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.

THIRD ORDER SHEAR DEFORMATION MODEL FOR LAMINATED SHELLS WITH FINITE ROTATIONS:FORMULATION AND CONSISTENT LINEARIZATION

The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.

New Method of Givens Rotations for Triangularization of Square Matrices

This paper describes a new method of QR-decomposition of square nonsingular matrices (real or complex) by the Givens rotations through the unitary discrete heap transforms. This transforms can be defined by a different path, or the order of processing components of input data, which leads to different realizations of the QR-decomposition. The heap transforms are fast, because of a simple form of decomposition of their matrices. The direct calculation of the N-point discrete heap transform requires no more than 5(N-1) multiplications, 2(N-1) additions, plus 3(N-1) trigonometric operations. The QR-decomposition of the square matrix N × N uses about 4/3N3 multiplications and N(N-1)/2 square roots. This number varies depending on the path of the heap transform, and it is shown that “the optimal path” allows for significant reduction of number of operations in QR-decomposition. The heap transform and its matrix can be described analytically, and therefore, this transform can also be applied to the QR-decomposition of complex matrices.

Cereal-forage crop rotations and irrigation treatment effect on water use efficiency and crops sustainability in Mediterranean environment

Agricultural systems based on crop rotations favour sustainability of cultivation and productivity of the crops. Wheat-forage crops rotations (annual winter binary mixture and perennial alfalfa meadow) combined with irrigation are the agronomical techniques able to better exploit the weather resources in Mediterranean environments. The experiment aimed to study the effect of 18 years of combined effect of irrigation and continuous durum wheat and wheat-forage rotations on productivities of crops and organic matter of topsoil. The experiments were established through 1991-2008 under rainfed and irrigated treatments and emphasized on the effect of irrigation and continuous wheat and wheat-forage crop rotations on water use efficiency and sustainability of organic matter. The effect of irrigation increased 49.1% and 66.9% the dry matter of mixture and meadow, respectively. Continuous wheat rotation reduced seed yield, stability of production, crude protein characteristics of kernel and soil organic matter. The yearly gain in wheat after forage crops was 0.04 t (ha·yr)-1 under rainfed and 0.07 t (ha·yr)-1 under irrigation treatments. The crude protein and soil organic matter of wheat rotations, compared to those of continuous wheat under rainfed and irrigated was increase in term of point percentage by 0.8 and 0.5 in crude protein and 5.1 and 4.4 in organic matter, respectively. The rotations of mixture and meadow under both irrigated treatments increased the point of percentage of organic matter over continuous wheat (9.3.and 8.5 in mixture and 12.5 and 9.5 meadow under rainfed and irrigation, respectively). Irrigation reduce the impact of weather on crop growing reducing water use efficiency (mean over rotations) for dry mater production (15.5 in meadow and 17.5 in mixture [L water (kg·dry·matter)-1 ]) and wheat seed yield. The effect of agronomic advantages achieved by forage crops in topsoil expire its effect after three years of continuous wheat rotation.

Bilaterally Symmetrical Transformation between Independent Operators and Rotations

This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation between unitary matrices. This approach could be used to modifying the controls to apply in a different basis.

Effect of various crop rotations on rice yield and nitrogen use efficiency in paddy–upland systems in southeastern China

To evaluate the effects of various rotation systems on rice grain yield and N use efficiency, a paddy–upland cropping experiment(2013–2016) was conducted in southeastern China. The experiment was designed using six different rice––winter crop rotations: rice–fallow(RF),rice–wheat(RW), rice–potato with rice straw mulch(RP), rice–green manure(Chinese milk vetch; RC–G), rice–oilseed rape(RO), and rice–green manure crop(oilseed rape with fresh straw incorporated into soil at flowering; RO–G) and three N rates, N0(0 kg N ha-1), N1(142.5 kg N ha-1), and N2(202.5 kg N ha-1). Average rice yields in the RF(5.93 t ha-1) rotation were significantly lower than those in the rotations with winter crops(7.20–7.48 t ha-1)under the N0 treatment, suggesting that incorporation of straw might be more effective for increasing soil N than winter fallow. The rice yield differences among the rotations varied by year with the N input. In general, the grain yields in the RP and RO–G rotations –were respectively 11.6–28.5% and 14.80–37.19% higher than those in the RF in plots with N applied. Increasing the N rate may have tended to minimize the average yield gap between the RF and the other rotations; the yield gaps were 18.55%, 4.14%, and 0.23% in N0, N1, and N2, respectively. However, the N recovery efficiency in the RF was significantly lower than that in other rotations, except for 2015 under both N1 and N2 rates, a finding that implies a large amount of chemical N loss. No significant differences in nitrogen agronomic efficiency(NAE) and physiological efficiency(NPE) were found between the rotations with legume(RC–G) and non–legume(RO and RW) winter crops, a result that may be due partly to straw incorporation. For this reason, we concluded that the return of straw could reduce differences in N use efficiency between rotations with and without legume crops. The degree of synchrony between the crop N demand and the N supply was evaluated by comparison of nitrogen balance degree(NBD) values. The NBD values in the RP and RW were significantly lower than those in the other rotations under both N1 and N2 rates. Thus,in view of the higher grain yield in the RP compared to the RW under the N1 rate, the RP rotation might be a promising practice with comparable grain yield and greater N use efficiency under reduced N input relative to the other rotations. The primary yield components of the RF and RP were identified as number of panicles m-2 and numbers of kernels panicle-1, respectively. The NAE and NPE were positively correlated with harvest index, possibly providing a useful indicator for evaluating N use efficiency.

Crustal block rotations in Chinese mainland revealed by GPS measurements

We simulate GPS horizontal velocity field in terms of rotations of crustal blocks to describe deformation behavior of the Chinese mainland and its neighboring areas. 31 crustal blocks are bounded primarily by -30 Quaternary faults with distinct geometries and variable long-term rates of 〈20 mm/a, and 1 683 GPS velocities were determined from decade-long observations mostly with an averaged uncertainty of 1-2 mm/a. We define GPS velocity at a site by the combination of motion of rigid block and elastic strain induced by the fault that is locking during a seismic cycle. Model velocities predicted from the preferable block model match well with the GPS velocities to an uncertainty of-l.7mm/a. The slip rates inferred from this model is in a range of 6-18 mm/a for the major faults in Tibet and its margins and 1-4 mm/a in eastern China, consistent with geological observations. Our numerical simulation suggests that the crustal blocks deform internally at a level of-10× 10^-9/a, quite small in comparison with significant deformation localized along fault zones of 50-100 km wide. We conclude that the pattern of continental deformation is not continuous-like but block-like, and the tenet of plate tectonics may be applicable to characterize the active deformation in Asia.

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

ON CORRECT ACCOUNT OF FINITE ROTATIONS IN FINITE PLASTICITY THEORY

The non-uniqueness of the transition from nonobjective constitutive relations to objective ones with the use of the principle of material frame-indifference(PMFI)is shown.To eliminate it,the concept of finite strain without rotations(FSWR)for a given material type and each strain component(elastic,plastic) is introduced.In FSWR the rotation is excluded with respect to the natural preferred configuration for a given material.Considered are a simple solid,a liquid,a mouocrystal,a polycrystal and a composite.The procedure is proposed lbr consistent generalization of known infinitesimal relations for finite strains and rota- tions.The structure of constitutive relations is derived for anisotropic elasto-plastic mono-and polycrystalline materials.

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated. The generalized linear elastic body is described in kine- matics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor. Thus, the balance equations of momentum and moment are used for the motion equations of the body. The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis. The motion-deformation coupled model is developed in which three types of inertia forces along with their incre- ments are elucidated. The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle. A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity. The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom. As an example with an application of the motion- deformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented. Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities. The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model. A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent. The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated. The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.

Cenozoic Vertical-Axis Rotations of the Hoh Xil Basin, Central–Northern Tibet

Understanding the Cenozoic vertical-axis rotation in the Tibetan Plateau is crucial for continental dynamic evolution. Paleomagnetic and rock magnetic investigations were carried out for the Oligocene and Miocene continental rocks of the Hoh Xii basin in order to better understand the tectonic rotations of central Tibet. The study area was located in the Tongtianhe area located in the southern part of the Hoh Xil basin and northern margin of the Tanggula thrust system in central-northern Tibet. A total of 160 independently oriented paleomagnetic samples were drilled from the Tongtianhe section for this study. The magnetic properties of magnetite and hematite have been recognized by measurements of magnetic susceptibility vs. temperature curves and unbiocking temperatures. The mean directions of the Oligocene Yaxicuo Group in stratigraphic coordinates （Declination/Inclination = 354.9°/29.3°, k = 33.0, a9s = 13.5°, N =5 Sites） and of the Miocene Wudaoliang Group in stratigraphic coordinates （Declination/Inclination = 3.60/36.4°, k = 161.0, a9s = 9.7°, N =3 Sites） pass reversal tests, indicating the primary nature of the characteristic magnetizations. Our results suggested that the sampled areas in the Tuotuohe depression of the Hoh Xil basin have undergone no paleomagnetically detectable rotations under single thrusting from the Tanggula thrust system. Our findings, together with constraints from other tectonic characteristics reported by previous paleomagnetic studies, suggest tectonic rotations in the Cuoredejia and Wudaoliang depressions of the Hoh Xil basin were affected by strike-slip faulting of the Fenghuo Shan-Nangqian thrust systems. A closer examination of geological data and different vertical-axis rotation magnitudes suggest the tectonic history of the Hoh Xil basin may be controlled by thrust and strike-slip faulting since the Eocene.

Soil Fertility Comparison between Rotations of Tobacco-Rice (TR) and Rape-Rice (RR)

Tobacco-planting plays an important role in ensuring the high-quality tobacco raw materials supply and the local social and economic development in Chenzhou City. In recent years whether tobacco-planting is better for the maintenance and improvement of soil fertility than other crop-planting has been highly concerned. In this study, 16 soil fertility indicators and soil integrated index (IFI) were compared by 21 pairs of fields in Chenzhou city under the rotations of tobacco-rice (TF) and rice-rice (RR), and results showed that, comparing the mean values of soil fertility indicators, the contents of OM, TN, AN, AK, S and IFI were extremely significantly higher in TR than those in RR (p < 0.01), the contents of Cu, Ca, Mg and Fe were significantly higher in TR than those in RR (p < 0.05), but Mn content was significantly lower in TR than those in RR (p < 0.05). Meanwhile the contents of TP, TK and AP were insignificantly higher in TR than those in RR, and the contents of B, Mo and Zn were insignificantly lower in TR than those in RR. The above significant differences in soil fertility indicators were mainly due to relatively higher fertilizer inputs and less nutrient removal during tobacco-growing season than during rape-growing season, the net increase of N, P2O5 and K2O are 8.61, 5.25 and 24.89 kg per 667 m2 respectively in tobacco-growing season, while the net decrease of N, P2O5 and K2O are 8.88, 4.70 and 4.62 kg per 667 m2 respectively in rape-growing season. C.V. of soil fertility indicators and IFI were meanly lower in TR (52.25% and 15.95%, respectively) than those in RR (63.07% and 22.12%, respectively). Comparatively, tobacco-planting can improve soil fertility better than rape-planting when rotated with late rice in Chenzhou city. For tobacco-planting, Mg fertilizer should be applied for 23.8% TR fields, while more N, K, Ca, Mg, S and B fertilizers should be applied for 42.86%, 23.81%, 14.29%, 47.62%, 80.95% and 47.62% RR fields, respectively.

TERTIARY BLOCK ROTATIONS AND PYRRHOTITE/ MAGNETITE GEOTHERMOMETRY IN THE TETHYAN HIMALAYA(SHIAR KHOLA,CENTRAL NEPAL)

In Mesozoic carbonates of the Tethyan Himalayas two characteristic remanent magnetisations(ChRM\-1 and ChRM\-2)were identified by their unblocking spectra.The ChRM\-1 is carried by pyrrhotite(unblocking spectra:270～340℃),acquired as a secondary thermoremanent magnetisation (TRM) during exhumation and cooling.The ChRM\-2 is carried by magnetite (unblocking spectra:430～580℃).A primary origin is indicated by calcite twin geothermometry and remanences consistent with the expected direction.Along an E—W profile of 10km length the ratio of remanence intensity of pyrrhotite to magnetite ( R PYR/MAG )changes systematically (from 0 38 to 1 00,Fig.1).It is known that pyrrhotite is formed in marly carbonates during low\|grade metamorphism (Rochette 1987).This occurs at the expense of magnetite.Thus the ratio R PYR/MAG is related to metamorphic temperatures and can be used as a geothermometer for temperatures≤300℃ in low\|grade metamorphic carbonates where other methods are rare.Stable remanence directions were used to estimate the amount of block rotation around vertical and horizontal axes(i.e.Klootwijk et al.1985,Appel et al.1991 & 1995).In the Shiar area the pyrrhotite remanence directions follow a small\|circle distribution with a best fit parallel to the N—S direction(Fig.2).

BLOCK ROTATIONS AT THE NORTHERN EDGE OF INDIA (SPITI,N-INDIA) AND THEIR CONTINUATION TO THE EAST (MALARI, N-INDIA)-REGIONAL SIGNIFICANCE FOR THE TECTONIC DEVELOPMENT OF THE TETHYAN HIMALAYAS

In carboniferous and triassic metacarbonates (anchizone to lower greenschist facies) of the Tethyan Himalayas the characteristic remanent magnetisations are carried by magnetite (ChRM\-1) and pyrrhotite (ChRM\-2;Klootwijk & Bingham,1980;Appel et al.,1991 & 1995;Schill et al.,1999).Magnetite may carry a primary remanent magnetisation whereas the pyrrhotite component is secondary and related to the last cooling event below 300℃. Pyrrhotite is formed in marly carbonates during low\|grade metamorphism.In Spiti the last cooling is represented by an 40 Ar/ 39 Ar age of 42～45Ma (Wiesmayr & Grasemann,1999).Five locations were sampled in the Spiti valley (Fig.1).Besides a present earth field direction,both remanent components (ChRM 1+2 ) are present in single specimens.The contribution to the total NRM is around 30% for the ChRM\-2 (coercivity of 20～100mT) and only around 8% for the ChRM\-2 (unblocking temperature of 250～330℃).Despite of the contribution stable remanence directions could be obtained for the ChRM\-2.For all sampling locations well grouping overall mean directions were obtained (Table 1,Fig.1).Results from Losar and the lower Pin valley are preliminary.They were estimated by great circle analyses or by taking the residual component after AF\|demagnetisation. Clockwise block rotations of around 10～40° in respect to stable India since 42 Ma are calculated by using the apparent polar wander path of Besse & Courtillot (1991).The α 95 \|angles show no overlapping (Fig.1 small figure).Therefore local rotations are not negligible.

Invalidity of Geometrical Interpretation of F-Spin Structure of Nuclear Rotations by Otsuka’s View

In Otsuka's view of nuclear rotations neutrons and protons are not rotating around a common axis,but rather around separate axis.In this letter,we pointed out that this invalidates the geometrical interpretation of F-spin structure of the neutron-proton interacting boson model,where the angle between the axis of symmetries of neutron ellipsoid and proton ellipsoid is used to determine whether a state is F-spin symmetric or mixed symmetric.

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Nematode infestation and N-effect of legumes on soil and crop yelds in legume-sorghum rotations

The effects of cowpea (Vignaunguiculata) and-groundnut (Arachis hypogea) on succeeding sorghum yields, soil mineral N and nematode infestationwere studied during five cropping seasons (2000 to 2004) in a weakly acid Ultisol of the agronomy research station of Farak?-Ba lo-cated in the Guinean zone of Burkina Faso, West Africa. A factorial 5x5 design of five crop rotations with five fertilizer treatments in a split-plot arrangement with four replications was used.Sorghum yields were affected by the two factors (rotation with legumes and fertilizer ap-plications) during the four years. But interactions were not observed between the two factors. Monocropping of sorghum produced the lowest yields and legume–sorghum rotations increased sorghum yields by50% to 300%. Ground-nut–sorghum and cowpea–sorghum rotations increased soil mineral N by36% and 52%, re-spectively. Crop rotation influenced nematode infestation but the effects on soil and sorghum root infestation differed according to the rotation. The cowpea–sorghum rotation increased soil and sorghum root infestationby nematodes while groundnut–sorghum decree-sed the nematode population. The soil of the cowpea-sorghum rotation contained 1.5 to 2 times more nematodes than the soil of the monocropping of sorghum. In contrast, the soil ofthe groundnut–sorghum rotation contained from 17 to 19 times fewernematodes than that of themonocropping of sorghum. However, nematode infestation did not affect any of the succeeding sorghum yields. It was concluded that the parasitic effect of nematodes was limited by the predominance of positive N-effects on the development of succeeding sorghum.

Collisions, or Reflections and Rotations, Leading to the Digits of π

We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.

Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.