This article develops applications of the generalized method of lines to numerical solutions of the time-independent, incompressible Navier-Stokes system in fluid mechanics. We recall that for such a method, the domain of the partial differential equation in question is discretized in lines (or more generally in curves), and the concerning solutions are written on these lines as functions of the boundary conditions and the domain boundary shape.

Uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the work by two of the present authors [Phys.\ Lett.\ A\textbf{382}, 1472 (2018)]. In this approach, the origin of the finite minimum value of uncertainty is attributed to the non-differentiable (virtual) trajectory of a quantum particle and then both of the Kennard and Robertson-Schr\"{o}dinger inequalities in quantum mechanics are reproduced. The same non-differentiable trajectory is applied to the motion of fluid elements in the Navier-Stokes-Fourier equation or the Navier-Stokes-Korteweg equation. By introducing the standard deviations of position and momentum for fluid elements, the uncertainty relations in hydrodynamics are derived. These are applicable even to the Gross-Pitaevskii equation and then the field-theoretical uncertainty relation is reproduced. We further investigate numerically the derived relations and find that the behaviors of the uncertainty relations for liquid and gas are qualitatively different. This suggests that the uncertainty relations in hydrodynamics are used as a criterion to classify liquid and gas in fluid.

The purpose of this paper is to bring to light a method through which the global in time existence for arbitrary large in H¹ initial data of a strong solution to 3D periodic Navier-Stokes equations follows. The method consists of subdividing the time interval of existence into smaller sub-intervals carefully chosen. These sub-intervals are chosen based on the hypothesis that for any wavenumber m, one can find an interval of time on which the energy quantized in low-frequency components (up to m) of the solution u is lesser than the energy quantized in high-frequency components (down to m) or otherwise the opposite. We associate then a suitable number m to each one of the intervals and we prove that the norm ||u(t)||_H1 is bounded in both mentioned cases. The process can be continued until reaching the maximal time of existence T_max which yields the global in time existence of strong solution.

In the early 1980s it was well established that Leray solutions of the unforced Navier-Stokes equations in Rn decay in energy norm for large time. With the works of T. Miyakawa, M. Schonbek and others it is now known that the energy decay rate cannot in general be any faster than t^-(n+2)/4 and is typically much slower. In contrast, we show in this note that, given an arbitrary Leray solution u(.,t), the difference of any two Stokes approximations to the Navier-Stokes flow u(.,t) will always decay at least as fast as t^-(n+2)/4, no matter how slow the decay of || u(.,t) ||_L2 might happen to be.

The paper is considering of the basic differential equations of hydrodynamics: the equation of continuity and motion. On the simplest example, it is shown that the equation of continuity in a system with the equation of motion leads to contradictions and erroneous results of modeling. A more correct form of the continuity equation is described. It is shown that the equations of motion can be written in the form of complete differentials. Three possible integral forms of the equations of motion are presented. As a conclusion, the existence and smoothness of the solution of the Navier-Stokes equations are considered.

We address the dynamics of two-dimensional Navier-Stokes models with infinite delay and hereditary memory, whose kernels are a much larger class of functions than the one considered in the literature, on a bounded domain. We prove the existence and uniqueness of weak solutions by means of Faedo-Galerkin method. Moreover, we establish the existence of global attractor for the system with the existence of a bounded absorbing set and asymptotic compact property.

We review a number of preconditioners for the advection-diffusion operator and for the Schur complement matrix which in turn constitute the building blocks for Constraint and Triangular Preconditioners to accelerate the iterative solution of the discretized and linearized Navier-Stokes equations. An intensive numerical testing is performed onto the driven cavity problem with low values of the viscosity coefficient. We devise an efficient multigrid preconditioner for the advection-diffusion matrix which, combined with the commuted BFBt Schur complement approximation, and inserted in a 2 x 2 block preconditioner, provides convergence of the GMRES method in a number of iteration independent of the meshsize for the lowest values of the viscosity parameter. The low-rank acceleration of such preconditioner is also investigated showing its great potential.

The gauge field equation for fluid mechanics established in Part 1 is developed into a first-order scattering theory in the simplified case of a two-dimensional incompressible flow over a flat plate. This is used to present a model for the origin of Tollmien-Schlichting (TS) waves based on scattering between fluid particles. As a result, analytical formulae for the maximum amplification factor and the transition point from laminar to turbulent flow in the boundary layer are obtained. The mathematical transformations from the stationary field equations in Part 1 to a scattering theory with time evolution along the flow axis using Wick rotation are elaborated in detail.

Cancers are complex, adaptive ecosystems. They remain the leading cause of disease-related death among children in North America. As we approach computational oncology and Deep Learning Healthcare, our mathematical models of cancer dynamics must be revised. Recent findings support the perspective that cancer-microenvironment interactions consist of turbulent flows. As such, cancer pattern formation, protein-folding and metastatic invasion are discussed herein as processes driven by chemical turbulence within the framework of complex systems theory. Current state-of-the-art quantitative approaches used in reconstructing cancer stem cell networks are reviewed. To conclude, cancer stem cells are presented as strange attractors of the Waddington landscape.

Nanopores with irregularities are promising tools for distinguishing nano-size objects by their shape, but the forces on the object that critically influence its axial and rotational movement are unclear. The physics of the situation was described using the Poisson-Nernst-Planck and Navier-Stokes equations. With uniformly charged object the axial Coulomb and dielectric pressure (which opposes it and is surprisingly important), control the object's axial movement and rotation. Even without external pressure the hydrodynamic pressure is significant (negative at its upper and positive at its lower surface), but its total value is almost zero. If the object is charged only on the upper surface the axial upper Coulomb pressure is near zero close to the center, but negative near its end (the pressure is zero at the lower surface). The total axial dielectric pressure, which is largely dominated by the pressure at the upper surface, is positive along the length of the object becoming pronounced near its end. The axial hydrodynamic pressure is negative and significant at the upper surface (zero at the lower surface), diminishes in value near the object's end, critically influencing its axial movement, which becomes much faster. At its end the axial dielectric pressure prevails, and controls its rotation.

We studies the initial value problem for the fractional Navier-Stokes-Coriolis equations, which obtained by replacing the Laplacian operator in the Navier-Stokes-Coriolis equation by the more general operator $(-\Delta)^\alpha$ with $\alpha>0$. We introduce function spaces of the Besove type characterized by the time evolution semigroup associated with the general linear Stokes-Coriolis operator. Next, we establish the unique existence of global in time mild solutions for small initial data belonging to our function spaces characterized by semigroups in both the scaling subcritical and critical settings.

For the solution existence condition of the Navier-Stokes equation, we propose a conjecture as follows: "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}+(\bm v\cdot \bm \nabla)$, used in most literature and textbooks, is incorrect. The correct expression $ \frac{d (:)}{dt}=\frac{\partial }{\partial t}(:)+\bm v\cdot [\bm \nabla (:)]$ is formulated. The solution existence condition of Navier-Stokes equation has been proposed from its form-solution, the conclusion is that "\emph{The Navier-Stokes equation has a solution if and only if the determinant of flow velocity gradient is not zero, namely $\det (\bm \nabla \bm v)\neq 0$.}"

Prediction of the likely evolution in the traffic scenes is a challenging task because of high uncertainty of sensing technology and dynamic environment. It leads to failure of planning for intelligent agents like autonomous vehicles. In this paper, we propose a fluid-based physical model to present the influence of surrounding object's motion on driving safety. In our pipeline, the input sensor could be LiDAR, camera, or multi-modal data. We use a Kalman filter to estimate the state space of each detected object, and adopt the properties of stable fluid to build a riskmap based on the density field. The noisy state space are then modeled as the boundary conditions in the simulation of advection and diffusion process. We test our approach on the public KITTI dataset and find this model could handle the short-term prediction in case of misdetection and tracking failure caused by object occlusion, which shows promising in collision risk assessment on road scenes.

Physics-informed neural networks are a promising method to yield surrogate models of flow fields. We present a metamodeling technique for variable geometries based on physics-informed neural networks. The method was applied to the DU99W350 airfoil at a Reynolds number of 1×10⁵. The model predicted the Reynolds-averaged velocity and pressure field around the airfoil for arbitrary angles of attack between 10.0° and 17.5°. The model was trained with data from CFD simulations for a limited set of angles of attack. Additionally, satisfaction of the a priori known boundary conditions as well as the Reynolds-averaged Navier-Stokes equations were trained. A sensitivity analysis concerning the Reynolds number, the amount and distribution of training data, and the turbulence model was conducted showing the superiority of the pseudo-Reynolds stress method and the demand of labeled training data in the domain. The trained network was capable of predicting the developing flow separation on the suction surface and exhibited excellent agreement with CFD results even in the proximity to the wall for interpolations as well as extrapolations from the labeled data set.

In this paper we study solutions and drift homogenization for a class of viscous lake equations by using the method of semigroups of bounded operators. Suppose that the initial value i.e.,for some Hölder continuous function onwith smooth function value satisfying and Then the initial value problem (2) for viscous lake equations has a unique smooth local strong solution. Using this result we study the drift homogenization for three-dimensional stationary Stokes equation in the usual sense

Based on the insight gained from single jet analysis performed earlier [1], CFD analysis on turbulent jets impinging on one another at an angle was performed. Multiple impingement angles were considered for this study to gain better understanding of the parameters affecting resultant jet growth and velocity distribution. From the study of single jet, it was concluded that the SST k-ω turbulence model was the ideal turbulence model capable of accurately predicting the flow physics of the jets exiting a fully developed pipe at low Reynolds number. Hence, for the study of impinging jets, SST k-ω turbulence model was used to study the velocity and jet growth characteristics. It became evident that the mesh alignment with the velocity vector at exit of the pipe domain plays a crucial role in the accuracy of the results. The parameter used to evaluate this condition was identified as False Diffusion and was observed to affect the TKE parameter significantly. Methods to reduce false diffusion are also discussed in this article. Based on the mesh obtained from the grid sensitivity study, jets impinging at 30, 45 and 60 degrees at Reynolds number of 7500 were numerically analyzed. It was observed that the profile of the resultant jet closely matched with the prediction of elliptical profile predicted by past researchers, [2] and [3]. Also, it was seen that higher jet growth was predicted in case of jets impinging at a higher impingement angle.

The time-resolved flowfield of a spatially oscillating jet emitted by a Sweeping Jet (SWJ) actuator is investigated numerically using three-dimensional Reynolds-averaged Navier-Stokes (3D-URANS) equations. Numerical simulations are performed for a practical range of mass flow rates providing flow conditions ranging from incompressible to subsonic compressible flows. A linear relationship between the mass flow rate and the jet oscillation frequency is found. The results of the numerical model are compared with the experimental data in the literature, and good agreement is found. Additionally, it is observed that the SWJ actuator frequency response switches from one linear mode to another linear mode when the compressibility effects become important.

Into the frame of the French TANDEM project (Tsunamis in the Atlantic and the English ChaNnel: Definition of the Effects through numerical Modelling) Principia has been working on the development and qualification of two in-house CFD software’s: the 2D EOLE-SV (Saint Venant) model for simulation of large scale tsunami propagation from the source up to coastal scale and the 3D EOLE-NS (Navier-Stokes) model dedicated to tsunami coastal impact modelling. This paper presents a large range of test cases carried out into the frame of the project and dedicated to the validation of numerical codes in various tsunami wave conditions. The main aspects of phenomena such as wave generation, propagation and coastal impact are investigated on academic situations. A real case simulation is concerned as well, the devastating 2011 Tohoku event which is compared with in-situ data.

In this perspective, we give an overview of several less explored structural and optical characterisation techniques useful for biomaterials. New insights into the structure of natural fibres such as spider silk can be gained with minimal sample preparation. Electromagnetic radiation (EMR) over a broad range of wavelengths (from X-ray to THz) provides information of the structure of the material at cor- respondingly different length scales (nm-to-mm). When the sample features, such as the alignment of certain fibres, cannot be characterised optically, polarisation analysis of the optical images can provide further information on feature alignment. The 3D complexity of biological samples necessitates that there be feature measure- ments and characterisation over a large range of length scales. We discuss the issue of characterising complex shapes by analysis of the link between the color and struc- ture of spider scales and silk. For example, it is shown that the green-blue color of a spider scale is dominated by the chitin slab’s Fabry-P ́erot type reflectivity rather than the surface nanostructure. The use of a chromaticity plot simplifies complex spectra and enables quantification of the apparent colors. All the experimental data presented herein are used to support the discussion on the structure-color link in the characterisation of materials.

Medium polarity plays a crucial role in charge-transfer processes and electrochemistry. The added supporting electrolyte in electrochemical setups, essential for attaining the needed electrical conductivity, sets challenges for estimating medium polarity. Herein, we resort to Lippert–Mataga–Ooshika (LMO) formalism for estimating the Onsager polarity of electrolyte organic solutions pertinent to electrochemical analysis. An amine derivative of 1,8-naphthalimide proves to be an appropriate photoprobe for LMO analysis. An increase in electrolyte concentration enhances the polarity of the solutions. This effect becomes especially pronounced for low-polarity solvents. Measured refractive indexes provide a means for converting Onsager to Born polarity, which is essential for analyzing medium effects on electrochemical trends. This study demonstrates a robust optical means, encompassing steady-state spectroscopy and refractometry, for characterizing solution properties important for charge-transfer science and electrochemistry.

Controllable, quantum-strong correlations of polarization states can be implemented with multi-photon independent states. Polarization-based photonic quantum correlations can be traced back to the overlap of the polarization Stokes vectors on the Poincaré sphere between two polarization filters. The quantum Rayleigh scattering prevents a single photon from propagating in a straight line inside a dielectric medium, and it also provides a mechanism for the projective measurement of polarization. Complexities associated with single-photon sources and detectors can be eliminated because the quantum Rayleigh scattering in a dielectric medium destroys entangled photons. Entanglement-free, identical sources and processing devices give rise to correlations rather than these being caused by “quantum nonlocality”. These analytic developments were prompted by the vanishing expectation values of the Pauli spin vector for a single photon of maximally entangled photonic Bell states.

We present the generation and nonlinear frequency conversion of nanosecond cylindrical vector beams (CVBs) in two-mode fiber (TMF). Based on the polarized dependence vector mode coupling characteristic and the precise wavelength tunability of an acoustically-induced fiber grating (AIFG), the nanosecond cylindrical vector beams (CVBs, 1064 nm, 10 ns) is directly generated in a TMF with convenient switching characteristics between the radial and azimuthal vector beams. Furthermore, the stimulated Raman scattering (SRS) is produced based on the transmission of the nanosecond CVBs in the 100-meters long TMF, and the spatial intensity and polarization distributions characteristics the 1st-order Stokes shifted component is consistent with the nanosecond CVBs pump pulse. This work provides a method for achieving wavelength conversion of the CVBs in optical fiber.

A physical scrutiny of experimental results published in Physical Review Letters (December 2015, M. Giustina, et al., Phys. Rev. Lett. 115, 250401, and L. K. Shalm et al., Phys. Rev. Lett. 115, 250402) is undertaken. These articles reported that measured outcomes were fitted with quantum states possessing a dominant component of non-entangled photons, thereby contradicting their own claim of quantum nonlocality. With probabilities of photon detections lower than 0.1 %, the alleged quantum nonlocality cannot be classified as a resource for developing quantum computing devices, despite recent publicity. Experimental evidence of a feasible process for quantum-strong correlations has been identified (M. Iannuzzi, et al., Phys. Lett. A, 384 (9), 126200, 2020) in terms of correlations between independent and multi-photon states evaluated as Stokes vectors on the Poincaré sphere. As single-photon sources are not needed, the design and implementation of quantum computing operations will be significantly streamlined.

It is shown that a Mueller quaternion can be formulated as a quaternion with matrix coefficients, and this Mueller quaternion transforms the Stokes quaternion for depolarizing process as well as for nondepolarizing process. Mueller quaternion keeps track of the phase acquired by the Stokes quaternion and, in general, quaternion states of optical media comprises all properties of Jones, Mueller-Jones and Mueller matrices.

Electron can tunnel between cofactor molecules positioned along biological electron transport chains up to the distance of ≃20 Å on the millisecond time scale of enzymatic turnover. This tunneling range mostly determines the design of biological energy chains facilitating cross-membrane transport of electrons. Tunneling distance and cofactors’ redox potentials become main physical parameters of this design. The protein identity, flexibility, or dynamics are missing from this picture assigning universal charge-transport properties to all proteins. This paradigm is challenged by dynamical models of electron transfer showing that the hopping rate is constant within the crossover distance R*≃12 Å, followed with an exponential tunneling falloff at longer distances. In this view, energy chains for electron transport are best designed by placing redox cofactors near the crossover distance R*. Protein flexibility and dynamics affect the magnitude of the maximum hopping rate within the crossover radius. Protein charge transport is not driven by universal parameters anymore and protein identity matters.

The method of regularized stokeslets is widely-used to model microscale biological propulsion. The method is usually implemented with only the single layer potential, with the double layer potential being neglected, despite this formulation often not being justified a priori due to non-rigid surface deformation. We describe a meshless approach enabling inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretization on a notebook computer with the inclusion of the double layer ranging from no-slip to free slip limits; neglect of the double layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a few percent error when the double layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and non-slender swimmers, whether or not the double layer is included, which may be due to the deformation’s `locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. Inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.

Here, we propose a novel scheme based on advanced techniques of digital modulation in optical communications to achieve a single-channel transmission rate above 100 Gb/s. We utilize a hybrid scheme amplitude/phase/frequency/dual polarization, combined with multidimensional dual lattice and a low-density parity-check-coded modulation. The Stokes parameters are applied to the proposed scheme to map the four-dimensional classical polarization \({I_X},{Q_X},{I_Y},{Q_Y}\) in a three-dimensional space. In addition, in the proposed system, the packing theory is applied to the bit interleaver process, three wavelengths are packaged before being transmitted over a wavelength-division multiplexing optical channel. This modulation process is carried out using symmetrical geometric shapes, such as a hypercube or a polyhedron, based on the molecular links theory using a grouping of 12 and 13/15 bits for the cubic and spherical lattices, respectively. The proposed technique is evaluated in the context of long distance communications over distances up to 100 km. The bit error rate results showed that the optical signal-to-noise ratio was approximately 4 dB over a distance of 50 km. In addition, the power spectral efficiency was found to be 3 lambda, which is considered good performance considering the effects of distance and the non-linear effects influencing the number of lambdas. Also, we use an optical time division multiplexing scheme (OTDM) in order to achieve a transmission rate beyond 1Tbit/s, where the speed effect is evaluated, taking into consideration that the power spectral efficiency is degraded. Furthermore, the average noise floor is -60dBm for all transmission distances. These findings are expected to contribute to the future implementation of robust long-distance optical communication infrastructure.

The bark of Rhus verniciflua Stokes (RVS) is used as a food additive and herbal medicine for various inflammatory disorders and cancer in Eastern Asia. RVS exerted anti-inflammatory effects in lipopolysaccharide (LPS)-stimulated RAW264.7 cells, but whether this effect occurs in macrophages after oral administration has not been determined. We used a thioglycollate-induced peritonitis model to obtain macrophages from mice given RVS. We examined the systemic inflammatory response to intraperitoneal LPS. RVS-treated mice had an increased population of peritoneal exudate cells expressing CD11b and SRA. Increased uptake of Alexa Fluor 488-labeled acetylated lipoprotein was observed in monocyte-derived macrophages from RVS-treated mice. When these cells from the RVS group were stimulated with LPS, the levels of tumor necrosis factor (TNF)- and interleukin (IL)-6 in the supernatant decreased, but the level of IL-12 increased. The surface expression of CD86 was reduced, but surface expression of class II MHC molecules was increased. RVS suppressed the serum levels of LPS-induced TNF- and IL-6. RVS enhanced monocyte differentiation in thioglycollate-induced peritonitis by increasing scavenger receptor expression and activity. Macrophages isolated from mice given RVS responded differently to LPS. These findings demonstrate that RVS confers selective anti-inflammatory activity without causing the overall inhibitory effects on immune cells.

The object of this paper is the bending analysis of isotropic rectangular Kirchhoff plates subjected to non-uniform heating (NUH) using the Fourier transform method. The bottom and top surfaces of the plate are assumed to have different changes in temperature, whereas the change in temperature of the mid-surface is zero. According to classical plate theory, the governing equation of the plate contains second derivatives of the NUH; these derivatives are zero by constant value of the NUH, which leads to its absence in the governing equation. This paper presented an approach by which Fourier sine transform was utilized to describe the NUH, while the double trigonometric series of Navier and the simple trigonometric series of Lévy were utilized to describe the deflection curve. Thus, the NUH appeared in the governing equation, which simplified the analysis. Rectangular plates simply supported along all edges were analyzed, bending moments, twisting moments, and deflections being determined. In addition, rectangular plates simply supported along two opposite edges were analyzed; the other edges having various support conditions (free, simply supported, and fixed).

A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely determined by the four parameters of the velocity gradient matrix, and vice-versa. This result, termed ellipse/flow equivalence, provides a stronger version of the well-known result that a linear velocity field maps an ellipse into another ellipse. Moreover, ellipse/flow equivalence is shown to be a manifestation of Stokes' theorem. This is done by deriving a matrix-valued relationship, called the geometric Stokes' theorem, that involves a spatial integral over the velocity gradient tensor, thus accounting for the two strain terms in addition to the divergence and vorticity. General expressions for various physical properties of an elliptical ring of fluid are also derived. The ellipse kinetic energy is found to be composed of three portions, associated respectively with the circulation, the rate of change of the moment of inertia, and the variance of parcel angular velocity around the ellipse. A particular innovation is the use of four matrices, termed the IJKL basis, that greatly facilitate the required calculations.

Fluid mechanics of flow in hydrophobic, rectangular microchannels with finite aspect ratios is of paramount importance. In such microchannels, not only the effect of the side walls should be taken into account, but also the classical assumption of no-slip boundary condition (BC) is no longer valid at the solid-liquid interface. Accordingly, slip flow can occur in microchannels fabricated from surfaces with low wetting conditions, hydrophobic surfaces. Determining the interactions of liquid molecules adjacent to solid surface is still a challenging issue, and it is especially important in small scale domains. Herein, the fluid mechanics of flow through rectangular hydrophobic microchannels has been reconsidered by taking into account the general Navier-slip BCs at the solid-liquid interface. For fully developed incompressible flow in microchannels at low Reynolds number, partial differential equation (PDE) of the momentum equation simplifies to the classical Poisson equation. Accordingly, by analytically solving the Poisson equations with general Navier-slip BCs, the most general forms of velocity distributions, flow rate, friction factor and Poiseuille number have been obtained.

In this study, five polyphenol compounds (reference substances, ref.) were added to Stokesia laevis (Slae26) ethanolic extract (5 mg GAE / mL) in order to test their antiproliferative effects on human colon tumor cell line Caco-2 (ATCC-HTB-37). The five phenolics (ref.) are luteolin-7-O-glucoside (orientin), luteolin-8-C-glucoside (cinnaroside), caffeic acid, gentisic acid and para-aminobenzoic acid (PABA), and they were combined in ratio 1:1 between the active compounds in samples (GAE : ref.). Results indicated certain antiproliferative effects of Slae26 (IC50=36 μg GAE/mL sample), of the five reference compounds, but mainly of Slae26 combinations with the five phenolics tested (ref.). Punctually, there were obtained IC50 values around 5 μg/mL sample, signifying real therapeutic usefulness and antitumor potency of Slae26 combinations with the five food bioactive compounds tested. In silico docking studies provided potential therapeutic agents to inhibit the catalytic domain of human tankyrase 1 (TNKS1) in the series of food bioactive compounds tested, and revealed luteolin-7-O-glucoside high effectiveness.

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.