Velocities In Different Directions Research Articles

Renormalization of Coulomb interactions in a system of two-dimensional tilted Dirac fermions

We investigate the effects of long-ranged Coulomb interactions in a tilted Dirac semimetal in two dimensions by using the perturbative renormalization-group method. Depending on the magnitude of the tilting parameter, the undoped system can have either Fermi points (type-I) or Fermi lines (type-II). Previous studies usually performed the renormalization-group transformations by integrating out the modes with large momenta. This is problematic when the Fermi surface is open, like type-II Dirac fermions. In this work, we study the effects of Coulomb interactions, following the spirit of Shankar\cite{Shankar}, by introducing a cutoff in the energy scale around the Fermi surface and integrating out the high-energy modes. For type-I Dirac fermions, our result is consistent with that of the previous work. On the other hand, we find that for type-II Dirac fermions, the magnitude of the tilting parameter increases monotonically with lowering energies. This implies the stability of type-II Dirac fermions in the presence of Coulomb interactions, in contrast with previous results. Furthermore, for type-II Dirac fermions, the velocities in different directions acquire different renormalization even if they have the same bare values. By taking into account the renormalization of the tilting parameter and the velocities due to the Coulomb interactions, we show that while the presence of a charged impurity leads only to charge redistribution around the impurity for type-I Dirac fermions, for type-II Dirac fermions, the impurity charge is completely screened, albeit with a very long screening length. The latter indicates that the temperature dependence of physical observables are essentially determined by the RG equations we derived. We illustrate this by calculating the temperature dependence of the compressibility and specific heat of the interacting tilted Dirac fermions.

Damage and wave propagation characteristics in thin GFRP panels subjected to impact by steel balls at relatively low-velocities

An experimental investigation was conducted to determine the damage and wave propagation characteristics in Glass Fibre Reinforced Polymer (GFRP) panels subjected to impact by steel balls at relatively low-velocities up to 91 ms−1. While maintaining the same impact energy level, the influence of ball mass on panel response was studied. The effects of composite lay-up sequence and successive impacts were also investigated. The wave propagation characteristics, including wave types, wave velocities, wave attenuations, and strain rates, were extracted from dynamic strain records measured at various locations on the panels. The results showed that, for the same level of impact energy, the small ball mass produced larger deformation and delamination than the large ball mass. Additionally, the resistance to impact was influenced by the composite lay-up sequence of similar fibre weight fraction. Test panels subjected to successive impacts showed an increase in cumulative delamination areas, whereas the tests indicated that successive impacts had a little effect on the perforation limit of the test panels. The impact velocity showed a pronounced influence on the measured peak strains and strain rates. The flexural wave was the predominant wave system, propagating at different velocities in different directions. In proximity to the impact site, both flexural wave and indentation predominated over the transient response. In addition to the flexural wave, impact induced low amplitude tensile longitudinal waves of high velocity.

Structure, electronic and mechanical properties of Ga1−xBxP alloys

The structural, electronic and mechanical properties of Ga1−xBxP ternary alloys are carried out by the first-principles based on density functional theory. We studied the effect of composition on the ground state properties such as lattice parameter, band gap and elastic modulus and anisotropy. The elastic anisotropy of Ga1−xBxP alloys have been described through different anisotropic factors. We analyzed elastic anisotropy by depicting the three-dimensional surface structure of elastic modulus. Due to the introduction of boron atoms, the Ga1−xBxP alloys become direct-gap semiconductors at x = 0.25, 0.50 and 0.75. At last, we calculated the average acoustic velocity in different directions and the Debye temperatures for the Ga1−xBxP alloys.

Wetting and electrowetting on corrugated substrates

Wetting and electrowetting (EW) on corrugated substrates are studied experimentally and theoretically in this paper. On corrugated substrates, because of the anisotropy of surface morphology, the droplet shows an elliptical shape and the spreading velocities in different directions are different. Spreading of a droplet is usually controlled not only by the surface tensions but also by hemi-wicking. Our experimental results indicated that liquids along the grooves propagate much faster than those in the direction vertical to the grooves. However, spreading in both directions obeys the same scaling law of l∼t4∕5. EW on corrugated substrates reveals some differences with that on smooth surfaces. The change of contact angles with an applied voltage follows a linear relationship in two stages instead of the smooth curve on flat surfaces. There exists a critical voltage which divides the two stages. The transition of a droplet from the Cassie state to the Wenzel state on corrugated substrates was also discussed. The extended EW equation was derived with the free energy minimization approach, and the anisotropic factor was introduced. From the extended equation, it is found that EW is affected by the anisotropic factor significantly. For the smooth surfaces, the extended EW equation will degenerate to the classical Lippmann-Young equation. Our research may help us to understand the wetting and EW of droplets on corrugated substrates and assist in their design for practical applications.

Geologic Evaluation of Kirkuk Underground Storage Project

Geologic evaluation of the Kirkuk underground was conducted by comparison of the geometric properties of the cavities derived from two surveys running during 1989 and 2015. The vertical cross sections of the cavities show that most cavities have shown that most cavities have irregular shape because of the presence of impurities in the salt bed that cause different leaching velocities in different directions. The relationship of the cavity roof with tilted salt bed was studied, that shows some of the cavities are not safe to store LPG.

The observation of AE events under uniaxial compression and the quantitative relationship between the anisotropy index and the main failure plane

In this paper, the P-wave velocities in different directions of sandstone samples under uniaxial compression are measured. The results indicate that the changes in the P-wave velocity in different directions are almost the same. In the initial stage of loading, the P-wave velocity exhibits a rising trend due to compaction and closure of preexisting fissures. As the stress increase, preexisting fissures are closed but induced fractures are not yet generated. The sandstone samples become denser and more uniform. The P-wave velocity remains in a steady state at a high level. In the late stage of loading, the P-wave velocity drops significantly due to the expansion and breakthrough of induced fractures. The P-wave velocity anisotropy index ε is analyzed during the process of loading. It can be observed that the change in the degree of wave velocity anisotropy can be divided into three stages: the AB stage, the BC stage and the CD stage, with a changing trend from decline to incline. In the initial stage of loading, the preexisting fissures have a randomized distribution, and the change is large-scale and uniform. The difference in each spatial point decreases gradually, and synchronization increases gradually. Thus, the P-wave velocity anisotropy declines. As the stress increases gradually, with the expansion and breakthrough of induced fractures, the difference in each spatial point increases. Before failure of rock samples, the violent change region of the rock samples' internal structure is focused on a narrow two-dimensional zone, and the rock samples' structural change is obviously local. Therefore, the degree of velocity anisotropy rises after declining, and it also has good corresponding relation among the AE count, the location of AE events and the degree of wave velocity anisotropy. The projection plane of the main fracture plane on the axis plane is recorded as M plane. Based on the AFF equation, for the CD stage, we analyze the quantitative relationship between the velocity anisotropy index ε and angle θ, which is the difference between the angle of the M plane and the X plane and the angle of the M plane and the Y plane from the theoretical point. The results indicate that 1ε and cotθ2 have good negative linear relationship that can be expressed as cotθ2=a∗1ε+b. According to experimental data, the linear fit of 1ε and cotθ2 is found, obtaining cotθ2=−0.04721ε+0.03, with a linear fit index of 0.908. From an experimental point of view, the linear relationship between 1ε and cotθ2 is verified. Through this research, we propose a new method for quantitatively predicting the main fracture occurrence position by P-wave velocity anisotropy. This work has an important significance for understanding buckling failure of rocks.

Asymmetry in Determinants of Running Speed During Curved Sprinting.

This study investigates the potential asymmetries between inside and outside legs in determinants of curved running speed. To test these asymmetries, a deterministic model of curved running speed was constructed based on components of step length and frequency, including the distances and times of different step phases, takeoff speed and angle, velocities in different directions, and relative height of the runner's center of gravity. Eighteen athletes sprinted 60 m on the curved path of a 400-m track; trials were recorded using a motion-capture system. The variables were calculated following the deterministic model. The average speeds were identical between the 2 sides; however, the step length and frequency were asymmetric. In straight sprinting, there is a trade-off relationship between the step length and frequency; however, such a trade-off relationship was not observed in each step of curved sprinting in this study. Asymmetric vertical velocity at takeoff resulted in an asymmetric flight distance and time. The runners changed the running direction significantly during the outside foot stance because of the asymmetric centripetal force. Moreover, the outside leg had a larger tangential force and shorter stance time. These asymmetries between legs indicated the outside leg plays an important role in curved sprinting.

The flow behavior of liquid Li in Cu micro-channels

The flow properties of liquid in microchannel have received more attention for their wide applications in different fields. Up to now, little work has focused on the flow behaviors of liquid metals. Recently, liquid lithium (Li) has been considered as one of the candidate plasma-facing materials (PFMs) because of its excellent properties in fusion reactor applications. Considering an accident condition, liquid Li may contact Cu components and erode them, which may cause a serious disaster. The study of the flow properites of liquid Li in Cu microchannel is crucial for the safe application of liquid Li working as a PFM. With the method of non-equilibrium molecular dynamics simulations, in this paper we investigate the flow behavior of liquid Li flowing in Cu microchannels. The density and velocity distributions of Li atoms are obtained. The influence of the dimension of Cu microchannel on the flowing behavior of liquid Li is studied. Comparative analyses are made in three different fluid-solid interfaces, i.e., Li-Cu(100), Li-Cu(110) and Li-Cu(111), respectively. Results show that the density distributions of liquid Li near the interface present an orderly stratified structure. Affected by a larger surface density, a more obviously stratification is found when Li atoms are near the fluid-solid interfaces of Li-Cu(100) and Li-Cu(111) and a wider vacuum gap appears between Li atoms and Cu(111) interface. When Li atoms are near the Li-Cu(110) interface, a lower stratification can be found and an alloy layer appears at Li-Cu(110) interface. Because of its lower surface density, Li atoms spread into the bulk Cu more easily. However, the density distributions have little difference when Li atoms are close to the same fluid-solid interface but with different flow directions. The velocity of Li atoms in microchannel has a parabolic distribution. Because there exists a wider vacuum gap and stratified structure, the Li atoms closed to the Li-Cu (111) interface have the largest velocity. Closed to the Li-Cu (110) interface, Li atoms have the smallest velocity because of the alloy layer and the lower stratified structure. Owing to the diversity of the atomic configurations of Cu (110) face, the liquid Li atoms flow with diverse velocities in different directions on the Li-Cu (110) interface. It is also found that the magnitude of flowing velocity of liquid Li is proportional to the square of microchannel dimension and increases with it. When liquid Li is flowing on the Li-Cu(100) interface, the simulation result reveals that the relationship between microchannel dimension and the largest velocity of Li atoms is in good agreement with Navier-Stokes theory result. It is noteweathy that the present result is smaller than the theoretical result when a negative slip occurs at the Li-Cu(110) interface. In contrast, the result is greater than the theoretical result in the presence of a positive slip at Li-Cu(111) interface.

Lattice stabilities, mechanical and thermodynamic properties of Al3Tm and Al3Lu intermetallics under high pressure from first-principles calculations**Project supported by the Scientific Technology Plan of the Educational Department of Liaoning Province and Liaoning Innovative Research Team in University, China (Grant No. LT2014004) and the Program for the Young Teacher Cultivation Fund of Shenyang University of Technology, China (Grant No. 005612).

The effects of high pressure on lattice stability, mechanical and thermodynamic properties of L12 structure Al3Tm and Al3Lu are studied by first-principles calculations within the VASP code. The phonon dispersion curves and density of phonon states are calculated by using the PHONONPY code. Our results agree well with the available experimental and theoretical values. The vibrational properties indicate that Al3Tm and Al3Lu keep their dynamical stabilities in L12 structure up to 100 GPa. The elastic properties and Debye temperatures for Al3Tm and Al3Lu increase with the increase of pressure. The mechanical anisotropic properties are discussed by using anisotropic indices AG, AU, AZ, and the three-dimensional (3D) curved surface of Young’s modulus. The calculated results show that Al3Tm and Al3Lu are both isotropic at 0 GPa and anisotropic under high pressure. In the present work, the sound velocities in different directions for Al3Tm and Al3Lu are also predicted under high pressure. We also calculate the thermodynamic properties and provide the relationships between thermal parameters and temperature/pressure. These results can provide theoretical support for further experimental work and industrial applications.

Prediction of novel phase of silicon and Si–Ge alloys

The structural, thermodynamic, elastic, anisotropic and electronic properties of P2221-Si have been studied using first-principles calculations. The elastic constants are satisfied with mechanical stability criteria. The mechanical anisotropy is predicted by anisotropic constants Poisson's ratio, shear modulus, Young's modulus and three dimensional curved surface of Young's modulus. These results show that P2221-Si and Si–Ge alloys are anisotropic. The sound velocities in different directions and Debye temperature for P2221-Si and Si–Ge alloys are also predicted. Electronic structure study shows that P2221-Si is an indirect semiconductor with band gap of 0.90eV. In addition, the band structures of Si–Ge alloys are investigated in this paper. Finally, we also calculate the thermodynamics properties and obtained the relationships between thermal parameters and temperature.

Reliability analysis of in-situ stress measurement using circumferential velocity anisotropy

In-situ stress measurement for deep reservoir formation is difficult in terms of security, reliability and technique. Acoustic velocity anisotropy test is a basic method for stress measurement of rock cores, which is based on the distribution of acoustic velocity in different directions around rock cores. The heterogeneity of core samples, such as fractures and gravel contained, can also lead to wave velocity anisotropy. Therefore, the corresponding reliability evaluation method is established to exclude some other anisotropy factors caused by non-tectonic stresses. In this paper, the reliability of testing results is evaluated from three aspects, i.e. phase difference, anisotropy index and waveform, to remove the factors caused by non-tectonic stresses.

Phase stability and anisotropic elastic properties of the Hf–Al intermetallics: A DFT calculation

The first-principles calculations based on density-functional theory were performed to investigate the structural properties, phase stability, and elastic properties of several selected Hf–Al intermetallics. The calculated formation enthalpies show that HfAl2 is the most stable in these intermetallics. The predicted elastic moduli results indicate that the order in the degree of elastic anisotropy is HfAl>Hf2Al>D022-HfAl3>Hf3Al2>Hf5Al3>Hf2Al3>D023-HfAl3>L12-HfAl3>Hf4Al3>HfAl2. By using the procedure of Brugger, the calculated sound velocities in different directions for the Hf–Al intermetallics are anisotropic. The Debye temperatures were also estimated from the elastic constant evaluations of Hf–Al intermetallics.

Computational investigations of mechanical and vibrational properties of quaternary semiconductor alloys MgxZn1-xSySe1-y

Physical properties like elastic constants, pressure derivative of bulk modulus, pressure derivative of elastic constants and acoustic wave velocities in different directions for Mg x Zn 1-x S , Mg x Zn 1-x Se and ZnS y Se 1-y semiconductor ternary alloys and Mg x Zn 1-x S y Se 1-y quaternary alloys with different concentrations of x and y are studied using our previously proposed potential based on the pseudopotential formalism. It is noticed from the present study that the physical properties under investigations depend on concentrations x and y of constitute compounds. The present results of various physical quantities of compounds presented here are compared with the available experimental data and other theoretical estimations and showed roughly reasonable agreement. The numerical values of same quantities for ternary alloys and MgZnSSe quaternary alloys were reported first time and hence such results may be useful for comparison purpose in future with either the experimental or the theoretical work.

First-principles investigation on the mechanical, vibrational and thermodynamics properties of AuCu3-type X3Sc (X = Al, Ga, In) intermetallic compounds

First-principles calculation is performed to systematically study the structural stabilities, mechanical properties, vibrational and thermodynamic properties for AuCu3-type Al3Sc, Ga3Sc and In3Sc compounds. The calculated formation enthalpy and cohesive energy indicate that these compounds all have the high thermodynamics stability. The elastic constants are satisfied with mechanical stability criteria. The mechanical parameters predict that Al3Sc has higher hardness than other two compounds. In the meantime, Al3Sc possess brittle nature, but Ga3Sc and In3Sc are ductile. The mechanical anisotropy is predicted by anisotropic constants AG, AU, AZ and 3D curved surface of Young’s moduli. These results show that Al3Sc is isotropic, but Ga3Sc and In3Sc are elastically anisotropic. The sound velocities in different directions and Debye temperature for Al3Sc, Ga3Sc and In3Sc are also predicted. The calculated vibrational properties indicate that three compounds would keep the dynamical stability in AuCu3 structure. Finally, we also calculate the thermodynamics properties and give out the relationships between thermal parameters and temperature.

Initial surface disturbance on a shear current: The Cauchy-Poisson problem with a twist

We solve for the first time the classical linear Cauchy-Poisson problem—the time evolution of an initial surface disturbance—when a shear current of uniform vorticity is present beneath the surface. The solution is general, including the effects of gravity, surface tension, and constant finite depth. The particular case of an initially Gaussian disturbance of width b is studied for different values of three system parameters: a “shear Froude number” \documentclass[12pt]{minimal}\begin{document}$S\sqrt{b/g}$\end{document}Sb/g (S is the vorticity), the Bond number and the depth relative to the initial perturbation width. Different phase and group velocity in different directions yield very different wave patterns in different parameter regimes when the shear is strong, and the well-known pattern of diverging ring waves in the absence of shear can take on very different qualitative behaviours. For a given shear Froude number, both finite depth and nonzero capillary effects are found to weaken the influence of the shear on the resulting wave pattern. The various patterns are analysed and explained in light of the shear-modified dispersion relation.

Moving Target Travelling Salesman Problem using Genetic Algorithm

ABSTRACT In this paper, the Moving Target Travelling Salesman Problem (MTTSP) is described. In MTTSP, several sites are required to be visited which are moving with constant velocity in different directions. The distance of the sites from origin, velocity and the angle of movement are known in advance. The goal is to find the fastest tour starting and ending at the origin which intercepts all the sites. The method implemented using genetic algorithm approach on the various data sets and the results are compared with greedy approach. General Terms Algorithm, complexity, Keywords Genetic Algorithm, Evolutionary Computation, Travelling Salesman Problem, Moving Target Travelling salesman problem, intercept, greedy method. 1. INTRODUCTION The traveling salesman problem (TSP) was originated by the studies of two mathematicians Sir William Rowam Hamilton from Ireland and Thomas Penyngton Kirkman from Briton in the 18th century. The general form of the TSP is believed to be studied further Kalr Menger in Vienna and promoted by Hassler, Whitney & Merrill at Princeton[2]. A detailed description about the connection between Menger & Whitney, and the development of the TSP can be found in Schrijver, 2005[3]. Given a set of cities and the cost of travel (or distance) between each possible pairs, the objective of the TSP is to find the best possible way of visiting all the cities and returning to the starting point that minimize the travel cost (or travel distance)[1]. Given

Study on Flow Velocity Field of Local Scour around the Pier Protected by the Sediment Storage Dam

Aimed at the representative project which is protected by the downstream sediment storage dam, three dimensional flow velocity field in local scour area around the separate bridge pier via physical model test was studied. The influences of shaping the eroded pit caused by the velocities in different directions were analyzed. The distribution results of flow velocity field in local scour pit near the pier protected by the sediment storage dam, deduced from the paper, will provide references for the defensive design of bridge projects.

Investigations on the structural, elastic and electronic properties of the orthorhombic Zirconium–Nickel alloy under different pressure

A theoretical study of structural, elastic, mechanical and electronic properties of the orthorhombic crystal ZrNi is presented for the first time by density functional theory method with the ultrasoft pseudopotential scheme in the frame of the generalized gradient approximation (GGA). The lattice constant, elastic constants and their pressure dependence are calculated. The bulk modulus, shear modulus, and Poisson’s ratio for ideal polycrystalline ZrNi are also successfully achieved. The shear and bulk modulus anisotropic factors are obtained from the single crystal elastic constants. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal. Band structure and density of states are also given in this work, which are in good agreement with available theoretical data.

Measurement Method of Graviton Velocity and Thought on Correcting Lorentz Transformation——The Superluminal Neutrino’s Influence on Special Relativity and Other Physical Theories

After discovery of the superluminal particle and consideration on development of contemporary physical theory research, also on the existing errors and omissions, the principle of constant light speed is found not a necessary condition in derivation of Lorentz Transformation; instead, this thesis proposes the velocity of graviton may feature superluminal, constant velocity in different directions, and independence of inertial reference frame speeds. This is an optional thought of correction. According serial hypothesis, an equation of graviton’s motion trace, i.e., the central curve of nebula density, is established for spiral galaxy. Thus we gain the method to measure velocity of graviton. If to totally avoid problem of limit speed, we have to search for independent of inertia frames, and relevant to space-time properties. Regarding current difficulties of singular points in the Theory of Limited Universe, this thesis points out that the document [1] is the best solution to these difficulties.

Free vibrations of drill strings in hyper deep vertical bore-wells

This paper considers the problems on investigation of the dynamic bending of elongated drill string tubes studied with allowance made for destabilizing effects of the longitudinal non-uniform preloading, action of torque, inertia forces of rotation and internal flows of washing liquid (mud). As a result of the completed analysis, natural wave and vibration modes are constructed, their frequencies are calculated. It is shown through the study of appropriate dispersion equations that free bending vibrations of unbounded rods can be realized only in the modes of regular dextral and sinistral spiral waves propagating with different velocities in different directions. The modes of free vibrations of the bounded drill strings possess more complicated irregular spiral shapes.