Direction Cosines Research Articles

Electron-acoustic waves by (modified) Zakharov–Kuznetsov equation and their multi-dimensional instability in the auroral zone

The feature of electron-acoustic waves (EAWs) in a magnetized plasma composed of stationary ions, nonthermal electrons and cold electron fluids is presented. The Zakharov–Kuznetsov (ZK) equation and modified Zakharov–Kuznetsov (mZK) equation are derived via reductive perturbation technique. The solitary wave solutions of ZK and mZK equations and the corresponding growth rates of multi-dimensional instability are given via small k perturbation method. The instability criterion and growth rate rely on obliqueness, magnetic field strength, temperature and density ratios of the hot-to-cold electron species, nonthermal parameter and direction cosines. It is apparent that, in the dayside auroral zone, there only exists negative potential solitary waves, and when the external magnetic field is larger and obliqueness is smaller, EAWs by mZK equation are more unstable than that by ZK equation. The results are beneficial to understand different nonlinear characteristics of unstable electrostatic disturbances in laboratory and space plasmas.

Directional Analytic Discrete Cosine Frames

Block frames called <i>directional analytic discrete cosine frames</i> (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

A Sweep-Based Low-Rank Method for the Discrete Ordinate Transport Equation

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and computational costs. This work extends the low-rank scheme for the time-dependent radiation transport equation in 2-D and 3-D Cartesian geometries with discrete ordinates discretization in angle (SN method). The reduced system that evolves on a low-rank manifold is constructed via an unconventional basis update and Galerkin integrator to avoid a substep that is backward in time, which could be unstable for dissipative problems. The resulting system preserves the information on angular direction by applying separate low-rank decompositions in each octant where angular intensity has the same sign as the direction cosines. Then, transport sweeps and source iteration can efficiently solve this low-rank-SN system. The numerical results in 2-D and 3-D Cartesian geometries demonstrate that the low-rank solution requires less memory and computational time than solving the full rank equations using transport sweeps without losing accuracy.

2D-DOD and 2D-DOA Estimation Using Sparse L-Shaped EMVS-MIMO Radar

It is well-known that EMVS-MIMO radar is an emerging technique that it allows for 2D-DOD and 2D-DOA estimation. Unfortunately, existing array geometries on the EMVS-MIMO radar can rarely reach a good compromise between the estimation accuracy and the computational burden. This paper is aimed at proposing an L-shaped sparse array topology for a bistatic EMVS-MIMO radar, whose inter-element distance is much larger than half-wavelength. A fast algorithm proposed herein to estimate the 2D-DOD and 2D-DOA. Firstly, the direction cosine estimates are obtained via the rotational invariance properties of the sparse subarrays, which are ambiguous yet exhibit high-resolution. Thereafter, the direction cosine estimates are achieved via the vector cross-product of the normalized Poynting vectors, which are unambiguous but have low-resolution. The unambiguous high-resolution direction cosine estimates are determined by combining the previous results, following which the 2D-DOD and 2D-DOA can be easily recovered. It is shown that the proposed framework can obtain a better accuracy of estimation than the other existing methods. Moreover, it is more flexible than the current sparse array methodologies. Finally, the theoretical derivations have been validated by simulation results.

Rotation vector and directional cosine matrix in problems of satellite attitude control

For many years, three rotation angles of moving vehicles: roll, pitch, and yaw have been used for attitude determination and control. However, in the last years due to appearance of new airspace applications such as strapdown inertial navigation systems (INS) and spacecrafts new quaternion (Q)-based methods appeared. Conventional and new modern methods have some features that can attract or repel developers. Nevertheless, some new techniques of classical mechanics can be tried to use them for vehicle attitude determination and control purposes with the expectation to get more effective results. The article presents a rotation vector (RV) and proposes a way of using it for satellite attitude control. This method is compared with conventional method of attitude control using three rotation angles. The ratio is shown between RV control and modern method of satellite attitude control using quaternion. Analytical and simulation results are presented.

Expressions of Euler Angles as Functions of the Directional Cosines of Three-Orthogonal Axes in Rigid Body Kinematics - II

Abstract In the rigid body kinematics, the position of the mobile frame in relation to the fixed frame is given by the base-change matrix. The elements of this orthogonal matrix are given by the Euler’s angles. This paper establishes the reverse link relations between the Euler’s angles and the elements of the base-change matrix (directional cosines).

Nonlinear dynamics in the jupiter magnetosphere: implications of dust-acoustic cnoidal mode

Different types of waves and their nature in the Jovian middle magnetosphere are still not clear or specified. For this purpose, a generalized hydrodynamic model for an arbitrary amplitude dust-acoustic waves is built for true Jovian magnetosphere. The plasma system consists of positive dust grains, Maxwellian ions and electrons. An evolution equation containing a Sagdeev potential is derived, and its numerical analysis is presented. Unexpectedly, the given data yielded cnoidal waves only with positive potential. The effect of the external magnetic field, Mach number, and directional cosine parameters are studied and manipulated. We think that the present results are important in realizing the main waves in the Jovian magnetosphere, and the possible correlation to its particles’ stability and pole acoustic waves.

SINS attitude algorithm based on moving-window overdetermined polynomial fitting of gyro outputs

The attitude algorithm is the most important part of the whole strapdown inertial navigation processing. It calculates the attitude of certain parameterization by integrating the gyro outputs or measurements in a specifically tailored way according to the attitude kinematic differential equation. The measurements or some angular velocity models obtained by fitting these measurements are often assumed free of errors in order to assess the numerical errors only. However, the gyro outputs and hence the models from them are by no means free of measurement errors. It is more often than not that the measurement errors dominate the numerical ones in practice. In this study, with coping with the measurement errors as the focus, we aim to improve the angular velocity model which is used as input in an attitude integration algorithm. This is achieved by exploiting the potential of overdetermined least-squares polynomial fitting. In order to avoid reducing the update rate by incorporating more measurements, the moving window trick is employed to re-use measurements in the previous update interval. The conventional attitude algorithm with second-order approximation in solving the differential equation of the equivalent rotation vector is employed as an example; however, the proposed method can be readily applied to other parameterizations such as direction cosine matrix, quaternion or Rodrigues parameters, and other high order approximations in solving the differential equation widely studied recently.

A general method for rotational averages

The theory of nonlinear spectroscopy on randomly oriented molecules leads to the problem of averaging molecular quantities over random rotation. We solve this problem for arbitrary tensor rank by deriving a closed-form expression for the rotationally invariant tensor of averaged direction cosine products. From it, we obtain some useful new facts about this tensor. Our results serve to speed the inherently lengthy calculations of nonlinear optics.

Optimization of gratings in a diffractive waveguide using relative-direction-cosine diagrams.

Designing diffractive waveguides for head-mounted displays requires wide-angle conical diffraction analysis of multiple gratings. In this work, diffractive waveguide design using the relative direction cosine space, which extends the direction cosine space to a relative space involving refractive indices and can describe grating diffraction through various media, is demonstrated. A diffractive waveguide was fabricated with grating periods of 382 and 270 nm, which generated a monochromatic virtual image image in green light (520 nm). The maximum field of view was measured as 39° with 0.5° deviation from the center of view.

Simultaneous analyses of fluorescence decay and anisotropy decay in green fluorescent protein dimer from jellyfish Clytia gregaria: FRET and molecular dynamics simulation

Structural and dynamic behaviors of the green fluorescent protein dimer from jellyfish Clytia gregaria (cgGFP) were investigated by means of molecular dynamics (MD) simulation. Both neutral and ionic forms of the chromophore, p-hydroxybenzylideneimidazolinone (GYS) were considered. The partial atomic charges of the chromophore were derived by BCC and RESP approaches. The structures were compared between the anionic and neutral cgGFP, and between the two subunits (Sub A and Sub B) of the protein dimer. The observed fluorescence intensity and anisotropy decays were further analyzed with theoretical expressions by employing the atomic coordinates of neutral cgGFP obtained by MD simulation. It was assumed that the fluorescence quenching of GYSA and GYSB is ascribed to HB formations between heteroatoms of GYSs and nearby amino acids. Excellent agreement between the observed and calculated intensity decays, and the observed and calculated anisotropy decays were obtained with RESP1 model. The agreements were better in RESP model than those in BCC one. Mean quenching constants of GYSA and GYSB were 0.27 and 0.59 ns−1 overall MD snapshots with RESP1. Mean value of square of direction cosine between the two transition moments of GYSs was 0.74, and that of square of orientation factor was 0.53, and the FRET rates from GYSA to GYSB, and from GYSB to GYSA were 0.87 and 1.87 ns−1.

On the wave instability of multi component electron acoustic plasma

The stability and instability properties of electron acoustic (EA) waves which was recorded during Viking orbit 1188 in the dayside auroral zone have been theoretically investigated in this manuscript. The system under consideration is a magnetized collisionless plasma consisting of cold electron fluid, non-thermal hot electrons, electron beam and a stationary ions. The reductive perturbation theory have been used to get Zakharov–Kuznetsov (ZK) equation, obliquely propagating solitary wave solution have been derived. Nonthermality population parameter μ, densities ratios (α, β), temperatures ratios (θ, σ) and obliqueness angle ϑ affect the amplitude and width of EA solitary waves. The small k perturbation technique have been applied to ZK equation to study instability criterion in this system and finally the growth rate of the predicted instability dependence on the plasma parameters have been introduced, it was shown that plsma parameters σ, α, μ, β and the direction cosine (ι ζ , ι η ) affects the instability growth rate Γ.

Fuzzy vector quantization with a step-optimizer to improve pattern classification

The paper proposes a novel supervised algorithm for data classification based on fuzzy vector quantization. The novelty here lies in including an optimization procedure to determine the step size of the quantization process. Adoption of fuzzy space for data exploration eliminates the problem of class-overlapping, while dealing with high dimensional non-linear data. In the proposed approach, the input data are first been transformed from the Euclidean space to the fuzzy space with three membership grades. Next, we have used uniform manifold approximation algorithm (UMAP), for projecting the data in visual space by selection of the most contrasting features from the fuzzy vectors. Then these features are passed through a quantization step with a novel step-optimization technique. Optimizing the quantization step and making it independent of data sets significantly speeds up the process. As the class information of all the feature vectors obtained by UMAP is known, majority voting principle has been used to locate the class-centroids in the subsequent step which in turn represent the class labels of the test samples. In test phase, after obtaining the test vectors, the Hyperspherical Direction Cosines (HDC) between the test vectors and the previously obtained class-centroids are evaluated. The test sample is finally assigned that class label where the sum of absolute differences (SAD) of these direction cosines is minimum. We have validated our classifier on various benchmark data sets and achieved higher accuracy with significantly low computation time than the existing state-of-the-art algorithms.

An algorithm for solving of Euler parameters differential equations system

The design an optimal numerical method for solving a system of ordinary differential equations simultaneously is described in this paper. System of differential equations was represented by a system of linear ordinary differential equations of Euler’s parameters called quaternions. The components of angular velocity were obtained by the experimental way. The angular velocity of the centre of gravity was determined from sensors of acceleration located in the plane of the centre of gravity of the machine. The used numerical method for solving was a fourth-order Runge-Kutta method. The stability of solving was based on the orthogonality of a direct cosine matrix. The numerical process was controlled on every step in numerical integration. The algorithm was designed in the C# programming language.

Construction of Structural Geological Model Using Monte Carlo Simulation

To optimize the prediction of structural geological conditions in the underground as of data collected at the surface, due to the usual great uncertainties involved, we discuss new perspectives for the construction of structural geological models, bearing in mind the common doubts involved and their implications in the safety of infrastructure works, mining, etc. This paper presents a statistical simulation applied to structural geological measures (dip-dip direction) obtained from schists during the design and construction of civil works through a correlation between surface data with different depth levels. Angular structural geological measures of joints and foliations converted in direction cosines were subjected to the PERMANOVA test to verify the amplitude of differences at different depth levels. The asymptotic results allowed to determine regions of confidence built around centroids through statistical simulation, allowable consistency was considered in regions where the differences in the simulated values were small enough from a practical point of view, considering that the difference between joint structures and foliation structures is smaller in the former. The foliation is a characteristic structure of rock deformation just like the joints.

ВЫПИСЫВАНИЕ ФОРМУЛ ВЫЧИСЛЕНИЯ СИЛ В СОЧЛЕНЕНИЯХ МАНИПУЛЯТОРОВ В СТАТИКЕ

The problem of bulkiness of mathematical models of manipulative systems of industrial robots is solved. Here we consider formulas for calculating static reactions in joints and formulas for active forces that balance the forces of gravity acting on the manipulator's bodies in its stationary state. The manipulator can be in such a state when it is before capturing the object of manipulation and releasing it, or when it is performing some assembly operations, or it is during spot welding and in slow (quasi-static) arc-welding and painting processes. Aim. The aim is to derive general recur-rence and finite formulas for calculating the reaction forces in joints and their projections to the ax-es of the coordinate system rigidly connected with the selected body. Express the formulas of force projections in terms of guiding cosines and justify their optimality in terms of the minimum of arithmetic operations. Derive general inverse recurrence formulas for writing out the guide cosines of the axes associated with the moving bodies of the coordinate system with respect to the stationary coordinate system. Research methods. The methods of research relate to vector mechanics and sys-tems analysis, and the algorithmization of calculations by reducing them to the use of recurrent formulas. Results. A systematic analysis of general formulas, in which all possible regular expres-sions are highlighted which are corresponding unambiguously to the kinematic parameters of ma-nipulators, is performed. These regular expressions are used in software for analytical modeling of manipulator, in particular, for the analytical solution of problems of statics of a manipulator. The method of analytical verification of the prescribed formulas is described. The tasks of writing out optimal formulas for calculating the projections of static reaction forces in joints have been solved. And the tasks of writing out optimal formulas for calculating active forces in progressive joints of universal manipulators with six degrees of freedom, operating in Cartesian, cylindrical, spherical and angular coordinate systems, have been solved also. Analytical verification of the derived equations of stat-ics is performed. Examples of the reuse of the derived formulas for manipulators with the same kin-ematic schemes of their subsystems. Conclusion. Expressions of the equations of statics of manipu-lators through the guide cosines of the axes of the associated coordinate systems of their bodies al-low us to write these equations through the known parameters of body orientation. The recurrent formulas for calculating directional cosines allows to use recursive functions in their software im-plementation, i.e. to increase the computational efficiency of the software.

Computational study of the geometric properties governing the linear mechanical behavior of fiber networks

Materials whose microstructure is formed by random fiber networks play an important role both in biology and engineering. So far, it still remains unclear which geometric properties of the fiber network determine the macroscopic mechanical properties of such materials. This paper presents a computational study based on a large number of representative volume elements of random fiber networks. Our study reveals that the linear mechanical properties of fiber networks (i.e., Young’s modulus and Poisson’s ratio) are largely determined by only four scalar key descriptors. These are the number of fibers per volume, the mean node valency, the mean fiber length, and the mean direction cosine between fibers adjacent to the same node. Number of fibers per volume and node valency were found to be responsible for around 80% of the variance of the mechanical properties, making them the two by far dominant microstructural descriptors. In the part of the configuration space covered by our study, we observed a linear or quadratic relationship between the above four scalar microstructural descriptors and the Young’s modulus. For the number of fibers per unit volume we propose a theoretical explanation for this simple relation.

Strain induced second-order Jahn–Teller reconstruction and magnetic moment modulation at monovacancy in graphene

Using density functional theory simulations, we examine the electronic structure of an isolated monovacancy defect in graphene under symmetry-breaking deformation. Results show that the defect experiences a second-order Jahn–Teller reconstruction at a critical strain of 1.7%. It stabilizes the orientation of the JT bond relative to the loading direction and breaks the threefold degeneracy of the defect structure. We call it Jahn–Teller re-reconstruction (JTRR), and it is mechanically reversible. The reversibility and stabilization of the orientation depend on the direction cosine between the JT bond and the loading direction. Also, a change in the loading direction by 90° can change the orientation of the JT bond by 120°. An atomic-scale analysis suggests that the maximum bond force arising from “the derivative of the kinetic energy of electrons” defines the critical strain. JTRR alters the electron occupation in the individual electronic orbitals at the defect site. The electronic charge redistribution and the density of states at the defective sites reveal that the pz orbitals dominate the reconstruction process. Furthermore, JTRR changes the magnitude of the magnetic moment at the defective site from 1.36 μB to 1.22 μB. This unravels a new way of controlling the magnetic behavior of monovacancy by applying symmetry-breaking mechanical strain. Results also show that passivation of the dangling bond can subside or eliminate the reconstruction process depending on the number of valence electrons available in the passivating atom.

Wireless Propagation Multipaths using Spectral Clustering and Three-Constraint Affinity Matrix Spectral Clustering

This study focused on spectral clustering (SC) and three-constraint affinity matrix spectral clustering (3CAM-SC) to determine the number of clusters and the membership of the clusters of the COST 2100 channel model (C2CM) multipath dataset simultaneously. Various multipath clustering approaches solve only the number of clusters without taking into consideration the membership of clusters. The problem of giving only the number of clusters is that there is no assurance that the membership of the multipath clusters is accurate even though the number of clusters is correct. SC and 3CAM-SC aimed to solve this problem by determining the membership of the clusters. The cluster and the cluster count were then computed through the cluster-wise Jaccard index of the membership of the multipaths to their clusters. The multipaths generated by C2CM were transformed using the directional cosine transform (DCT) and the whitening transform (WT). The transformed dataset was clustered using SC and 3CAM-SC. The clustering performance was validated using the Jaccard index by comparing the reference multipath dataset with the calculated multipath clusters. The results show that the effectiveness of SC is similar to the state-of-the-art clustering approaches. However, 3CAM-SC outperforms SC in all channel scenarios. SC can be used in indoor scenarios based on accuracy, while 3CAM-SC is applicable in indoor and semi-urban scenarios. Thus, the clustering approaches can be applied as alternative clustering techniques in the field of channel modeling.

Supernonlinear wave and multistability in magneto-rotating plasma with (r, q) distributed electrons

Supernonlinear ion-acoustic waves (IAWs) and their multistability are studied under the Zakharov-Kuznetsov (ZK) and modified ZK (mZK) equations in a rotating magnetized electron-ion plasma that consists of generalized (r, q)-distributed electrons. Bifurcation of IAW is presented through phase plane analysis and existence of IAW solutions is also shown through graphs of potential energy function. Supernonlinear wave exists for system corresponding to mZK equation with nonlinear periodic and solitary wave solutions. Effects of strength (q) and flatness (r) of the (r, q)-distribution on IAW solutions are shown along with other parameters, such as speed of the wave (V) and direction cosine (n). Furthermore, introducing an extraneous periodic perturbation, multistability property of the perturbed dynamical system is examined, and it is displayed using phase space and time series plots. Features of coexisting trajectories are examined for different values of spectral indices (r, q). Existence of two different types of chaos are supported through Lyapunov exponent graphs. Here, acceptable parametric values of spectral indices (r, q) are considered from data values of slow solar wind streams. Hence, supernonlinear periodic IAW and multistability property under the modified ZK equation are reported for the first time in rotating electron-ion magnetized plasma with (r, q)-distributed electrons. This study is applicable to understand supernonlinear wave features and multistability property of ion-acoustic wave motions featured in slow solar wind streams.