Denys Dutykh

Khalifa University of Science and Technology · Mathematics Department

The Lesser Antilles subduction zone delineates the boundary where the Caribbean Plate meets the Atlantic segment of the North American Plate. It features the extensive Barbados complex, an impressive accretionary prism. This region is known for its potential to generate megathrust earthquakes and tsunamis. This research focuses on the tsunami hazar...

Earthquakes imprint their signatures on lake sediments through event deposits, which serve as valuable paleoseismological archives. Among these deposits, homogenite layers are commonly associated with lake oscillations, i.e., seiches; however, the underlying mechanisms driving these oscillations remain insufficiently understood. This study investig...

This study presents an innovative approach to solar photovoltaic (PV) performance analysis through the integration of temperature and solar irradiance data using a graph-based community detection method. While previous research often considered these factors independently, our method captures their complex interactions, offering a more comprehensiv...

The state of health of solar photovoltaic (PV) systems is assessed by measuring the current-voltage (I-V) curves, which present a collection of three cardinal points: the short-circuit point, the open-circuit point, and the maximum power point. To understand the response of PV systems, the I-V curve is typically modeled using the well-known single-...

In this paper, we undertake a comprehensive examination of quasinormal modes linked to Lee-Wick black holes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Such black holes can display a rich structure of horizons, and our analysis considers all the representative scenarios, including extremal and n...

In this paper, we undertake a comprehensive examination of quasinormal modes (QNMs) linked to Morris-Thorne, also known as Bronnikov-Ellis wormholes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Our research corrects inaccuracies previously reported in the literature and addresses areas where the...

This study explores an ancient landslide and its ability to potentially generate a tsunami. This event took place approximately 11,700 years ago in Lake Aiguebelette, located in the northwestern Alps, France. By applying advanced underwater mapping techniques and computer modelling, we were able to reconstruct the origins and impact of this underwa...

In this paper, we undertake a comprehensive examination of quasinormal modes (QNMs) linked to Morris–Thorne, also known as Bronnikov–Ellis wormholes, delving into scalar, electromagnetic, and gravitational perturbations using the spectral method. Our research corrects inaccuracies previously reported in the literature and addresses areas where the...

We propose a scheme to enhance the sensitivity of non-Hermitian optomechanical mass sensors. The benchmark system consists of two coupled optomechanical systems where the mechanical resonators are mechanically coupled. The optical cavities are driven either by a blue-detuned or red-detuned laser to produce gain and loss, respectively. Moreover, the...

In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic one-step numerical method of order p in this part, and for the class of Backward Difference Formulas schemes in the...

The route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize and evolve into chaos. Two distinct transitions into chaotic behaviour were identified as energy levels incre...

Preliminary results on the application of polar coordinates for estimating the single-diode model

The route to chaos and the phase dynamics of the large scales in a rotating shallow-water model have been rigorously examined through the construction of an autonomous five-mode Galerkin truncated system employing complex variables, useful in investigating how large/meso-scales are destabilized and how their dynamics evolves and transits to chaos....

This article explores the exceptional integrability property of a family of higher‐order Benjamin–bona–mahony (BBM)‐type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann‐type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case whi...

We present the irreversibility generated by a stationary cavity magnomechanical system composed of a yttrium iron garnet (YIG) sphere with a diameter of a few hundred micrometers inside a microwave cavity. In this system, the magnons, i.e., collective spin excitations in the sphere, are coupled to the cavity photon mode via magnetic dipole interact...

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous cl...

This article explores the exceptional integrability property of a family of higher-order Benjamin-Bona-Mahony (BBM)-type nonlinear dispersive equations. Here, we highlight its deep relationship with a generalized infinite hierarchy of the integrable Riemann-type hydrodynamic equations. A previous Lie symmetry analysis revealed a particular case whi...

We present a comprehensive analysis of quasinormal modes (QNMs) for noncommutative geometry-inspired Schwarzschild black holes, encompassing both non-extreme and extreme cases. By employing a spectral method, we calculate the QNMs in the context of scalar, electromagnetic, and gravitational perturbations. Our findings not only challenge previous cl...

Mass 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...

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the application of high-order Finite Element (FE) to certain classes of PDEs, such as diffusion equations and the Navier...

Over the past decade, Finite Element Method (FEM) has served as a foundational numerical framework for approximating the terms of Time Series Expansion (TSE) as solutions to transient Partial Differential Equation (PDE). However, the application of high-order Finite Element (FE) to certain classes of PDEs, such as diffusion equations and the Navier...

Makran Subduction Zone (MSZ), located in the northwestern Indian Ocean, is susceptible to tsunamis through various mechanisms. With its history of tsunamis and potential for seismogenic activity, MSZ holds the potential to generate tsunamigenic earthquakes in the future. Traditionally, megathrust events have been the main tsunami generators. Howeve...

This study investigates a 12,000-year-old palaeotsunami in Lake Aiguebelette, France, using sedimentary records and numerical models to simulate the tsunami generated by underwater landslide during Younger Dryas to the Early Holocene climatic transition. The simulations suggest that the event produced substantial tsunami waves, providing new insigh...

The route to chaos in a truncated rotating shallow-water model has been investigated by constructing an autonomous five-mode Galerkin truncated system with complex variables. Two distinct transitions to chaos were observed as the energy injected into the system increased. The first transition is characterized by forming a continuous sequence of bif...

We present the irreversibility generated by a stationary cavity magnomechanical system composed of a yttrium iron garnet (YIG) sphere with a diameter of a few hundred micrometers inside a microwave cavity. In this system, the magnons, i.e., collective spin excitations in the sphere, are coupled to the cavity photon mode via magnetic dipole interact...

This Water Monograph shows the benefit of using relaxed variational methods for the water waves problem. It illustrates the advantage of using a variational principle involving as many dependent variables as possible. Its primary purpose here is to provide a generalized framework for deriving model equations for water waves. This methodology is elu...

A scheme that harnesses magnon squeezing under weak pump driving within a cavity magnomechanical system to achieve a robust magnon (photon) blockade is proposed. Through meticulous analytical calculations of optimal parametric gain and detuning values, the objective is to enhance the second‐order correlation function. The findings demonstrate a sub...

We propose a scheme to enhance the sensitivity of Non-Hermitian optomechanical mass-sensors. The benchmark system consists of two coupled optomechanical systems where the mechanical resonators are mechanically coupled. The optical cavities are driven either by a blue or red detuned laser to produce gain and loss, respectively. Moreover, the mechani...

Muscle fatigue is the decay in the ability of muscles to generate force, and results from neural and metabolic perturbations. This article presents an integrative mathematical model that describes the decrease in maximal force capacity (i.e. fatigue) over exercises performed at intensities above the critical force Fc (i.e. severe domain). The model...

We present a scheme for controlling quantum correlations by applying feedback to the cavity mode that exits a cavity while interacting with a mechanical oscillator and magnons. In a hybrid cavity magnomechanical system with a movable mirror, the proposed coherent feedback scheme allows for the enhancement of both bipartite and tripartite quantum co...

Mass movements and delta collapses are significant sources of tsunamis in lacustrine environments, impacting human societies enormously. Palaeotsunamis play an essential role in understanding historical events and their consequences along with their return periods. Here, we focus on a palaeo event that occurred during the Younger Dryas to Early Hol...

The I-V curves of solar photovoltaic (PV) systems have been widely used as a tool to determine their electrical operation. Usually, I-V curves are described by means of three cardinal points: the short-circuit point ( 0 , I sc ) , the open-circuit point ( V oc , 0 ) , and the maximum power point ( V mp , I mp ) . In this context, to study the I-V c...

We propose a scheme to achieve magnon (photon) blockade by using magnon squeezing within a cavity magnomechanical system under weak pump driving. Under ideal conditions, we observe a substantial magnon blockade effect, as well as simultaneous photon blockade. Moreover, both numerical and analytical results match perfectly, providing robust evidence...

Muscle fatigability corresponds to the decrease in the ability of muscles to generate force. The Critical Power (Pc) concept [1] predicts the point at which fatigue develops in such a way that the required constant intensity will no longer be sustainable (W’ reserve is emptied). During all-out tests, the power plateau is reached at the end of the t...

Procédé d’estimation de l’état de charge d’une batterie au plomb en situation d’autodécharge Procédé d’estimation de l’état de charge d’une batterie rechargeable au plomb électriquement au repos, la batterie comportant au moins une cellule électrochimique comportant un électrolyte acide, au moins une électrode négative en plomb et au moins une élec...

Procédé d'estimation de l'état de charge d'une batterie au plomb en situation d'autodécharge Procédé d'estimation de l'état de charge d'une batterie rechargeable au plomb électriquement au repos, la batterie comportant au moins une cellule électrochimique comportant un électrolyte acide, au moins une électrode négative en plomb et au moins une élec...

The Lesser Antilles subduction zone marks the convergence between the Caribbean Plate and the oceanic Atlantic part of the America Plate. A specificity of this subduction is the development of a huge accretionary prism, the Barbados complex. As other subduction zones, the Lesser Antilles one has the potential to produce megathrust-associated earthq...

Slides of a mini-lecture given to Master and PhD students of the Solar Academy, France. This theoretical presentation was followed by examples given by Dr. Sylvain Lespinats (CEA/INES, France).

Responding to the need of a growing community of students and researchers who want to get involved in the field of electrochemical storage systems, NEOLAB offers a new tool dedicated to a modeling domain where almost no open-source solutions exist. Physics-based models of batteries require extensive knowledge in thermodynamics, electro-chemistry, m...

A method for determining the state of a system among a plurality of states, includes acquiring values of a reference physical quantity of the system corresponding to a plurality of points in an original space, each value being paired with one point of the plurality of points and with one state of the system; embedding a portion of the points in a r...

The reduction modulo p of a family of lacunary integer polynomials, associated with the dynamical zeta function ζβ(z)of the β-shift, for β> 1 close to one, is investigated. We briefly recall how this family is correlated to the problem of Lehmer. A variety of questions is raised about their numbers of zeroes in 𝔽p and their factorizations, via Kron...

The purpose of the work is revolved around presenting a literature review applied to wave-structure interactions. During this literature review, three types of breakwaters are presented: Bottom submerged breakwater, submerged plate, and seawalls breakwaters. Further, a numerical method used recently to study wave-structure interactions is presented...

In this paper, the spectral method is developed as a reduced-order model for the solution of parametric problems within the building refurbishment framework. We propose to use the spectral reduced-order method to solve parametric problems in an innovative way, integrating the unknown parameter as one of the coordinates of the decomposition. The res...

This work proposes a novel calculus method that goes deeper into the nature of photovoltaic technology. For this purpose, a distributed solar cell model is used to calculate the IV curves of a solar module. The main advance of this approach is that the user can set the topology of the solar module, as well as each parameter of the solar cells that...

Un aspect de l’invention concerne un procédé de détermination de l’état d’un système parmi une pluralité d’états comprenant une étape (E1) d’acquisition d’une pluralité de valeurs d’au moins une grandeur physique de référence du système correspondant à une pluralité de points dans un espace d’origine, chaque valeur de la pluralité de valeurs étant...

Nonlinear dynamics have become a new perspective on model human movement variability; however, it is still a debate whether chaotic behavior is indeed possible to present during a rhythmic movement. This paper reports on the nonlinear dynamical behavior of coupled and synchronization models of a planar rhythmic arm movement. Two coupling schemes be...

Fault detection and diagnosis (FDD) are important tools to perform on-going monitoring of the systems and help in their building commissioning. An innovative method is investigated based on combined data-driven and knowledge-based approaches. This article presents the method. In the first phase, a so-called operating map of the system is built usin...

In this manuscript we perform an extensive numerical study of the long wave interaction problem with a fixed partially immersed body into a fluid layer. The incident wave is assumed to be an isolated solitary wave. The body in this study is assumed to be fixed with a rectangular section which is not touching the bottom of the channel. The mathemati...

There is studied the integrability of a generalized Gurevich-Zybin dynamical system based on the differential-algebraic and geometrically motivated gradient-holonomic approaches. There is constructed the corresponding Lax type represenation, compatible Poisson structures as well as the integrability of the related Hunter-Saxton reduction. In partic...

This paper addresses an optimization of Unmanned Aerial Vehicle (UAV) flight trajectories by bank-turn mechanism for a fixed-wing UAV at a constant altitude. The flight trajectories should be optimal and stay in the UAV flight operational area. The maneuver planning is conducted in two steps, which are UAV path planning and UAV flight trajectory pl...

CANWA (Comparative Analytical Numerical Wave Algorithm), written in MATLAB, provides a fast, direct comparison of a general finite volume solution to the 1+1 shallow water wave equations with a robust analytical solution recently presented by Nicolsky et al. (2018). The implementation of the method for data projection, introduced in Nicolsky et al....

The reduction modulo $p$ of a family of lacunary integer polynomials, associated with the dynamical zeta function $\zeta_{\beta}(z)$ of the $\beta$-shift, for $\beta > 1$ close to one, is investigated. We briefly recall how this family is correlated to the problem of Lehmer. A variety of questions is raised about their numbers of zeroes in $\mathbb...

High dimensional data are subject to the curse of dimensionality defined in Sect. 2.1, which hinders their analysis. Yet, in practice, data may be assumed to live in a manifold whose dimensionality is lower than that of the data space dimensionality. The effective dimensionality of data is called intrinsic dimensionality. Its estimation is detailed...

This Chapter presents a few examples of applications of dimensionality reduction for the analysis of data towards the diagnosis of energy systems. These systems encompass smart-buildings (Sect. 8.1), photovoltaic systems (Sect. 8.2) and batteries (Sect. 8.3). Diagnosis aims at identifying the occurrence of faults in a system. These faults are chara...

This chapter positions Dimensionality Reduction (DR) in the broader context of data science, considering both its use as an automated pre-processing tool extracting variable (manifold learning) for other automated tasks (e.g., classification, clustering, regression), and as a mapping technique allowing to visualize multidimensional data in a low-di...

This book proposes tools for analysis of multidimensional and metric data, by establishing a state-of-the-art of the existing solutions and developing new ones. It mainly focuses on visual exploration of these data by a human analyst, relying on a 2D or 3D scatter plot display obtained through Dimensionality Reduction (DR). Performing diagnosis of...

Exploratory visual analysis of multidimensional labeled data is challenging. Multidimensional Projections for labeled data attempt to separate classes while preserving neighborhoods. In this work, we consider the case where instances are assigned multiple labels with probabilities or weights: for example, the output of a probabilistic classifier, f...

An analytical solution of deformation of a homogeneous, isotropic elastic layer of uniform thickness overlying a homogeneous, isotropic viscoelastic half-space of Burger medium due to movement of an infinite fault for different types of crack surface has been studied. The deformation by this fault has been compared with the deformation by an infini...

For \(\beta > 1\) a real algebraic integer (the base), the finite alphabets \({\mathcal {A}} \subset {\mathbb {Z}}\) which realize the identity \({\mathbb {Q}}(\beta ) = \mathrm{Per}_{{\mathcal {A}}}(\beta )\), where \(\mathrm{Per}_{{\mathcal {A}}}(\beta )\) is the set of complex numbers which are \((\beta , {\mathcal {A}})\)-eventually periodic re...

Since the seminal paper by Korteweg and deVries deriving the celebrated Korteweg-de Vries (KdV) equation, there has been a strong push to include extra effects which are prescribed. Such extra effects include moving pressure distribution, topography, electric/magnetic fields, hydro-elasticity and more recently flows with constant vorticity. This ar...

The present study evaluates the tsunami hazard from splay thrust and normal faults in the western Makran, Gulf of Oman for the first time. We interpret splay thrust and normal faults in the Gulf of Oman using reflection seismic data and analyze the implied regional deterministic and probabilistic tsunami hazards. The tsunami hazards associated with...

The purpose of the work presented in this paper is to study the reflection and transmission coefficients resulting from the interactions of regular waves with a rectangular breakwater sited at the bottom of a tank. The present investigation is devoted to the analysis of the reflection and transmission coefficients within the framework of linearized...

The intentions of this paper are revolved around discussing the limitation of the Direct Numerical Simulation (DNS). To resolve the equations governing the problem of a jet emitted from the bottom of a numerical tank, the investigation has been made in the context of an unsteady, viscous, and incompressible fluid. The numerical resolution of the eq...

The application of coal ash (CA) in construction industries has grown rapidly, posing risk to the environment due to heavy metals leaching from the material. This research presents a simulation of ecological risk assessment and model risk indicators (ERI) of leached heavy metals (lead (Pb), copper (Cu), zinc (Zn) and arsenic (As)) from CA (FA: fly...

The classical Benjamin-Bona-Mahony equation (BBM equation) models unidirectional propagation of long gravity surface waves of small amplitude. Unlike many other water wave models, it lacks the Galilean invariance, which is an essential classical physical property. It is shown that by an addition of a higher asymptotic order nonlinear term, this def...

In 1895, Korteweg and de Vries (KdV), derived their celebrated equation describing the motion of waves of long wavelength in shallow water. In doing so they made a number of quite reasonable assumptions, incompressibility of the water and irrotational fluid. The resulting equation, the celebrated KdV equation, has been shown to be a very reasonable...

Dimensionality Reduction (DR) represents a set of points {ξi} in a high dimensional metric data space D by associated points {xi} in a low-dimensional embedding space ℰ. This representation defines a mapping Φ:D→ℰ such that Φ(ξi) = xi for all i. This mapping must preserve as much as possible the structure of data.

The purpose of map evaluation is to assess the overall quality of a map. Most often, this quality is quantified by scalar indicators allowing to compare several maps. This may be used to select the best of several techniques for embedding a dataset or to tune the hyper-parameters of a given technique. It strives to measure the amount of distortions...

This chapter details the challenges involved for the optimization of the stress functions presented in the previous chapters, as well as the solutions effectively used (Sect. 7.1). It then addresses the issue of time and space complexity and DR techniques acceleration (Sect. 7.2). Finally, it dives into out of sample extension of the mapping, which...

In the general case, Dimensionality Reduction (DR) is an unsupervised task. Indeed, it does not necessitate data annotations, as opposed to classification for which the desired output must be provided for a training set. Yet, DR is sometimes applied to datasets for which such annotations are available (e.g., class-information). In this context, sup...

Map interpretation encompasses several tools enhancing the map with additional information. Some allow to study the link between axes of the data and embedding space, as detailed Sect. 4.1, while other perform local evaluation of distortions deriving concepts of global map evaluation, as described in Sects. 4.2 and 4.3.

In this paper, the goal is to revolve around discussing the stability of the Method of Fundamental Solutions (MFS) for the use case of wave-current interactions. Further, the reliability of Generating-Absorbing Boundary Conditions (GABCs) applied to the wave-current interactions is investigated using the Method of Fundamental Solutions (MFS), in a...