Narrow Results

Tidal turbine arrays have undergone extensive research to determine the optimal spacing for efficient performance and reduced wake generation. Small-scale laboratory tests are typically conducted to analyze wake structures prior to deployment. These tests often result in conditions of extreme blockage due to channel narrowing in comparison to turbine size. The primary objective of this study is to investigate flow behavior around turbines under blockage conditions and their performance close to the free surface, both in current-only and wave-and-current scenarios. The methodology employed a combination of blade element momentum theory and computational fluid dynamics (CFD) integrating a virtual blade model (VBM) code. The findings of this study indicate potential enhancements in tidal turbine array performance of up to 7% in lateral arrangements and 11% in streamwise arrangements under blockage conditions. The wake is significantly influenced by surface waves, which also contribute to increased downstream turbine performance.

Pulsar winds are the ideal environment for the study of non-linear electromagnetic waves. It is generally thought that a pulsar launches a striped wind, a magnetohydrodynamic entropy wave, where plasma sheets carried along with the flow separate regions of alternating magnetic field. But when the density drops below a critical value, or equivalently for distances from the pulsar greater than a critical radius, a strong superluminal wave can also propagate. In this contribution we discuss the conversion of the equatorial striped wind into a linearly polarized superluminal wave, and we argue that this mode is important for the conversion of Poynting flux to kinetic energy flux before the outflow reaches the termination shock.

Complex systems, as interwoven miscellaneous interacting entities that emerge and evolve through self-organization in a myriad of spiraling contexts, exhibit subtleties on global scale besides steering the way to understand complexity which has been under evolutionary processes with unfolding cumulative nature wherein order is viewed as the unifying framework. Indicating the striking feature of non-separability in components, a complex system cannot be understood in terms of the individual isolated constituents’ properties per se, it can rather be comprehended as a way to multilevel approach systems behavior with systems whose emergent behavior and pattern transcend the characteristics of ubiquitous units composing the system itself. This observation specifies a change of scientific paradigm, presenting that a reductionist perspective does not by any means imply a constructionist view; and in that vein, complex systems science, associated with multiscale problems, is regarded as ascendancy of emergence over reductionism and level of mechanistic insight evolving into complex system. While evolvability being related to the species and humans owing their existence to their ancestors’ capability with regards to adapting, emerging and evolving besides the relation between complexity of models, designs, visualization and optimality, a horizon that can take into account the subtleties making their own means of solutions applicable is to be entailed by complexity. Such views attach their germane importance to the future science of complexity which may probably be best regarded as a minimal history congruent with observable variations, namely the most parallelizable or symmetric process which can turn random inputs into regular outputs. Interestingly enough, chaos and nonlinear systems come into this picture as cousins of complexity which with tons of its components are involved in a hectic interaction with one another in a nonlinear fashion amongst the other related systems and fields. Relation, in mathematics, is a way of connecting two or more things, which is to say numbers, sets or other mathematical objects, and it is a relation that describes the way the things are interrelated to facilitate making sense of complex mathematical systems. Accordingly, mathematical modeling and scientific computing are proven principal tools toward the solution of problems arising in complex systems’ exploration with sound, stimulating and innovative aspects attributed to data science as a tailored-made discipline to enable making sense out of voluminous (-big) data. Regarding the computation of the complexity of any mathematical model, conducting the analyses over the run time is related to the sort of data determined and employed along with the methods. This enables the possibility of examining the data applied in the study, which is dependent on the capacity of the computer at work. Besides these, varying capacities of the computers have impact on the results; nevertheless, the application of the method on the code step by step must be taken into consideration. In this sense, the definition of complexity evaluated over different data lends a broader applicability range with more realism and convenience since the process is dependent on concrete mathematical foundations. All of these indicate that the methods need to be investigated based on their mathematical foundation together with the methods. In that way, it can become foreseeable what level of complexity will emerge for any data desired to be employed. With relation to fractals, fractal theory and analysis are geared toward assessing the fractal characteristics of data, several methods being at stake to assign fractal dimensions to the datasets, and within that perspective, fractal analysis provides expansion of knowledge regarding the functions and structures of complex systems while acting as a potential means to evaluate the novel areas of research and to capture the roughness of objects, their nonlinearity, randomness, and so on. The idea of fractional-order integration and differentiation as well as the inverse relationship between them lends fractional calculus applications in various fields spanning across science, medicine and engineering, amongst the others. The approach of fractional calculus, within mathematics-informed frameworks employed to enable reliable comprehension into complex processes which encompass an array of temporal and spatial scales notably provides the novel applicable models through fractional-order calculus to optimization methods. Computational science and modeling, notwithstanding, are oriented toward the simulation and investigation of complex systems through the use of computers by making use of domains ranging from mathematics to physics as well as computer science. A computational model consisting of numerous variables that characterize the system under consideration allows the performing of many simulated experiments via computerized means. Furthermore, Artificial Intelligence (AI) techniques whether combined or not with fractal, fractional analysis as well as mathematical models have enabled various applications including the prediction of mechanisms ranging extensively from living organisms to other interactions across incredible spectra besides providing solutions to real-world complex problems both on local and global scale. While enabling model accuracy maximization, AI can also ensure the minimization of functions such as computational burden. Relatedly, level of complexity, often employed in computer science for decision-making and problem-solving processes, aims to evaluate the difficulty of algorithms, and by so doing, it helps to determine the number of required resources and time for task completion. Computational (-algorithmic) complexity, referring to the measure of the amount of computing resources (memory and storage) which a specific algorithm consumes when it is run, essentially signifies the complexity of an algorithm, yielding an approximate sense of the volume of computing resources and seeking to prove the input data with different values and sizes. Computational complexity, with search algorithms and solution landscapes, eventually points toward reductions vis à vis universality to explore varying degrees of problems with different ranges of predictability. Taken together, this line of sophisticated and computer-assisted proof approach can fulfill the requirements of accuracy, interpretability, predictability and reliance on mathematical sciences with the assistance of AI and machine learning being at the plinth of and at the intersection with different domains among many other related points in line with the concurrent technical analyses, computing processes, computational foundations and mathematical modeling. Consequently, as distinctive from the other ones, our special issue series provides a novel direction for stimulating, refreshing and innovative interdisciplinary, multidisciplinary and transdisciplinary understanding and research in model-based, data-driven modes to be able to obtain feasible accurate solutions, designed simulations, optimization processes, among many more. Hence, we address the theoretical reflections on how all these processes are modeled, merging all together the advanced methods, mathematical analyses, computational technologies, quantum means elaborating and exhibiting the implications of applicable approaches in real-world systems and other related domains.

Predicting trajectories of fluid parcels on the water surface perturbed by waves is a difficult mathematical and theoretical problem. It is even harder to model flows generated on the water surface due to complex three-dimensional wave fields, which commonly result from the modulation instability of planar waves. We have recently shown that quasi-standing, or Faraday, waves are capable of generating horizontal fluid motions on the water surface whose statistical properties are very close to those in two-dimensional turbulence. This occurs due to the generation of horizontal vortices. Here we show that progressing waves generated by a localized source are also capable of creating horizontal vortices. The interaction between such vortices can be controlled and used to create stationary surface flows of desired topology. These results offer new methods of surface flow generation, which allow engineering inward and outward surface jets, large-scale vortices and other complex flows. The new principles can be also be used to manipulate floaters on the water surface and to form well-controlled Lagrangian coherent structures on the surface. The resulting flows are localized in a narrow layer near the surface, whose thickness is less than one wavelength.

In this paper, a stochastic dynamic analysis method for cable-stayed bridges subjected to multi-dimensional and multi-supported earthquake and waves is established based on the pseudo-excitation method. The Monte Carlo method is used to analyze the influence of excitation nonlinearity on the bridge structure response, and the applicability of this method is verified. Stochastic response characteristic of coastal cable-stayed bridges subjected to multi-dimensional and multi-supported earthquake and waves is studied. The influence of water–structure interaction on the stochastic seismic response of main components of the cable-stayed bridge is described, and the influence of key parameters is analyzed. The results show that the influence of excitation nonlinearity on the response of the cable-stayed bridge can be neglected. A greater energy input caused by the rigid additional mass of the hydrodynamic pressure is the reason for the increasing of the seismic response. The influence of stochastic response of the underwater structure of the tower is changed with the site conditions. For the ground motion acceleration input energy being distributed in the high-frequency domain, the water–structure interaction has a greater effect on stochastic seismic response of the underwater structure of the tower. The influence of water–structure interaction on the stochastic seismic response of the underwater structure of the cable-stayed bridge increases with the increasing of the wave height and water depth.

The convective wave equation deals with wave propagation in a moving media. We focus on the underwater acoustic wave equation where the convective element is the flow of water inside a river, along its length. The main thrust of this paper is the ill-posed “refocusing” problem. The initial condition simulates an explosion in a small compact region and the response is recorded over time at several microphones. Having only partial and noisy information we expect that small perturbations will destroy the ability to recover the complete initial data. We use the time reversal (TR) technique to determine the location of the original explosion, given limited spatial observations. We test the effectiveness of this scheme under conditions including dissipation, dispersion, etc. We use finite differences and implement absorbing boundary conditions to simulate an unbounded region.

In this paper, we will present an approach to constructing of dynamical spatial Green’s function (elementary solutions, dominant function) for a thin infinite elastic plate of constant thickness. The plate material is anisotropic with a single plane of symmetry, geometrically coinciding with plate’s middle plane. The Timoshenko theory was used for describing the plate movement. Transient spatial Green’s functions for normal displacements and angles of orthogonal alteration to middle surface before deformation of material fiber are built in the Cartesian coordinate system.

To construct Green’s function, direct and inverse Laplace and Fourier integral transformations are applied. The originals of Laplace Green’s functions were analytically found with the theorem of residues. To construct Fourier originals, a specific method was used based on Fourier series transformation inversion integral connection with Fourier series on a variable interval.

Green’s function found for normal displacement made it possible to represent the normal transient function as three-fold convolution of Green function with distant load function. The functions of normal distant displacements were constructed in case of the impact of transient total loads concentrated and distributed across rectangular courts. The numerical method of rectangles was used to calculate the convolution integrals. The influence of the concentrated load speed on transient normal displacements of the anisotropic plate was analyzed.

As a verification of constructed transient spatial Green’s functions, the results of numerical solutions were compared with the results found using known transient Green’s functions for isotropic thin elastic rectangular simply supported Timoshenko’s plate which solutions are constructed using Laplace integral transformation in time and its decomposition into Fourier series on coordinates. Besides, its confidence was proved analyzing the nature of waves in anisotropic, orthotropic and isotropic plate, found in the process of numerical calculations. The results are represented as diagrams. Examples of calculations are given.

Self-phase modulation (SPM) induces a varying refractive index of the medium due to the optical Kerr effect. The optical waves propagation (OWP) in a medium with SPM occupied a remarkable area of research in the literature. A model equation to describe OWP in the absence of SPM was proposed very recently by Biswas–Arshed equation (BAE). This work is based on constructing the solutions that describe the waves which arise from soliton-periodic wave collisions. A variety of geometric optical wave structures are observed. Here, a transformation that allows to investigate the multi-geometric structures of OW’s result from soliton-periodic wave collisions is introduced. Chirped, conoidal, breathers, diamond and W-shaped optical waves are shown to propagate in the medium in the absence of SPM. The exact solutions of BAE are obtained by using the unified method, which was presented recently. We mention that the results found here, are completely new.

In the Ellis wormhole metrics, we study the characteristics of fluid dynamics and the properties of linear sound waves. By implying the energy–momentum equation and the continuity equation in the general relativistic manner, we examine the flow dynamics and solve the corresponding equations for a relatively simple case — radial flow. To study the linear sound waves, the equations governing the mentioned physical system are linearized and solved and interesting characteristic properties are found.

A new high-order local Absorbing Boundary Condition (ABC) has been recently proposed for use on an artificial boundary for time-dependent elastic waves in unbounded domains, in two dimensions. It is based on the stress–velocity formulation of the elastodynamics problem, and on the general Complete Radiation Boundary Condition (CRBC) approach, originally devised by Hagstrom and Warburton in 2009. The work presented here is a sequel to previous work that concentrated on the stability of the scheme; this is the first known high-order ABC for elastodynamics which is long-time stable. Stability was established both theoretically and numerically. The present paper focuses on the accuracy of the scheme. In particular, two accuracy-related issues are investigated. First, the reflection coefficients associated with the new CRBC for different types of incident and reflected elastic waves are analyzed. Second, various choices of computational parameters for the CRBC, and their effect on the accuracy, are discussed. These choices include the optimal coefficients proposed by Hagstrom and Warburton for the acoustic case, and a simplified formula for these coefficients. A finite difference discretization is employed in space and time. Numerical examples are used to experiment with the scheme and demonstrate the above-mentioned accuracy issues.

We analyze guided waves in the linear media separated nonlinear interface. The mathematical formulation of the model is a one-dimensional boundary value problem for the nonlinear Schrödinger equation. The Kerr type nonlinearity in the equation is taken into account only inside the waveguide. We show that the existence of nonlinear stationary waves of three types is possible in defined frequency ranges. We derive the frequency of obtained stationary states in explicit form and find the conditions of its existence. We show that it is possible to obtain the total wave transition through a plane defect. We determine the condition for realizing of such a resonance. We obtain the reflection and transition coefficients in the vicinity of the resonance. We establish that complete wave propagation with nonzero defect parameters can occur only when the nonlinear properties of the defect are taken into account.

Using 5D membrane/induced-matter theory as a basis, we derive the equations of motion for a novel gauge. The latter admits both particle and wave behaviour, as well as super-communication (wherein there is causal contact in the higher-dimensional manifold among points which are disjoint in spacetime). Possible ways to test this model are suggested, notably using particle mass.

We refute a physical model, recently proposed by Gunn, Allison and Abbott (GAA) [http://arxiv.org/pdf/1402.2709v2.pdf], to utilize electromagnetic waves for eavesdropping on the Kirchhoff-law–Johnson-noise (KLJN) secure key distribution. Their model, and its theoretical underpinnings, is found to be fundamentally flawed because their assumption of electromagnetic waves violates not only the wave equation but also the second law of thermodynamics, the principle of detailed balance, Boltzmann's energy equipartition theorem, and Planck's formula by implying infinitely strong blackbody radiation. We deduce the correct mathematical model of the GAA scheme, which is based on impedances at the quasi-static limit. Mathematical analysis and simulation results confirm our approach and prove that GAA's experimental interpretation is incorrect too.

The continuous increment in the performance of classical computers has been driven to its limit. New ways are studied to avoid this oncoming bottleneck and many answers can be found. An example is the Belousov–Zhabotinsky (BZ) reaction which includes some fundamental and essential characteristics that attract chemists, biologists, and computer scientists. Interaction of excitation wave-fronts in BZ system, can be interpreted in terms of logical gates and applied in the design of unconventional hardware components. Logic gates and other more complicated components have been already proposed using different topologies and particular characteristics. In this study, the inherent parallelism and simplicity of Cellular Automata (CAs) modeling is combined with an Oregonator model of light-sensitive version of BZ reaction. The resulting parallel and computationally-inexpensive model has the ability to simulate a topology that can be considered as a one-bit full adder digital component towards the design of an Arithmetic Logic Unit (ALU).

In complex scalar fields, singularities of the phase (optical vortices, wavefront dislocations) are lines in space, or points in the plane, where the wave amplitude vanishes. Phase singularities are illustrated by zeros in edge diffraction and amphidromies in the heights of the tides. In complex vector waves, there are two sorts of polarization singularity. The polarization is purely circular on lines in space or points in the plane (C singularities); these singularities have index ±1/2. The polarization is purely linear on lines in space for general vector fields, and surfaces in space or lines in the plane for transverse fields (L singularities); these singularities have index ±1. Polarization singularities (C points and L lines) are illustrated in the pattern of tidal currents.

Though the concept of a dark energy driven accelerating universe was introduced by the author in 1997, to date dark energy itself, as described below has remained a paradigm. We quickly review these and find a second cosmological signature of the 1997 model, consistent with latest observations.

A parametric study of composite strips leads to systems of partial differential equations, coupled through interface conditions, that are naturally solved in Laplace transform space. Because of the complexity of the solutions in transform space and the potential variations due to geometry and materials, a systematic approach to inversion is necessarily numerical. The Dubner-Abate-Crump (DAC) algorithm is the standard in such problems and is implemented. The presence of discontinuous wavefronts in the problems considered leads to Gibbs phenomenon; which, in turn, overestimates the values of maximum stress. These errors are mitigated by use of Lanczos' σ-factors, which combine naturally with the DAC algorithm.

Two wave transformation models, SWAN and CGWAVE, are used to simulate wave conditions at the Field Research Facility, Duck (North Carolina). The motivation is to examine how well these models reproduce observations and to determine the level of consistency between the two models. Stationary wave conditions pertaining to three different storm-induced bathymetric representations are modelled. It was found that SWAN and CGWAVE reproduced the observed wave behavior to a large extent, but CGWAVE results tended to be somewhat smaller than the SWAN results and the measurements. The differences were attributed to wave-wave interactions and breaking. Otherwise the models showed a high level of consistency. SWAN and CGWAVE were also used to explore other mechanisms reported in recent literature; the results were either consistent with some observations (in the case of the nonlinear mechanisms) or they shed more light on others (in case of the role of the research pier legs).

Open coast storm surge water levels consist of a wind shear forcing component generally referred to as a wind setup; a wave setup component caused by wind induced waves transferring momentum to the water column; an atmospheric pressure head component due to the atmospheric pressure deficit over the spatial extent of the storm system; a Coriolis forced component due to the effects of the rotation of the earth acting on the wind driven alongshore current at the coast; and, if astronomical tides are present, an astronomical tide component (although the tide is not really a direct part of the meteorological driven component of storm surge). Typically, the most important component of a storm surge is the wind setup component, especially on the East Coast of the US and in the Gulf of Mexico. The importance of bathymetry to this wind setup storm surge component is considered herein with special reference to the coastline of Florida where eight Florida transects consisting of a cross-section of bathymetric data perpendicular to the shoreline were investigated. Effects of Coriolis, wave setup, atmospheric pressure head, and astronomical tide are not considered herein but will be addressed in future papers. The present study findings show that the wind setup component can vary over an order of magnitude for the same wind speed depending on the bathymetry leading up to the coast.

We discuss a stochastic model for the behavior of electrons in a magnetically confined plasma having axial symmetry. The aim of the work is to provide an explanation for the density limit observed in the Frascati Tokamak Upgrade (FTU) machine. The dynamical framework deals with an electron embedded in a stationary and uniform magnetic field and affected by an orthogonal random electric field. The behavior of the average plasma profile is determined by the appropriate Fokker–Planck equation associated to the considered model and the disruptive effects of the stochastic electric field are shown. The comparison between the addressed model and the experimental data allows to fix the relevant spatial scale of such a stochastic field. It is found to be of the order of the Tokamak micro-physics scale, i.e. few millimeters. Moreover, it is clarified how the diffusion process outlines a dependence on the magnetic field as $\sim B^{-3/2}$.