Large Wave Numbers Research Articles

A normal-mode approach for high-speed rarefied plane Couette flow

Based on gas kinetic theory, a linear stability analysis method for low-speed rarefied flows was developed by Zou et al. [“A new linear stability analysis approach for microchannel flow based on the Boltzmann Bhatnagar–Gross–Krook equation,” Phys. Fluids 34, 124114 (2022) and “A novel linear stability analysis method for plane Couette flow considering rarefaction effects,” J. Fluid Mech. 963, A33 (2023)]. In the present study, we extended the method to high-speed rarefied flows using the Bhatnagar–Gross–Krook model. The Chebyshev spectral method is employed to discretize physical space, and the Gauss–Hermite and fourth-order Newton–Cotes quadrature methods are used to discretize velocity space. The fourth-order Newton–Cotes quadrature method was found to have sufficient accuracy for the stability analysis, laying the foundation for future research on hypersonic flows. The stability analysis of compressible rarefied Couette flow showed that acoustic modes are reflected between the wall and the relative sonic line, and the variation in their phase speed and growth rate with the wavenumber is not affected by the Mach number (Ma) and the Knudsen number (Kn). Increasing Kn has a stabilizing effect on both the acoustic and viscous modes, but as Ma increases, the attenuation rate of each mode's growth rate gradually decreases. In subsonic and sonic flows, the least stable viscous mode dominates in the case of small numbers. As Kn increases, the viscous mode gradually dominates over all wavenumber ranges considered in subsonic flow. In sonic flow, mode 1 is dominant in the region beyond the range of small wavenumbers. In supersonic flow, mode 2 is the least stable in the large wavenumber ranges, while mode 1 is the least stable in other wavenumber ranges. At a fixed wavenumber, as Kn increases, the decay rate of the growth rate of mode 2 is the highest. Additionally, under different Knudsen numbers, the growth rates of mode 1, mode 2, and the least stable viscous mode monotonically increase with an increase in Ma, with mode 2 showing the most significant increase.

Entropy generation in a ciliary flow of an Eyring-Powell ternary hybrid nanofluid through a channel with electroosmosis and mixed convection.

Drug delivery systems, where the nanofluid flow with electroosmosis and mixed convection can help in efficient and targeted drug delivery to specific cells or organs, could benefit from understanding the behavior of nanofluids in biological systems. In current work, authors have studied the theoretical model of two-dimensional ciliary flow of blood-based (Eyring-Powell) nanofluid model with the insertion of ternary hybrid nanoparticles along with the effects of electroosmosis, magnetohydrodynamics, thermal radiations, and mixed convection. Moreover, the features of entropy generation are also taken into consideration. The system is modeled in a wave frame with the approximations of large wave number and neglecting turbulence effects. The problem is solved numerically by using the shooting method with the assistance of computational software "Mathematica" for solving the governing equation. According to the temperature curves, the temperature will increase as the Hartman number, fluid factor, ohmic heating, and cilia length increase. It is also disclosed that ternary hybrid nanoparticles result in a change in flow rate when other problem parameters are varied, and the same is true for temperature graphs. Engineers and scientists can make better use of nanofluid-based cooling systems in electronics, automobiles, and industrial processes with the aid of the study's findings.

Unpredicted Scaling of the One-Dimensional Kardar-Parisi-Zhang Equation.

The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree. Yet recent numerical simulations in the tensionless (or inviscid) limit of the KPZ equation [C. Cartes et al., The Galerkin-truncated Burgers equation: Crossover from inviscid-thermalized to Kardar-Parisi-Zhang scaling, Phil. Trans. R. Soc. A 380, 20210090 (2022).PTRMAD1364-503X10.1098/rsta.2021.0090; E. Rodríguez-Fernández et al., Anomalous ballistic scaling in the tensionless or inviscid Kardar-Parisi-Zhang equation, Phys. Rev. E 106, 024802 (2022).PRESCM2470-004510.1103/PhysRevE.106.024802] unveiled a new scaling, with a critical dynamical exponent z=1 different from the KPZ one z=3/2. In this Letter, we show that this scaling is controlled by a fixed point which had been missed so far and which corresponds to an infinite nonlinear coupling. Using the functional renormalization group (FRG), we demonstrate the existence of this fixed point and show that it yields z=1. We calculate the correlation function and associated scaling function at this fixed point, providing both a numerical solution of the FRG equations within a reliable approximation, and an exact asymptotic form obtained in the limit of large wave numbers. Both scaling functions accurately match the one from the numerical simulations.

Stabilizing two-dimensional turbulent Kolmogorov flow via selective modification of inviscid invariants

We stabilize 2D turbulent Kolmogorov flow by selectively altering the time rate of change of inviscid invariants (energy and enstrophy) of the flow. This method has earlier been demonstrated to modify the 2D unforced decaying turbulent flow to reach steady states. However, Kolmogorov flow exhibits flow unsteadiness over a range of spatial and temporal scales which are driven by constant external forcing at wave number kf. The energy injected at scale (k≈kf) is distributed to large (k>kf) and small (k<kf) wave numbers through interactions of different scales called direct and inverse energy cascading, respectively. The selective modification strategy autonomously identifies additional forcing inputs into the governing equations which results in the transformation of Kolmogorov flow into a non-trivial steady state. We demonstrate that this method is highly effective in altering the inverse energy cascading, a particularly intricate challenge in fluid dynamics. Intriguingly, we have also found that the steady states achieved through this approach resemble an invariant solution of the original Kolmogorov flow, highlighting the potential significance of our method.

Functional renormalisation group approach to shell models of turbulence

Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (FRG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.

Covalent bonds formed in MoS2–C60/Ferrocene heterostructure under high pressure

Constructing mixed dimensional heterostructure can create the possibility for obtaining new structures and properties by combining the advantages of both materials. Further introducing external means to control intermolecular/atomic distance and configuration may affect the bonding form, band structure, and interfacial interaction, which brings more novel function materials. In this work, high pressure Raman studies and theoretical research have been carried out on monolayer MoS2–C60/Ferrocene (C60/Fc) heterostructures to explore the possible phase transitions and interfacial bonding changes. We found that the interaction between C60/Fc and MoS2 molecules gradually enhanced as pressure increased, accompanying by a large wavenumber splitting of Ag (2) mode and the appearance of new peaks around 700-800 cm−1. These phenomena indicated that not only the polymeric structure was formed between C60 molecules, but some C atoms connected with adjacent S atoms at the interface to form covalent bonds with the help of pressure. The theoretical studies further indicated the possible bonds formation between C and S atoms. Surprisingly, the covalent bonds can still be observed at lower pressure when pressure decompressed, while the long-range ordered polymer structure between C60s can be maintained at atmospheric pressure.

Supergrowth and sub-wavelength object imaging.

We further develop the concept of supergrowth [Quantum Stud.: Math. Found.7, 285 (2020)10.1007/s40509-019-00214-5], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function higher than its largest wavenumber. We identify a canonical oscillatory function's superoscillating and supergrowing regions and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation-based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging.

Pressure-dependent cationic associations of ionic liquids with bentonite nanoclay

Pressure-dependent IR spectroscopy is used to investigate the possibility of stabilizing ionic liquid (IL)–hydrophilic bentonite (Bent) composites with the application of high pressures. Ambient-pressure experiments suggest IL hydrophilicity/hydrophobicity impacts cation and anion interactions with Bent. For example, both the cation and anion of hydrophilic 1-butyl-3-methylimidazolium dicyanamide ([BMIM][DCA]) experience composition-dependent vibrational mode wavenumber shifts. However, anion–Bent interactions are suppressed at ambient pressure when the nanoclay is paired with hydrophobic 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([BMIM][NTf2]). Compression to high pressures triggers significant blue shifts for ring-bound C–H stretching bands. The rates of these changes upon pressurization indicate the two ILs experience different interaction motifs with the Bent surface. Large wavenumber shifts for C4–H and C5–H stretching modes of [BMIM][NTf2] imply preferential coordination to Bent surface sites through these groups. This presumably leaves the C2–H group available for hydrogen bonding with the NTf2 anion. The situation is different for [BMIM][DCA], where all three C–H groups on the imidazolium ring appear to interact with Bent surface sites. Depressurization reveals further differences between the two systems. Spectroscopic features are reversible for [BMIM][NTf2], whereas the C–H stretching mode blue shifts for [BMIM][DCA] are either irreversible or the relaxation is kinetically hindered upon return to ambient pressure. Taken together, the spectroscopic data strongly suggests that IL–Bent interactions are pressure sensitive, and IL assemblages along the interface may be manipulated through the application of high pressure.

Broadband unidirectional surface plasmon polaritons with low loss.

Unidirectional surface plasmon polaritons (SPPs) have been proven to truly exist at an interface between a magnetized semiconductor and an opaque isotropic material, however, they suffer rather serious leakage loss (with propagation length shorter than two wavelengths) caused by nonlocality. In this work, we investigate an alternative category of unidirectional SPPs existing on a nonreciprocal plasmonic platform with a cladding composed of a dielectric heterostructure transversely terminated by metal. This unidirectional SPP mode exists for small wavenumbers within the entire upper bulk-mode bandgap of the magnetized semiconductor, hence it is robust against nonlocal effects over a broad band. In contrast to previous unidirectional SPPs, the leakage loss of the present unidirectional SPPs is significantly reduced by more than five times, since the portion of modal energy distributed in the cladding is substantially increased. A similar reduction in absorption losses associated with semiconductor dissipation is observed. Though the nonlocality induces a backward-propagating SPP with extremely large wavenumbers, it can be suppressed even at very small level of dissipation. Therefore, our proposed plasmonic waveguide actually exhibits exceptional unidirectional characteristics.

High-frequency instabilities in supersonic compression-ramp flow

We consider high Reynolds number supersonic flow over a compression ramp in the triple-deck formulation. Previous studies of compression-ramp stability have shown rapid growth of high-frequency disturbances in initial-value computations; however, no physical or numerical origin has yet been identified robustly. By considering linear perturbations to steady compression-ramp solutions, we show that instabilities observed in previous studies do not have a growth rate that is described by the integral eigenrelation of Tutty & Cowley (J. Fluid Mech., vol. 168, 1986, pp. 431–456) for a (long-wave) Rayleigh instability. We solve both the temporal and spatial instability problems in the limit of asymptotically large wavenumber $K$ (or equivalently frequency) and show that the growth rate of the instability remains $o(K)$ , being dominated by higher-order terms in the expansion at moderate ramp angles.

Bacterial turbulence in gradient confinement

We investigate a novel form of non-uniform living turbulence at an extremely low Reynolds number using a bacterial suspension confined within a sessile droplet. This turbulence differs from homogeneous active turbulences in two or three-dimensional geometries. The heterogeneity arises from a gradient of bacterial activity due to oxygen depletion along the droplet’s radial direction. Motile bacteria inject energy at individual scales, resulting in local anisotropic energy fluctuations that collectively give rise to isotropic turbulence. We find that the total kinetic energy and enstrophy decrease as distance from the drop contact line increases, due to the weakening of bacterial activity caused by oxygen depletion. While the balance between kinetic energy and enstrophy establishes a characteristic vortex scale depending on the contact angle of the sessile drop. The energy spectrum exhibits diverse scaling behaviors at large wavenumber, ranging from k −1/5 to k −1, depending on the geometric confinement. Our findings demonstrate how spatial regulation of turbulence can be achieved by tuning the activity of driving units, offering insights into the dynamic behavior of living systems and the potential for controlling turbulence through gradient confinements.

Thermodynamics of Highly Interacting Blend PCHMA/dPS by TOF-SANS.

We investigate the thermodynamics of a highly interacting blend of poly(cyclohexyl methacrylate)/deuterated poly(styrene) (PCHMA/dPS) with small-angle neutron scattering (SANS). This system is experimentally challenging due to the proximity of the blend phase boundary (>200 °C) and degradation temperatures. To achieve the large wavenumber q-range and flux required for kinetic experiments, we employ a SANS diffractometer in time-of-flight (TOF) mode at a reactor source and ancillary microscopy, calorimetry, and thermal gravimetric analysis. Isothermal SANS data are well described by random-phase approximation (RPA), yielding the second derivative of the free energy of mixing (G″), the effective interaction (χ̅) parameter, and extrapolated spinodal temperatures. Instead of the Cahn-Hilliard-Cook (CHC) framework, temperature (T)-jump experiments within the one-phase region are found to be well described by the RPA at all temperatures away from the glass transition temperature, providing effectively near-equilibrium results. We employ CHC theory to estimate the blend mobility and G″(T) conditions where such an approximation holds. TOF-SANS is then used to precisely resolve G″(T) and χ̅(T) during T-jumps in intervals of a few seconds and overall timescales of a few minutes. PCHMA/dPS emerges as a highly interacting partially miscible blend, with a steep dependence of G″(T) [mol/cm3] = -0.00228 + 1.1821/T [K], which we benchmark against previously reported highly interacting lower critical solution temperature (LCST) polymer blends.

Dynamics of certain Euler-Bernoulli rods and rings from a minimal coupling quantum isomorphism.

In some parameter and solution regimes, a minimally coupled nonrelativistic quantum particle in one dimension is isomorphic to a much heavier, vibrating, very thin Euler-Bernoulli rod in three dimensions with ratio of bending modulus to linear density (ℏ/2m)^{2}. For m=m_{e}, this quantity is comparable to that of a microtubule. Axial forces and torques applied to the rod play the role of scalar and vector potentials, respectively, and rod inextensibility plays the role of normalization. We show how an uncertainty principle ΔxΔp_{x}≳ℏ governs transverse deformations propagating down the inextensible, force and torque-free rod, and how orbital angular momentum quantized in units of ℏ or ℏ/2 (depending on calculation method) emerges when the force and torque-free inextensible rod is formed into a ring. For torqued rings with large wave numbers, a "twist quantum" appears that is somewhat analogous to the magnetic flux quantum. These and other results are obtained from a purely classical treatment of the rod, i.e., without quantizing any classical fields.

Influence of the beta-effect on dynamics of frontal temperature jets

The theory of temperature jets gets extended to account for the influence of the beta effect on their dynamics. Including this effect noticeably changes symmetry properties and laws of conservation inherent to models without the beta effect. Specifically nontrivial, the dynamics of jets become near the equator, where the model admits multi-valued solutions that look like jets crossing the equator. For example, the so-called loop solitons moving along the equator with velocities inversely proportional to the cube of their amplitude turn out among them. Estimates based on simple qualitative considerations show that, owing to the beta effect, the temperature jets can form a specific equatorial turbulence, in which they play the role of structural elements. Notably, the spectral slope of the energy density at large wave numbers in such turbulence becomes equal to unity.

Application of Adapted-Bubbles to the Helmholtz Equation with Large Wavenumbers in 2D

An adapted bubble approach which is a modifiation of the residual-free bubbles (RFB) method, is proposed for the Helmhotz problem in 2D. A new two-level finite element method is introduced for the approximations of the bubble functions. Unlike the other equations such as the advection-diffusion equation, RFB method when applied to the Helmholtz equation, does not depend on another stabilized method to obtain approximations to the solutions of the sub-problems. Adapted bubbles (AB) are obtained by a simple modification of the sub-problems. This modification increases the accuracy of the numerical solution impressively. The AB method is able to solve the Helmholtz equation efficiently in 2D up to ch = 3.5 where c is the wave number and h is the mesh size. We provide analysis to show how the AB method mitigates the pollution error.

On the Surface Plasmonic Waves Excited by a Dipole Above Anisotropic and Spatially Dispersive Two-Dimensional Surfaces of Infinite Extent in Planarly Layered Media

The surface plasmonic waves excited by a vertical or horizontal oriented Hertzian dipole above anisotropic and spatially dispersive two-dimensional surfaces of infinite extent embedded in planarly layered uniaxial media are investigated using the dyadic Green function approach. The spectral-domain transmission line analogy Green function formulation and iso-frequency-contour equations are derived. The methods to accurately and efficiently evaluate the two-dimensional Fourier integral arising from the spatial-domain Green function computation are also developed. To resolve the numerical inefficiency due to the highly oscillatory integrand and singularities of surface plasmonic waves that possess large wavenumber, the methods of extrapolating the real-axis integration combined with singularity subtraction are proposed and found to be applicable to a wide range of observation distances. As an application example of the proposed formulation, we compute the scattered fields of a vertical dipole above the graphene biased by drift current which exhibits significant spatial dispersion. It is shown that the light-matter interaction of graphene plasmons can be significantly reinforced when placed above uniaxially anisotropic epsilon-near-zero substrates. The proposed formulation may provide the methodology for the computational analysis of two-dimensional materials and surface plasmonic waves.

Boundary-Layer Disruption and Heat-Transfer Enhancement in Convection Turbulence by Oscillating Deformations of Boundary.

In this Letter, we propose a novel strategy for significantly enhancing the heat transfer in convection turbulence. By introducing a boundary deformation of the standing-wave type, flow modulation can be realized when the amplitude is comparable or larger than the boundary-layer thickness. For a fixed moderate frequency, the entire fluid layer follows the boundary motion at small wave numbers, while only the near-wall regions are affected by the boundary deformation at large wave numbers. The heat-flux enhancement happens for the latter. For a fixed wave number and gradually increasing frequency, the vortical flows inside the wave valleys exhibit nonlinear transition and alter the distribution of boundary heat flux, and the global heat flux increases significantly at large enough frequencies. The current findings suggest that oscillating deformations of boundary can efficiently break the boundary layers, which serves as the bottleneck of global heat transfer, and open a new venue for modulating the convection turbulence.

Efficient electromagnetic interference shielding of three-dimensional hydrophobic Cu/wood/Cu porous composites

Three-dimensional hydrophobic and efficient electromagnetic shielding Cu/wood/Cu laminated composites were prepared by a simple one-step electroless Cu process. The number of electroless Cu on wood surface and the treatment time of electroless Cu were used as variables. The effects of independent variables in the range from 0.3 ×10−3 to 3.0 GHz (L-band) on the conductivity, water contact angle and electromagnetic shielding effectiveness of the composite were analyzed. The Cu particles are fully filled in the wood hierarchical porous structure, and the metal coating uniformly covers the entire wood surface. After three times of electroless Cu, the conductivity of the composite can reach 7255 S/cm, the contact angle is 130.8° when the time is 12 min, showing good hydrophobic properties, and the average electromagnetic shielding effectiveness is as high as 96 dB. Compared with the L-band (94 dB), the twice electroless sample has a maximum shielding effectiveness of 85.6 dB in the X-band (8.2-12.4 GHz), which can shield a large number of incident electromagnetic waves to achieve high absorption and low reflection. The anisotropic internal porous structure of wood matrix and the multi-interface polarization between wood and Cu are the main reasons for the effective electromagnetic interference shielding performance of Cu/wood/Cu laminated composites.

Upscale transfer of waves in one-dimensional rotating shallow water

We study the inverse flux of waves in one of the simplest geophysical fluid dynamics models: one-dimensional rotating shallow water equations. Based on direct numerical integration of the governing equations, we find that waves injected at small scales get transferred upscale predominantly via resonant quartic interactions between wave modes. The waves’ upscale transfer is non-local and involves turbulent transfer between disparate scales of the flow. Our analysis reveals that the upscale transfer of waves is extremely intermittent and is a result of localized-in-time bursts in wave action flux. These intermittent events of flux bursts lead to shallower waves’ spectrum and relatively higher amplitude wave fields in physical space. On examining statistics of the flow fields, we find that low-energy high wavenumbers more or less comply with the assumptions used in wave turbulence theory, such as uniformly distributed wave phases and the Gaussian distribution of fields, while non-uniform distribution of wave phases and non-Gaussian statistics dominate at large scales or low wavenumbers that contain a major share of the flow energy. Our findings point out that the one-dimensional rotating shallow water equations, despite being a simple geophysical fluid dynamic model, harbour complex and intricate features associated with the upscale transfer of waves that have not been recognized in the past.

The enriched quadrilateral overlapping finite elements for time-harmonic acoustics

The pronounced numerical dispersions and numerical anisotropy make solutions from the finite element model using low-order elements unreliable for the time-harmonic acoustic problems with fairly large wavenumber. In this work we propose a novel enriched quadrilateral overlapping elements for Helmholtz problems. In this scheme, the original overlapping elements are strengthened by the harmonic trigonometric functions stemming from the spectral techniques. Since all additional degrees of freedom are aligned on the vertex node of every overlapping element, the proposed method can be directly applied to the original finite element model without changing the mesh topology. Because of the enriched approximation space, the proposed method can significantly suppress the numerical dispersions with practically negligible numerical anisotropy, and can be more computationally efficient in providing comparable solution accuracy compared to the original scheme and the classic finite element method. Besides, the linear dependence issue is completely avoided and these enriched overlapping elements are distortion-insensitive. In this work, the original variational formulation is perturbed using the penalty method to impose the essential boundary conditions. Numerical experiments show that the developed method can reduce user interventions in mesh creation and adjustment, and is promising in practical engineering applications for time-harmonic acoustics.