NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

Rotational Inertial Physics in Non-Classical Thermoviscous Fluent Continua Incorporating Internal Rotation Rates

In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.

Variations of the Earth＇s rotation rate and cyclic processes in geodynamics

The authors analyzed the relationship between variations of the Earth＇s rotation rate and the geodynamic processes within the Earth＇s body, including seismic activity, The rotation rate of a planet determines its uniaxial compression along the axis of rotation and the areas of various surface elements of the body. The Earth＇s ellipticity variations, caused naturally by the rotation rate variations, are manifested in vertical components of precise GPS measurements. Comparative analysis of these variations is considered in view of modern theoretical ideas concerning the Earth＇s figure. The results justify further research that is of interest for improvement of space svstems and technologiesi.

Effect of Rotation Rate on the Formation of Platinum-modified Polyaniline Film and Electrocatalytic Oxidation of Methanol

The oxidation of methanol was investigated on platinum-modified polyaniline electrode. Changes in the electrode rotation rates (Ω) during platinum electrodeposition remarkably affect the formation and distribution of platinum in the polymer matrix and consequently lead to different currents of methanol oxidation. The results show that platinum loading is proportional to rotation ratesΩ1/2.

Target rotation parameter estimation for ISAR imaging via frame processing

Frame processing method offers a model-based approach to Inverse Synthetic Aperture Radar(ISAR) imaging. It also provides a way to estimate the rotation rate of a non-cooperative target from radar returns via the frame operator properties. In this paper, the relationship between the best achievable ISAR image and the reconstructed image from radar returns was derived in the framework of Finite Frame Processing theory. We show that image defocusing caused by the use of an incorrect target rotation rate is interpreted under the FP method as a frame operator mismatch problem which causes energy dispersion. The unknown target rotation rate may be computed by optimizing the frame operator via a prominent point. Consequently, a prominent intensity maximization method in FP framework was proposed to estimate the underlying target rotation rate from radar returns. In addition, an image filtering technique was implemented to assist searching for a prominent point in practice. The proposed method is justified via a simulation analysis on the performance of FP imaging versus target rotation rate error.Effectiveness of the proposed method is also confirmed from real ISAR data experiments.

USEFUL RELATIVE MOTION DESCRIPTION METHOD FOR PERTURBATIONS ANALYSIS IN SATELLITEFORMATION FLYING

A set of parameters called relative orbital elements were defined to describe the relative motion of the satellites in the formation flying. With the help of these parameters, the effect of the perturbations on the relative orbit trajectory and geometric properties of satellite formation can be easily analyzed. First, the relative orbital elements are derived, and pointed out： if the eccentricity of the leading satellite is a small value, the relative orbit trajectory is determined by the intersection between an elliptic cylinder and a plane in the leading satellite orbit frame reference; and the parameters that describe the elliptic cylinder and the plane can be used to obtain the relative orbit trajectory and the relative orbital elements. Second, by analyzing the effects of gravitational perturbations on the relative orbit using the relative orbital elements,it is found that the propagation of a relative orbit consists of two parts ： one is the drift of the elliptic cylinder; and the other is the rotation of the plane resulted from the rotation of the normal of the plane. Meanwhile, the analytic formulae for the drift and rotation rates of a relative trajectory under gravitational perturbations are presented. Finally, the relative orbit trajectory and the corresponding changes were analyzed with respect to the J2 perturbation.

Observation of tiny polarization rotation rate in total internal reflection via weak measurements

In this paper,we examine the tiny polarization rotation effect in total internal reflection due to the spin–orbit interaction of light.We find that the tiny polarization rotation rate will induce a geometric phase gradient,which can be regarded as the physical origin of photonic spin Hall effect.We demonstrate that the spin-dependent splitting in position space is related to the polarization rotation in momentum space,while the spin-dependent splitting in momentum space is attributed to the polarization rotation in position space.Furthermore,we introduce a quantum weak measurement to determine the tiny polarization rotation rate.The rotation rate in momentum space is obtained with 118 nm,which manifests itself as a spatial shift,and the rotation rate in position space is achieved with 38 μrad∕λ,which manifests itself as an angular shift.The investigation of the polarization rotation characteristics will provide insights into the photonic spin Hall effect and will enable us to better understand the spin–orbit interaction of light.

Generation and imaging of a tunable ultrafast intensity-rotating optical field with a cycle down to femtosecond region

A tunable ultrafast intensity-rotating optical field is generated by overlapping a pair of 20Hz,800 nm chirped pulses with a Michelson interferometer(MI).Its rotating rate can be up to 10 trillion radians per second(Trad/s),which can be flexibly tuned with a mirror in the MI.Besides,its fold rotational symmetry structure is also changeable by controlling the difference from the topological charges of the pulse pair.Experimentally,we have successfully developed a twopetal lattice with a tunable rotating speed from 3.9 Trad/s up to 11.9 Trad/s,which is confirmed by our single-shot ultrafast frame imager based on noncollinear optical-parametric amplification with its highest frame rate of 15 trillion frames per second(Tfps).This work is carried out at a low repetition rate.Therefore,it can be applied at relativistic,even ultrarelativistic,intensities,which usually operate in low repetition rate ultrashort and ultraintense laser systems.We believe that it may have application in laser-plasma-based accelerators,strong terahertz radiations and celestial phenomena.

AN ATMOSPHERIC MOTION EQUATION BUILT ON THE CONSERVATIVE RELATIONSHIP OF THE ANGULAR MOMENTUM EXCHANGE BETWEEN THE SOLID EARTH AND THE ATMOSPHERE ON SEASONAL-ANNUAL TIMESCALE

Within the seasonal-annual timeseale,there exists an angular momentum conservative exchange relationship be- tween the solid earth and the atmosphere,and their angular momentum exchange not only can cause variations in length-of-day(LOD)but also can express anomalies in atmospheric general circulation.Therefore,their angular mo- mentum exchange mechanism should be introduced into the general circulation model. Considering the angular momentum anomalous exchange caused by the air-earth interface friction effect,a whole-layer atmospheric motion equation is derived in this paper including the earth spin anomalous friction force parameterized by using the change in the earth rotation rate.Through analysing the equation,it shows that the magni- tude of the earth spin anomalous friction force is the same as that of Coriolis force on seasonal-annual timescale.

Non-classical continuum theories for solid and fluent continua and some applications

This paper presents two specific thermodynamically consistent nonclassical continuum theories for solid and fluent continua.The first non-classical continuum theory for solid continua incorporates Jacobian of deformation in its entirety in the conservation and the balance laws and the derivation of the constitutive theories.The second non-classical continuum theory for solid continua considers Jacobian of deformation in its entirety as well as the Cosserat rotations in the conservation and balance laws as well as the constitutive theories.The first non-classical continuum theory for fluent continua presented here considers velocity gradient tensor in its entirety.The second non-classical continuum theory for fluent continua considers velocity gradient tensor in its entirety as well as Cosserat rotation rates in the derivation of the conservation and balance laws and the constitutive theories.Since the non-classical continuum theories for solid and fluent continua considered here incorporate additional physics of deformation due to rotations and rotation rates compared to classical continuum mechanics,the conservation and balance laws of classical continuum mechanics are shown to require modification as well as a new balance law balance of moment of moments is required to accommodate the new physics due to rotations and rotation rates.Eringen’s micropolar,micromorphic and microstretch theories,couple stress theories and nonlocal theories are also discussed within the context of the non-classical theories presented here for solid and fluent continua.Some applications of these theories are also discussed.