Constant Gradient Research Articles

Flows in the space of interacting chiral boson theories

We study interacting theories of N left-moving and N¯ right-moving Floreanini-Jackiw bosons in two dimensions. A parametrized family of such theories is shown to enjoy (nonmanifest) Lorentz invariance if and only if its Lagrangian obeys a flow equation driven by a function of the energy-momentum tensor. We discuss the canonical quantization of such theories along classical stress tensor flows, focusing on the case of the root-TT¯ deformation, where we obtain perturbative results for the deformed spectrum in a certain large-momentum limit. In the special case N=N¯, we consider the quantum effective action for the root-TT¯-deformed theory by expanding around a general classical background, and we find that the one-loop contribution vanishes for backgrounds with constant scalar gradients. Our analysis can also be interpreted via dual U(1) Chern-Simons theories in three dimensions, which might be used to describe deformations of charged AdS3 black holes or quantum Hall systems. Published by the American Physical Society 2024

Marangoni Droplets of Dextran in PEG Solution and Its Motile Change Due to Coil-Globule Transition of Coexisting DNA.

Motile droplets using Marangoni convection are attracting attention for their potential as cell-mimicking small robots. However, the motion of droplets relative to the internal and external environments that generate Marangoni convection has not been quantitatively described. In this study, we used an aqueous two-phase system [poly(ethylene glycol) (PEG) and dextran] in an elongated chamber to generate motile dextran droplets in a constant PEG concentration gradient. We demonstrated that dextran droplets move by Marangoni convection, resulting from the PEG concentration gradient and the active transport of PEG and dextran into and out of the motile dextran droplet. Furthermore, by spontaneously incorporating long DNA into the dextran droplets, we achieved cell-like motility changes controlled by coexisting environment-sensing molecules. The DNA changes its position within the droplet and motile speed in response to external conditions. In the presence of Mg2+, the coil-globule transition of DNA inside the droplet accelerates the motile speed due to the decrease in the droplet's dynamic viscosity. Globule DNA condenses at the rear part of the droplet along the convection, while coil DNA moves away from the droplet's central axis, separating the dipole convections. These results provide a blueprint for designing autonomous small robots using phase-separated droplets, which change the mobility and molecular distribution within the droplet in reaction with the environment. It will also open unexplored areas of self-assembly mechanisms through phase separation under convections, such as intracellular phase separation.

Stress–diffusion coupling. Application to interstitial diffusion

A numerical study of the stress–diffusion coupling theory based on the Cahn–Larché method is presented in the case of interstitial diffusion. Indeed, the interaction between diffusion and stress fields has been widely studied in the past. Most of the studies focused on the effect of chemical stress due to mass transport on diffusion. The majority of the studies have been focusing on the coupling between external mechanical and chemical stresses with diffusion. In this study, the effect of stress/strain on mobility and stress gradient mobility and driving forces are presented, based on the model of Voorhees and Larché. The analytical solutions are detailed, from general equations (interstitial diffusion, elastic material) to a macroscopic model (interstitial diffusion, isotropic elastic material, infinite dilute solution, 2D axisymmetric). Numerical simulations for different samples thickness and β parameter helped to better understand and then experimentally identify the prevailing effect of stress on mobility or diffusion driving forces. These studies demonstrated the impact of constant compressive and tensile stress on diffusion kinetics through the mobility term of the equation, as well as the effects of negative and positive stress gradients via the Nernstian term. The results show that constant compressive stress and negative stress gradient hinder the diffusion. On the contrary, tensile stress and positive stress gradient promote the diffusion. This work also demonstrates the importance of coupling between mobility and Nernstian effect on the diffusion promotion.

Ultrashort echo time magnetic resonance elastography for quantification of the mechanical properties of short T2 tissues via optimal control-based radiofrequency pulses.

The aim of the current study is to demonstrate the feasibility of radiofrequency (RF) pulses generated via an optimal control (OC) algorithm to perform magnetic resonance elastography (MRE) and quantify the mechanical properties of materials with very short transverse relaxation times (T2 < 5 ms) for the first time. OC theory applied to MRE provides RF pulses that bring isochromats from the equilibrium state to a fixed target state, which corresponds to the phase pattern of a conventional MRE acquisition. Such RF pulses applied with a constant gradient allow to simultaneously perform slice selection and motion encoding in the slice direction. Unlike conventional MRE, no additional motion-encoding gradients (MEGs) are needed, enabling shorter echo times. OC pulses were implemented both in turbo spin echo (OC rapid acquisition with refocused echoes [RARE]) and ultrashort echo time (OC UTE) sequences to compare their motion-encoding efficiency with the conventional MEG encoding (classical MEG MRE). MRE experiments were carried out on agar phantoms with very short T2 values and on an ex vivo bovine tendon. Magnitude images, wave field images, phase-to-noise ratio (PNR), and shear storage modulus maps were compared between OC RARE, OC UTE, and classical MEG MRE in samples with different T2 values. Shear storage modulus values of the agar phantoms were in agreement with values found in the literature, and that of the bovine tendon was corroborated with rheometry measurements. Only the OC sequences could encode motion in very short T2 samples, and only OC UTE sequences yielded magnitude images enabling proper visualization of short T2 samples and tissues. The OC UTE sequence produced the best PNRs, demonstrating its ability to perform anatomical and mechanical characterization. Its success warrants in vivo confirmation in further studies.

Effect of Solid/Liquid and Eutectic Front Velocities on Microstructure Evolution in Al-20%Cu Alloys

During the solidification process, microstructures are affected by the experimental conditions, the thermophysical characteristics of the alloy, and the type of grain-refining particles. Unidirectional solidification experiments were performed in a vertical Bridgman-type furnace to investigate the effect of the solidification front velocity on the solidified microstructure of a non-refined and refined Al-20%Cu alloy. The samples were solidified by rapidly increasing the sample velocity (v) range from 0.02 mm/s to 0.2 mm/s while maintaining an almost constant temperature gradient (~5 K/mm). As a result, despite changes in the solid/liquid front velocity along the sample, the microstructure of the non-refined alloys remained columnar. In the refined alloy, the columnar structure changed into an equiaxed structure at two different front velocities.

Dynamic deformation characteristics of lightweight soil based on Davidenkov model

The dynamic deformation characteristics of lightweight soil were studied using consolidated-undrained dynamic triaxial tests to predict its non-linear stress and strain behaviour under a traffic load. The results showed that the influence of confining pressure on the attenuation of the dynamic shear modulus ratio became significant with increasing expanded polystyrene (EPS) particle content or cement content. The attenuation curve of the dynamic shear modulus ratio was evaluated using Davidenkov model parameters, A, B and γ 0. It was proved that the parameter A was mostly affected by EPS particle content and confining pressure, with its value ranging between 1.1 and 1.85. The parameter γ 0 was affected by cement content and confining pressure, and its value ranged between 0.0007 and 0.0016. The parameter B was found to range between 0.38 and 0.55, in general. The relationship curves between damping ratio and dynamic shear strain revealed two forms, S shaped and bell shaped. The verification tests showed that the Davidenkov model could predict accurately the dynamic deformation characteristics of lightweight soil both under a changing stress state and under constant gradient loading conditions. These results provide a theoretical basis for determining the deformation of a lightweight soil subgrade under a traffic load.

Self-Oscillation of a Liquid Crystal Elastomer String-Mass System Under Constant Gradient Temperature

Abstract Recent experiments have found that a fiber-mass system can self-oscillate along the vertical direction under a non-uniform temperature field, which necessitates significant vertical space. To address the challenge in adapting to situations with limited vertical space, the current work introduces a self-oscillating string-mass system, comprising of a mass ball and a thermally responsive liquid crystal elastomer string exposed to a constant gradient temperature. By employing theoretical modeling and numerical simulation, we have identified two motion regimes of the system, namely, the static regime and the self-oscillation regime, and elucidated the mechanism of self-oscillation. Utilizing the analytical method, we derived the expressions for bifurcation point, amplitude, and frequency of the self-oscillation, and investigated the impact of system parameters on these aspects, which were verified by numerical solutions. Compared to a fiber-mass system, the string-mass system has superior stability to deal with small horizontal disturbances, can amplify its amplitude and frequency limited by small thermal deformation of material, and saves a significant amount of vertical space. Given these attributes, such self-oscillating string-mass system presents novel possibilities for designing energy harvesters, active machinery, and soft robots.

Numerical modelling of pore water pressure response beneath a raft foundation during real river floods

Tall buildings with basement levels are increasingly being built due to need for space in large cities. Frequently, such structures are built involving a raft foundation and diaphragm walls below the water table. In addition, sometimes such buildings are located on floodplains. Therefore, if a river flood event occurs, the building can be exposed to pore water pressure (due to the fluctuation of water table) acting beneath its raft foundation. The generated subpressures will depend on the water table changes with time, and on the way such pressures are transmitted through the ground. Previous works have studied this behavior through laboratory and small-scale tests or numerically; however, many of them have used a constant hydraulic gradient and the water table fluctuations with time have been ignored. In this work, the evolution of pore water pressures with time mobilized beneath a raft foundation of a building built in a floodplain is studied. To do that, full-scale numerical models capable of simulate a river flooding and its corresponding overflow are developed. Such models incorporate data from water table change–time curves recorded during real river floods associated with a set of river regimes. Additionally, the effect of factors such as the soil permeability, the diaphragm wall length, and the soil thicknesses on water pore pressures beneath a raft foundation are also analyzed. Results suggest numerical models developed herein are capable of reproducing pore pressures induced beneath a raft foundation during river flooding. Furthermore, it was found that the above-mentioned factors could impact the percentage of pore water pressure mobilized beneath the raft foundation with respect to the maximum pore water pressure that could be induced during river flooding, and that the principal risk arises in buildings near large catchments where the flow increases over an extended period. Finally, practical implications and recommendations to practitioners are provided.

Stability patterns in plane porous Poiseuille flow with uniform vertical cross-flow: A dual approach

In this study, we examine the effects of a porous parameter and a uniform vertical cross-flow on the onset of instability in a plane Poiseuille flow (PPF) subjected to infinitesimal disturbances. The linearized Navier-Stokes (N–S) equations, which govern the stability of the fluid flow system, are addressed using the Chebyshev collocation method (CCM). Our approach includes both modal and non-modal analyses, each providing distinct insights into the system's behavior. The modal analysis involves a linear stability assessment using both non-normalized and normalized basic velocity approaches. Assuming a constant pressure gradient, the first approach aligns with the traditional Poiseuille flow framework, where a uniform pressure difference drives the flow. This simplifies calculations and aids in predicting flow characteristics. The second approach, which varies the pressure gradient to maintain a constant maximum streamwise velocity, offers a different perspective by focusing on a specific flow velocity profile through the porous medium. This variation in the pressure gradient allows us to explore changes in flow behavior and the system's responses under these conditions. This analysis includes examining the eigenspectrum, neutral stability curves, and determining critical triplets. On the non-modal front, we explore the intricacies of the non-normal Orr-Sommerfeld (O–S) operator. This involves studying the pseudospectrum and transient energy growth rate (G(t)) plots for optimal perturbations. Identification of regions of stability, potential instability, and instability is achieved using contour plots of maximum transient energy growth (Gmax). Interestingly, our results reveal that the porous parameter acts as a stabilizing agent, mitigating instability. In contrast, the uniform vertical cross-flow plays a dual role, contributing to both stabilization and destabilization of the system. Additionally, our study highlights the impact of examining basic velocity through both normalized and non-normalized approaches, leading to different stability predictions.

Power modulation and its effect on microstructural evolution during laser oscillating welding of steel to aluminum alloy

The control of intermetallic compounds (IMCs) poses a challenge in welding Al–Fe joints. To tackle this issue, power-modulated laser welding was utilized to join 6061 aluminum (6061Al) and AISI-304 stainless steel (304SS) in an overlap configuration. This research compares the impacts of two power modes: constant power (CP) and gradient power (GP) on weld formation and interface IMCs to demonstrate the superior performance of the GP mode. The GP mode alters the energy distribution pattern, resulting in distinct weld formation and interface microstructures compared to the CP mode. Notably, the research confirms that the GP mode enhances the tensile shear strength of the joints, highlighting the effectiveness of the GP mode.

Polymer nanocomposites with concurrently enhanced dielectric constant and breakdown strength at high temperature enabled by rationally designed core-shell structured nanofillers

Polymer dielectrics are required to maintain high energy density at elevated temperatures for advanced power and electronic systems. Herein, we report a novel solution-processed core-shell structured polyimide (PI) nanocomposite with moderate dielectric constant HfO2 core and wide-bandgap Al2O3 shell, effectively addressing the typical trade-off between dielectric constant and breakdown strength in dielectric nanocomposites predominant at elevated temperatures. The formation of improved dielectrically matching interfaces by the rationally designed dielectric constant gradient from core-shell-matrix remarkably mitigates the distortion of the electric field around the interfaces, resulting in a high breakdown strength. Wide band gap Al2O3 shell also introduces deeper traps to impede the conduction loss. The validity of Al2O3 shell has been proved via experiments and simulations. Accordingly, HfO2@Al2O3/PI nanocomposite exhibits an excellent charge-discharge efficiency of 91.7 % at 300 MV/m and a maximum discharged energy density of 2.94 J/cm3 at 150 °C, demonstrating its potential for high-temperature energy storage.

Geometric mechanics of the vertical slice model

The goals of this work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Models (VSMs) of ocean dynamics and (ii) illustrate the versatility and utility of deterministic and stochastic variational approaches by deriving several variants of wave–current interaction models which describe the effects of internal waves propagating within a vertical planar slice embedded in a 3D region of constant horizontal gradient of buoyancy in the direction transverse to the vertical plane.

Generalised Couette flow of nanoliquid among two concentric channels with particles injection

In the presence of nanoparticle injection, buoyancy power, constant pressure gradient, variable viscosity coefficient, magnetic field, mass diffusivity of thermophoresis, and Brownian motion, the hydrodynamic nanoliquid conducted with electric current flows through the gap between two concentric cylindrical channels of infinite length. The focus of this article was on generalised Couette flow that is flow in which the outer channel plate moves at a uniform velocity while still being subjected to a pressure gradient. Here we use the RKF45 numerical method and the shooting technique to solve dimensionless momentum, energy, and concentration equations. How the obtained parameters controlled on flow rate, temperature and concentration of the fluid have been investigated and appearances through respective graphs. The high magnitude of nanoliquid flow rate with outer channel wall motion and pressure gradient parameters has been observed. The nanoliquid temperature declines with an annular gap parameter while amplified thermophoresis and magnetic parameter values enrich the fluid temperature. In addition, loftier values of variable viscosity and Brownian motion parameters boost the nanoliquid concentration.

Suppressing effect of shortening vapor cell stem on polarization-induced magnetic gradient relaxation of Xe in NMR co-magnetometers

The Rb polarization-induced magnetic field gradient is one of the crucial sources of Xe spin relaxation in NMR co-magnetometers. The additional volume of the atomic vapor cell stem can enhance the effective magnetic field gradient through the diffusion effect of the optically polarized-Rb atoms, which affects the spin relaxation properties of Xe and degrades the long-term stability of NMR co-magnetometers. Based on the discrete steps random walk diffusion model, the magnetic gradient relaxation properties of Xe diffusing in an asymmetric cell composed of a cubic part and a cylindrical tube (stem) are characterized. Simulation results indicate that a shorter stem can effectively prolong the nuclear spin relaxation time under a constant magnetic field gradient. To verify this conclusion, a cell stem truncating actuator is developed using a high-power CO2 laser to shorten the cell stem, and the magnetic field gradient coil is used to perform the gradient compensation to examine the impact of various stem lengths on the spin relaxation rate. Experiments indicate that under the influence of atomic diffusive motions, shortening the stem length can effectively suppress the polarization-induced magnetic gradient and increase the 129Xe transverse relaxation time from 4.5 s to 21 s. The study posts practical applications for vapor cells with a stem, which is expected to enhance the performance of atomic spin co-magnetometers.

Effect of slip boundary conditions on unsteady pulsatile nanofluid flow through a sinusoidal channel: an analytical study

A novel analysis of the pulsatile nano-blood flow through a sinusoidal wavy channel, emphasizing the significance of diverse influences in the modelling, is investigated in this paper. This study examines the collective effects of slip boundary conditions, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat source on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research that assumed a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient that significantly influences several associated parameters. The mathematical model characterising nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameter values. The findings obtained for various parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, Knudsen number due to the slip boundary, volume fraction of nanoparticles, radiation parameter, Prandtl number, and heat source parameters on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with increasing permeability and slip parameters. Additionally, the temperature increases with increasing nanoparticle volume fraction and radiation parameter, while it decreases with increasing Prandtl number.

Impact of heat and mass transfer on the magnetohydrodynamic two-phase flow of couple stress fluids through a porous walled curved channel using Homotopy Analysis Method

The analysis of heat and mass transfer in the movement of immiscible couple stress fluids through a curved channel whose walls are at two different temperatures is the focus of the current work. Immiscible fluids are subjected to an external magnetic field that is taken normal to the fluid’s flow. For suction or injection in the flow, the channel walls are presumed to be porous. The buoyancy force, which is modelled using the Boussinesq approximation, and a constant pressure gradient cause the flow of the couple stress fluids in the curved channel. The highly non-linear coupled differential equations associated with the proposed work are solved with the use of the semi-analytic Homotopy Analysis Method. The semi-analytical expression of the various flow variables such as flow velocity, temperature, concentration, etc. is obtained by solving these non-linear differential equations after they have been non-dimensionalized by taking into account non-dimensional parameters. From the obtained results authors have noted how the two immiscible couple stress fluids’ flow velocity, temperature, and concentration behaviour depend on the flow-effecting parameters, including the couple stress parameter, curvature parameter, Schmidt number, and so on. Further, the authors of the proposed work have analysed the effect of various flow parameters on heat and mass transfer. Since the authors have studied the two-phase flow of couple stress fluids in a porous walled curved channel together with the effect of magnetic field, the current model has various applications in the fields of crude oil extraction, filtration, nuclear reactor, and bio-mechanics.

Suppression of Mesoscale Eddy Mixing by Topographic PV Gradients

Abstract Oceanic mesoscale eddy mixing plays a crucial role in Earth’s climate system by redistributing heat, salt, and carbon. For many ocean and climate models, mesoscale eddies still need to be parameterized. This is often done via an eddy diffusivity , which sets the strength of turbulent downgradient tracer fluxes. A well-known effect is the modulation of in the presence of background potential vorticity (PV) gradients, which suppresses cross-PV gradient mixing. Topographic slopes can induce such suppression through topographic PV gradients. However, this effect has received little attention, and topographic effects are often not included in parameterizations for . In this study, we show that it is possible to describe the effect of topography on analytically in a barotropic framework, using a simple stochastic representation of eddy–eddy interactions. We obtain an analytical expression for the depth-averaged as a function of the bottom slope, which we validate against diagnosed eddy diffusivities from a numerical model. The obtained analytical expression can be generalized to any constant barotropic PV gradient. Moreover, the expression is consistent with empirical parameterizations for eddy diffusivity over topography from previous studies and provides a physical rationalization for these parameterizations. The new expression helps to understand how eddy diffusivities vary across the ocean, and thus how mesoscale eddies impact ocean mixing processes. Significance Statement Large oceanic “whirls,” called eddies, can mix and transport ocean properties such as heat, salt, carbon, and nutrients. Mixing plays an important role for oceanic ecosystems and the climate system. In numerical simulations of Earth’s climate, eddy mixing is typically represented using a simplified expression. However, an effect that is often not included is that eddy mixing is weaker over a sloping seafloor. In most areas of the ocean the bottom slope is steep enough for this effect to be significant. In this study we derive an expression for eddy mixing that accounts for oceanic bottom slopes. The present effort provides a physical basis for eddy mixing over oceanic bottom slopes, justifying their use in climate models.

Ultra-fast calculation method of incident angle based on underwater acoustic round-trip positioning

In underwater acoustic round-trip positioning, the incident angle calculation in constant gradient acoustic ray tracing significantly hinders the efficiency of positioning calculation. To address this issue, we proposed an ultra-fast calculation method for determining incident angle based on underwater acoustic round-trip positioning. Specifically, the method employs the k-mean++ clustering algorithm to streamline the sound velocity profile. Additionally, a function formula for the incident angle is constructed, and its partial derivative with respect to Snell's constant is derived. Finally, Newton's method is applied to iteratively calculate the incident angles of the signal emission and reception, respectively. The simulation test results demonstrate that the proposed method reduces the positioning calculation time by 80.123%, 80.105%, 80.136%, and 80.104% on four transponders compared to the traditional method. In the field experiment, the proposed method is superior to the traditional method by 81.693% in positioning calculation time. These findings indicate the significant superiority of the proposed method in positioning calculation efficiency compared to the traditional method.

Pulsatile nanofluid flow with variable pressure gradient and heat transfer in wavy channel

This research contributes to the comprehension of nanofluid behaviour through a wavy channel, emphasizing the significance of considering diverse influences in the modelling process. The study explores the collective influence of pressure gradient variation, magnetic field, porosity, channel waviness, nanoparticle concentration, and heat transfer on nano-blood flow in a two-dimensional wavy channel. In contrast to prior research assuming a constant pulsatile pressure gradient during channel waviness, this innovative study introduces a variable pressure gradient, significantly influencing several associated parameters. The mathematical model characterizing nano-blood flow in a horizontally wavy channel is solved using the perturbation technique. Analytical solutions for fundamental variables such as stream function, velocity, wall shear stress, pressure gradient, and temperature are visually depicted across different physical parameters values. The findings obtained for differing parameter values in the given problem demonstrate a significant influence of the amplitude ratio parameter of channel waviness, Hartmann number of the magnetic field, permeability parameter of the porous medium, volume fraction of nanoparticles, radiation parameter, Prandtl number, and the suction/injection parameter on the flow dynamics. The simulations provide valuable insights into the decrease in velocity with increasing magnetic field and its increase with higher permeability. Additionally, the temperature is observed to escalate with a rising nanoparticle volume fraction and radiation parameter, while it declines with increasing Prandtl number.

Investigation of heat and mass transfer of oldroyd – 8 constant fluid in wire coating process employing response surface methodology

Wire coating is widely used for electrical insulation, shock protection, preventing leakage, and facilitating smooth current flow. This study aims to evaluate the applicability of Oldroyd-8 constant fluid for wire applications in a magnetic field using a pressure-type die. Based on the Buongiorno model with a constant pressure gradient and temperature-dependent thermophysical properties, governing equations are developed. These equations are transformed into dimensionless form and solved numerically. The study thoroughly investigates key features, including momentum, thermal distribution, nanoparticle volume fraction, and shear stress rate. Also, this study employs Response Surface Methodology to optimize heat transfer and shear stress rates in coated wire. Quadratic models, developed through a central-composite design, determine optimal levels for the Oldroyd-8 constant fluid parameter and nanofluid parameters, ensuring optimal heat transfer and shear stress rates for the melt. Nanofluid parameters contribute to an improvement in the thermal distribution profile. Optimal heat transfer and shear stress rate occur when the nanofluid parameters are minimized, and non – Newtonian fluid parameter is maximized.