Numerical Simulation of the Whole Three-Dimensional Flow in a Stirred Tank with Anisotropic Algebraic Stress Model

In accordance to the anisotropic feature of turbulent flow, ananisotropic algebraic stress model is adopted to predict theturbulent flow field and turbulent characteristics generated by aRushton disc turbine with the improved inner-outer iterativeprocedure. The predicted turbulent flow is compared with experimentaldata and the simulation by the standard k-ε turbulence model. Theanisotropic algebraic stress model is found to give better predictionthan the standard k-ε turbulence model. The predicted turbulent flowfield is in accordance to experimental data and the trend of theturbulence intensity can be effectively reflected in the simulation.

Phenomenological Anisotropic Study of Surface Finish in Pack Rolling

A phenomenological anisotropic model has been presented for the surface roughness modeling of pack rolling. The model is an assembly of grains in different orientations and sizes. The grain size is assumed to be in log-normal distribution. To model the macro anisotropic mechanical behavior of the grains induced by the slip deformation, the grains are assumed as isolated anisotropic units. The units have different mechanic behavior, and depend on the crystallographic orientations and the external loading as well as the interaction of the adjunctive grains. In the paper, the material properties of the grains are assumed as uniform distributions. The roughness of the contact surfaces depends on the distribution types and the scatters of the distributions. It is found that the initial roughness of the contact surfaces has a little influence on the surface roughness when the rolling deformation is large. The comparison between the phenomenological model and crystallographic model shows that the phenomenological model can also give out a reasonable result, while it only takes much less CPU time. The agreement between the single sheet model and the pack rolling model shows that in a certain degree the pack rolling model can be replaced by the single sheet model to decrease the CPU time.

Anisotropic diffusion of volatile pollutants at air-water interface

The volatile pollutants that spill into natural waters cause water pollution. Air pollution arises from the water pollution because of volatilization. Mass exchange caused by turbulent fluctuation is stronger in the direction normal to the air-water interface than in other directions due to the large density difference between water and air. In order to explore the characteristics of anisotropic diffusion of the volatile pollutants at the air-water interface, the relationship between velocity gradient and mass transfer rate was established to calculate the turbulent mass diffusivity. A second-order accurate smooth transition differencing scheme （STDS） was proposed to guarantee the boundedness for the flow and mass transfer at the air-water interface. Simulations and experiments were performed to study the trichloroethylene （C2HC13） release. By comparing the anisotropic coupling diffusion model, isotropic coupling diffusion model, and non-coupling diffusion model, the features of the transport of volatile pollutants at the air-water interface were determined. The results show that the anisotropic coupling diffusion model is more accurate than the isotropic coupling diffusion model and non-coupling diffusion model. Mass transfer significantly increases with the increase of the air-water relative velocity at a low relative velocity. However, at a higher relative velocity, an increase in the relative velocity has no effect on mass transfer.

Calculating the shading reduction coefficient of photovoltaic system efficiency using the anisotropic sky scattering model

The front-row shading reduction coefficient is a key parameter used to calculate the system efficiency of a photovoltaic(PV)power station.Based on the Hay anisotropic sky scattering model,the variation rule of solar radiation intensity on the surface of the PV array during the shaded period is simulated,combined with the voltage-current characteristics of the PV modules,and the shadow occlusion operating mode of the PV array is modeled.A method for calculating the loss coefficient of front shadow occlusion based on the division of the PV cell string unit and Hay anisotropic sky scattering model is proposed.This algorithm can accurately evaluate the degree of influence of the PV array layout,wiring mode,array spacing,PV module specifications,and solar radiation on PV power station system efficiency.It provides a basis for optimizing the PV array layout,reducing system loss,and improving PV system efficiency.

Effect of Quantum Fluctuation on Two-Dimensional Spatially Anisotropic Heisenberg Antiferromagnet with Integer Spin

In the present paper, we calculate the Gaussian correction to the critical value J^c⊥ caused by quantum spin fluctuation in a two-dimensional spatially anisotropic Heisenberg antiferromagnet with integer spin S. Previously, some authors computed this quantity by the mean-field theory based on the Sehwinger boson representation of spin operators. However, for S = 1, their result is much less than the one derived by numerical calculations. By taking the effect of quantum spin fluctuation into consideration, we are able to produce a greatly improved result.

Elasto-plastic analysis of masonry with anisotropic plastic material model

This paper establishes an anisotropic plastic material model to analyze the elasto-plastic behavior of masonry in plane stress state.Being an anisotropic material,masonry has different constitutive relation and fracture energies along each orthotropic axes.Considering the unique material properties of masonry,a new yield criterion for masonry is proposed combining the Hill's yield criterion and the Rankine's yield criterion.The new yield criterion not only introduces compression friction coefficient of shear but also considers yield functions for independent stress state along two material axes of tension.To solve the involved nonlinear equations in numerical analysis,several nonlinear methods are implemented,including Newton-Raphson method for nonlinear equations and Implicit Euler backward mapping algorithm to update stresses.To verify the proposed material model of masonry,a series of tests are operated.The simulation results show that the new developed material model implements successfully.Compared with isotropic material model,the proposed model performs better in elasto-plastic analysis of masonry in plane stress state.The proposed anisotropic model is capable of simulating elasto-plastic behavior of masonry and can be used in related applications.

A Gaussian Model for Anisotropic Strange Quark Stars

For studying the anisotropie strange quark stars, we assume that the radial pressure inside an anisotropic star can be obtained simply by isotropie pressure plus an additional Gaussian term with three free parameters （A, μ and X）. According to recent observations, a pulsar in a mass range of 1.97±0.04M has been measured. Hence, we take this opportunity to set the free parameters of our model. We fix X by applying boundary and stability conditions and then search the A - μ parameter space For a maximum mass range of 1.9M 〈 Mmax 〈 2.1M. Our results indicate that anisotropy increases the maximum mass M and also its corresponding radius R for a typical strange quark star. Furthermore, our model shows magnetic field and electric charge increase the anisotropy factor △. In fact, △ has a maximum on the surface and this maximum goes up in the presence of magnetic field and electric charge. Finally, we show that anisotropy can be more effective than either magnetic field or electric charge in raising maximum mass of strange quark stars.

Force-constant-decayed anisotropic network model:An improved method for predicting RNA flexibility

RNA is an important biological macromolecule,which plays an irreplaceable role in many life activities.RNA functions are largely determined by its tertiary structure and the intrinsic dynamics encoded in the structure.Thus,how to effective extract structure-encoded dynamics is of great significance for understanding RNA functions.Anisotropic network model(ANM)is an efficient method to investigate macromolecular dynamical properties,which has been widely used in protein studies.However,the performance of the conventional ANM in describing RNA flexibility is not as good as that on proteins.In this study,we proposed a new approach,named force-constant-decayed anisotropic network model(fcdANM),to improve the performance in investigating the dynamical properties encoded in RNA structures.In fcd-ANM,nucleotide pairs in RNA structure were connected by springs and the force constant of springs was decayed exponentially based on the separation distance to describe the differences in the inter-nucleotide interaction strength.The performance of fcd-ANM in predicting RNA flexibility was evaluated using a non-redundant structure database composed of 51 RNAs.The results indicate that fcd-ANM significantly outperforms the conventional ANM in reproducing the experimental B-factors of nucleotides in RNA structures,and the Pearson correlation coefficient between the predicted and experimental nucleotide B-factors was distinctly improved by 21.05%compared to the conventional ANM.Fcd-ANM can serve as a more effective method for analysis of RNA dynamical properties.

Effects of Staggered Magnetic Field on Entanglement in the Anisotropic XY Model

We investigate effects of staggered magnetic field on thermal entanglement in the anisotropic XY model. The analytic results of entanglement for the two-site cases are obtained. For the general case of even sites, we show that when the anisotropic parameter is zero, the entanglement in the XY model with a staggered magnetic field is the same as that with a uniform magnetic field.

Anisotropic Plane Symmetric Two-Fluid Cosmological Model with Time-Varying G and A

We investigate a two-fluid anisotropic plane symmetric cosmological model with variable gravitational constant G（t） and cosmological term A（t）. In the two-fluid model, one fluid is chosen to be that of the radiation field modeling the cosmic microwave background and the other one a perfect fluid modeling the material content of the universe. Exact solutions of the field equations are obtained by using a special form for the average scale factor which corresponds to a specific time-varying deceleration parameter. The model obtained presents a cosmological scenario which describes an early acceleration and late-time deceleration. The gravitation constant increases with the cosmic time whereas the cosmological term decreases and asymptotically tends to zero. The physical and kinematical behaviors of the associated fluid parameters are discussed.

Modelling Magnetoresistance Effect in Limited Anisotropic Semiconductors

A macroscopic model of the magnetoresistance effect in fimited anisotropic semiconductors is built. This model allows us to solve the problem of measurement of physical magnetoresistance components of crystals and films. Based on a unified mathematical model the method is worked out enabling us to measure tensor components of the specific electrical resistance and the relative magnetoresistance of anisotropic semiconductors simultaneously.

Structural, Anisotropic and Thermodynamic Properties of Imm2-BCN

Structural, anisotropic, and thermodynamic properties of Imm2-BCN were studied based on density function theory with the ultrasoft psedopotential scheme in the frame of the generalized gradient approximation（GGA）. The elastic constants were confirmed that the predicted Imm2-BCN is mechanically stable. The anisotropy of elastic properties were also studied systematically. The anisotropy studies of Young＇s modulus, shear modulus, linear compressibility, and Poisson＇s ratio show that the Imm2-BCN exhibits a large anisotropy. Through the quasi-harmonic Debye model, the relations between the equilibrium volume V, thermal expansion α, the heat capacity C_V and CP, the Grüneisen parameter γ, and the Debye temperature Θ_D with pressure P and temperature T were also studied systematically.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

A Numerical Study on the Structure and Dynamics of Turbulence in Oscillatory Bottom Layer Flow over A Flat or Rippled Bed

This paper is mainly concerned with the turbulence in oscillatory bottom boundary layers over flat or rippled seaheds. Owing to the strong shear and anisotmpy of oscillatory flow, an anisotropic turbulence mathematical model is set up using the finite difference method, and the computational results of the model are verified by comparisons with wellknown experiments. Turbulent energy, dissipation and Reynolds stress can all be computed with this mathematical model, and the development processes of a large coherent vortex structure over a rippled bed, such as main flow separation, coherent vortex formation and curling, coherent vortex ejection and breaking up, are successfully simulated.

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferrornagnetic Heisenberg model of S =1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J⊥^c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J⊥^c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.

A Comprehensive Study of Solar Energy Components by Using Various Models on Horizontal and Inclined Surfaces for Different Climate Zones

The main objective of this research is to analyze the monthly average daily of global (H), beams (B) and diffuses (D) solar irradiance on a horizontal surface at four selected sites (El-Kharga, Hurghada in Egypt and Dammam, Hail in Saudi Arabia) during the period time from 1980 to 2020. The empirical models between (H/Ho) and meteorological parameters along with the values of (MBE), (RMSE), MPE, R2 and the t-Test statics are discussed. The results in this study indicate good agreement between observed and calculated values of total solar energy and diffuse solar fraction. The results for south facing surfaces of the (RMSE) for different slope at different models in the present research are discussions. Nine different models between isotropic and anisotropic used to estimate the diffuse solar radiation on a tilted surface at selected sites in this study. The absolute relative values of RMSE for the south-facing surface ranges from 7 to 41.3 at El-Kharga and Hurghada sites, Egypt in the present study for Koronakis and Stevenand Unsworth (SU) models respectively. The values of (RMSE), for the south-facing surface ranges from 9.3 to 39.7 at Dammam and Hail sites, Saudi Arabia in the present research for Koronakis and Klucher models respectively. For west-facing surface the values of RMSE range from 11.2 to 47.3 for Badescu and Koronakis models at El-Kharga and Hurghada sites, Egypt respectively, while values of RMSE range from 6.5 to 38.5 for Klucher and Reindl et al. models at Dammam and Hail sites, Saudi Arabia. The models Koronakis, Klucher and Stevenand Unsworth (SU) models are given the most accurate estimate for the south-facing surface, and Badescu, Koronakis, Klucher and Reindl et al. models are good performs better estimated for the west-facing surface.

Polarizabilities and Orientational Order Parameter in N-(p-n-Ethoxybenzylidene)- p-n-Alkoxy Anilines, 2O.Om LC Compounds

n.m, n.Om, nO.m and nO.Om compounds play an important role in the fundamental and applied aspects. As a part of our systematic studies of the above homologous series regarding the synthesis, characterization and phase transition studies, here the authors report the polarizabilities and orientational order parameter, S in N-(p-n-ethoxybenzylidene)-p-n-alkoxy anilines, 2O.Om with m = 3 to 10 liquid crystalline compounds except with m = 5 which has been already published. The rest of the compounds exhibit the nematic LC phase except with m = 10 which shows the smectic-C phase along the nematic phase which is originally not detected by Godzwon et al. But the author’s observations with TM and differential scanning calorimeter have shown the existence on SmC phase in addition to nematic phase. Further, SmC is clarified using the histogram technique whose details are given below and are published elsewhere. The orientstonal order parameter, S is estimated using different methods and compared with the value obtained from birefringence, δn = (ne – no) where no field model is used. It is observed in these compounds case as in other LC compounds Vuks isotropic model is favored compared to that of anisotropic model proposed by Neugebauer.

Effect of Water Content and Grains Size Distribution on the Characteristic Resilient Young’s Modulus (<i>E_c</i>) Obtained Using Anisotropic Boyce Model on Gravelly Lateritic Soils from Tropical Africa (Burkina Faso and Senegal)

This research was carried out to determine the rheological parameters of lateritic soils in order to contribute to the improvement of the technical documents used for pavement design in tropical Africa. The study is based on the loading repeated of cyclic triaxial tests (LRT) performed at University Gustave Eiffel (formerly Institut Français des Sciences et Technologies des Transports de l’Aménagement et des Réseaux (IFSTTAR)) in Nantes with the application of the European standard EN 13286-7: 2004 [1]. The tests were performed at constant confinement stress and using the stepwise method to determine the resilient axial () and radial () deformation as a function of the axial and radial stresses. Four gravel lateritic soils from different sites selected in Burkina Faso and Senegal were the subject of this research for the triaxial tests. These materials have a maximum diameter of 20 mm and a percentage of fines less than 20%. The LRT tests were carried out on samples compacted at three moisture contents (wopm - 2%, wopm and wopm + 2%) and at 95% and 100% of optimal dry density (γdopm). Test results showed that the characteristic resilient Young’s modulus (Ec) of gravelly laterites soils depends on the compacted water content and the variation of the grains size distribution (sand (ø < 2 mm), motor (ø < 0.5 mm) and fines content (ø < 0.063 mm) obtained after (LRT). Materials with a high percent of fines (>20%), mortar and sand (Sindia and Lam-Lam) are more sensitive to variations in water content. The presence of water combined with the excess of fines leads to a decrease in modulus around 25% for Lam-Lam and 20.2% for Sindia. Materials containing a low percent of fines, mortar and sand (Badnogo and Dedougou) behave differently. And the resilient modulus increases about 225.67% for Badnogo and 312.24% for Dedougou with the rise of the water content for approximately unchanged the percentage of fines, mortar and sand. Granularity therefore has an indirect influence on the resilient modulus of the lateritic soils by controlling the effects of water on the entire system. Results of statistical analysis and coefficients of correlation (0.659 to 0.865) showed that the anisotropic Boyce’s model is suitable to predict the volumetric () and deviatoric strain () with stress path (Δq/Δp) of the lateritic soils. The predicted Er resilient Young’s modulus from anisotropic Boyce’s model varies according to the evolution of the bulk stress (). A correlation around 0.9 is obtained from the power law model.

Derivation of Lower Critical Magnetic Field for Anisotropic Ginzburg-Landau Model in Superconductivity

In this paper, the authors discuss the vortex structure of an anisotropic Ginzburg-Landau model for superconducting thin film proposed by Du. We obtain the estimate for the lower critical magnetic field Hc1 which is the first critical value of hex corresponding to the first phase transition in which vortices appear in the superconductor. We also find local minimizers of the anisotropic superconducting thin film with a large parameter k, and for the applied magnetic field near the critical field we discuss the asymptotic behavior of the local minimizers.

Out-of-time-ordered correlation in the anisotropic Dicke model

Out-of-time-ordered correlation(OTOC)functions have been used as an indicator of quantum chaos in a lot of physical systems.In this work,we numerically demonstrate that zero temperature OTOC can detect quantum phase transition in the anisotropic Dicke model.The phase diagram is given with OTOC.The finite-size effect is studied.Finally,the temperature effect is discussed.