Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation,we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses.By changing the relative phase between the fundamental frequency field and the second one,it is found that the harmonic intensity in the platform region can be significantly modulated.In the higher order,the harmonic intensity can be increased by about one order of magnitude.Through time-frequency analysis,it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase,and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability.In addition,near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields.With the change of the relative phase,the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one.Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity,which provides an opportunity for syntheses of circularly polarized attosecond pulses.

Dynamics of a rotating ring-stiffened sandwich conical shell with an auxetic honeycomb core

The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the rotation.The governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s principle.Utilizing trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied.The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.

Effects of multiple shapes for steady flow with transformer oil+Fe_(3)O_(4)+TiO_(2) between two stretchable rotating disks

In this study,we examine the effects of various shapes of nanoparticles in a steady flow of hybrid nanofluids between two stretchable rotating disks.The steady flow of hybrid nanofluids with transformer oil as the base fluid and Fe_(3)O_(4)+TiO_(2)as the hybrid nanofluid is considered.Several shapes of Fe_(3)O_(4)+TiO_(2)hybrid nanofluids,including sphere,brick,blade,cylinder,and platelet,are studied.Every shape exists in the same volume of a nanoparticle.The leading equations(partial differential equations(PDEs))are transformed to the nonlinear ordinary differential equations(ODEs)with the help of similarity transformations.The system of equations takes the form of ODEs depending on the boundary conditions,whose solutions are computed numerically by the bvp4c MATLAB solver.The outputs are compared with the previous findings,and an intriguing pattern is discovered,such that the tangential velocity is increased for the rotation parameter,while it is decreased by the stretching values because of the lower disk.For the reaction rate parameter,the concentration boundary layer becomes shorter,and the activation energy component increases the rate at which mass transfers come to the higher disk but have the opposite effect on the bottom disk.The ranges of various parameters taken into account are Pr=6.2,Re=2,M=1.0,φ_(1)=φ_(2)=0.03,K=0.5,S=-0.1,Br=0.3,Sc=2.0,α_(1)=0.2,γ=0.1,E_(n)=2.0,and q=1.0,and the rotation factor K is within the range of 0 to 1.

Single atom Cu-N-C catalysts for the electro-reduction of CO_(2) to CO assessed by rotating ring-disc electrode

The electrochemical CO_(2) reduction reaction(CO_(2)RR) to controllable chemicals is considered as a promising pathway to store intermittent renewable energy. Herein, a set of catalysts based on copper-nitrogendoped carbon xerogel(Cu-N-C) are successfully developed varying the copper amount and the nature of the copper precursor, for the efficient CO_(2)RR. The electrocatalytic performance of Cu-N-C materials is assessed by a rotating ring-disc electrode(RRDE), technique still rarely explored for CO_(2)RR. For comparison, products are also characterized by online gas chromatography in a H-cell. The as-synthesized Cu-NC catalysts are found to be active and highly CO selective at low overpotentials(from -0.6 to -0.8 V vs.RHE) in 0.1 M KHCO_(3), while H_(2) from the competitive water reduction appears at larger overpotentials(-0.9 V vs. RHE). The optimum copper acetate-derived catalyst containing Cu-N_(4) moieties exhibits a CO_(2)-to-CO turnover frequency of 997 h^(-1) at -0.9 V vs. RHE with a H_(2)/CO ratio of 1.8. These results demonstrate that RRDE configuration can be used as a feasible approach for identifying electrolysis products from CO_(2)RR.

Multiparameter Numerical Investigation of Two Types of Moving Interactions Between the Deep-Sea Mining Vehicle Track Plate and Seabed Soil:Digging and Rotating Motions

To ensure the safe performance of deep-sea mining vehicles(DSMVs),it is necessary to study the mechanical characteristics of the interaction between the seabed soil and the track plate.The rotation and digging motions of the track plate are important links in the contact between the driving mechanism of the DSMV and seabed soil.In this study,a numerical simulation is conducted using the coupled Eulerian–Lagrangian(CEL)large deformation numerical method to investigate the interaction between the track plate of the DSMV and the seabed soil under two working conditions:rotating condition and digging condition.First,a soil numerical model is established based on the elastoplastic mechanical characterization using the basic physical and mechanical properties of the seabed soil obtained by in situ sampling.Subsequently,the soil disturbance mechanism and the dynamic mechanical response of the track plate under rotating and digging conditions are obtained through the analysis of the sensitivity of the motion parameters,the grouser structure,the layered soil features and the soil heterogeneity.The results indicate that the above parameters remarkably influence the interaction between the DSMV and the seabed soil.Therefore,it is important to consider the rotating and digging motion of the DSMV in practical engineering to develop a detailed optimization design of the track plate.

Synthesis of NO by rotating sliding arc discharge reactor with conical-spiral electrodes

The present work investigates the potential applications of nitrogen oxides(NO_(x)),particularly nitric oxide(NO)and nitrogen dioxide(NO_(2)),generated through discharge plasma in diverse sectors such as medicine,nitrogen fixation,energy,and environmental protection.In this study,a rotating sliding arc discharge reactor was initially employed to produce high concentrations of gaseous NO_(x),followed by the utilization of a molybdenum wire redox reactor for NO_(2)-to-NO conversion.The outcomes reveal that the discharge states and generations of NO_(x) are affected by varying parameters,including the applied energies,frequencies and airflow states(1.3-2.6 m/s are the laminar flow,2.6-5.2 m/s are the transition state,5.2-6.5 m/s are the turbulent flow),and the concentrations of NO_(x) within the arc discharge are higher than that in the spark discharge.Moreover,the concentrations of NO,NO_(2) and NO_(x) gradually increased,and the concentration ratios of NO/NO_(2) and NO_(x)/NO_(2) decreased with increasing the applied energy for one cycle from 14.8 mJ to 24.3 mJ.Meanwhile,the concentrations of NO,NO_(2) and NO_(x) gradually decreased,and the concentration ratios of NO/NO_(2) and NO_(x)/NO_(2) first decreased and then increased with increasing the applied frequencies from 5.0 kHz to 9.0 kHz.Further,the concentrations of NO,NO_(2) and NO_(x) gradually decreased,and the concentration ratios of NO/NO_(2) and NO_(x)/NO_(2) first increased and then decreased with increasing the air flow speeds from 1.3 m/s to 6.5 m/s.Lastly,the concentrations of NO increased and NO_(2) decreased with increasing temperature from 25℃ to 400℃ using molybdenum converted.These findings provide experimental support for the application of plasma in the fields of medicine,nitrogen fixation,energy and environmental protection.

Rotating magnetic field inhibits Aβ protein aggregation and alleviates cognitive impairment in Alzheimer’s disease mice

Amyloid beta(Aβ)monomers aggregate to form fibrils and amyloid plaques,which are critical mechanisms in the pathogenesis of Alzheimer’s disease(AD).Given the important role of Aβ1-42 aggregation in plaque formation,leading to brain lesions and cognitive impairment,numerous studies have aimed to reduce Aβaggregation and slow AD progression.The diphenylalanine(FF)sequence is critical for amyloid aggregation,and magnetic fields can affect peptide alignment due to the diamagnetic anisotropy of aromatic rings.In this study,we examined the effects of a moderate-intensity rotating magnetic field(RMF)on Aβaggregation and AD pathogenesis.Results indicated that the RMF directly inhibited Aβamyloid fibril formation and reduced Aβ-induced cytotoxicity in neural cells in vitro.Using the AD mouse model APP/PS1,RMF restored motor abilities to healthy control levels and significantly alleviated cognitive impairments,including exploration and spatial and non-spatial memory abilities.Tissue examinations demonstrated that RMF reduced amyloid plaque accumulation,attenuated microglial activation,and reduced oxidative stress in the APP/PS1 mouse brain.These findings suggest that RMF holds considerable potential as a non-invasive,high-penetration physical approach for AD treatment.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Rotating tank experiments for the study of geophysical fluid dynamics

Geophysical fluid dynamics(GFD)is an interdisciplinary field that studies the large-scale motion of fluids in the natural world.With a wide range of applications such as weather forecasts and climate prediction,GFD employs various research approaches including in-situ observations,satellite measurements,numerical simulations,theoretical analysis,artificial intelligence,and physical model experiments in laboratory.Among these approaches,rotating tank experiments provide a valuable tool for simulating naturally-occurring fluid motions in laboratories.With proportional scaling and proper techniques,scientists can reproduce multi-scale physical processes of stratified fluids in the rotation system,which allows for the simulation of essential characteristics of fluid motions in the atmosphere and oceans.In this review,rotating tanks of various scales in the world are introduced,as these tanks have been actively used to explore fundamental scientific questions in ocean and atmosphere dynamics.To illustrate the GFD experiments,three representative cases are presented to demonstrate the frontier achievements in the the GFD study by using rotating tank experiments:mesoscale eddies in the ocean,convection processes,and plume dynamics.Detailed references for the experimental procedures are provided.Future studies are encouraged to further explore the utilization of rotating tanks with improvements in experimental design and integration of other research methods.This is a promising direction of GFD to help enhance our understanding of the complex nature of fluid motions in the natural world and to address the challenges posed by global environmental changes.

Effect of power supply parameters on discharge characteristics and sterilization efficiency of magnetically driven rotating gliding arc

Plasma sterilization is a new generation of high-tech sterilization method that is fast,safe,and pollution free.It is widely used in medical,food,and environmental protection fields.Home air sterilization is an emerging field of plasma application,which puts higher requirements on the miniaturization,operational stability,and operating cost of plasma device.In this study,a novel magnetically driven rotating gliding arc(MDRGA)discharge device was used to sterilize Lactobacillus fermentation.Compared with the traditional gas-driven gliding arc,this device has a simple structure and a more stable gliding arc.Simulation using COMSOL Multiphysics showed that adding permanent magnets can form a stable magnetic field,which is conducive to the formation of gliding arcs.Experiments on the discharge performance,ozone concentration,and sterilization effect were conducted using different power supply parameters.The results revealed that the MDRGA process can be divided into three stages:starting,gliding,and extinguishing.Appropriate voltage was the key factor for stable arc gliding,and both high and low voltages were not conducive to stable arc gliding and ozone production.In this experimental setup,the sterilization effect was the best at 6.6 kV.A high modulation duty ratio was beneficial for achieving stable arc gliding.However,when the duty ratio exceeded a certain value,the improvement in the sterilization effect was slow.Therefore,considering the sterilization effect and energy factors comprehensively,we chose 80%as the optimal modulation duty ratio for this experimental device.

Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

A Comprehensive 3-Steps Methodology for Vibration-Based Fault Detection,Diagnosis and Localization in Rotating Machines

In any industry,it is the requirement to know whether the machine is healthy or not to operate machine further.If the machine is not healthy then what is the fault in the machine and then finally its location.The paper is proposing a 3-Steps methodology for the machine fault diagnosis to meet the industrial requirements to aid the maintenance activity.The Step-1 identifies whether machine is healthy or faulty,then Step-2 detect the type of defect and finally its location in Step-3.This method is extended further from the earlier study on the 2-Steps method for the rotor defects only to the 3-Steps methodology to both rotor and bearing defects.The method uses the optimised vibration parameters and a simple Artificial Neural Network(ANN)-based Machine Learning(ML)model from the earlier studies.The model is initially developed,tested and validated on an experimental rotating rig operating at a speed above 1st critical speed.The proposed method and model are then further validated at 2 different operating speeds,one below 1st critical speed and other above 2nd critical speed.The machine dynamics are expected to be significantly different at these speeds.This highlights the robustness of the proposed 3-Steps method.

The Whole Theory of This Universe—A Step Forward to Einstein. Part-4: “Concept Map of Rotating Universe”

The article collectively proposes a revolutionary perspective on the universe, intertwining concepts of time, spatial positioning, and cosmic dynamics. We introduce the idea of a rotating universe centered around Mega Central Energy Pools (MCEPs), where time varies relative to the distance from the universe’s center, potentially enabling time travel. This model challenges conventional notions of time and cosmology, suggesting that black holes and white holes act as cosmic recycling factories. Additionally, this model unveils a novel theory of dark matter, positing photons as its constituents and highlighting their role in energy transfer across the cosmos. Furthermore, the investigation into Venus’s unique day-length-to-year-length ratio unveils a microscopic mechanism involving swirling energy droplets, charged particles, and field interactions, offering insights into planetary dynamics on both micro and macro scales.

Research on Rotating Machinery Fault Diagnosis Based on Improved Multi-target Domain Adversarial Network

Aiming at the problems of low efficiency,poor anti-noise and robustness of transfer learning model in intelligent fault diagnosis of rotating machinery,a new method of intelligent fault diagnosis of rotating machinery based on single source and multi-target domain adversarial network model(WDMACN)and Gram Angle Product field(GAPF)was proposed.Firstly,the original one-dimensional vibration signal is preprocessed using GAPF to generate the image data including all time series.Secondly,the residual network is used to extract data features,and the features of the target domain without labels are pseudo-labeled,and the transferable features among the feature extractors are shared through the depth parameter,and the feature extractors of the multi-target domain are updated anatomically to generate the features that the discriminator cannot distinguish.The modelt through adversarial domain adaptation,thus achieving fault classification.Finally,a large number of validations were carried out on the bearing data set of Case Western Reserve University(CWRU)and the gear data.The results show that the proposed method can greatly improve the diagnostic efficiency of the model,and has good noise resistance and generalization.

Magneto-Photo-Thermoelastic Excitation Rotating Semiconductor Medium Based on Moisture Diffusivity

In this research,we focus on the free-surface deformation of a one-dimensional elastic semiconductor medium as a function of magnetic field and moisture diffusivity.The problem aims to analyze the interconnection between plasma and moisture diffusivity processes,as well as thermo-elastic waves.The study examines the photothermoelasticity transport process while considering the impact of moisture diffusivity.By employing Laplace’s transformation technique,we derive the governing equations of the photo-thermo-elastic medium.These equations include the equations for carrier density,elastic waves,moisture transport,heat conduction,and constitutive relationships.Mechanical stresses,thermal conditions,and plasma boundary conditions are used to calculate the fundamental physical parameters in the Laplace domain.By employing numerical techniques,the Laplace transform is inverted to get complete time-domain solutions for the primary physical domains under study.Referencemoisture,thermoelastic,and thermoelectric characteristics are employed in conjunction with a graphical analysis that takes into consideration the effects of applied forces on displacement,moisture concentration,carrier density,stress due to forces,and temperature distribution.

Libration-Generated Average Convection in a Rotating Flat Layer with Horizontal Axis

The study of average convection in a rotating cavity subjected to modulated rotation is an interesting area for the development of both fundamental and applied science.This phenomenon finds application in the field of mass transfer and fluid flow control,relevant examples being crystal growth under reduced gravity and fluid mixing in microfluidic devices for cell cultures.In this study,the averaged flow generated by the oscillating motion of a fluid in a planar layer rotating about a horizontal axis is experimentally investigated.The boundaries of the layer are maintained at constant temperatures,while the lateral cylindrical wall is thermally insulated.It is demonstrated that libration results in intense oscillatory fluid motion,which in turn produces a time-averaged flow.For the first time,quantitative measures for the instantaneous velocity field are obtained using the Particle Image Velocimetry technique.It is revealed that the flow has the form of counter-rotating vortices.The vortex circulations sense changes during a libration cycle.An increase in the rotation rate and amplitude of the cavity libration results in an increase in the flow intensity.The heat transfer and time-averaged velocity are examined accordingly as a function of the dimensionless oscillation frequency,and resonant excitation of heat transfer and average oscillation velocity are revealed.The threshold curve for the onset of the averaged convection is identified in the plane of control parameters(dimensionless rotational velocity and pulsation Reynolds number).It is found that an increase in the dimensionless rotational velocity has a stabilizing effect on the onset of convection.

Dynamics of Low-Viscosity Liquids Interface in an Unevenly Rotating Vertical Layer

The behavior of two immiscible low-viscosity liquids differing in density and viscosity in a vertical flat layer undergoing modulated rotation is experimentally studied.The layer has a circular axisymmetric boundary.In the absence of modulation of the rotation speed,the interphase boundary has the shape of a short axisymmetric cylinder.A new effect has been discovered,under the influence of rotation speed modulation,the interface takes on a new dynamic equilibrium state.A more viscous liquid covers the end boundaries of the layer in the form of thin films,which have the shape of round spots of almost constant radius;with increasing amplitude of the velocity modulation,the wetting boundary expands.It is found that upon reaching the critical amplitude of oscillations,the film of a viscous liquid loses stability,and the outer edge of the wetting spot collapses and takes on a feathery structure.It is shown that this threshold is caused by the development of the Kelvin-Helmholtz oscillatory instability of the film.The spreading radius of a spot of light viscous liquid and its stability are studied depending on the rotation rate,amplitude,and frequency of rotation speed modulation.The discovered averaged effects are determined by different oscillatory interaction of fluids with the end-walls of the cell,due to different viscosities.The effect of films forming can find application in technological processes to intensify mass transfer at interphase boundaries.

Experimental Study of Thermal Convection and Heat Transfer in Rotating Horizontal Annulus

A genuine technological issue–the thermal convection of liquid in a rotating cavity–is investigated experimentally.The experiments are conducted within a horizontal annulus with isothermal boundaries. The inner boundaryof the annulus has a higher temperature, thus exerting a stabilising influence on the system. It is shown that whenthe layer rotation velocity diminishes, two-dimensional azimuthally periodic convective rolls, rotating togetherwith the cavity, emerge in a threshold manner. The development of convection is accompanied by a significantintensification of heat transfer through the layer. It is shown that the averaged thermal convection excitation inthe form of a system of two-dimensional rolls occurs against the background of oscillations of a non-isothermalfluid in the cavity reference frame caused by the gravity field. The excitation threshold and the structure ofconvective rolls are consistent with the results of the earlier theoretical studies by the authors performed usingthe equations of “vibrational” convection obtained by the averaging method. Furthermore, the experiments haverevealed a new type of averaged flow in the form of a spatially periodic system of toroidal vortices. It is shown thata steady streaming, excited by the inertial oscillations of the fluid, is responsible for the generation of the toroidalvortices. These flows develop in a non-threshold manner and are most clearly manifested in a case of resonantexcitation of one of the inertial modes.

Vibrational Suspension of Two Cylinders in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of rotating hydrodynamic systems containing phase inclusions are interesting due to the related widespread occurrence in nature and technology.The influence of external force fields on rotating systems can be used to control the dynamics of inclusions of various types.Controlling inclusions is of current interest for space technologies.In low gravity,even a slight vibration effect can lead to the appearance of a force acting on phase inclusions near a solid boundary.When vibrations are applied to multiphase hydrodynamic systems,the oscillating body intensively interacts with the fluid and introduces changes in the related flow structure.Asymmetries in the fluid flow lead to the appearance of an averaged force.As a result,the body is repelled from the cavity boundary and takes a position at a certain distance from it.The vibrationally-induced movement of phase inclusions in liquids can be used to improve various technological processes(for example,when degassing and cleaning liquids from solid inclusions,mixing various components,etc.).This study presents a relevant methodology to study the averaged vibrational force acting on a pair of free cylindrical bodies near the oscillating wall of a cavity.Attention is paid to the region of moderate and low dimensionless frequencies when the size of the inclusion is consistent with the thickness of the Stokes boundary layer.The dynamics of these bodies is considered in a horizontal cylindrical cavity with a fluid undergoing modulated rotation.The average lift force of a vibrational nature is measured by the method of quasi-stationary suspension of bodies whose density differs from the density of the liquid in a static centrifugal force field.The developed technique makes it possible to determine the dependence of the lift force on vibration parameters and the distance from the oscillating boundary at which solid inclusions are located.It is shown that in the region of moderate dimensionless frequencies,the average lift force acting on an inclusion near the boundary undergoing modulated rotation almost linearly depends on the dimensionless frequency.

Linear and Non-Linear Dynamics of Inertial Waves in a Rotating Cylinder with Antiparallel Inclined Ends

This work is devoted to the experimental study of inertial wave regimes in a non-uniform rotating cylinder with antiparallel inclined ends.In this setting,the cross-section of the cylinder is divided into two regions where the fluid depth increases or decreases with radius.Three different regimes are found:inertial wave attractor,global oscillations(the cavity’s resonant modes)and regime of symmetric reflection of wave beams.In linear wave regimes,a steady single vortex elongated along the rotation axis is generated.The location of the wave’s interaction with the sloping ends determines the vortex position and the vorticity sign.In non-linear regimes several pairs of the triadic resonance subharmonics are detected simultaneously.The instability of triadic resonance is accompanied by the periodic generation of mean vortices drifting in the azimuthal direction.Moreover,the appearance frequency of the vortices is consistent with the low-frequency subharmonic of the triadic resonance.The experimental results shed light on the mechanisms of the inertial wave interaction with zonal flow and may be useful for the development of new methods of mixing.