Search

The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone. Although theoretical descriptions exist for idealized conditions, computing the stochastic multimodal dynamics for the complex conditions of an experiment is very challenging. We show that this is possible using deterministic finite-element calculations with the fluctuation dissipation theorem by exploring the multimodal stochastic dynamics of a doubly clamped nanobeam. We use a very general, and flexible, finite-element computational approach to quantify the stochastic dynamics of multiple modes simultaneously using only a single deterministic simulation. We include the experimentally relevant features of an intrinsic tension in the beam and the influence of a nearby rigid boundary on the dynamics through viscous fluid interactions. We quantify the stochastic dynamics of the first 11 flexural modes of the beam when immersed in air or water. We compare the numerical results with theory, where possible, and find excellent agreement. We quantify the limitations of the computational approach and describe its range of applicability. These results pave the way for computational studies of the stochastic dynamics of complex 3D elastic structures in a viscous fluid where theoretical descriptions are not available. [ABSTRACT FROM AUTHOR]

In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid–liquid phase separation and a further transition into a gel-like state. In the present work, we formulate a thermodynamically consistent kinetic framework to study the interplay between phase separation, chemical reaction, and aging in spatially inhomogeneous macromolecular mixtures. A numerical algorithm is also proposed to simulate domain growth from collisions of liquid and gel domains via passive Brownian motion in both two and three spatial dimensions. Our results show that the coarsening behavior is significantly influenced by the degree of gelation and Brownian motion. The presence of a gel phase inside condensates strongly limits the diffusive transport processes, and Brownian motion coalescence controls the coarsening process in systems with high area/volume fractions of gel-like condensates, leading to the formation of interconnected domains with atypical domain growth rates controlled by size-dependent translational and rotational diffusivities. [ABSTRACT FROM AUTHOR]

The translocation of polymers through nanopores is a complex process influenced by various factors. In this study, the translocation behavior of a two-dimensional active polymer chain, comprised of a head active Brownian particle (ABP) and a tail passive polymer chain, through a nanopore is studied using Langevin dynamics simulations. Results show that the effect of the self-propulsion force of the ABP on the translocation differs significantly from the driving force inside the pore for traditional polymer translocations. Specifically, the translocation time τ initially increases with increasing the magnitude fs of the self-propulsion force and then decreases with a further increase in fs. A small fs lowers the potential barrier for the translocation and thus promotes slow translocations, whereas a large fs directly pulls the polymer chain through the nanopore following the scaling relation τ ∝ fs−1. Moreover, two asymptotic scaling relations between τ and polymer length N, τ ∝ Nα, are found, with the exponent α of about 2.5 for small fs or long N and the exponent α of about 1.4 for short active polymers with large fs. We discover that the slow rotation of the ABP accelerates the translocation process. [ABSTRACT FROM AUTHOR]

Biased and accelerated molecular simulations (BAMS) are widely used tools to observe relevant molecular phenomena occurring on time scales inaccessible to standard molecular dynamics, but evaluation of the physical time scales involved in the processes is not directly possible from them. For this reason, the problem of recovering dynamics from such kinds of simulations is the object of very active research due to the relevant theoretical and practical implications of dynamics on the properties of both natural and synthetic molecular systems. In a recent paper [A. Rapallo et al., J. Comput. Chem. 42, 586–599 (2021)], it has been shown how the coupling of BAMS (which destroys the dynamics but allows to calculate average properties) with Extended Diffusion Theory (EDT) (which requires input appropriate equilibrium averages calculated over the BAMS trajectories) allows to effectively use the Smoluchowski equation to calculate the orientational time correlation function of the head–tail unit vector defined over a peptide in water solution. Orientational relaxation of this vector is the result of the coupling of internal molecular motions with overall molecular rotation, and it was very well described by correlation functions expressed in terms of weighted sums of suitable time-exponentially decaying functions, in agreement with a Brownian diffusive regime. However, situations occur where exponentially decaying functions are no longer appropriate to capture the actual dynamical behavior, which exhibits persistent long time correlations, compatible with the so called subdiffusive regimes. In this paper, a generalization of EDT will be given, exploiting a fractional Smoluchowski equation (FEDT) to capture the non-exponential character observed in the relaxation of intramolecular distances and molecular radius of gyration, whose dynamics depend on internal molecular motions only. The calculation methods, proper to EDT, are adapted to implement the generalization of the theory, and the resulting algorithm confirms FEDT as a tool of practical value in recovering dynamics from BAMS, to be used in general situations, involving both regular and anomalous diffusion regimes. [ABSTRACT FROM AUTHOR]

We propose a Brownian ratchet for the unidirectional transport of stimuli-responsive molecules confined in a series of asymmetric geometries. It relies on repetitive cycles of aggregation and dispersion, which cause significant changes in molecular distribution within the confining geometry and enable the Brownian motion of the molecules to be ratcheted in a specific direction. To demonstrate the feasibility of the proposed Brownian ratchet, we conducted Brownian dynamics simulations where stimuli-responsive molecules were repeatedly aggregated and dispersed in a series of truncated conical tubes by altering intermolecular interactions. These simulations demonstrated the unidirectional transport of the molecules, indicating the efficacy of the proposed Brownian ratchet. Furthermore, we found that it becomes more effective with higher concentrations of molecules. This study suggests that, through the deliberate control of molecular assembly and disassembly by stimuli-responsive intermolecular interactions, it is possible to achieve directional and controlled molecular transport in various nanoscale applications. [ABSTRACT FROM AUTHOR]

As the physicochemical properties of ultrafine bubble systems are governed by their size, it is crucial to determine the size and distribution of such bubble systems. At present, the size or size distribution of nanometer-sized bubbles in suspension is often measured by either dynamic light scattering or the nanoparticle tracking analysis. Both techniques determine the bubble size via the Einstein–Stokes equation based on the theory of the Brownian motion. However, it is not yet clear to which extent the Einstein–Stokes equation is applicable for such ultrafine bubbles. In this work, using atomic molecular dynamics simulation, we evaluate the applicability of the Einstein–Stokes equation for gas nanobubbles with a diameter less than 10 nm, and for a comparative analysis, both vacuum nanobubbles and copper nanoparticles are also considered. The simulation results demonstrate that the diffusion coefficient for rigid nanoparticles in water is found to be highly consistent with the Einstein–Stokes equation, with slight deviation only found for nanoparticle with a radius less than 1 nm. For nanobubbles, including both methane and vacuum nanobubbles, however, large deviation from the Einstein–Stokes equation is found for the bubble radius larger than 3 nm. The deviation is attributed to the deformability of large nanobubbles that leads to a cushioning effect for collision-induced bubble diffusion. [ABSTRACT FROM AUTHOR]

Beyond well-documented confinement and surface effects arising from the large internal surface and severely confining porosity of nanoporous hosts, the transport of nanoconfined fluids remains puzzling in many aspects. With striking examples such as memory, i.e., non-viscous effects, intermittent dynamics, and surface barriers, the dynamics of fluids in nanoconfinement challenge classical formalisms (e.g., random walk, viscous/advective transport)—especially for molecular pore sizes. In this context, while molecular frameworks such as intermittent Brownian motion, free volume theory, and surface diffusion are available to describe the self-diffusion of a molecularly confined fluid, a microscopic theory for collective diffusion (i.e., permeability), which characterizes the flow induced by a thermodynamic gradient, is lacking. Here, to fill this knowledge gap, we invoke the concept of "De Gennes narrowing," which relates the wavevector-dependent collective diffusivity D0(q) to the fluid structure factor S(q). First, using molecular simulation for a simple yet representative fluid confined in a prototypical solid (zeolite), we unravel an essential coupling between the wavevector-dependent collective diffusivity and the structural ordering imposed on the fluid by the crystalline nanoporous host. Second, despite this complex interplay with marked Bragg peaks in the fluid structure, the fluid collective dynamics is shown to be accurately described through De Gennes narrowing. Moreover, in contrast to the bulk fluid, the departure from De Gennes narrowing for the confined fluid in the macroscopic limit remains small as the fluid/solid interactions in severe confinement screen collective effects and, hence, weaken the wavevector dependence of collective transport. [ABSTRACT FROM AUTHOR]

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft–soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈ 10 − 20 n m in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈ 0.05 τ d (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a stochastic semilinear differential equations driven by both Brownian motion and fractional Brownian motion. Firstly, we establish an inequality for the distance between finite‐dimensional distributions of a random process at two different moments. Then, using the properties of stochastic integrals, fixed point theorems, and based on this inequality, we establish the existence and uniqueness of Besicovich almost automorphic solutions in finite‐dimensional distributions for this type of semilinear equation. Finally, we provide an example to demonstrate the effectiveness of our results. Our results are new to stochastic differential equations driven by Brownian motion or stochastic differential equations driven by fractional Brownian motion. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how particles settle in a one-dimensional deterministic model. We leverage a model for deterministic Brownian motion and introduce boundary conditions to simulate particle settling. By adjusting parameters in the Jerk equation, we explore how different diffusion, and the size of the settling space affect the particles’ behavior. We analyze how these parameters influence the settling time and its relationship to the dispersion medium. Additionally, we examine statistical properties as follows: the average settling time, the probability distributions for mean displacement, and how the probability distribution of settling times changes with the size of the space. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we provide some analytical results about the finiteness of the reduced first collision time between a Brownian and Gaussian jump particles in the interactive medium. These results depend on the influence of discounted effort-reward parameter on the jumping distance. More than using the effectiveness of this parameter on uniform integrability conditions, we study the behavior of the triangular arrays of the random sequence with this discount parameter that represents the probable positions of the first collision at any time t∈R+. This will give more stronger finite moment conditions which are sufficient for the existence of finiteness of this reducing time. [ABSTRACT FROM AUTHOR]

Abstract.The data distributions of many financial and econometric sequences always exhibit heavy-tailed phenomena, which trigger distinct difficulty in parameter estimation by classical least squares method. This article aims to construct a new ratio-typed test based on least absolute deviation estimation that effectively circumvents the problem of long-run variance estimation and has robustness on detecting structural changes under strong mixing sequences with heavy-tailed innovations. This is because the least absolute deviation estimation can allow for processes within the domain of attraction of a stable law with an index κ∈(0,2), not limited to (1, 2). Under some regular conditions, the asymptotic distribution under the null hypothesis is derived as a functional of Brownian motion, not a functional of lévy process, and the divergence rate under the alternative hypothesis is also provided. Furthermore, the consistency of a ratio-typed change point estimator is given and its convergence rate is established. The numerical simulation indicates that empirical sizes are undistorted, and empirical powers exhibit significant performance. Finally, two practical application examples are presented to illustrate the validity of the proposed test procedures. [ABSTRACT FROM AUTHOR]

In this article, we study the approximate solution of a class of singular perturbation systems driven by additive fractional Gaussian noise with the Hurst parameter H ∈ (1 / 2 , 1) by the renormalization group (RG) method. We combine the pathwise approach with the fractional Itô formula to identify the convergence order of diffusion terms. Then, we obtain a simplified system, denoted as the RG equation, by utilizing the RG method. Furthermore, we prove that the solution of the original system is approximated by the solution constructed by the RG equation. [ABSTRACT FROM AUTHOR]

We mainly focus on the willow algorithm which can be used to solve the optimal dynamic multi-cycle investment and consumption problem under the jump-diffusion stochastic volatility model. First we obtain the moment generating function of the risky asset and then coalescing the Johnson-Curve transformation theory to generate the willow algorithm, which solving the multi-cycle dynamic investment and consumption problem is designed based on the two-dimensional willow framework. Moreover, through comparing our proposed solution with the optimal investment and consumption display solutions under the geometric Brownian motion model, we further discuss the analysis of the willow algorithm sensitivity. The willow algorithm for optimal investment and consumption proposed in this paper is able to extend the willow method which is effective from the field of option pricing to the field of investment portfolio, and it also provides a new idea for numerically solving the multi-period optimal investment and consumption decision. [ABSTRACT FROM AUTHOR]

In this paper, we propose a collocation scheme for efficiently solving the mixed time-fractional Black-Scholes (MTF-BS) model and obtaining the option price. Our approach involves deriving the mixed fractional Black-Scholes (MF-BS) partial differential equation (PDE) considering the delta hedging strategy and the mixed fractional Geometric Brownian motion (MFGBM) model. To simplify the problem, we transform the MTF-BS PDE into a modified Riemann-Liouville derivative form. Subsequently, a collocation method is employed to numerically solve the transformed equation, where the solution is represented as a series of fractional Jaiswal functions with unknown coefficients. By utilizing operational matrices and collocation points, we convert the problem into a linear system of equations, allowing for the examination of convergence and stability in the Sobolev spaces. Finally, we present four examples to demonstrate the method's effectiveness and accuracy. [ABSTRACT FROM AUTHOR]

This study focuses on the valuation of geometric Asian power options and presents an efficient numerical algorithm for solving the option price PDE. The analytical methodology utilizes the fractional Ito formula and replicating portfolio techniques to derive a PDE that characterizes the option price. However, due to the lack of an analytical solution for this PDE, a numerical method is proposed to solve it. The numerical solution involves implementing a time-semi-discrete scheme obtained through forward time difference approximation, while the other derivatives in the equation are approximated using cubic B-spline quasi-interpolation approximation. By employing the respective scheme and incorporating the initial and boundary conditions, the numerical solution for the equation is obtained. Subsequently, the stability of the method is investigated, and numerical results are presented. The main advantages of the presented method are its simplicity for computer implementation and its suitability for multi-dimensional problems. [ABSTRACT FROM AUTHOR]

In the current work, we develop and analyse a prey–predator model as a semi-Kolmogorov population model in which the predator has an indirect effect on the prey. The functional response of the model is investigated as Holling type (II). We construct a stochastic environment because of the parameter's random essence to study the influence of environmental fluctuations on this model and introduce a stochastic version of the prey–predator model. Then we present a dynamical analysis of solutions, including existence, uniqueness, positivity, stochastic boundedness, and stochastic extinction of all prey. Finally, some numerical simulations are carried out to validate our theoretical findings and confirm the efficiency and adaptation of our stochastic model. [ABSTRACT FROM AUTHOR]

Purpose: The main purpose here is to explore the unsteadiness characteristics in magnetized flow of Reiner–Rivlin nanofluid. Energy and concentration expressions are modeled by utilizing Buongiorno model for nanoscale particles. Additionally, Joule heating and activation energy are also deliberated. Design/methodology/approach: The bvp4c solver in MATLAB is employed for graphical and numerical outcomes. Findings: A similar trend of temperature field is seen against thermophoresis and Brownian movement parameters. Thermal transport rate decreases via Prandtl number. Augmentation in mass transport rate is noted through unsteadiness parameter. Originality/value: To the best of author's knowledge, no such consideration has been given in the literature yet. [ABSTRACT FROM AUTHOR]

This work has broad applications in areas such as materials engineering, particularly in the manufacturing of polymers, textile fibers, and nanocomposites, thus, inspired the study to examine a continuous two‐dimensional flow of micropolar fluid steadily fluctuated in an oblique impinging on a stretched surface theoretically and computationally. In addition, heat radiation and chemical reactions are taken into account in this work. The flow is composed of a uniform shear flow parallel to the sheet surface and a stagnation‐point flow. Assuming a linear variation in surface temperature, the sheet is extending at a velocity proportionate to the distance from the stagnation point. In terms of partial differential equations, the boundary‐layer regime under discussion is modeled. The nondimensional ordinary differential equations were developed using appropriate similarity variables via a similarity transformation approach. The most effective and powerful too of the numerical approach, known as the pseudospectral collocation technique, is used to solve the micropolar flow model problem. The velocity, angular velocity, temperature, and concentration profiles are portrayed through graphs. Moreover, the impression of the input values on the wall drag coefficient, thermal, and solutal transfer rate are computed in a table. A table is used to compare the numerical findings with the results found in the literature to verify the correctness of the results. It is noted that there is great agreement between the found answer and the earlier investigations. Graphs are used to show the impacts of the relevant factors in the problem, which include the magnetic parameter, the impinging angle heat transfer characteristics, the Prandtl number, the Lewis number, Brownian motion, and the thermophoresis parameter. [ABSTRACT FROM AUTHOR]

This study comprehensively examines magnetohydrodynamic heat transport characteristics within a thin nanofluid film on a stretchable sheet embedded in a composite medium. By considering factors such as the unsteady nature of sheet velocity, Brownian motion, thermophoresis, thermally radiative heat, irregular heat generation/sink, chemical reactions, and dissipation due to viscous fluid, the research provides valuable insights into the variations in fluid velocity, temperature, and nanoparticles concentration. The computational solution utilizes the efficient numerical method that enables accurate predictions of system behavior under varying conditions. Notable findings include the influence of Schmidt numbers on nanoparticle concentration distribution, the opposing impact of thermophoresis parameter values, and the influence of Brownian motion and heat source/sink on temperature profiles in thin nanofluid film. Also, nanoliquid film thickness is reduced by enhancing the porous parameter values and Hartmann number values. The nanoliquid film becomes thinner when the space‐dependent heat source/sink parameter is considered compared to the temperature‐dependent heat source/sink coefficient. In space‐dependent and temperature‐dependent cases, the increase in these parameters leads to a decrease in the temperature gradient. Furthermore, it is observed that higher thermophoresis values correspond to reduced nanoparticle concentration gradient profiles. Also, enhancement in the chemical reaction values leads to an expansion in the solutal boundary region surrounding nanoparticles, and as a consequence, the concentration gradient of nanoparticles is enhanced. This research has significant potential for optimizing heat performance and advancing innovation in industrial and engineering processes. [ABSTRACT FROM AUTHOR]

This study implements the comparative study of Casson and Williamson nanofluids by considering the impacts of linear thermal radiation and inclined magnetohydrodynamics. Here, we employ graphs to compare the variables affecting the behavior of non‐Newtonian and Newtonian fluids for a range of physical and dimensionless parameter values. The flow's coupled equations, which contain multiple independent variables, these equations can then be changed into a single independent variable by adding similarity variables and can be solved by applying the shooting method. The effects of thermomigration and Brownian motion on nonlinear flow equations are graphically examined. For an array of radiation parameter values, we have observed that the Newtonian fluid's concentration is lesser than that of both the non‐Newtonian fluids and also noticed that Newtonian fluids converge a little sooner than Casson and Williamson fluids. The primary innovation is shown in Table 1, where the mass transfer and heat transfer values are contrasted with the limiting circumstances of previous research findings that are documented in the literature. [ABSTRACT FROM AUTHOR]

This article extends recent asymptotic theory developed for the Hodrick Prescott (HP) filter and boosted HP (bHP) filter to long-range dependent time series that have fractional Brownian motion (fBM) limit processes after suitable standardization. Under general conditions, it is shown that the asymptotic form of the HP filter is a smooth curve, analogous to the finding in Phillips and Jin for integrated time series and series with deterministic drifts. Boosting the filter using the iterative procedure suggested in Phillips and Shi leads under well-defined rate conditions to a consistent estimate of the fBM limit process or the fBM limit process with an accompanying deterministic drift when that is present. A stopping criterion is used to automate the boosting algorithm, giving a data-determined method for practical implementation. The theory is illustrated in simulations and two real data examples that highlight the differences between simple HP filtering and the use of boosting. The analysis is assisted by employing a uniformly and almost surely convergent trigonometric series representation of fBM. [ABSTRACT FROM AUTHOR]

In this article, the authors set up an optimal control of neutral stochastic integro-differential equations (NSIDEs) driven by fractional Brownian motion (fBm) in a Hilbert space by using Grimmer resolvent operators. Sufficient conditions for mild solutions are formulated and proved by using the Banach contraction mapping principle and stochastic analytic techniques. We have extended the problem in [Issaka et al. (2020) Results on nonlocal stochastic integro-differential equations are driven by a fractional Brownian motion. Open Mathematics, 18(1), 1097–1112] to NSIDEs driven by fBm and have used modified techniques to make them compatible with optimal controls of stochastic integro-differential systems. In addition, the optimal control of the proposed problem is presented using Balder's theorem. Such optimal control of NSIDEs with fBm is widely used in automatic control, aircraft and air traffic control, electrical networks, wavelet expansions, etc. Finally, an example illustrates the potential of the main results. [ABSTRACT FROM AUTHOR]

In this paper, we aim to interpret the background gravitational effects appearing in quantum field theory on curved space-time by studying the Brownian motion of quantum states along with the Hamilton–Perelman Ricci flow. It has been shown that the Wiener measure automatically contains the Einstein–Hilbert action and the path-integral formulation of the scalar quantum field theory on curved space-time at the first order of local approximations. This provides a well-defined formulation of the path-integral measure for quantum field theory in the presence of gravity. However, we establish that the emergence of Einstein–Hilbert action is independent of the matter field interactions and is a merely entropic/geometric effect stemming from the nature of the Ricci flow of the universe geometry. We also extract an explicit formula for the cosmological constant in terms of the Ricci flow and Hamilton’s theorem for 3-manifolds. Then, we discuss the cosmological features of the FLRW solution in ΛCDM Model via the derived equations of the Ricci flow. We also argue the correlation between our formulations and the entropic aspects of gravity. Finally, we provide some theoretical evidence that proves the second law of thermodynamics is the basic source of gravity and probably a more fundamental concept. [ABSTRACT FROM AUTHOR]

The efficiency of solar cells based on organic–inorganic hybrid perovskite materials has already met the standards for commercial applications. However, there remains an efficiency gap of ≈30% between small‐area devices and industrial‐scale devices. Large‐area devices, in particular, tend to exhibit lower optoelectronics and reduced environmental stability. The ink fluid behavior significantly influences the crystal process of large‐area perovskite films during printing fabrication, which cannot be disregarded. As the manufacturing area and total solvent volatilization increase, the impact of inhomogeneous migration by perovskite colloidal particles gradually intensifies. This work focuses on elucidating the impact of the rheological properties of perovskite colloidal particles on the crystalline quality and device optoelectronic performance of perovskite films during deposition. It explores the fluid behavior of colloidal particles in the ink and throughout the printing process, the effects of additives on the motion of perovskite colloidal particles, and how the ink's rheological properties change when modifying agents interact with perovskite particles. Additionally, the functional aspects of controlling perovskite film formation and optimizing photovoltaic performance in perovskite solar cells (PSCs) are thoroughly discussed. Ultimately, the preparation process improvement of perovskite precursor solution and the current technical barriers to commercialization are summarized and prospected. [ABSTRACT FROM AUTHOR]

Endoscopy, in medical sciences, is a modern mechanism for the examination of internal remote organs by the direct insertion of the illuminated tube inside the body. It also transports the fluid with the movement of contraction and relaxation. The current study aims to explore the peristaltic propulsion of ethylene glycol‐based graphene oxide nanofluid through an endoscope. The considered nanofluid depicts shear‐thinning aspects, which are described by the Carreau–Yasuda fluid model. The modified Darcy's law is employed to describe the porosity of the medium. For a precise calculation, the modified Buongiorno model is adopted with the incorporated Maxwell's model, Brownian motion parameter, and variable for the thermophoresis effect. The mathematical problem linearized under the lubrication approach is solved numerically through Mathematica. After using the experimentally found values of Carreau–Yasuda fluid parameters for different levels of nanoparticle proportion, It is concluded that there is a slight decline in the velocity and the temperature of the nanofluid. Furthermore, a larger Biot number contributes significantly to the heat transfer coefficient. Fluid flow is assisted by a rise in the Darcy porosity parameter. For an increment in the strength of the buoyancy forces, there is a significant uplift in the fluid's temperature and the velocity. [ABSTRACT FROM AUTHOR]

Spatial patterns in genetic diversity are shaped by individuals dispersing from their parents and larger-scale population movements. It has long been appreciated that these patterns of movement shape the underlying genealogies along the genome leading to geographic patterns of isolation-by-distance in contemporary population genetic data. However, extracting the enormous amount of information contained in genealogies along recombining sequences has, until recently, not been computationally feasible. Here, we capitalize on important recent advances in genome-wide gene-genealogy reconstruction and develop methods to use thousands of trees to estimate per-generation dispersal rates and to locate the genetic ancestors of a sample back through time. We take a likelihood approach in continuous space using a simple approximate model (branching Brownian motion) as our prior distribution of spatial genealogies. After testing our method with simulations we apply it to Arabidopsis thaliana. We estimate a dispersal rate of roughly 60 km2/generation, slightly higher across latitude than across longitude, potentially reflecting a northward post-glacial expansion. Locating ancestors allows us to visualize major geographic movements, alternative geographic histories, and admixture. Our method highlights the huge amount of information about past dispersal events and population movements contained in genome-wide genealogies. [ABSTRACT FROM AUTHOR]