Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave model

Before going further with fractional derivative which is constructed by Rabotnov exponential kernel,there exist many questions that are not addressed.In this paper,we try to recapitulate all the fundamental calculus,which we can obtain with this new fractional operator.The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions,polynomial functions,exponential functions,trigonometric functions,or Mittag-Leffler functions.For all the fractional differential equations,the obtained solutions are represented graphically.The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations.Finally,we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel.

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

Bifurcation analysis and exact traveling wave solutions for (2+1)-dimensional generalized modified dispersive water wave equation

We investigate (2+1)-dimensional generalized modified dispersive water wave (GMDWW) equation by utilizing the bifurcation theory of dynamical systems. We give the phase portraits and bifurcation analysis of the plane system corresponding to the GMDWW equation. By using the special orbits in the phase portraits, we analyze the existence of the traveling wave solutions. When some parameter takes special values, we obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation.

Large-scale inverted-V channels of upflowing oxygen ions pumped by Alfvén waves

Large-scale inverted-V channels of upflowing oxygen ions are frequently identified in data collected by Cluster,at all local times,near the open-closed field line boundary over Earth’s high-latitude ionosphere-occur with downward propagating MHD Alfvén waves which have cascaded into kinetic regimes of plasma.The transverse acceleration of the oxygen ions in the center of these structures is interpreted as the integrated energization by these waves along the channels.Also observed within the channels are upward parallel electric fields,a key characteristic of kinetic Alfvén waves,which may contribute not only to lifting the ions but also to precipitating aurora electrons that might initiate ion upflow in the ionosphere below.Statistics on five-year observations of Cluster show that the channels typically form during geomagnetic perturbations,particularly when solar-wind dynamic pressure is high or highly fluctuated.Near the open-closed field line boundary,the stronger the wave power,the higher the upward oxygen flux and the higher the beam energy,indicating that these waves provide a simple but efficient way to drive oxygen upflows.

Dispersion of Axisymmetric Longitudinal Waves in A Bi-Material Compound Solid Cylinder Made of Viscoelastic Materials

The paper studies the dispersion of axisymmetric longitudinal waves in the bi-material compound circular cylinder made of linear viscoelastic materials.The investigations are carried out within the scope of the piecewise homogeneous body model by utilizing the exact equations of linear viscoelasto-dynamics.The corresponding dispersion equation is derived for an arbitrary type of hereditary operator and the algorithm is developed for its numerical solution.Concrete numerical results are obtained for the case where the relations of the constituents of the cylinder are described through fractional exponential operators.The influence of the viscosity of the materials of the compound cylinder on the wave dispersion is studied through the rheological parameters which indicate the characteristic creep time and long-term values of the elastic constants of these materials.Dispersion curves are presented for certain selected dispersive and non-dispersive attenuation cases under various values of the problem parameters and the influence of the aforementioned rheological parameters on these curves is discussed.As a result of the numerical investigations,in particular,it is established that in the case where the rheological parameters of the components of the compound cylinder are the same,the viscosity of the layers’materials causes the axisymmetric wave propagation velocity to decrease.

Shear Wave Speed Dispersion Characteristics of Seafloor Sediments in the Northern South China Sea

To accurately characterize the shear wave speed dispersion of seafloor sediments in the northern South China Sea,five types of sediments including silty clay,clayey silt,sandy silt,silty sand,and clayey sand were selected,on which the measurements of the shear wave speed at 0.5-2.0 kHz and related physical properties were performed.Results reveal that the shear wave speed of sediments increases as the frequency increases,and the dispersion enhanced in the sediments in the order of silty clay,clayey silt,sandy silt,silty sand,and clayey sand,at a linear change rate of 0.727,0.787,3.32,4.893,and 6.967 m s−1 kHz−1,respectively.Through regression analysis,linear and logarithmic regression equations for the correlation between shear wave speed and frequency were established for each sediment type and the determination coefficients of regression equations indicate that the correlation is closer to a logarithmic relationship.The Grain-Shearing(GS)and Biot-Stoll models were used to calculate the shear wave speed dispersion of the five sediment types,and the comparison between theoretical prediction and measured results of shear wave speeds shows that the GS model can more accurately describe the shear wave speed dispersion characteristics of these sediments in the frequency band of 0.5-2.0 kHz.In the same band,the predictions obtained by using the Biot-Stoll model are significantly different from the measured data.

Numerical simulation for recognition of coalfield fire areas by Rayleigh waves

Effective recognition of a coalfield fire area improves fire-fighting efficiency and helps avoid potential geological hazards. Coalfield fire areas are hard to detect accurately using general geophysical methods. This paper describes simulations of shallow, buried coalfield fires based on real geological conditions. Recognizing the coalfield fire by Rayleigh wave is proposed. Four representative geological models are constructed, namely; the non-burning model, the pseudo-burning model, the real-burning model, and the hidden-burning model. Numerical simulation using these models shows many markedly different characteristics between them in terms of Rayleigh wave dispersion and Eigen displacement. These characteristics, as well as the shear wave velocity obtained by inverting the fundamental dispersion, make it possible to distinguish the type of the coalfield fire area and indentify the real and serious coalfield fire area. The results are very helpful for future application of Rayleigh waves for the detection of coalfield fire area.

Increased P wave duration in patients with depression or anxiety disorder

BACKGROUND: Activation of the sympathetic nervous system plays an important role in regulating cardiovascular actions. P wave parameters can provide general information on central cardiovascular autonomic regulatory responses, which are altered in patients with anxiety disorders and depression. In particular, there are no reports addressing changes in P wave duration and dispersion. OBJECTIVE: To compare the differences in P wave duration and P wave dispersion between patients with anxiety disorders and depression, because patients with anxiety disorders and depression develop abnormal electrocardiograms. DESIGN, TIME AND SETTING: A non-randomized concurrent controlled study was performed. Patients with depression and general anxiety disorders were admitted at the psychiatry outpatient clinics of the Medical Faculty of Düzce University of Turkey between May 2005 and October 2006. PARTICIPANTS: A total of 71 consecutive patients with depression and anxiety disorders, as well as 50 physically and mentally healthy age- and gender-matched controls were selected. METHODS: Electrocardiogram records were obtained at the time of admission to the outpatient clinics. MAIN OUTCOME MEASURES: P wave duration and P wave dispersion were measured. RESULTS: Both the maximum (Pmax) and minimum (Pmin) P wave duration were greater in patients with psychiatric disorders than in healthy controls. Pmax was significantly greater in patients with depression or anxiety disorders (Bonferroni test, P < 0.017). The P wave dispersion was similar between patients and controls (P > 0.017). P waves were similar between panic patients and other anxiety patients. Beck depression results were positively correlated with Pmin and Pmax (r = 0.374, 0.302, P = 0.013, 0.049, respectively), and not associated with P wave dispersion (P > 0.05). CONCLUSION: Psychiatric disorders are associated with increases in Pmax, but not with P wave dispersion. The P wave changes were associated with the degree of depression.

S-wave velocity structure in Tangshan earthquake region and its adjacent areas from joint inversion of receiver functions and surface wave dispersion

Using the seismic records of 83 temporary and 17 permanent broadband seismic stations deployed in Tangshan earthquake region and its adjacent areas(39°N–41.5°N,115.5°E–119.5°E),we conducted a nonlinear joint inversion of receiver functions and surface wave dispersion.We obtained some detailed information about the Tangshan earthquake region and its adjacent areas,including sedimentary thickness,Moho depth,and crustal and upper mantle S-wave velocity.Meanwhile,we also obtained the vP/vS structure along two sections across the Tangshan region.The results show that:(1)the Moho depth ranges from 30 km to 38 km,and it becomes shallower from Yanshan uplift area to North China basin;(2)the thickness of sedimentary layer ranges from 0 km to 3 km,and it thickens from Yanshan uplift region to North China basin;(3)the S-wave velocity structure shows that the velocity distribution of the upper crust has obvious correlation with the surface geological structure,while the velocity characteristics of the middle and lower crust are opposite to that of the upper crust.Compared with the upper crust,the heterogeneity of the middle and lower crust is more obvious;(4)the discontinuity of Moho on the two sides of Tangshan fault suggests that Tangshan fault cut the whole crust,and the low vS and high vP/vS beneath the Tangshan earthquake region may reflect the invasion of mantle thermal material through Tangshan fault.

Crustal thickness,V_(P)/V_(S) ratio,and shear wave velocity structures beneath Myanmar and their tectonic implications

The crustal structure in Myanmar can provide valuable information for the eastern margin of the ongoing IndoEurasian collision system.We successively performed H-k stacking of the receiver function and joint inversion of the receiver function and surface wave dispersion to invert the crustal thickness(H),shear wave velocity(V_(S)),and the V_(P)/V_(S) ratio(k)beneath nine permanent seismic stations in Myanmar.H was found to increase from 26 km in the south and east of the study area to 51 km in the north and west,and the V_(P)/V_(S) ratio was complex and high.Striking differences in the crust were observed for different tectonic areas.In the Indo-Burma Range,the thick crust(H~51 km)and lower velocities may be related to the accretionary wedge from the Indian Plate.In the Central Myanmar Basin,the thin crust(H=26.9-35.5 km)and complex V_(P)/V_(S) ratio and V_(S) suggest extensional tectonics.In the Eastern Shan Plateau,the relatively thick crust and normal V_(P)/V_(S) ratio are consistent with its location along the western edge of the rigid Sunda Block.

Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-agation in a bar supported on a spring foundation.The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure.The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation.For each term,a corresponding substructure composed of dampers and masses is constructed.Finally,the equivalent mechan-ical structure is obtained by parallelly connecting these substructures.The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements.Numerical examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.

On similarity solutions to (2+1)-dispersive long-wave equations

This work is devoted to get a new family of analytical solutions of the(2+1)-coupled dispersive long wave equations propagating in an infinitely long channel with constant depth,and can be observed in an open sea or in wide channels.The solutions are obtained by using the invariance property of the similarity transformations method via one-parameter Lie group theory.The repeated use of the similarity transformations method can transform the system of PDEs into system of ODEs.Under adequate restrictions,the reduced system of ODEs is solved.Numerical simulation is performed to describe the solutions in a physically meaningful way.The profiles of the solutions are simulated by taking an appropriate choice of functions and constants involved therein.In each animation,a frame for dominated behavior is captured.They exhibit elastic multisolitons,single soliton,doubly solitons,stationary,kink and parabolic nature.The results are significant since these have confirmed some of the established results of S.Kumar et al.(2020)and K.Sharma et al.(2020).Some of their solutions can be deduced from the results derived in this work.Other results in the existing literature are different from those in this work.

Novel multi-parametric diagnosis of non-alcoholic fatty liver disease using ultrasonography,body mass index,and Fib-4 index

BACKGROUND Shear wave speed(SWS),shear wave dispersion(SWD),and attenuation imaging(ATI)are new diagnostic parameters for non-alcoholic fatty liver disease.To differentiate between non-alcoholic steatohepatitis(NASH)and non-alcoholic fatty liver(NAFL),we developed a clinical index we refer to as the“NASH pentagon”consisting of the 3 abovementioned parameters,body mass index(BMI),and Fib-4 index.AIM To investigate whether the area of the NASH pentagon we propose is useful in discriminating between NASH and NAFL.METHODS This non-invasive,prospective,observational study included patients diagnosed with fatty liver by abdominal ultrasound between September 2021 and August 2022 in whom shear wave elastography,SWD,and ATI were measured.Histological diagnosis based on liver biopsy was performed in 31 patients.The large pentagon group(LP group)and the small pentagon group(SP group),using an area of 100 as the cutoff,were compared;the NASH diagnosis rate was also investigated.In patients with a histologically confirmed diagnosis,receiveroperating characteristic(ROC)curve analyses were performed.RESULTS One hundred-seven patients(61 men,46 women;mean age 55.1 years;mean BMI 26.8 kg/m2)were assessed.The LP group was significantly older(mean age:60.8±15.2 years vs 46.4±13.2 years;P<0.0001).Twenty-five patients who underwent liver biopsies were diagnosed with NASH,and 6 were diagnosed with NAFL.On ROC curve analyses,the areas under the ROC curves for SWS,dispersion slope,ATI value,BMI,Fib-4 index,and the area of the NASH pentagon were 0.88000,0.82000,0.58730,0.63000,0.59333,and 0.93651,respectively;the largest was that for the area of the NASH pentagon.CONCLUSION The NASH pentagon area appears useful for discriminating between patients with NASH and those with NAFL.

A fully nonlinear and weakly dispersive water wave model for simulating the propagation,interaction,and transformation of solitary waves

This paper presents the development of a theoretical model of fully nonlinear and weakly dispersive(FNWD)waves and numerical techniques for simulating the propagation,interaction,and transformation of solitary waves.Using the standard expansion method and without the limit of small nonlinear parameter defined as the ratio of the wave height versus water depth,a set of model equations describing the FNWD waves in a domain of moderately varying bottom topography are formulated.Exact solitary wave solutions satisfying the FNWD equations are also derived.Numerically,a time-accurate and stabilized finite-element code to solve the governing equations is developed for wave simulations.The solitary wave solutions of FNWD,weakly nonlinear and weakly dispersive(WNWD),and Laplace equations based models in terms of wave profile and phase speed are compared to examine their related features and differences.Investigations on the overtaking collision of two unidirectional solitary waves of different amplitudes,i.e.,ax and a2 where a1>a2,are carried out using both the FNWD and WNWD water wave models.Selected cases by running the FNWD and WNWD models are performed to identify the critical values of a1/a2 for forming a flattened merging wave peak,which is the condition used to determine if the stronger wave is to pass through the weaker one or both waves are to remain separated during the encountering process.It is interesting to note the critical values of a1/a2 obtained from the FNWD and WNWD models are found to be different and greater than the value of 3 proposed by Wu through the theoretical analysis of the Korteweg-de Vries(KdV)equations.Finally,the phenomena of wave splitting and nonlinear focusing of a solitary wave propagating over a three-dimensional semicircular shoal are simulated.The results obtained from both the FNWD and WNWD models showing the fission process of separating a main solitary wave into multiple waves of decreasing amplitudes are presented,compared,and discussed.

Dissipative Kerr solitons in optical microresonators with Raman effect and third-order dispersion

Using the mean-field normalized Lugiato-Lefever equation,we theoretically investigate the dynamics of cavity soliton and comb generation in the presence of Raman effect and the third-order dispersion.Both of them can induce the temporal drift and frequency shift.Based on the moment analysis method,we analytically obtain the temporal and frequency shift,and the results agree with the direct numerical simulation.Finally,the compensation and enhancement of the soliton spectral between the Raman-induced self-frequency shift and soliton recoil are predicted.Our results pave the way for further understanding the soliton dynamics and spectral characteristics,and providing an effective route to manipulate frequency comb.

Dispersive Shallow Water Wave Modelling.Part II:Numerical Simulation on a Globally Flat Space

In this paper we describe a numerical method to solve numerically the weakly dispersive fully nonlinear SERRE-GREEN-NAGHDI(SGN)celebrated model.Namely,our scheme is based on reliable finite volume methods,proven to be very efficient for the hyperbolic part of equations.The particularity of our study is that we develop an adaptive numerical model using moving grids.Moreover,we use a special form of the SGN equations where non-hydrostatic part of pressure is found by solving a linear elliptic equation.Moreover,this form of governing equations allows to determine the natural form of boundary conditions to obtain a well-posed(numerical)problem.

Dispersive Shallow Water Wave Modelling.Part I:Model Derivation on a Globally Flat Space

In this paperwe reviewthe history and current state-of-the-art in modelling of long nonlinear dispersive waves.For the sake of conciseness of this review we omit the unidirectional models and focus especially on some classical and improved BOUSSINESQ-type and SERRE-GREEN-NAGHDI equations.Finally,we propose also a unified modelling framework which incorporates several well-known and some less known dispersive wave models.The present manuscript is the first part of a series of two papers.The second part will be devoted to the numerical discretization of a practically important model on moving adaptive grids.

P波时限、P波离散度对特发性心房颤动的预测价值初探(英文)

Objective:To assess the sensitivity and the specifity of predicting idiopathic AF with P wave duration and P wave dispersion. Methods:The maximum P wave duration and P wave dispersion in 36 patients with idiopathic AF were measured and compared with those of sex - and age - matched healthy subjects. Results:The maximum P wave duration and P wave dispersion were higher in patients with idiopathic Af than in control group. The maximum P wave duration ＞ 110ms or P wave dispersion ＞40ms was used to differentiate patients from healthy subjects, the sensitivity and the specifity value were 88% vs 82% and 75 % vs 86%, respectively. When the above two parameters were integrated, the sensitivity was 76 %, the specifity 88 %. Conclusion: The maximum P.wave duration and P wave dispersion are simple and practical ECG indexes for idiopathic AF patients.

Typical Circulation Patterns and Associated Mechanisms for Persistent Heavy Rainfall Events over Yangtze–Huaihe River Valley during 1981–2020

Persistent heavy rainfall events(PHREs)over the Yangtze–Huaihe River Valley(YHRV)during 1981–2020 are classified into three types(type-A,type-B and type-C)according to pattern correlation.The characteristics of the synoptic systems for the PHREs and their possible development mechanisms are investigated.The anomalous cyclonic disturbance over the southern part of the YHRV during type-A events is primarily maintained and intensified by the propagation of Rossby wave energy originating from the northeast Atlantic in the mid–upper troposphere and the northward propagation of Rossby wave packets from the western Pacific in the mid–lower troposphere.The zonal propagation of Rossby wave packets and the northward propagation of Rossby wave packets during type-B events are more coherent than those for type-A events,which induces eastward propagation of stronger anomaly centers of geopotential height from the northeast Atlantic Ocean to the YHRV and a meridional anomaly in geopotential height over the Asian continent.Type-C events have“two ridges and one trough”in the high latitudes of the Eurasian continent,but the anomalous intensity of the western Pacific subtropical high(WPSH)and the trough of the YHRV region are weaker than those for type-A and type-B events.The composite synoptic circulation of four PHREs in 2020 is basically consistent with that of the corresponding PHRE type.The location of the South Asian high(SAH)in three of the PHREs in 2020 moves eastward as in the composite of the three types,but the position of the WPSH of the four PHREs is clearly westward and northward.Two water vapor conveyor belts and two cold air conveyor belts are tracked during the four PHREs in 2020,but the water vapor path from the western Pacific is not seen,which may be caused by the westward extension of the WPSH.

Stress dependence of elastic wave dispersion and attenuation in fluid-saturated porous layered media

The fluid-saturated porous layered(FSPL)media widely exist in the Earth's subsurface and their overall mechanical properties,microscopic pore structure and wave propagation characteristics are highly relevant to the in-situ stress.However,the effect of in-situ stress on wave propagation in FSPL media cannot be well explained with the existing theories.To fill this gap,we propose the dynamic equations for FSPL media under the effect of in-situ stress based on the theories of poroacoustoelasticity and anisotropic elasticity.Biot loss mechanism is considered to account for the stress-dependent wave dispersion and attenuation induced by global wave-induced fluid flow.Thomsen's elastic anisotropy parameters are used to represent the anisotropy of the skeleton.A plane-wave analysis is implemented on dynamic equations yields the analytic solutions for fast and slow P waves and two S waves.Modelling results show that the elastic anisotropy parameters significantly determine the stress dependence of wave velocities.Vertical tortuosity and permeability have remarkable effects on fast and slow P-wave velocity curves and the corresponding attenuation peaks but have little effect on S-wave velocity.The difference in velocities of two S waves occurs when the FSPL medium is subjected to horizontal uniaxial stress,and the S wave along the stress direction has a larger velocity,which implies that the additional anisotropy other than that induced by the beddings appears due to horizontal stress.Besides,the predicted velocity results have the reasonable agreement with laboratory measurements.Our equations and results are relevant to a better understanding of wave propagation in deep strata,which provide some new theoretical insights in the rock physics,hydrocarbon exploration and stress detection in deep-strata shale reservoirs.