Long-wavelength Approximation Research Articles

Entropy Production in Electroosmotic Cilia Facilitated Stream of Thermally Radiated Nanofluid with Ohmic Heating.

No thermal process, even the biological systems, can escape from the long arms of the second law. All living things preserve entropy since they obtain energy from the nutrition they consume and gain order by producing disorder. The entropy generation in a biological and thermally isolated system is the main subject of current investigation. The aim is to examine the entropy generation during the convective transport of a ciliated nano-liquid in a micro-channel under the effect of a uniform magnetic field. Joint effects of electroosmosis and thermal radiation are also brought into consideration. To attain mathematical simplicity, the governing equations are transformed to wave frame where the inertial parts of the transport equations are dropped with the use of a long-wavelength approximation. This finally produces the governing equations in the form of ordinary differential equations which are solved numerically by a shooting technique. The analysis reports that the cilia motion contributes to enhance the flow and heat transfer phenomena. An enhancement in the flow is observed near the channel surface for higher cilia length and for smaller values of the electroosmotic parameter. The entropy generation in the ciliated channel is observed to be lessened by intensifying the thermal radiation and decreasing the Ohmic heating. The extended and flexible cilia structure contributes to augment the volumetric flow rate and to drop the total entropy generation in the channel.

Lubrication analysis of peristaltic motion in non-axisymmetric annular tubes

This paper addresses peristaltic flow induced in a non-axisymmetric annular tube by a periodic small-amplitude wave of arbitrary shape propagating axially along its inner surface, assumed to be a circular cylinder. The study is motivated by recent in vivo experimental observations pertaining to the flow of cerebrospinal fluid along the perivascular spaces of cerebral arteries. The analysis employs the lubrication approximation, describing low-Reynolds-number peristaltic flow in the long-wavelength approximation. Closed-form analytic expressions are derived for the average pumping rate in infinitely long tubes and also in tubes of finite length. Consideration is also given to the transverse motion arising in non-axisymmetric tubes. For small-amplitude waves, the solution is reduced to the integration of a parameter-free Stokes-flow problem, which is solved for relevant cross-sectional shapes, with closed-form analytical results derived for thin canals.

Accuracy of parameter estimations with a spaceborne gravitational wave observatory

Employing the Fisher information matrix analysis, we estimate parameter errors of TianQin and Laser Interferometer Space Antenna (LISA) for monochromatic gravitational waves. With the long-wavelength approximation, we derive analytical formulas for the parameter estimation errors. We separately analyze the effects of the amplitude modulation due to the changing orientation of the detector plane and the Doppler modulation due to the translational motion of the center of the detector around the Sun. We disclose that in the low-frequency regime there exist different patterns in angular resolutions and estimation errors of sources' parameters between LISA and TianQin, the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ for TianQin but ${S}_{n}(f)$ for LISA, and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}/f$ for TianQin but $\sqrt{{S}_{n}(f)}$ for LISA. In the medium-frequency regime, we observe the same pattern where the angular resolution falls off as ${S}_{n}(f)/{f}^{2}$ and the estimation errors of the other parameters fall off as $\sqrt{{S}_{n}(f)}$ for both TianQin and LISA. In the high-frequency regime, the long-wavelength approximation fails; we numerically calculate the parameter estimation errors for LISA and TianQin and find that the parameter estimation errors measured by TianQin are smaller than those by LISA.

MENP: an open-source MATLAB implementation of multipole expansion for nanophotonics

In modern nanophotonics, multipolar interference plays an indispensable role to realize novel optical devices represented by metasurfaces with unprecedented functionalities. Not only to engineer sub-wavelength structures that constitute such devices but also to realize and interpret unnatural phenomena in nanophotonics, a program that efficiently carries out multipole expansion is highly demanded. MENP is a MATLAB program for computation of multipole contributions to light scattering from current density distributions induced in nanophotonic resonators. The main purpose of MENP is to carry out post-processing of a rigid multipole expansion for full-field simulations that in principle provide the information of all near- and far-field interactions (e.g., as a total scattering cross section). MENP decomposes total scattering cross sections into partial ones due to electric and magnetic dipolar and quadrupolar terms based on recently developed exact multipole expansion formulas. We validate the program by comparing results for ideal and realistic nanospheres with those obtained with the Mie theory. We also demonstrate the potential of MENP for analysis of anapole states by calculating the multipole expansion under the long-wavelength approximation, which enables us to introduce toroidal dipole moments.

Numerical Treatment for Dynamics of Second Law Analysis and Magnetic Induction Effects on Ciliary Induced Peristaltic Transport of Hybrid Nanomaterial

The presented communication provides the analysis of entropy generation and heat transport rate in peristalsis of hybrid nanofluid induced by metachronal ciliary beating under magnetic environment for sufficiently large magnetic Reynolds number. Nanoparticles of Cu and Al2O3 are suspended in water. Features of their structures are determined by using long-wavelength approximation with zero Reynolds number. Adams Bashforth method has been applied to compute the results of the flow variables as well as entropy generation number from the formulated differential system which are then interpreted graphically to establish physical significance for different values of physical interest. This investigation reveals that thermal performance of fluid can be boosted by utilizing hybrid nanomaterial about the strength of a wall for stability. Irreversibility analysis ensures that entropy reduced for strong magnetic field while thermal heat generation results in an increase in temperature causing an enhancement in entropy of the system. Error analysis has been performed with reasonably accurate tolerance level. The comparative outcomes of both numerical approaches are presented with plentiful graphical as well as numerical demonstrations which demonstrate the importance in terms of robustness, accuracy and stability.

Porosity and dissipative effects in Peristalsis of hydro-magneto nanomaterial: Application of biomedical treatment

The non-uniformity value which currently many applications of magneto-hydrodynamics are found in medicine where drug deliverance happens through peristaltic pumping phenomena, various magnetic drugs are released to target tumor diseases and to control the drug flow movement to the desired area. Owing to these facts, the aims of this article is to examine the simultaneous influence of magneto-hydrodynamics (MHD) and slip effect on unsteady peristaltic nanofluid flow in a non-uniform porous channel of finite length. The constituent governing equations for the model have been examined under the approximation of long wave length and small Reynolds value. Keeping kerosene oil and ethylene glycol as base fluids with polystyrene chosen as nanoparticle. The current analysis is carried out for the peristaltic flow transferal which carries innumerable industrialized employments. The incompressible, viscous, electrically conducting flow is studied in wave form. Here, exact method is employed to obtained closed form solutions. We have implemented computational software packages “Mathematica” as a main tool in order to obtain explicit expressions for axial velocity, temperature, stream function, pumping phenomenon and bolus formation. Obtained solutions are used for graphical analysis against different physical parameters. It is concluded that axial velocity increments for higher Hartmann number and slip parameter near the walls. The porosity effects increases the temperature whereas the temperature field shows increasing behavior for larger Brinkman number.

Universality of the spherical collapse with respect to the matter type: the case of a barotropic fluid with linear equation of state

We study the spherical collapse of an over-density of a barotropic fluid with linear equation of state in a cosmological background. Fully relativistic simulations are performed by using the Baumgarte-Shibata-Shapiro-Nakamura formalism jointly with the Valencia formulation of the hydrodynamics. This permits us to test the universality of the critical collapse with respect to the matter type by considering the constant equation of state parameter $\omega$ as a control parameter. We exhibit, for a fixed radial profile of the energy-density contrast, the existence of a critical value $\omega^*$ for the equation of state parameter under which the fluctuation collapses to a black hole and above which it is diluting. It is shown numerically that the mass of the formed black hole, for subcritical solutions, obeys a scaling law $M\propto |\omega - \omega^*|^\gamma$ with a critical exponent $\gamma$ independent on the matter type, revealing the universality. This universal scaling law is shown to be verified in the empty Minkoswki and de Sitter space-times. For the full matter Einstein-de Sitter universe, the universality is not observed if conformally flat sub-horizon initial conditions are used. But when super-horizon initial conditions computed from the long-wavelength approximation are used, the universality appears to be true.

An Exploratory Approach to Study Electro-Osmotic of Non-Newtonian Bio-Bi-Phase Flow Due to Peristaltic Transport of Particulate Fluid

The present article aims to probe the impacts of electro-magneto-hydrodynamics (EMHD) peristaltic flow of in-compressible, dusty, non-Newtonian fluid in a hose of predetermined dimension together with homogeneously scattered analogous rigid particles. In the presence of transversal static magnetic field, Navier-Stokes’s equations are employed to design a flow problem for the particulate phase. Governing flow problem is simplified by approximation of long wavelength and zero Reynolds number. The analytical solution for both velocities (solid-liquid) and pressure rise is computed by using well known computational software Mathematica. Perturbation method is employed to extract analytical solution of the resulting ordinary differential equations. Impacts of different physical parameters, expansion in trapped bolus for fluid and particulate velocity profile by increasing Hartmann number are displayed and explained through graphs. Furthermore, a rise in skin friction is noticed with the rise in particle effect and electro-osmotic parameter. This study may have greater significance and viable applications to improve the quality of micro-fluidic devices.

Remarkable Predictive Power of the Modified Long Wavelength Approximation

The modified long-wavelength approximation (MLWA), a next order approximation beyond the Rayleigh limit, has been applied usually only to the dipole $\ell=1$ contribution and for the range of size parameters $x$ not exceeding $x\lesssim 1$ to estimate far- and near-field electromagnetic properties of plasmonic nanoparticles. Provided that the MLWA functional form for the $T$-matrix in a given channel $\ell$ is limited to the ratio $T\sim iR/(F+D-iR)$, where $F$ is the familiar size-independent Fr\"ohlich term and $R\sim {\cal O}(x^{2\ell+1})$ is a radiative reaction term, there is a one-parameter freedom in selecting the dynamic depolarization term $D\sim {\cal O}(x^2)$ which preserves the fundamental feature of the MLWA that its predictions coincide with those of the Mie theory up to the order ${\cal O}(x^2)$. By exploiting this untapped design freedom, we demonstrate on a number of different metals (Ag, Al, Au, Mg), and using real material data, that the MLWA may surprisingly yield very accurate results for plasmonic spheres both for (i) $x$ up to $\gtrsim 1$ and beyond, and (ii) higher order multipoles ($\ell>1$), essentially doubling its expected range of validity. Because the MLWA obviates the need of using spherical Bessel and Hankel functions and allows for an intuitive description of (nano)particle properties in terms of a driven damped harmonic oscillator parameters, a significantly improved analysis and understanding of nanoparticle scattering and near-field properties can be achieved.

Thermal and concentration convection in nanofluids for peristaltic flow of magneto couple stress fluid in a nonuniform channel

This article addresses the influence of double-diffusivity convection in nanofluids in relation to peristaltic flow of magneto couple stress fluid in a nonuniform channel. Firstly, mathematical formulations of magneto couple stress fluid in the presence of double-diffusivity convection in nanofluids for 2-dimensional and 2-directional flows are described in detail. The highly nonlinear equations are simplified using approximation of long wavelength and low but finite Reynolds number. Exact solutions of stream function, axial induced magnetic field, axial pressure gradient, nanoparticle volume fraction temperature and concentration are computed. Graphical representations of numerous physical parameters of interest are presented to explain the conduct of flow quantities. It is observed from graphical plots that temperature profile and solutal concentration increases by increasing values of thermophoresis, Brownian motion, Soret and Dufour parameters.

Calculable Microscopic Theory for $$^{12}$$C($$\alpha , \gamma $$)$$^{16}$$O Cross Section near Gamow Window

$^{12}$C$(\alpha, \gamma)^{16}$O radiative-capture process is a key reaction to produce the element of oxygen in stars. Measuring the cross section near the Gamow window is extremely hard because it is too small. To make a theoretical contribution towards resolving the long-standing problem, I present a microscopic formulation that aims at providing all materials needed to calculate the cross section. The states of $^{12}$C and $^{16}$O relevant to the reaction are respectively described with fully microscopic 3 $\alpha$-particle and 4 $\alpha$-particle configurations, in which the relative motion among the $\alpha$ particles is expanded in terms of correlated Gaussian basis functions. The configuration space has the advantage of being able to well describe the reduced $\alpha$-width amplitudes of the states of $^{16}$O. Both electric dipole and electric quadrupole transitions are responsible for the radiative-capture process. The $\alpha$ particle is described with a $(0s)^4$ configuration admixed with a small amount of an isospin $T=1$ impurity component, which is crucially important to account for the isovector electric dipole transition. The isoscalar electric dipole operators are also taken into account up to the first order beyond the long-wavelength approximation. All the necessary ingredients are provided to make the paper self-contained and ready for numerical computations.

The Binary Powell-Eyring Nanofluid of Peristaltic Flow with Heat Transfer in a Ciliated Tube

These articles show the mathematical investigation of the binary Powell- Eyring Nanofluid of peristaltic flow with heat transfer in a ciliated tube. The approximation of long wavelength and low Reynolds number is taken into consideration. We obtain a system of partial differential equations which solved by using the perturbation method. The velocity and the temperature are computed for various values of the physical parameters. The results are illustrated graphically through a set of Figures. We found that the increase of Grashof number causes an increase in the velocity, then the velocity decrease near the wall of the tube. When the volume fraction of the Nanoparticles increase the velocity increase and decrease near the wall of the tube. The increase in the cilia length leads to an increase in the velocity, then a decrease near the wall of the tube. The increase of the first Eyring-Powell parameter gives an increase in the velocity and decrease near the wall of the tube. The increase of the second Eyring-Powell parameter cause decrease in the velocity. The temperature parameter increase then decreases with the increase of the Sink parameter. The increase of the volume fraction of the Nanoparticles leads to decreases then increase in the temperature parameter. The increase of the cilia length parameter causes an Increase in the temperature.

Extinction cross section of dimer array of metallic nanoparticles

<sec>Surface lattice resonance (SLR) relies on both the lattice structure and its unit cell, which usually contains metallic nanoparticles. Since the full width half maximum of the lattice resonance is much narrower than that of localized surface plasmon resonance of a single particle, it is receiving attention increasingly. Based on the modified long-wavelength approximation, in this paper we derive an analytical expression for the extinction cross section of the dimer array of metallic nanoparticles.</sec><sec>Comparing with the single particle array, good tunability can be achieved by the lattice resonance of the dimer array, which is influenced by more factors, including the arrangement of the array, the structural parameter and the rotation of the dimer, the shape and size of the particles, etc. First, the polarizabilities of the two kinds of particles in the dimer array are adjusted by introducing a matrix of the array factors, which take into account the influence of dipole fields of every particle. Then a simple expression of the resonance condition for the SLR of the dimmer array is obtained. The proposed model can be applied to a wide variety of dimer arrays of ellipsoid particles, and the applied method can be generalized to more complicated structure like polymer arrays. In this paper we further discuss the polarization dependence and ability to modulate the lattice resonance, by changing the excitation condition and the structural parameters of the dimer array. It is found that the resonances of the dimmer array can be classified as three main categories. The resonance related to the particles is independent of the variation of the dimmer arrangement or the array structure. On the other hand, the resonances corresponding to the dimmer and the array rely crucially on the structural parameters. By carefully adjusting the structural parameters, we can modulate the specific resonance effectively. This research is of theoretical importance for studying the SLR for more complicated structures and may find potential applications in the design of new photoelectric chip via nanoparticle array.</sec>

Parameter estimation of stellar-mass black hole binaries with LISA

Stellar-mass black hole binaries (SBHBs), like those currently being detected with the ground-based gravitational-wave (GW) observatories LIGO and Virgo, are also an anticipated GW source for LISA. LISA will observe them during the early inspiral stage of evolution; some of them will chirp through the LISA band and reappear some time later in the band of $3^{rd}$ generation ground-based detectors. SBHBs could serve as laboratories for testing the theory of General Relativity and inferring the astrophysical properties of the underlying population. In this study, we assess LISA's ability to infer the parameters of those systems, a crucial first step in understanding and interpreting the observation of those binaries and their use in fundamental physics and astrophysics. We simulate LISA observations for several fiducial sources and perform a full Bayesian analysis. We demonstrate and explain degeneracies in the parameters of some systems. We show that the redshifted chirp mass and the sky location are always very well determined, with typical errors below $10^{-4}$ (fractional) and $0.4 \ {\rm deg^2}$. The luminosity distance to the source is typically measured within $40-60\%$, resulting in a measurement of the chirp mass in the source frame of $\mathcal{O}(1 \%)$. The error on the time to coalescence improves from $\mathcal{O}(1 \ {\rm day})$ to $\mathcal{O}(30 \ {\rm s})$ as we observe the systems closer to their merger. We introduce an augmented Fisher-matrix analysis which gives reliable predictions for the intrinsic parameters compared to the full Bayesian analysis. Finally, we show that combining the use of the long-wavelength approximation for the LISA instrumental response together with the introduction of a degradation function at high frequencies yields reliable results for the posterior distribution when used self-consistently, but not in the analysis of real LISA data.

Mathematical Modelling Of Extraction Of The Underground Fluids: Application To Peristaltic Transportation Through A Vertical Conduit Occupied With Porous Material

This paper gives a theoretical idea for extracting the underground fluids through peristalsis. Due to the similarity in aforesaid problem, peristaltic transportation of a viscous Newtonian fluid over a vertical porous conduit is studied by considering the impact of heat transfer. Presuming the long-wavelength approximation, explicit solutions are found as asymptotic expansions with reference to free convection and porosity parameters. Mathematical expressions for coefficient of heat transfer, temperature and mean flux are derived. It is experiential that for few precise values of dissimilar parameters under contemplation, the coefficient of heat transfer increases significantly as Grashof number and Eckert number increases. This narrates to optimization of heat transfer in some processes. Further, it has been observed that mean flow enhances with amplitude ratio, porosity in addition to pressure drop. This authorizes auxiliary research on the impacts of peristalsis on the flow features in vertical channels.

ПРОЦЕССЫ ПЕРЕНОСА В ДИСПЕРСНЫХ СИСТЕМАХ И НАНОСИСТЕМАХ, СОДЕРЖАЩИХ ЧАСТИЦЫ СФЕРИЧЕСКОЙ И ЦИЛИНДРИЧЕСКОЙ ФОРМЫ

There is considered a transfer of electromagnetic emission in the systems of spherical dispersion particles with different optical characteristics. A numerical method for definition of thermal source density for two spherical particles is offered. The method is applicable both for particles with constant optical characteristics, and for particles the dielectric permittivity of which follows Kerr’s Law or depends upon even degrees of the module of an electric vector. A model of electromagnetic emission transfer in cylindrical particles having inclusions of other chemical composition is developed. The substance of the inclusion differs considerably from the material of the particle by a factor of emission absorption for the wave length under consideration in long-wavelength approximation. For the calculation of a temperature field of the spherical particle system in two-dimensional approximation there was used a finite element method. The configurations of the particle location of the system were chosen in a random way; as typical dimensions of the system there were considered longitudinal and transverse diameters of clusters, the distance between the centers of two largest particles and similar natural geometrical properties. A possibility for heat transfer control in such systems is considered. It follows from our model calculations obtained that both electromagnetic and thermal interaction of dispersion articles may be visible at larger distances between their centers; that close to the border of a dispersion particle there is a thermal surface layer of the particle, where temperature distribution bears considerably a heterogeneous character. It is defined that in a poly-dispersion system the impact of group effects can change temperature by one and a half times and more.

Electronic properties of \u03b1 \u2212 \U0001d4af3 quantum dots in magnetic fields

We address the electronic properties of quantum dots in the two-dimensional α − \U0001d4af3 lattice when subjected to a perpendicular magnetic field. Implementing an infinite mass boundary condition, we first solve the eigenvalue problem for an isolated quantum dot in the low-energy, long-wavelength approximation where the system is described by an effective Dirac-like Hamiltonian that interpolates between the graphene (pseudospin 1/2) and Dice (pseudospin 1) limits. Results are compared to a full numerical (finite-mass) tight-binding lattice calculation. In a second step we analyse charge transport through a contacted α − \U0001d4af3 quantum dot in a magnetic field by calculating the local density of states and the conductance within the kernel polynomial and Landauer-Büttiker approaches. Thereby the influence of a disordered environment is discussed as well.Graphical abstract

Effect of Surface Roughness during Peristaltic Movement in a Nonuniform Channel

In this study, the effect of the roughness parameter during the peristaltic transport of a Newtonian fluid in a nonuniform channel has been explored. The motivation of this study comes from various research studies in the area of life sciences and engineering, which reveal that the wall of living beings’ arteries and all other surfaces have roughness to some extent. As peristalsis is a major mode of transporting biological fluids in various organs, the effect of surface roughness during peristaltic flow becomes very significant. The problem of peristaltic motion of a Newtonian fluid through a rough nonuniform channel having sinusoidal-shaped roughness has been investigated in the current work. To analyze the flow, analytic formulation of pressure rise, friction force, velocity, and pressure gradient has been carried out under the low Reynolds number and long-wavelength approximation. Results obtained for zero surface roughness from the current model are in complete agreement with previous studies available in the literature that have been carried out without considering the surface roughness of the wall. Numerical outcomes for the properties mentioned above have been plotted for analyzing the impact of roughness on the physical and flow parameters.

Thermal radiation and Hall effects in mixed convective peristaltic transport of nanofluid with entropy generation

The enhancement of energy by introducing nanoparticles is a hot topic in the present century, due to industrial and technological applications. Therefore, current article investigates the peristaltic flow of $$\mathrm{Ag}{-}\mathrm{H}_2\mathrm{O}$$ nanofluid with entropy generation through a uniform channel. Hall and Radiation effects are incorporated. Two-phase formulation for nanofluid is employed. Long-wavelength approximation is used in the mathematical modelling. Built-in numerical solver NDSolve is utilized. Numerical results of the coupled equations are sketched for several quantities of interest. Outcomes of the study reveals that entropy significantly reduces for large values of Hall parameter, whereas opposite behaviour is noted for velocity. Increase in the values of radiation parameter reduces the velocity, temperature, and entropy generation. Increase in Bejan number is observed for enhancement in Brinkman number. Rate of heat transfer at walls increases when heat source parameter is increased. Additionally, comparison of different nanoparticles is also furnished through tables.

Influence of Joule heating and wall slip in electroosmotic flow via peristalsis: second law analysis

Electrokinetic peristaltic slip transport in an asymmetric porous microchannel is studied to explore the entropy production in steady magnetohydrodynamic Jeffery fluid under simulation of Debye and long-wavelength approximations. The emerging two-dimensional bounded problem with electrokinetic body forces is solved numerically. Appropriate combination of heat and momentum equations with Jeffery model, after non-dimensionalization, generated controlling parameters in order to determine velocity, pressure gradient, temperature, entropy production and Bejan number. The trapping mechanism is also visualized by drawing streamlines against governing parameters. The zeta potential signifies the flow and heat response of the system. Former parameters like Brinkman number and Joule heating are compatibly liable for the increase in thermal irreversibilities. The outcomes of the present analysis are applicable in designing the thermofluidic micropumps and biomicrofluidic devices for separation processes and diagnosis.