Non-dispersive Model Research Articles

Numerical Reconstruction of Landslide Paleotsunami Using Geological Records in Alpine Lake Aiguebelette

AbstractMass movements and delta collapses are significant sources of tsunamis in lacustrine environments, impacting human societies enormously. Paleotsunamis studies play an essential role in understanding historical events and their consequences, along with their return periods. This study investigates a paleotsunami induced by a subaqueous mass movement during the Younger Dryas to Early Holocene transition, ca. 11,700 years ago in Lake Aiguebelette (NW Alps, France). Utilizing high‐resolution seismic and bathymetric surveys associated with sedimentological, geochemical, and magnetic analyses, we uncovered a paleotsunami triggered by a seismically induced mass transport deposit. Numerical simulations of mass movement have been conducted using a visco‐plastic Herschel‐Bulkley rheological model and corresponding tsunami wave modeled with dispersive and nondispersive models. Our findings reveal for the first time that dispersive effects may be negligible for subaqueous landslides in a relatively small lake. This research reconstructs a previously unreported paleotsunami event and enhances our understanding of tsunami dynamics in lacustrine environments.

On periodic and finite genus solutions to the integrable Kaup–Broer system for capillary waves

The Kaup–Broer (KB) system is a weakly nonlinear and weakly nondispersive model for gravity-capillary waves. We consider the case of capillary waves, which we will call the KB 1 system. We begin by computing the elliptic traveling waves. We then demonstrate the complete integrability of this system by finding a matrix Lax pair. We use the Lax pair to construct infinitely many conservation laws, the forward scattering transform for periodic solutions, and the inverse scattering transform for periodic boundary conditions using finite genus solutions to the KB system. This paper is a follow up to [14], and demonstrates how some standard implications of the integrability of the KB 1 system can be established using the formalism therein.

A non-hydrostatic multi-phase mass flow model

Modeling mass flows is classically based on the hydrostatic, depth-averaged balance equations. However, if the momentum transfers scale similarly in the slope parallel and the flow depth directions, then the gravity and the acceleration can have the same order of magnitude effects. This urges for a non-hydrostatic model formulation. Here, I extend existing single-phase Boussinesq-type gravity wave models by developing a new non-hydrostatic model for multi-phase mass flows consisting of the solid and fine-solid particles, and viscous fluid (Pudasaini and Mergili, 2019 [1]). The new model includes enhanced gravity and dispersion effects taking into account the interfacial momentum transfers due to the multi-phase nature of the mass flow. I outline the fundamentally new contributions in the non-hydrostatic Boussinesq-type multi-phase gravity waves emerging from the phase-interactions including buoyancy, drag, virtual mass and Newtonian as well as non-Newtonian viscous effects. So, this contribution presents a more general, well-structured framework of the multi-phase flows with enhanced gravity and dispersion effects, setting a foundation for a comprehensive simulation of such flows. I discuss some particular situations where the non-hydrostatic and dispersive effects are more pronounced for multi-phase mass flows. Even the reduced models demonstrate the importance of non-hydrostatic contributions for both the solid and fine-solid particles, and the viscous fluid. Analytical solutions are presented for some simple situations demonstrating how the new dispersive model can be reduced to non-dispersive motions, yet largely generalizing the existing non-dispersive models. I postulate a novel, spatially varying dissipative force, called the prime-force, which physically controls the dynamics, run-out and the deposition of the mass flow in a precise way. The practitioners and engineers may find this force very useful in relevant technical applications. This illuminates the need of formally including the prime-force in the momentum balance equation. A simple dispersion equation is derived. I highlight the essence of dispersion on the mass flow dynamics. Dispersion consistently produces a wavy velocity field about the reference state without dispersion. Emergence of such a dispersive wave is the first of this kind for the avalanching debris mass. It is revealed that the dispersion intensity increases energetically as the solid volume fraction or the friction decreases.

Comparison between linear frequency-modulated ultrasonic excitation signals and pure tones for concrete applications

Non-destructive testing has supported prognosis and health management in the construction industry for decades. Among them, ultrasonic tests (UT) are increasingly used to assess the structural integrity of the concrete. Typically, the UT uses pure tones as the excitation signal. However, an alternative is to use a linear frequency-modulated pulse (LFMP) followed by compression. This process improves the signal-to-noise ratio, provides broadband frequency responses, and is less susceptible to propagation dispersion. This work compared the ultrasonic transit times (UTT) of LFMP and pure tones. Three nondispersive models for concrete materials were numerically simulated using the k-Wave MATLAB toolbox. Additionally, a sample of reactive powder concrete (RPC) was experimentally tested. The frequencies ranged from 50 kHz to 750 kHz for both simulations and experiments. The simulation results presented LFMP relative errors in UTTs ranging from 0.0 % to 2.7 % compared to the theoretical values, whereas for pure tones, the RE was 2 % to 63 %. Experimentally, as no theoretical value can be considered, the quantitative comparison was the measurement dispersion under repeatability conditions. LFMPs disclosed a standard deviation in transit time of 35 ns, whereas for pure tones, it ranged from 43 to 51 ns. This research reinforces the potential of LFMP excitation compared to traditional pure tones, providing more accurate and precise ultrasonic velocity measurements in heterogeneous environments.

Frequency dispersion amplifies tsunamis caused by outer-rise normal faults

Although tsunamis are dispersive water waves, hazard maps for earthquake-generated tsunamis neglect dispersive effects because the spatial dimensions of tsunamis are much greater than the water depth, and dispersive effects are generally small. Furthermore, calculations that include non-dispersive effects tend to predict higher tsunamis than ones that include dispersive effects. Although non-dispersive models may overestimate the tsunami height, this conservative approach is acceptable in disaster management, where the goal is to save lives and protect property. However, we demonstrate that offshore frequency dispersion amplifies tsunamis caused by outer-rise earthquakes, which displace the ocean bottom downward in a narrow area, generating a dispersive short-wavelength and pulling-dominant (water withdrawn) tsunami. We compared observational evidence and calculations of tsunami for a 1933 Mw 8.3 outer-rise earthquake along the Japan Trench. Dispersive (Boussinesq) calculations predicted significant frequency dispersion in the 1933 tsunami. The dispersive tsunami deformation offshore produced tsunami inundation heights that were about 10% larger than those predicted by non-dispersive (long-wave) calculations. The dispersive tsunami calculations simulated the observed tsunami inundation heights better than did the non-dispersive tsunami calculations. Contrary to conventional practice, we conclude that dispersive calculations are essential when preparing deterministic hazard maps for outer-rise tsunamis.

Comparison of Dispersive and Nondispersive Models for Wave Run-Up on a Beach

The applicability of dispersive and nondispersive wave models for describing long-wave propagation and run-up on a beach in the case of composite bottom topography is investigated: a plane beach transforms into a zone of constant depth. Numerical simulations are performed in the framework of two models: (1) nonlinear shallow-water theory and (2) the dispersive model in the Boussinesq approximation based on modified Peregrine equations. Simulations are compared with the data of a laboratory experiment for different types of waves: regular waves, biharmonic signals, and “vessel-like” wave trains strongly modulated by frequency and amplitude. Conclusions about the applicability of the corresponding theories for describing considered types of waves are drawn based on this comparison.

Stripping induced polarization effects from airborne electromagnetics to improve 3D conductivity inversion of a narrow palaeovalley

The electrical conductivity distribution within wide palaeochannels is usually well-mapped from airborne electromagnetic data using stitched 1D algorithms. Such stitched 1D solutions are, however, inappropriate for narrow valleys. An alternative option is to consider 2D or 3D models to allow for finite lateral extent of conductors. In airborne electromagnetic data within the Musgrave block near the well-studied Valen conductor, strong induced polarization (IP) and superparamagnetic (SPM) effects make physical property and structure estimation even more uncertain for deep channel clays, particularly those whose channel widths are comparable to their depth of burial. We developed a recursive data fitting algorithm based on dispersive thin sheet responses. The separate IP and SPM components of the fit provide near-surface chargeability and SPM distributions, and the associated electromagnetic (EM) fit provides stripped data with monotonic decays compatible with a simple nondispersive conductivity model. The validity of this stripped data prediction was tested through a comparison of 1D conductivity-depth imaging and 3D inversion applied to the original data and the stripped data. Due to the forked geometry of the deep conductivity structure in the region we investigated, we successfully used 3D rather than 2D inversion to predict the conductivity distribution related to the EM data. We recovered from the stripped data a continuous conductivity structure consistent with a branching, clay-filled palaeovalley under cover.

Far-Field Characteristics of Linear Water Waves Generated by a Submerged Landslide over a Flat Seabed

Understanding the propagation of landslide-generated water waves is of great help against tsunami hazards. In order to investigate the effects of landslide shapes on the far-field leading wave generated by a submerged landslide at a constant depth, three linear wave models with different degrees of dispersive properties are employed in this study. The linear fully dispersive model is then validated by comparing the results against the experimental data available for landslides with a low Froude number. Three simplified shapes of landslides with the same volume, which are unnatural for a body of incoherent material, are used to investigate the effects of landslide shapes on the far-field properties of the generated leading wave over a flat seabed. The results show that the far-field leading crest over a constant depth is independent of the exact landslide shape and is invalid at a shallow water depth. Therefore, the most popular non-dispersive model (also called the shallow water wave model) cannot be used to reproduce the phenomenon. The weakly dispersive wave model can predict this phenomenon well. If only the leading wave is considered, this model is accurate up to at least μ = h0/Lc = 0.6, where h0 is the water depth and Lc denotes the characteristic length of the landslide.

A dispersive homogenization model for composites and its RVE existence

An asymptotic homogenization model considering wave dispersion in composites is investigated. In this approach, the effect of the microstructure through heterogeneity-induced wave dispersion is characterised by an acceleration gradient term scaled by a “dispersion tensor”. This dispersion tensor is computed within a statistically equivalent representative volume element (RVE). One-dimensional and two-dimensional elastic wave propagation problems are studied. It is found that the dispersive multiscale model shows a considerable improvement over the non-dispersive model in capturing the dynamic response of heterogeneous materials. To test the existence of an RVE for a realistic microstructure for unidirectional fiber-reinforced composites, a statistics study is performed to calculate the homogenized properties with increasing microstructure size. It is found that the convergence of the dispersion tensor is sensitive to the spatial distribution pattern. A calibration study on a composite microstructure with realistic spatial distribution shows that convergence is found although only with a relatively large micromodel.

Nonlinear Dispersive Model of Electroporation for Irregular Nucleated Cells.

In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non-local, dispersive, and space-time multiphysics model based on Maxwell's and asymptotic Smoluchowski's equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi-relaxation Debye-based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non-dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331-342. © 2019 Wiley Periodicals, Inc.

Performance Benchmarking Tsunami Models for NTHMP’s Inundation Mapping Activities

The coastal states and territories of the United States (US) are vulnerable to devastating tsunamis from near-field or far-field coseismic and underwater/subaerial landslide sources. Following the catastrophic 2004 Indian Ocean tsunami, the National Tsunami Hazard Mitigation Program (NTHMP) accelerated the development of public safety products for the mitigation of these hazards. In response to this initiative, US coastal states and territories speeded up the process of developing/enhancing/adopting tsunami models that can be used for developing inundation maps and evacuation plans. One of NTHMP’s requirements is that all operational and inundation-based numerical (OI since they are considered as sufficiently comprehensive. Average relative errors associated with expected parameters values such as maximum surface amplitude/runup are estimated. The level of agreement with the reference data, reasons for discrepancies between model results, and some of the limitations are discussed. In general, dispersive models were found to perform better than nondispersive models, but differences were relatively small, in part because the BPs mostly featured long waves, such as solitary waves. The largest error found (e.g., the laboratory experiment case of a solitary wave on a simple beach) was 10 % for non-breaking wave conditions and 12 % for breaking conditions; these errors are equal or smaller than the thresholds (10 % and 20 %, respectively) defined by the OAR-PMEL-135 for predicting the surface profile; hence, all models examined here are deemed acceptable for inundation mapping purposes.

Ground-roll subtraction from common-shot gathers with significant trace-to-trace variations in the energy of random noise

Conventional f–k filtering and filtering based on singular value decomposition (SVD) or on some related transformations have proved to be effective tools to eliminate ground roll from seismic records. These methods, however, operate successfully when the energy of additive random noise is quite stable or relatively low on different traces. Otherwise, when some traces are contaminated by anomalous noise, the methods become ineffective or even deleterious and require pre-editing of the noisy traces. This process, however, is somewhat subjective and results in gaps, which are harmful to further seismic imaging, processing and interpretation techniques. To avoid these drawbacks, we propose the two-stage weighted stacking recently developed for optimally estimating the signal from seismic data contaminated by both spatially coherent and random noise. The first stage is targeted for the ground-roll subtraction and is performed with respect to the amplitudes and arrival times of ground roll and the variances of random noise. In the second stage, intended for ultimate signal reconstruction, the residual data undergo optimum stacking with respect to the amplitudes and arrival times of the signal and the variances of random noise. We compare f–k filtering, SVD-based filtering and optimum stacking on two common-shot gathers contaminated by different types of severe ground rolls, with one being almost non-dispersive and the other mildly dispersive. With these data, the three methods give comparable results. To mimic significant trace-to-trace variations in the noise energy, we add synthetic noise to some traces on both shot gathers. In this case, SVD-based filtering and f–k filtering fail, whereas one-stage optimum stacking efficiently subtracts the ground roll but leaves the random noise on the anomalous traces almost untouched. In turn, two-stage optimum stacking greatly diminishes the random noise, considerably refines the data and therefore outperforms SVD-based filtering and f–k filtering. When handling the dispersive ground roll, we combine SVD-based filtering and optimum stacking with a special pre-conditioning linear transform. It is intended to reduce the deviation of such surface waves from their idealized non-dispersive model, and thus to favor both ground-roll subtraction methods.

Wave Propagation in a Timoshenko Beam Building Model

This study analyzes wave propagation in a Timoshenko beam model of a high-rise building excited by base motion. This model accounts for wave dispersion caused by bending and is more realistic for analysis of wave propagation in high-rise buildings than shear beam and other discrete nondispersive models. The model transfer functions and impulse response functions are obtained from the analytical solution for a forced vibration response of the beam excited by base motion. The impulse response functions represent the model response to a virtual input pulse; a set of such functions at different levels is used to study pulse propagation in the beam. A parametric study of dispersion and its effects on the model transfer functions and impulse response functions is presented in terms of dimensionless parameters and in ranges corresponding to buildings. The model is validated for a 9-story full-scale RC building and smaller earthquake excitation. The results provide insight into dispersive wave propagation in buildings caused by bending, which is useful for the interpretation of impulse responses of buildings obtained from earthquake records and for the development and testing of wave methods for structural health monitoring. The results can also be used for testing numerical models for pulse propagation in buildings.

Minimum variance guided wave imaging in a quasi-isotropic composite plate

Ultrasonic guided waves are capable of rapidly interrogating large, plate-like structures forboth nondestructive evaluation and structural health monitoring (SHM) applications.Distributed sparse arrays of inexpensive piezoelectric transducers offer a cost-effective wayto automate the interrogation process. However, the sparse nature of the array limits theamount of information available for performing damage detection and localization.Minimum variance techniques have been incorporated into guided wave imaging to reducethe magnitude of imaging artifacts and improve the imaging performance for sparse arraySHM applications. The ability of these techniques to improve imaging performance isrelated to the accuracy of a priori model assumptions, such as scattering characteristics anddispersion. This paper reports the application of minimum variance imaging under slightlyinaccurate model assumptions, such as are expected in realistic environments.Specifically, the imaging algorithm assumes an isotropic, non-dispersive, single modepropagating environment with a scattering field independent of incident angle andfrequency. In actuality, the composite material considered here is not only slightlyanisotropic and dispersive but also supports multiple propagating modes, andadditionally, the scattering field is dependent on the incident angle, scattered angle,and frequency. An isotropic propagation velocity is estimated via calibrationprior to imaging to implement the non-dispersive model assumption. Imagingperformance is presented under these inaccurate assumptions to demonstrate therobustness of minimum variance imaging to common sources of imaging artifacts.

Modeling tsunamis generated by submerged landslides using depth integrated equations

We present a depth integrated numerical model for the simulation of the generation and the propagation of tsunamis generated by submerged landslides. The model is able to reproduce at low computational costs the full frequency dispersion of the waves and uses an ad hoc treatment for the incorporation of the effects of the moving seafloor to reproduce the generation of the waves. We also compare the present approach with some simplified techniques used in the past for the generation of these waves in depth integrated models, and we highlight the different behavior of frequency-dispersive and non-dispersive model equations. Reference solutions for comparison and discussion are obtained from the application of a three dimensional solver of the Laplace equation. All the numerical models used in this research are based on linearized model equations and boundary conditions and are therefore expected to provide reliable results for problems involving small amplitude waves and small thickness landslides. The model seems to be useful for rapid and accurate estimation of the properties of landslide generated waves, and can be used to support a tsunami early warning system.

Wave localization in one-dimensional periodic-on-average disordered system composed of single-negative metamaterials

By using the transfer-matrix method,we study the Anderson localization behavior in one-dimensional periodic-on-average disordered system composed of two different single-negative(SNG) metamaterials. Non-dispersive and dipersive models have been studied respectively. It was found that the disorder has great effect on waves with frequency in the pass band of the corresponding periodic structure. However,inside the gap,the effect can be almost ignored. These features are different from those we ever found in the random single-negative system. The main reason of the difference should be the number of the interfaces between two kinds of single negative metamateirals,which should be the basic mechanism of the wave propagation in systems made of single negative metamaterials. In periodic-on-average disordered systems,the number of the interface is the same as that in periodic one. However,there is an obvious decrease in random systems,which will have a great effect on the ability of wave transport,leading to small localization length. In the case of a dispersive model,it has been proved that the randomness has no effect on the wave propagation with frequency at the center of the gap. Especially,this special point becomes a delocalization point when the ratio of effective optical thickness of two single negative materials equals one. The results facilitates further understanding of the wave transport mechanism in systems composed of metamaterials.

Wave dispersion study for tsunami propagation in the Sea of Marmara

In this paper the aim is to investigate whether there are differences between the dispersion and non-dispersion solutions on tsunami propagation. For this purpose, two numerical models of tsunami propagation are compared. One of these numerical models is a nondispersive model that uses Saint Venant equations and the other is a dispersive model that uses Boussinesq equations. The tsunamis resulting from a submarine mass failure (SMF) which is settled at the bottom of the north eastern Sea of Marmara are examined. An analytical solution considering wave dispersion is developed for obtaining near-field tsunami amplitudes above the submarine mass failure. Numerical modeling is used at the sea surface from the common boundary called as liquid boundary with incident waves up to the coastal regions to get the tsunami amplitudes. The output of the analytical model is taken as the disturbances for the numerical method. In the numerical solutions TELEMAC-2D software system is used for both dispersive and nondispersive modeling. The results of the dispersive and nondispersive models are compared to each other. Both temporal and spatial differences in the amplitudes and wave shapes are examined. The obtained results demonstrate that there are no noticeable differences between the dispersion and non-dispersion solutions except some special cases and some special landslide velocities.

Study of dispersive mobility in polyimide by surface voltage decay measurements

In order to study charge trapping and transport in polyimide, we have submitted samples of Kapton HN to corona charging and measured its surface potential decay with an electrostatic voltmeter. We propose a two terms mobility to explain the experimental data: a non-dispersive contribution based on Toomer and Lewis model added to a dispersive process, which is associated with the disordered structure of the material. The non-dispersive model alone did not fit well to the data for short times, but our assumption makes the theoretical expression fit successfully to the experimental data. Some important parameters related to the charge transport properties of the material are determined and discussed.

Advective transport of CO2in permeable media induced by atmospheric pressure fluctuations: 1. An analytical model

Advective flows within soils and snowpacks caused by pressure fluctuations at the upper surface of either medium can significantly influence the exchange rate of many trace gases from the underlying substrate to the atmosphere. Given the importance of many of these trace gases in understanding biogeochemical cycling and global change, it is crucial to quantify (as much as possible) any impact these flows can have on the transport of these gases. This study (part 1 of 2) details a new model describing the influence that naturally occurring, pressure‐driven, oscillatory advective flows have on CO2profiles within soils and snowpacks and on the associated CO2fluxes emanating from the underlying source. This model, which consists of two layers with differing permeability and CO2source strength, is developed for both a dispersive and a nondispersive medium. The pressure forcing and the CO2response, modeled as plane waves in time and the horizontal direction, have amplitudes that vary in the vertical direction as described by analytical solutions to the diffusion equation (for pressure) and the advective‐diffusive and dispersive‐diffusive equations (for CO2). In the case of a dispersive medium, the dispersion coefficient is derived in terms of the horizontal wave number and amplitude of the pressure forcing at the upper surface and the vertical structure and dispersivity of the medium. Diffusive flux enhancement factors, developed for the dispersive and nondispersive models, are expressed as functions of the surface amplitude of the pressure forcing, the permeability and cross‐sectional shape and dimension of the pore tubes of the medium, and the vertical structure of the medium. Results indicate that advective flows induced by naturally occurring atmospheric pressure fluctuations are likely to enhance diffusive fluxes more in a dispersive medium than a nondispersive medium. However, such pressure forcing can significantly enhance diffusive fluxes in either medium.

On-Chip Millionfold Sample Stacking Using Transient Isotachophoresis

We present a simple and robust isotachophoresis (ITP) method that can be integrated with microchip-based capillary electrophoresis (CE) devices to achieve millionfold sample stacking. We performed an experimental parametric study to show the effects of initial sample ion concentration, leading ion concentration, and trailing ion concentration on ITP stacking. We also discuss the usefulness and limitations of a simple one-dimensional nondispersive model and a scaling analysis for dispersion rate. We found that a single-column ITP configuration together with electroosmotic flow suppression and high leading ion concentration provide high-performance ITP and can be integrated readily with CE separation. We demonstrated detection of trace of 100 fM Alexa Fluor 488 (signal-to-noise ratio of 11) with a concentration increase of a factor of 2 x 10(6). Application of our ITP/CE protocol to the stacking and separation of negatively charged fluorescent tracers (Alexa Fluor 488 and bodipy) resulted in a concentration increase of 6.4 x 10(4) and a signal increase of 4.5 x 10(5). The ITP/CE protocol can be performed with a standard microchannel cross design or simple flow control. The method can be implemented with available off-the-shelf chip systems using off-the-shelf voltage control systems and buffer chemistries.