scholarly journals A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 920
Author(s):  
Chukwuma Ogbonnaya ◽  
Chamil Abeykoon ◽  
Adel Nasser ◽  
Ali Turan
Keyword(s):  
Numerical Models ◽  
Problem Formulation ◽  
Science And Engineering ◽  
Physical Systems ◽  
Engineering Problems ◽  
Parametric Studies ◽  
Independent Variable ◽  
Transcendental Equations ◽  
The Waves ◽  
Modelling Approach

A system of transcendental equations (SoTE) is a set of simultaneous equations containing at least a transcendental function. Solutions involving transcendental equations are often problematic, particularly in the form of a system of equations. This challenge has limited the number of equations, with inter-related multi-functions and multi-variables, often included in the mathematical modelling of physical systems during problem formulation. Here, we presented detailed steps for using a code-based modelling approach for solving SoTEs that may be encountered in science and engineering problems. A SoTE comprising six functions, including Sine-Gordon wave functions, was used to illustrate the steps. Parametric studies were performed to visualize how a change in the variables affected the superposition of the waves as the independent variable varies from x1 = 1:0.0005:100 to x1 = 1:5:100. The application of the proposed approach in modelling and simulation of photovoltaic and thermophotovoltaic systems were also highlighted. Overall, solutions to SoTEs present new opportunities for including more functions and variables in numerical models of systems, which will ultimately lead to a more robust representation of physical systems.

On modelling physical systems with stochastic models: diffusion versus Lévy processes

2008 ◽  
Vol 366 (1875) ◽  
pp. 2455-2474 ◽  
Author(s):  
Cécile Penland ◽  
Brian D Ewald
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Lévy Processes ◽  
Numerical Models ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Physical Systems ◽  
Random Forcing ◽  
Weather And Climate ◽  
Made In

Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

Numerical simulation of submarine landslide and generated tsunamis : Application to the Mayotte seismo-volcanic crisis

2021 ◽  
Author(s):  
Pablo Poulain ◽  
Anne Le Friant ◽  
Rodrigo Pedreros ◽  
Anne Mangeney ◽  
Andrea Filippini ◽  
...  
Keyword(s):  
Ground Deformation ◽  
Numerical Models ◽  
Morphological Data ◽  
Submarine Landslides ◽  
Submarine Slide ◽  
Seismic Swarms ◽  
Submarine Slides ◽  
High Resolution Bathymetry ◽  
The Impact ◽  
The Waves

<p>Since May 2018, Mayotte island has experienced an important seismic activity linked to the on-going sismo-volcanic crisis. The epicenters of the seismic swarms are located between 5 and 15 km east of Petite Terre for the main swarm, and 25 km east of Petite Terre for the secondary swarm. Although variations in the number of earthquakes and their distribution have been observed since the start of the eruption in early July 2018 [Lemoine A.(2020), Cesca et al.(2020)], a continuous seismicity persists and could generate several earthquakes of magnitudes close to M4 widely felt by the population. This recurrent seismicity could weaken the steep submarine slopes of Mayotte, as highlighted by the high resolution bathymetry data collected during the MAYOBS cruise in May 2019 (Feuillet et al.,submitted) and trigger submarine landslides with associated tsunamis.</p><p>To address the hazards associated with such events, we analyzed morphological data to define 8 scenarios of potential submarine slides with volumes ranging from 11,25.10<sup>6</sup> to 800.10<sup>6</sup> m<sup>3</sup> and we simulate the landslide dynamics and generated waves. We use two complementary numerical models: (i) the code HYSEA to simulate the dynamic of the submarine granular flows and the water wave generation, and (ii) the Boussinesq FUNWAVE- TVD model simulate the waves propagation and the inundation on Mayotte. The effect of the time at which the models are coupled is investigated.</p><p>The most impacting submarine slide scenarios are located close to Petite Terre at a shallow depth. They can locally generate a sea surface elevation more than a meter in local areas especially at Petite Terre. The various simulations show that parts of the island are particularly sensitive to the risk of tsunamis. Indeed, some scenarios that does not cause significant coastal flooding still seems to cause significant hazards in these exposed areas. The barrier reef around Mayotte has a prominent role in controlling the wave propagation towards the island and therefore reducing the impact on land. It should be noted that the arrival of tsunamis on the coastline is not necessarily preceded by a retreat from the sea and the waves can reach the coasts of Mayotte very quicky (few minutes).</p><p> </p><p>Cesca, S., Letort, J., Razafindrakoto, H.N.T. et al. Drainage of a deep magma reservoir near Mayotte inferred from seismicity and deformation. Nat. Geosci. <strong>13, </strong>87–93 (2020). https://doi.org/10.1038/s41561-019-0505-5</p><p>Feuillet, N, Jorry, S. J., Crawford, W, Deplus, C. Thinon, I, Jacques, E. Saurel, J.M., Lemoine, A., Paquet, F., Daniel, R., Gaillot, A., Satriano, C., Peltier, A., Aiken, C., Foix, O., Kowalski, P., Laurent, A., Beauducel, F., Grandin, R., Ballu, V., Bernard, P., Donval, J.P., Geli, L., Gomez, J. Guyader, V., Pelleau, P., Rinnert, E., Bertil, D., Lemarchand, A., Van der Woerd, J.et al. (in rev). Birth of a large volcano offshore Mayotte through lithosphere-scale rifting, Nature.</p><p>Anne Lemoine, Pierre Briole, Didier Bertil, Agathe Roullé, Michael Foumelis, Isabelle Thinon, Daniel Raucoules, Marcello de Michele, Pierre Valty, Roser Hoste Colomer, The 2018–2019 seismo-volcanic crisis east of Mayotte, Comoros islands: seismicity and ground deformation markers of an exceptional submarine eruption, Geophysical Journal International, Volume 223, Issue 1, October 2020, Pages 22–44, https://doi.org/10.1093/gji/ggaa273</p>

scholarly journals Determination of coupled sway, roll, and yaw motions of a floating body in regular waves

2004 ◽  
Vol 2004 (41) ◽  
pp. 2181-2197 ◽  
Author(s):  
S. N. Das ◽  
S. K. Das
Keyword(s):  
Dynamic Equilibrium ◽  
Numerical Models ◽  
Equations Of Motion ◽  
System Stability ◽  
Floating Body ◽  
Regular Waves ◽  
Laplace Transform Technique ◽  
Restoring Forces ◽  
The Waves

This paper investigates the motion response of a floating body in time domain under the influence of small amplitude regular waves. The governing equations of motion describing the balance of wave-exciting force with the inertial, damping, and restoring forces are transformed into frequency domain by applying Laplace transform technique. Assuming the floating body is initially at rest and the waves act perpendicular to the vessel of lateral symmetry, hydrodynamic coefficients were obtained in terms of integrated sectional added-mass, damping, and restoring coefficients, derived from Frank's close-fit curve. A numerical experiment on a vessel of19190ton displaced mass was carried out for three different wave frequencies, namely,0.56rad/s,0.74rad/s, and1.24rad/s. The damping parameters (ςi) reveal the system stability criteria, derived from the quartic analysis, corresponding to the undamped frequencies (βi). It is observed that the sway and yaw motions become maximum for frequency0.56rad/s, whereas roll motion is maximum for frequency0.74rad/s. All three motions show harmonic behavior and attain dynamic equilibrium for timet>100seconds. The mathematical approach presented here will be useful to determine seaworthiness characteristics of any vessel when wave amplitudes are small and also to validate complex numerical models.

scholarly journals Investigating the Effect of Stepped Scarf Repair Ratio in Repaired CFRP Laminates under Compressive Loading

2020 ◽  
Vol 4 (4) ◽  
pp. 153
Author(s):  
Spyridon Psarras ◽  
Theodoros Loutas ◽  
Magdalini Papanaoum ◽  
Orestis Konstantinos Triantopoulos ◽  
Vasilis Kostopoulos
Keyword(s):  
Numerical Models ◽  
Compressive Loading ◽  
Composite Plates ◽  
Step Length ◽  
Critical Threshold ◽  
Cfrp Laminates ◽  
Threshold Size ◽  
Repair Patch ◽  
Parametric Studies ◽  
Strength And Stiffness

In this work the effectiveness of stepped repairs to damaged fiber reinforced composite materials is investigated by using previously validated numerical models which were compared with tested repaired composite plates. Parametric studies were carried out in order to assess the scarf ratio (i.e., step length to ply thickness ratio) influence on ultimate forces, displacements, stresses and stiffnesses. FE models with repair scarf ratios varying from the value of 20 to the value 60 with a step increase of 10 were developed. The numerical models allowed a direct comparison of the influence that the scarf ratio had to the strength and stiffness restoration of the repaired composite structure. The study verifies that the restoration of the strength of a damaged laminate depends largely on the size of the repair patch. Generally, the bigger the size of a patch, the stronger the repaired structure is, up to a critical threshold size. To maximize the strength restoration, it is advised that the number of steps in each patch are no less than the number of plies on the base laminate.

Modeling of Fabric Impact With High Speed Imaging and Nickel-Chromium Wires Validation

2011 ◽  
Vol 78 (5) ◽  
Author(s):  
Sidney Chocron ◽  
Trenton Kirchdoerfer ◽  
Nikki King ◽  
Christopher J. Freitas
Keyword(s):  
Numerical Simulations ◽  
High Speed ◽  
Numerical Models ◽  
Single Layer ◽  
Diagnostic Techniques ◽  
High Speed Photography ◽  
High Speed Imaging ◽  
Nickel Chromium ◽  
Validation Set ◽  
The Waves

Ballistic tests were performed on single-yarn, single-layer and ten-layer targets of Kevlar® KM2 (600 and 850 denier), Dyneema® SK-65 and PBO® (500 denier). The objective was to develop data for validation of numerical models so, multiple diagnostic techniques were used: (1) ultra-high speed photography, (2) high-speed video and (3) nickel-chromium wire technique. These techniques allowed thorough validation of the numerical models through five different paths. The first validation set was at the yarn level, where the transverse wave propagation obtained with analytical and numerical simulations was compared to that obtained in the experiments. The second validation path was at the single-layer level: the propagation of the pyramidal wave observed with the high speed camera was compared to the numerical simulations. The third validation consisted of comparing, for the targets with ten layers, the pyramid apex and diagonal positions from tests and simulations. The fourth validation, which is probably the most relevant, consisted of comparing the numerical and experimental ballistic limits. Finally for the fifth validation set, nickel-chromium wires were used to record electronically the waves propagating in the fabrics. It is shown that for the three materials the waves recorded during the tests match well the waves predicted by the numerical model.

scholarly journals The Use Of STEM Approaches To Widen Formula Derivation Steps In Material Science And Engineering Programmes At Higher Education Institutions

2021 ◽  
Vol 17 (29) ◽  
pp. 38
Author(s):  
Charles Darko
Keyword(s):  
Higher Education ◽  
Material Science ◽  
Higher Education Institutions ◽  
Cognitive Learning ◽  
Science And Engineering ◽  
Derivation Step ◽  
Ongoing Work ◽  
Self Study ◽  
Engineering Problems ◽  
Formula Derivation

Many complex formula derivation steps found within material science and engineering programmes are essential skill-developing activities that enhance students’ learning. However, most students lack the required mathematical knowledge to fully comprehend some of those derivation steps. This work developed a framework of clarifying some of the formula derivations steps by adding further mathematical steps that support the students’ constructive and cognitive learning. Some derivation steps were added to the derivations of the theoretical tensile strength model as well as the Maxwell’s and the Voigt-Kelvin models. The idea was not to disrupt students’ constructive or cognitive learning processes but to facilitate their learning since their ultimate aim is not to derive but to apply the steps of the modified derivations in solving other material science and engineering problems. The students benefited from the activities in two folds; firstly, they understood the reasons behind each derivation step and secondly, it improved their self-study activities by reducing their study periods. These activities provide a platform to widen STEM activities at higher education institutions. The ongoing work will look at other important formula derivation steps within material science and engineering that can enhance students’ learning.

scholarly journals NATURAL WAVE TRAINS: DESCRIPTION AND REPRODUCTION

1978 ◽  
Vol 1 (16) ◽  
pp. 16 ◽  
Author(s):  
H. Lundgren ◽  
S.E. Sand
Keyword(s):  
Numerical Models ◽  
Wave Train ◽  
Three Dimensional ◽  
Correct Description ◽  
Linear Superposition ◽  
Natural Wave ◽  
Wave Trains ◽  
Steep Waves ◽  
Deterministic Description ◽  
The Waves

In many applications there is a great need for a correct description of the natural, irregular three-dimensional sea and its reproduction in physical and numerical models. Because of the tremendous difficulties inherent in the nonlinearities, the science of coastal engineering is still very far from this ultimate goal. Indeed, the scope of this paper is comparatively very modest: To describe and reproduce natural, irregular two-dimensional waves, i.e. waves propagating in one direction in a flume. In addition, this scope is fulfilled only by assuming linear superposition of Fourier terms. As opposed to the usual spectral description, the deterministic description presented here does not eliminate the phase information in the wave train recorded. Because of the nonlinearities, however, the linear deterministic description invariably degenerates with the distance travelled by the waves. It appears though from the present paper that the degeneration is fairly slow even for rather steep waves.

scholarly journals NUMERICAL MODELING OF WAVE PENETRATION IN OSTEND HARBOUR

2011 ◽  
Vol 1 (32) ◽  
pp. 42 ◽  
Author(s):  
Vasiliki Stratigaki ◽  
Dieter Vanneste ◽  
Peter Troch ◽  
Stefaan Gysens ◽  
Marc Willems
Keyword(s):  
Numerical Model ◽  
Numerical Models ◽  
Boussinesq Equations ◽  
Propagation Model ◽  
Model Based ◽  
The North ◽  
The North Sea ◽  
Rubble Mound Breakwaters ◽  
The Waves ◽  
Integrated Study

The initial Ostend harbour entrance at the North Sea coast of Belgium is being modified and extended with two new rubble-mound breakwaters. Through an integrated study of the wave penetration in Ostend harbour, the waves are being acquired by prototype measurements and physical and numerical modelling is carried out. Two numerical models are used. SimWave is a numerical model based on Nwogu’s extended Boussinesq equations. The second numerical model is MILDwave, a mild-slope wave propagation model based on the equations of Radder and Dingemans. The present study concentrates on applications of the numerical models, throughout the different design stages and construction phases of the new breakwaters.

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