GPU parallel computation of dendrite growth competition in forced convection using the multi-phase-field-lattice Boltzmann model

A graphics-processing-unit(GPU)-parallel-based computational scheme is developed to realize the competitive growth process of converging bi-crystal in two-dimensional states in the presence of forced convection conditions by coupling a multi-phase field model and a lattice Boltzmann model.The elimination mechanism in the evolution process is analyzed for the three conformational schemes constituting converging bi-crystals under pure diffusion and forced convection conditions,respectively,expanding the research of the competitive growth of columnar dendrites under melt convection conditions.The results show that the elimination mechanism for the competitive growth of converging bi-crystals of all three configurations under pure diffusion conditions follows the conventional Walton-Chalmers model.When there is forced convection with lateral flow in the liquid phase,the anomalous elimination phenomenon of unfavorable dendrites eliminating favorable dendrites occurs in the grain boundaries.In particular,the anomalous elimination phenomenon is relatively strong in conformation 1 and conformation 2 when the orientation angle of unfavorable dendrites is small,and relatively weak in conformation 3.Moreover,the presence of convection increases the tip growth rate of both favorable and unfavorable dendrites in the grain boundary.In addition,the parallelization of the multi-phase-field-lattice Boltzmann model is achieved by designing the parallel computation of the model on the GPU platform concerning the computerunified-device-architecture parallel technique,and the results show that the parallel computation of this model based on the GPU has absolute advantages,and the parallel acceleration is more obvious as the computation area increases.

THREE-DIMENSIONAL CHARACTERISTICS AND HOMOGENIZATION OF ELECTROMAGNETIC FIELD IN SOFT-CONTACT CONTINUOUS CASTING MOLD

The three-dimensional electromagnetic characteristics and non-uniform distribution of electromagnetic field in soft-contact continuous casting mold have been analyzed by numerical simulation. The results show that the maximum electromagnetic flux density is found in front of slit; the electromagnetic flux density becomes large as the coil current and slit number increase. In a certain frequency range, the electromagnetic flux density increases with the increase of frequency and the frequency range is different with the change of azimuthal position along the inner wall of mold. The uniformity of electromagnetic field is influenced mainly by frequency and mold structure parameters. Increasing slit number and adjusting slit arrangement position can improve the electromagnetic flux density and the uniformity of electromagnetic field. For a soft-contact mold with 16 slits, when frequency is 20 kHz, the optimal slit arrangement parameter is a:b=1:2, c=0.

Three dimensional tectonic stress field in North China

According to the latest data of geological structure, geophysics, in-situ stress measurement and focal mechanism,3-D tectonic stress field model in North China is built and 3-D tectonic stress field pattern of North China aresimulated by finite element method. Then the overall characteristics and regional specific feature of North Chinaare studied. Finally, the influences of the valid dynamic boundary conditions of North China Block, active faultsand the inhomogeneity of crustal medium on tectonic stress field of North China are investigated.

SURFACE INTEGRAL OF THREE－DIMENSIONAL VELOCITY FIELD FOR SQUARE BAR DRAWING THROUGH CONICAL DIE

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Numerical study on three-dimensional flow field of continuously rotating detonation in a toroidal chamber

Gaseous detonation propagating in a toroidal chamber was numerically studied for hydrogen/oxygen/nitrogen mixtures. The numerical method used is based on the three-dimensional Euler equations with detailed finiterate chemistry. The results show that the calculated streak picture is in qualitative agreement with the picture recorded by a high speed streak camera from published literature. The three-dimensional flow field induced by a continuously rotating detonation was visualized and distinctive features of the rotating detonations were clearly depicted. Owing to the unconfined character of detonation wavelet, a deficit of detonation parameters was observed. Due to the effects of wall geometries, the strength of the outside detonation front is stronger than that of the inside portion. The detonation thus propagates with a constant circular velocity. Numerical simulation also shows three-dimensional rotating detonation structures, which display specific feature of the detonation- shock combined wave. Discrete burning gas pockets are formed due to instability of the discontinuity. It is believed that the present study could give an insight into the interest- ing properties of the continuously rotating detonation, and is thus beneficial to the design of continuous detonation propulsion systems.

Numerical simulation of recalescence of 3-dimensional isothermal solidification for binary alloy using phase-field approach

A accelerated arithmetic algorithm of the dynamic computing regions was designed,and 3-dimensional numerical simulation of isothermal solidification for a binary alloy was implemented.The dendritic growth and the recalescence of Ni-Cu binary alloy during the solidification at different cooling rates were investigated.The effects of cooling rate on dendritic patterns and microsegregation patterns were studied.The computed results indicate that,with the increment of the cooling rate,the dendritic growth velocity increases,both the main branch and side-branches become slender,the secondary dendrite arm spacing becomes smaller,the inadequate solute diffusion in solid aggravates,and the severity of microsegregation ahead of interface aggravates.At a higher cooling rate,the binary alloy presents recalescence;while the cooling rate is small,no recalescence occurs.

Cosmic Dark Energy from ‘t Hooft’s Dimensional Regularization and Witten’s Topological Quantum Field Pure Gravity

We utilize two different theories to prove that cosmic dark energy density is the complimentary Legendre transformation of ordinary energy and vice versa as given by E(dark) = mc2 (21/22) and E(ordinary) = mc2/22. The first theory used is based on G ‘t Hooft’s remarkably simple renormalization procedure in which a neat mathematical maneuver is introduced via the dimensionality of our four dimensional spacetime. Thus, ‘t Hooft used instead of D = 4 and then took at the end of an intricate and subtle computation the limit to obtain the result while avoiding various problems including the pole singularity at D = 4. Here and in contradistinction to the classical form of dimensional and renormalization we set and do not take the limit where and is the theoretically and experimentally well established Hardy’s generic quantum entanglement. At the end we see that the dark energy density is simply the ratio of and the smooth disentangled D = 4, i.e. (dark) = (4 -k)/4 = 3.8196011/4 = 0.9549150275. Consequently where we have ignored the fine structure details by rounding 21 + k to 21 and 22 + k to 22 in a manner not that much different from of the original form of dimensional regularization theory. The result is subsequently validated by another equally ingenious approach due mainly to E. Witten and his school of topological quantum field theory. We notice that in that theory the local degrees of freedom are zero. Therefore, we are dealing essentially with pure gravity where are the degrees of freedom and is the corresponding dimension. The results and the conclusion of the paper are summarized in Figure 1-3, Table 1 and Flow Chart 1.

Field-effect transistors based on two-dimensional materials for logic applications

Field-effect transistors （FETs） for logic applications, graphene and MoS2, are discussed. These materials have based on two representative two-dimensional （2D） materials, drastically different properties and require different consider- ations. The unique band structure of graphene necessitates engineering of the Dirac point, including the opening of the bandgap, the doping and the interface, before the graphene can be used in logic applications. On the other hand, MoS2 is a semiconductor, and its electron transport depends heavily on the surface properties, the number of layers, and the carrier density. Finally, we discuss the prospects for the future developments in 2D material transistors.

A contrastive study on the influences of radial and three-dimensional satellite gravity gradiometry on the accuracy of the Earth's gravitational field recovery

The accuracy of the Earth＇s gravitational field measured from the gravity field and steady-state ocean circulation explorer（GOCE）,up to 250 degrees,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij from the satellite gravity gradiometry（SGG） are contrastively demonstrated based on the analytical error model and numerical simulation,respectively.Firstly,the new analytical error model of the cumulative geoid height,influenced by the radial gravity gradient V zz and three-dimensional gravity gradient V ij are established,respectively.In 250 degrees,the GOCE cumulative geoid height error measured by the radial gravity gradient V zz is about 2 1/2 times higher than that measured by the three-dimensional gravity gradient V ij.Secondly,the Earth＇s gravitational field from GOCE completely up to 250 degrees is recovered using the radial gravity gradient V zz and three-dimensional gravity gradient V ij by numerical simulation,respectively.The study results show that when the measurement error of the gravity gradient is 3×10 12 /s 2,the cumulative geoid height errors using the radial gravity gradient V zz and three-dimensional gravity gradient V ij are 12.319 cm and 9.295 cm at 250 degrees,respectively.The accuracy of the cumulative geoid height using the three-dimensional gravity gradient V ij is improved by 30%-40% on average compared with that using the radial gravity gradient V zz in 250 degrees.Finally,by mutual verification of the analytical error model and numerical simulation,the orders of magnitude from the accuracies of the Earth＇s gravitational field recovery make no substantial differences based on the radial and three-dimensional gravity gradients,respectively.Therefore,it is feasible to develop in advance a radial cold-atom interferometric gradiometer with a measurement accuracy of 10 13 /s 2-10 15 /s 2 for precisely producing the next-generation GOCE Follow-On Earth gravity field model with a high spatial resolution.

On the Rotation of a Vector Field in a Four-Dimensional Space

Recently I published a paper in the journal ALAMT (Advances in Linear Algebra & Matrix Theory) and explored the possibility of obtaining products of vectors in dimensions higher than three [1]. In continuation to this work, it is proposed to develop, through dimensional analogy, a vector field with notation and properties analogous to the curl, in this case applied to the space IR4. One can see how the similarities are obvious in relation to the algebraic properties and the geometric structures, if the rotations are compared in spaces of three and four dimensions.

Numerical study of growth competition between twin grains during directional solidification by using multi-phase field method

A multi-phase field model is established to simulate the growth competition and evolution behavior between seaweed and columnar dendrites during directional solidification.According to the effects of surface tension and interfacial energy,we quantitatively analyze the influences of factors such as inclination angles,pulling velocity,and anisotropic strength on twin growth.The results demonstrate that the pulling velocity and anisotropic strength have an important influence on the morphology and evolution of the seaweed and dendritic growth.The low pulling velocity and anisotropic strength are both key parameters for maintaining the stable morphology of seaweed during competitive growth in a bicrystal,showing that the lateral branching behavior is the root of the dendrites that can ultimately dominate the growth.And it is clarified that the lateral branching behavior and lateral blocking are the root causes of the final dominant growth of dendrites.With the increase of anisotropy strength,the seaweed is eliminated fastest in case 1,the seaweed is transformed into degenerate dendritic morphology,and eliminates the seaweed by promoting the generation and lateral growth of the lateral branches of the dendrites.The increase of pulling velocity is to increase the undercooling of favorable oriented grain and accelerate the growth rate of dendrites,thus producing more new primary dendrites for lateral expansion and accelerating the elimination rate of unfavorable oriented grain.

Multi-phase field simulation of competitive grain growth for directional solidification

The multi-phase field model of grain competitive growth during directional solidification of alloy is established.Solving multi-phase field models for thin interface layer thickness conditions,the grain boundary evolution and grain elimination during the competitive growth of SCN-0.24-wt%camphor model alloy bi-crystals are investigated.The effects of different crystal orientations and pulling velocities on grain boundary microstructure evolution are quantitatively analyzed.The obtained results are shown below.In the competitive growth of convergent bi-crystals,when favorably oriented dendrites are in the same direction as the heat flow and the pulling speed is too large,the orientation angle of the bi-crystal from small to large size is the normal elimination phenomenon of the favorably oriented dendrite,blocking the unfavorably oriented dendrite,and the grain boundary is along the growth direction of the favorably oriented dendrite.When the pulling speed becomes small,the grain boundary shows the anomalous elimination phenomenon of the unfavorably oriented dendrite,eliminating the favorably oriented dendrite.In the process of competitive growth of divergent bi-crystal,when the growth direction of favorably oriented dendrites is the same as the heat flow direction and the orientation angle of unfavorably oriented grains is small,the frequency of new spindles of favorably oriented grains is significantly higher than that of unfavorably oriented grains,and as the orientation angle of unfavorably oriented dendrites becomes larger,the unfavorably oriented grains are more likely to have stable secondary dendritic arms,which in turn develop new primary dendritic arms to occupy the liquid phase grain boundary space,but the grain boundary direction is still parallel to favorably oriented dendrites.In addition,the tertiary dendritic arms on the developed secondary dendritic arms may also be blocked by the surrounding lateral branches from further developing into nascent main axes,this blocking of the tertiary dendritic arms has a random nature,which can have aninfluence on the generation of nascent primary main axes in the grain boundaries.

Three-dimensional Holographic Vector of Atomic Interaction Field(3D-HoVAIF) for the QSPR/QSAR of Polychlorinated Naphthalenes

Three-dimensional holographic vector of atomic interaction field（3D-HoVAIF） is used to describe the chemical structures of polychlorinated naphthalenes（PCNs）.After variable screening by stepwise multiple regression（SMR） technique,the liner relationships between gas-chromatographic relative retention time（RRT）,298 K supercooled liquid pressures（logPL）,n-octanol/air partition coefficient（logKOA）,n-octanol/water partition coefficient（logKOW）,aqueous solubilities（logSW）,relative in vitro potency values（-logEROD） of PCNs and 3D-HoVAIF descriptors have been established by partial least-square（PLS） regression.The result shows that the 3D-HoVAIF descriptors can be well used to express the quantitative structure-property（activity） relationships of PCNs.Predictive capability of the models has also been demonstrated by leave-one-out cross-validation.Moreover,the predicted values have been presented for those PCNs which are lack of experimentally physico-chemical properties and biological activity by the optimum models.

Investigation of dimensionality in superconducting NbN thin film samples with different thicknesses and NbTiN meander nanowire samples by measuring the upper critical field

We study superconducting properties of NbN thin film samples with different thicknesses and an ultra-thin NbTiN meander nanowire sample.For the ultra-thin samples,we found that the temperature dependence of upper critical field(Hc2)in parallel to surface orientation shows bending curvature close to critical temperature Tc,suggesting a two-dimensional(2D)nature of the samples.The 2D behavior is further supported by the angular dependence measurements of Hc2 for the thinnest samples.The temperature dependence of parallel upper critical field for the thick films could be described by a model based on the anisotropic Ginzburg-Landau theory.Interestingly,the results measured in the field perpendicular to the film surface orientation show a similar bending curvature but in a much narrow temperature region close to Tc for the ultra-thin samples.We suggest that this feature could be due to suppression of pair-breaking caused by local in-homogeneity.We further propose the temperature dependence of perpendicular Hc2 as a measure of uniformity of superconducting ultra-thin films.For the thick samples,we find that Hc2 shows maxima for both parallel and perpendicular orientations.The Hc2 peak for the perpendicular orientation is believed to be due to the columnar structure formed during the growth of the thick films.The presence of columnar structure is confirmed by transmission electron microscopy(TEM).In addition,we have measured the angular dependence of magneto-resistance,and the results are consistent with the Hc2 data.

Three dimensional K-Tz stress fields around the embedded center elliptical crack front in elastic plates

Through detailed three-dimensional （3D） finite element （FE） calculations, the out-of-plane constraints Tz along embedded center-elliptical cracks in mode I elastic plates are studied. The distributions of Tz are obtained near the crack front with aspect ratios （a/c） of 0.2, 0.4, 0.5, 0.6, 0.8 and 1.0. Tz decreases from an approximate value of Poisson ratio v at the crack tip to zero with increasing normalized radial distances （r/a） in the normal plane of the crack front line, and increases gradually when the elliptical parameter angle φ changes from 0° to 90°at the same r/a. With a/c rising to 1.0, Tz is getting nearly independent of φ and is only related to r/a. Based on the present FE calculations for Tz, empirical formulas for Tz are obtained to describe the 3D distribution of Tz for embedded center-elliptical cracks using the least squares method in the range of 0.2 ≤ a/c ≤ 1.0. These Tz results together with the corresponding stress intensity factor K are well suitable for the analysis of the 3D embedded centerelliptical crack from field, and a two-parameter K-Tz principle is proposed.

EXPERIMENTAL INVESTIGATION FOR THE EFFECT OF ROTATION ON THREE-DIMENSIONAL FLOW FIELD IN FILM-COOLED TURBINE

An experimental investigation of three-dimensional flow field in a film-cooled turbine model is carried out by using particle image velocimeter （PIV） in a low-speed wind tunnel. The effects of different blowing ratios （M=1.5, 2） on the flow field are studied. The experimental results reveal the classical phenomena of the formation of kidney vortex pair and secondary flow in wake region behind the jet hole. And the changes of the kidney vortex pair and the wake at different locations away from the hole on the suction and pressure sides are also studied. Compared with the flow field in stationary cascade, there are centrifugal force and Coriolis force existing in the flow field of rotating turbine, and these forces bring the radial velocity in the jet flow. The effect of rotatien on the flow field of the pressure side is more distinct than that on the suction side from the measured flow fields in Y-Z plane and radial velocity contours. The increase of blowing ratio makes the kidney vortex pair and the secondary flow in the wake region stronger and makes the range of the wake region enlarged.

An easy way to controllably synthesize one-dimensional Sm B_6 topological insulator nanostructures and exploration of their field emission applications

A convenient fabrication technique for samarium hexaboride（SmB6） nanostructures（nanowires and nanopencils） is developed, combining magnetron-sputtering and chemical vapor deposition. Both nanostructures are proven to be single crystals with cubic structure, and they both grow along the [001] direction. Formation of both nanostructures is attributed to the vapor-liquid-solid（VLS） mechanism, and the content of boron vapor is proposed to be the reason for their different morphologies at various evaporation distances. Field emission（FE） measurements show that the maximum current density of both the as-grown nanowires and nanopencils can be several hundred μA/cm^2, and their FN plots deviate only slightly from a straight line. Moreover, we prefer the generalized Schottky-Nordheim（SN） model to comprehend the difference in FE properties between the nanowires and nanopencils. The results reveal that the nonlinearity of FN plots is attributable to the effect of image potential on the FE process, which is almost independent of the morphology of the nanostructures.All the research results suggest that the SmB6 nanostructures would have a more promising future in the FE area if their surface oxide layer was eliminated in advance.

Effects of external fields on a two-dimensional Klein-Gordon particle under pseudo-harmonic oscillator interaction

We study the effects of the perpendicular magnetic and Aharonov-Bohm （AB） flux fields on the energy levels of a two-dimensional （2D） Klein Gordon （KG） particle subjected to an equal scalar and vector pseudo-harmonic oscillator （PHO）. We calculate the exact energy eigenvalues and normalized wave functions in terms of chemical potential param- eter, magnetic field strength, AB flux field, and magnetic quantum number by means of the Nikiforov Uvarov （NU） method. The non-relativistic limit, PHO, and harmonic oscillator solutions in the existence and absence of external fields are also obtained.

High-order harmonic generation spectrum of an excited one-dimensional Coulomb atom in an intense laser field

Response of the wave packet of a one-dimensional Coulomb atom to an intense laser field is calculated using the symmetrized split operator fast Fourier method. The high-order harmonic generation （HHG） of the initial state separately being the ground and excited states is presented. When the hardness parameter a in the soft Coulomb potential V（x） =-1√x^2＋α is chosen to be small enough, the so-called hard Coulomb potential V（x）=1/｜x｜ can be obtained. It is well known that the hard one-dimensional Coulomb atom has an unstable ground state with an energy eigenvalue of - 0.5 and it has no states corresponding to physical states in the true atoms, and has the first and second excited states being degenerate. The parity effects on the HHG can be seen from the first and second excited states of the hard one-dimensional Coulomb atom. The HHG spectra of the excited states from both the soft and hard Coulomb atom models are shown to have more complex structures and to be much stronger than the corresponding HHG spectrum of the ground state of the soft Coulomb model with a = 2 in the same laser field. Laser-induced non-resonant one-photon emission is also observed.

Atomic coherent states as energy eigenstates of a Hamiltonian describing a two-dimensional anisotropic harmonic potential in a uniform magnetic field

In this paper we find that a set of energy eigenstates of a two-dimensional anisotropic harmonic potential in a uniform magnetic field is classified as the atomic coherent states ｜τ） in terms of the spin values of j in the Schwinger bosonic realization. The correctness of the above conclusions can be verified by virtue of the entangled state 〈η｜ representation of the state ｜τ）.