Abstract The problem concerning water wave scattering by a floating breakwater has been an interesting subject of study under linearized water wave theory in the past few decades due to the reason that not only do these structures allow better water circulation to have smaller impact on sediment transport and fish migration, but also their construction is cost effective compared with the bottom founded structures. Modern study observes that thick breakwaters, with their larger and bulkier structure, are more effective at reducing wave energy compared with thin breakwaters. However, recent research reveals that breakwaters that combine both thin and thick parts offer enhanced performance by providing effective wave attenuation and reducing the construction costs. We may mention that these problems are primarily studied when the depth of water is uniform. However, in practice, the bathymetry of the water region is not uniform. This motivated us to study the problem of water wave scattering by a $ \boldsymbol \sqcap $ -shaped floating breakwater (which is a combination of thick and thin parts) in the presence of a rectangular submarine trench. For analytical solution of the corresponding boundary value problem, the geometric symmetry of the problem simplifies the mathematical difficulty considerably. For this, the domain of definition is divided into smaller subdomains and by suitable matching conditions at the various boundaries of the subdomains, the corresponding boundary value problem is formulated in terms of two Fredholm-type integral equations. The multi-term Galerkin approximation technique, involving Chebyshev polynomials and ultraspherical Gegenbauer polynomials as basis functions, is employed to solve the integral equations. It is important to note here that the choice of basis functions depends on the types of singularities at the corner of the trench and at the submerged sharp edge of the breakwater. The solutions of the integral equations are then employed to evaluate reflection and transmission coefficients. Graphical illustrations show that the length, width of the trench and the width of the breakwater have definite impact on the reflected wave, transmitted wave and the force on the breakwater. It is observed that the presence of trench produces oscillations in the reflection and transmission coefficients. When the width of the trench is equal to the width of the breakwater, reflection and transmission coefficients show smooth uniform oscillations. However, when the width of the trench and the width of the breakwater are unequal, nonuniform, nonsmooth oscillations in the reflection and transmission coefficients are observed. It is interesting to note that for a particular width of the breakwater, the reflected wave of certain wavelength shows resonating behaviour. Also, with the increase of submerged length of the side wall of the $\large \boldsymbol \sqcap $ -shaped breakwater, the horizontal force on the breakwater enhances and the vertical force diminishes. Additionally, it is observed that when the breakwater is present in a water region with a trench, the horizontal force is more than the vertical force. However, when the breakwater is present in uniformly deep water without a trench, the vertical force is more than the horizontal force.
Abstract The present study characterizes the impact of brash ice present at the topmost surface of an ocean on a submerged stationary prolate spheroidal body (both axisymmetric and nonaxisymmetric) within the framework of linear water wave theory. The brash ice cover is assumed to behave as an inertial surface composed of uniformly distributed, noninteracting particles in the presence of surface tension. Taking advantage of the body’s symmetry, we adopt a prolate spheroidal coordinate system. The solution is constructed through the method of image singularities, using Havelock’s theorem to transform the fundamental Green’s function into a prolate spheroidal coordinate system. The diffraction potentials are expanded in terms of the multipoles of the Green’s function using spherical harmonics. The zero-velocity condition, along with suitable orthogonality relations, is used to derive the final linear system. The hydrodynamic forces (such as surge, heave and sway) and moment acting on the spheroid are numerically evaluated, and analysed for different values of the brash ice parameter, coefficients of surface tension, depths of submergence, eccentricity of the body and wave-heading angles. We observe reduction in the magnitudes of forces due to the presence of brash ice and further reduction has been noticed as the layer of brash ice gets heavier. The yaw moment is found to attain its maximum value at a specific angle of wave incidence.
We investigate the dynamics arising from an idealized model of a spherical active particle immersed in a cubic Poiseuille field inspired by fluid flow through an equilateral triangular duct. Starting from a general Hamiltonian formulation, we describe the equations of motion, analyse equilibrium points and their stability and classify trajectories based on their initial position. Motion of an active particle within the Poiseuille flow of an equilateral triangular duct is an interesting case to examine given its symmetry group and a velocity field described by a cubic polynomial. In addition to trajectory types previously identified in other duct geometries, including central and vertical swinging, tumbling, off-centred trapping and wandering, we observe some exotic orbits within the triangular geometry. We also examine the chaotic behaviour by using Poincar & eacute; maps and Lyapunov exponents over a range of parameter values and initial conditions. This work enhances the broader understanding of idealized microswimmer motion via a case where the fluid flow has a straightforward closed-form description.
If a rectangular object is dipped into a liquid, the contact line normally rises up the surface and dips near the corner, often an undesirable outcome in an industrial dip-coating context. Is it possible to round the corners of the object in such a way that the contact line curve becomes horizontal? We find that just rounding the corner is not sufficient to accomplish this, but by additionally roughening the surface in a prescribed way, one can indeed achieve the desired horizontal contact line.
We study the semi-infinite Neumann problem, which models the variation law of a cline in a semi-infinite habitat. Using the bifurcation analysis method, we find that there is a unique solution curve emanating from (arctan alpha, 0) with alpha > 0, which is strictly increasing and approaches 1 in C[0, +infinity). Furthermore, we show that any cline (bifurcation solution) is stable, thereby providing a confirmed answer to a conjecture. Moreover, we also establish the stability of the trivial solution. Our conclusions are consistent with the related numerical results and biological reality.
Within the framework of small-amplitude water wave theory, the scattering of obliquely incident monochromatic surface waves by dual thick vertical barriers over an arbitrary bottom topography is analysed. A numerical model based on the finite element method is developed by formulating the governing well-posed mixed boundary value problem over each element within a truncated finite domain. This domain is obtained by limiting the originally infinite domain to a finite distance. Two types of bottom profiles, namely parabolic and rectangular, are considered for the numerical analysis. To ensure the accuracy of the present numerical results, an energy identity relation is derived using Green's identity and verified numerically. Additionally, for validation purposes, the numerical results are compared with existing results available in the literature. The number of zeros on the reflection and transmission coefficient curves is investigated with respect to the gap between identical and nonidentical barriers. The effects of various physical parameters, including the gap between the vertical barriers, the height of the bottom topography, the thickness and length of the barriers, and the angle of wave incidence on the reflection and transmission coefficients, as well as on the nondimensional horizontal force acting on the front and rear barriers, are examined using the proposed numerical model. This study contributes to understanding of wave-structure interaction and will be useful in addressing similar problems in applied mathematics and fluid mechanics.
In this paper, the pricing problem of geometric average Asian options under the Vasicek interest rate based on a time-changed mixed fractional Brownian motion is considered. A stochastic process similar to the renewal process is applied to characterize the constant periodicity of the financial asset price in emerging financial markets. The time-changed mixed fractional Brownian motion model $M_{\alpha ,H}(t) = aB(T_\alpha (t)) + bB_H(T_\alpha (t))$ is introduced to describe the underlying asset process of Asian options. When the Hurst exponent satisfies certain conditions, the model is used to price options without arbitrage. By using the hedging and no-arbitrage principle, the partial differential equation satisfied by the price of an Asian option is given. The pricing formula of an Asian call and a put option, and the corresponding parity formula, are obtained, along with their explicit solution.
Interval consensus is an important generalization of conventional consensus problems by allowing each agent to individually nominate an acceptable interval for their consensus value. However, as other consensus problems, agents in the network exchange information explicitly among neighbours and disclose their values without any protection for sensitive information causing serious privacy concerns in many applications in distributed multiagent systems. We propose a privacy-preserving approach consisting of decomposition and weighting mechanisms. Based on this approach, we show that the agents in the network can achieve interval consensus with the final consensus value within the intersection of all proposed intervals if the intersection is nonempty and the network is connected. Moreover, the privacy of the initial states of the agents is guaranteed against internal and external adversaries. The proposed consensus protocol is simple and efficient, and it can be implemented in a distributed manner over the network.
The fuzzy set theory has several types of extensions. Bipolar fuzzy sets are fuzzy set extensions that have been developed by several researchers and applied in various settings. The satisfaction levels of a property and its counter-property define the membership degrees in bipolar fuzzy sets. These sets are useful in expert systems and decision-making, because they provide a refined representation of uncertainty by enabling both positive and negative membership degrees to exist simultaneously. This paper deals with calculating the knowledge passed by a bipolar fuzzy set; a knowledge-measure in the bipolar fuzzy framework is proposed here. Its validity is examined together with its mathematical characteristics and its performance is assessed with different examples. In addition, novel dissimilarity, similarity and accuracy measures are derived from the proposed measure in the bipolar fuzzy framework. The basic properties of the derived measures are outlined and their validity is evaluated. The proposed accuracy measure based on a new approach is discussed for solving cluster analysis issues. Furthermore, a case study about air pollution in different regions of the world in the year 2022 is examined. The proposed approach uses the information gathered from this investigation to generate clusters. In addition, medical diagnosis and pattern detection issues are addressed using the proposed measures in the bipolar fuzzy framework.
A global spectral method is presented for unsteady incompressible fluid flow in smoothly varying channels. Recombined Chebyshev bases are implemented with numerical conformal mapping, ensuring boundary conditions are met for both straight walls and smoothly varying walls. The pressure calculation reduces to matrix operations that comprise 8% of runtime, while maintaining spectral accuracy and mass continuity. The method is demonstrated for Reynolds numbers from $Re=1$ up to $Re=10<^>5$ . The method is verified by comparison with known results for a straight-walled channel, and with lubrication theory and linearization estimates for a channel with a periodic wavy lower wall. Some simple wall shapes are modelled at low Reynolds number. Long term stability is demonstrated for high Reynolds number flow, with an analysis of convergence against grid spacing.
The problem concerning water wave scattering by a floating breakwater has been an interesting subject of study under linearized water wave theory in the past few decades due to the reason that not only do these structures allow better water circulation to have smaller impact on sediment transport and fish migration, but also their construction is cost effective compared with the bottom founded structures. Modern study observes that thick breakwaters, with their larger and bulkier structure, are more effective at reducing wave energy compared with thin breakwaters. However, recent research reveals that breakwaters that combine both thin and thick parts offer enhanced performance by providing effective wave attenuation and reducing the construction costs. We may mention that these problems are primarily studied when the depth of water is uniform. However, in practice, the bathymetry of the water region is not uniform. This motivated us to study the problem of water wave scattering by a Pi -shaped floating breakwater (which is a combination of thick and thin parts) in the presence of a rectangular submarine trench. For analytical solution of the corresponding boundary value problem, the geometric symmetry of the problem simplifies the mathematical difficulty considerably. For this, the domain of definition is divided into smaller subdomains and by suitable matching conditions at the various boundaries of the subdomains, the corresponding boundary value problem is formulated in terms of two Fredholm-type integral equations. The multi-term Galerkin approximation technique, involving Chebyshev polynomials and ultraspherical Gegenbauer polynomials as basis functions, is employed to solve the integral equations. It is important to note here that the choice of basis functions depends on the types of singularities at the corner of the trench and at the submerged sharp edge of the breakwater. The solutions of the integral equations are then employed to evaluate reflection and transmission coefficients. Graphical illustrations show that the length, width of the trench and the width of the breakwater have definite impact on the reflected wave, transmitted wave and the force on the breakwater. It is observed that the presence of trench produces oscillations in the reflection and transmission coefficients. When the width of the trench is equal to the width of the breakwater, reflection and transmission coefficients show smooth uniform oscillations. However, when the width of the trench and the width of the breakwater are unequal, nonuniform, nonsmooth oscillations in the reflection and transmission coefficients are observed. It is interesting to note that for a particular width of the breakwater, the reflected wave of certain wavelength shows resonating behaviour. Also, with the increase of submerged length of the side wall of the Pi -shaped breakwater, the horizontal force on the breakwater enhances and the vertical force diminishes. Additionally, it is observed that when the breakwater is present in a water region with a trench, the horizontal force is more than the vertical force. However, when the breakwater is present in uniformly deep water without a trench, the vertical force is more than the horizontal force.
We study a robust optimal reinsurance and investment problem for an ambiguity-averse insurer, where decisions are influenced by past capital flows (delay). The insurer's surplus is modelled via diffusion approximation, and the financial market comprises a risk-free asset and a risky asset following geometric Brownian motion. To capture ambiguity aversion toward both insurance and financial risks, we employ the alpha-max/min mean-variance criterion, which generalizes the classical mean-variance approach by weighting worst-case and best-case scenarios under model uncertainty. Incorporating a time-delay structure into the wealth dynamics leads to an infinite dimensional stochastic control problem. Using stochastic control theory for delay systems, we derive an extended Hamilton-Jacobi-Bellman equation and a verification theorem. Explicit, closed-form solutions for the robust optimal time-consistent reinsurance and investment strategies, along with the equilibrium value function, are obtained. Key findings include: (i) the equilibrium reinsurance strategy becomes more conservative as ambiguity aversion increases; (ii) the impact of ambiguity aversion of an individual on the investment strategy depends on the correlation between insurance and financial risks. When this dependence is weak, higher ambiguity aversion leads to a more conservative investment strategy. However, if the insurance market is highly ambiguous, a more ambiguity-averse insurer may surprisingly adopt a more aggressive investment strategy to diversify overall portfolio risk. Numerical analyses illustrate the effects of crucial parameters such as the ambiguity aversion coefficient, delay parameters and market coefficients of the optimal strategies, providing further economic interpretation and validation.
This paper introduces a parallelizable lossless image compression algorithm designed for three-channel standard images and two-channel pathology images. The proposed algorithm builds on the Quite OK Image Format (QOI) by addressing its limitations in parallelizability and compression efficiency, thereby enhancing both the compression ratio and processing speed. By incorporating image context and optimizing pixel traversal sequences, the algorithm enables effective parallel processing, achieving rapid compression of million-pixel pathology images within milliseconds, and is scalable to larger whole-slide images. It also delivers exceptional performance in terms of both speed and compression ratio for standard images. Additionally, the low complexity lossless compression for images (LOCO-I) context prediction algorithm used in joint photographic experts group lossless standard (JPEG-LS) is parallelized to improve compression efficiency and speed. By implementing full-process parallelization across the entire compression workflow rather than confining parallelization to individual steps, this approach significantly enhances overall time performance.
This study investigates the hydroelastic interaction of flexural gravity waves with multiple porous elastic plates of varying lengths in finite-depth water, employing an integral equation approach. The floating ice sheet is modelled as a flexible plate of uniform thickness, governed by the Euler-Bernoulli beam equation. The primary objective is to evaluate the effectiveness of porous elastic plates as wave barriers for shoreline protection in ice-covered regions. Within the framework of linearized theory, the problem is formulated as a boundary value problem (BVP) and solved using an eigenfunction expansion method with nonorthogonal eigenfunctions. The mode-coupling relation is utilized to transform the BVP into a system of Fredholm-type integral equations, which is subsequently solved using the multi-term Galerkin approximation technique with Chebyshev polynomials. The numerical analysis evaluates the reflection and transmission coefficients, hydrodynamic forces, and wave energy dissipation, with a particular focus on the influence of the permeability and flexibility of the submerged plates, along with other relevant parameters. Validation is conducted by comparing the results with those of previous studies under specific conditions. This research underscores the practical benefits of incorporating porosity and flexibility into the model, demonstrating improved wave reflection and energy dissipation. Additionally, the findings reveal that the thickness of the ice sheet plays a crucial role in optimizing breakwater performance. The research delivers key insights into mitigating wave-induced forces and offers a reliable framework for designing effective and sustainable coastal protection systems that safeguard shorelines from high waves.
Intense vortices have been observed within large-scale bushfires, and have been likened to "fire tornadoes". This paper presents a simple mathematical model of such an event, and is based on a Boussinesq approximation relating temperature and density in the air. A linearized model is derived under the assumption that the temperature varies only slightly from ambient, and a solution to that model is presented in closed form. The nonlinear equations are solved in axisymmetric geometry, using a semi-numerical approach based on Fourier-Bessel series. The nonlinear and linearized results are in good agreement for small temperature excursions above ambient, but when larger deviations occur, nonlinear effects cause a type of flow reversion within the fire vortex. The cause of this effect is discussed in the paper.
Yeast species have several adaptations that enable them to survive in harsh environments. These adaptations include biofilm formation, where the secretion of extracellular polymeric substances can protect the cells from a hostile environment, or, under nutrient-limited conditions, pseudohyphal or hyphal growth, where the colony can send out long tendrils to explore the environment and seek nutrients. Recently, we observed a spiral colony morphology emerge in an isolate of the hyphae-forming yeast Magnusiomyces magnusii (M. magnusii) grown under laboratory conditions. We use an off-lattice agent-based model (ABM) that simulates colony development to investigate the hypothesis that bias in the angle between successive hyphal segments causes the spiral morphology. The model involves biologically motivated rules of hyphal extension, with key model parameters including the colony size at the onset of hyphal filaments, and the angle between the penultimate and the apical segments. Using one example of an experimentally grown colony, we use a sequential neural likelihood method to perform likelihood-free Bayesian inference to infer the model parameters. Our results indicate a mean angle between hyphal segments of ${2.3}<^>{\circ } [{1.1}<^>{\circ }, {3.6}<^>{\circ }]$ (95% credible interval). To confirm the model's applicability to colony growth, we use biologically feasible parameter values to yield morphologies observed in M. magnusii experiments.
The transient response of an ice shelf to an incident wave packet from the open ocean is studied with a model that allows for extensional waves in the ice shelf, in addition to the standard flexural waves. Results are given for strains imposed on the ice shelf by the incident packet, over a range of peak periods in the swell regime and a range of packet widths. In spite of large differences in speeds of the extensional and flexural waves, it is shown that there is generally an interval of time during which they interact, and the coherent phases of the interactions generate the greatest ice shelf strain magnitudes. The findings indicate that incorporating extensional waves into models is potentially important for predicting the response of Antarctic ice shelves to swell, in support of previous findings based on frequency-domain analysis.
A semi-analytical study of oblique wave interaction with two $\boldsymbol {\sqcap }$ -shaped breakwater designs—floating and bottom-fixed structures—incorporating two thin porous plates is presented using linearized theory. Wave potential for both configurations is developed using the eigenfunction expansion method, considering both progressive and evanescent wave modes. The problem of oblique wave scattering by $\boldsymbol {\sqcap }$ -shaped breakwaters is reduced to a set of coupled integral equations of first kind, based on horizontal velocity components. These equations are solved using the multi-term Galerkin approximation with appropriate basis functions to handle the square-root singularities at sharp edges of the porous barriers. The performance of the models is evaluated by examining reflection, transmission and energy dissipation coefficients, along with free surface elevation and horizontal drift force. We observe that increasing the plate length of the breakwaters attenuates the incident waves more effectively than increasing the width. Additionally, the floating $\boldsymbol {\sqcap }$ -shaped breakwater significantly reduces the free surface elevation in the transmitted region. The results from the developed model can provide valuable insights for the design of wave–structure systems in shallow waters.
