against recent reservoir failure observations and contrasted with traditional two-dimensional models. The results revealed that the suggested three-dimensional methodology achieved a significant 84.4% reproducibility when juxtaposed with actual inundation traces. It was 35.5%p more accurate than the two-dimensional diffusion wave equation (DWE) and 17.1%p more than the shallow water equation (SWE) methods in predicting flood waves. This suggests that the reproducibility of the DWE and SWE decreases compared to the three-dimensional approach when considering more complex floodplains. These results demonstrate that three-dimensional flood wave analysis with the SfM methodology is optimal for effectively minimising topographic and flood wave reproduction errors across extensive areas. This dual reduction in errors significantly enhances the reliability of flood hazard assessments and improves risk management by providing more precise and realistic predictions of flood waves.

Singularities of Diffuse Wave Fields in Scattering Media with Refractive Index Gradients

The subject of this paper is the radiative transfer in media with gradients of the refractive index. Asymptotic expressions of the intensity distributions in the vicinity of singular directions are derived. Critical conditions for the appearance of singular intensity distributions in fields of scattered radiation in a medium are formulated. It is shown that singular radiation fields in such media can be generated, among other things, by non-singular configurations of radiation sources. The obtained results are verified by direct comparison with the results of numerical calculations using the Monte Carlo statistical modeling method.

Reconstruction of direct waves between passive flexible sensors using diffuse ultrasonic waves

The sensing system that enables generation and sensing of guided ultrasonic waves (GUWs) serves as a pivotal cornerstone for the structural health monitoring based on GUWs. Traditional sensing systems have been constrained by inherent limitations including substantial mass addition and limited flexibility, and this leads to an increasing research efforts for the emerging nano-composite sensors. Despite the superior properties of lightweight and flexibility, the nano-composite sensors is incapable of active wave excitation, and thus waves propagating directly between sensors cannot be obtained. To tackle this deficiency, an approach grounded in representation theorem to reconstruct signals using diffuse ultrasonic waves is proposed. In this approach, the waves propagating between two passive sensors can be approximated through the cross-correlation of wave signals in a diffused status. On this basis, the passive sensors can be virtually converted to active actuators, enabling the acquisition of waves virtually excited and captured by a pair of passive sensors. In experimental validations, the wave signals between passive sensors are retrieved and the damage close to the sensing path is detected. The proposed method enhances signal acquisition capability of sensing networks based on flexible passive sensors and opens avenues for the monitoring of previously inaccessible blind areas within complex structures.

Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations

Superconvergence analysis of spectral volume methods for one-dimensional diffusion and third-order wave equations