A Simplified Method for Predicting Tunneling-Induced Ground Movement considering Nonuniform Deformation Boundary

Stochastic medium (SM) theory is a practical method in ground settlement prediction, while its nonintegrable double integral form makes the solution process complicated. A simplified analytical solution based on the SM theory is developed to predict the ground movement in tunneling excavation. With the simplified solution, the ground movement for single tunnel and twin tunnels could be predicted based on the gap parameter G and influence angle β. A feasible approach is developed to estimate these two parameters using the maximum ground settlement Smax and tunnel design parameters, including tunnel depth H and diameter R. The proposed approach can be used to predict the ground movement curve for both circular and noncircular cross section tunnels. To validate its accuracy, the results predicted by the simplified procedure are compared with those obtained by the SM theory and measured in situ. The comparisons show that the current results agree well with those obtained by the SM theory and measured in situ. The comparison of five tunnels in literature illustrates that the simplified method can provide a more reasonable prediction for the ground movement induced by tunneling.

Pelatihan pemanfaatan teknologi sebagai media pendukung pembelajaran untuk guru di Kecamatan Sembalun

The involvement of lecturers, students, and teaching staff is an integral form of the Tri Dharma of higher education. Education has a crucial role and is the primary key to producing quality human resources. In the current practice of teaching and learning activities, many teachers have not used media or technology in teaching. Therefore, it is necessary to increase teacher competence through Community Service Activities to adapt to the industrial era 4.0, which is more likely to use technology in various fields of life, one of which is the world of education. PKM activities were carried out for six villages in Sembalun District to equalize the competence of teachers in the village so that they were equal to teachers in the city in presenting technology-based learning media. This interactive learning media creation training produced enjoyable visual and graphic-based learning to become more exciting and not dull. With the implementation of this activity, teachers have more competence in using technology and have succeeded in building their learning media. Apart from that, the creativity of the teacher increases with this activity.

Joint Channel Allocation and Power Control for Uplink NOMA-Assisted Multi-UAV Networks

The explosive growth of data leads to that the traditional wireless networks cannot enable various quality of service (QoS) communication for cellular-connected multi-UAV (unmanned aerial vehicle) networks. To overcome this obstacle, we solve the joint optimization problem of channel allocation and power control for uplink NOMA-assisted multi-UAV networks. Firstly, we design a mixed integer nonlinear programming framework, where the channel gains are characterized with integral form in time interval and sorted in nondescending order as the priority index of the decoded signal. In order to propose a feasible algorithm, the initial power levels of UAVs are obtained and integrated into the original problem which is reduced to integer programming problem. Then, the UAVs whose channel gain differences satisfy the constraints will be divided into a group to share the same channel, while the initial power levels of UAVs are adjusted to get a more satisfactory initial solution for power control. Combining the solution of channel allocation and the initial power levels, we solve power control problem with asynchronous update mechanism until the power levels of UAVs remain unchanged. Finally, we propose a channel allocation algorithm and a power control algorithm with the asynchronous optimization mechanism, respectively. Simulation results show that the proposed algorithms can effectively improve the network performance in terms of the aggregated rate.

Engineering spectral properties of non-interacting lattice Hamiltonians

We investigate the spectral properties of one-dimensional lattices with position-dependent hopping amplitudes and on-site potentials that are smooth bounded functions of the position. We find an exact integral form for the density of states (DOS) in the limit of an infinite number of sites, which we derive using a mixed Bloch-Wannier basis consisting of piecewise Wannier functions. Next, we provide an exact solution for the inverse problem of constructing the position-dependence of hopping in a lattice model yielding a given DOS. We confirm analytic results by comparing them to numerics obtained by exact diagonalization for various incarnations of position-dependent hoppings and on-site potentials. Finally, we generalize the DOS integral form to multi-orbital tight-binding models with longer-range hoppings and in higher dimensions.

Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F=F(x,y′) and when F=F(y,y′). For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for Jyx−Jy0x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied.

On a force balance and role of cathode plasma in Hall Effect Thruster

The cathode plasma is a specific transition region in the Hall Effect Thruster (HET) discharge that localizes between the strongly magnetized acceleration layer (magnetic layer or B-layer) and non-magnetized exhaust plume. Cathode plasma provides a flow of electron current that supplies losses in the magnetic layer (due to ionization, excitation, electron-wall interactions, etc.). The electrons' transport in this region occurs in collisionless mode through the excitation of plasma instabilities. This effect is also known as "anomalous transport/conductivity". In this work, we present the results of a 2d (drift-plane) kinetic simulation of the HET discharge, including the outside region that contains cathode plasma. We discuss the process of cathode plasma formation and the mechanisms of "anomalous transport" inside it. We also analyze how fluid force balance emerges from collisionless kinetic approach. The acceleration mechanism in Hall Effect Thrusters (HETs) is commonly described in terms of force balance. Namely, the reactive force produced by accelerated ions has the same value as Ampère's force acting on a drift current loop. This balance written in integral form provides the basis for quantitative estimations of HETs' parameters and scaling models.

Strict convexity of the objective function and uniqueness of the maximum point in a model with three arbitrary random priorities

The main result of this paper is the proof of the strict concavity of some function of integral form depending on three random variables, which we call priorities. This function is an objective function in the so-called model with priorities, in which the arbiter, following expert opinions, distributes funds among the enterprises and institutions under his jurisdiction. This result implies an important corollary about the existence and uniqueness of a local maximum point (which is also a global maximum point) of the objective function. This is a significant generalization of the corresponding result of N.V. Neumezhitskaia, S.I. Uglich and T.A. Volosatova, published in December 2020.

Crossover scaling functions in the asymmetric avalanche process

We consider the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. The exact expressions for the first two scaled cumulants of the particle current are obtained in the large time limit t ! ∞ via the Bethe ansatz and a perturbative solution of the TQ-equation. The results are presented in an integral form suitable for the asymptotic analysis in the large system size limit N ! ∞. In this limit the first cumulant, the average current per site or the average velocity of the associated interface, is asymptotically finite below the critical density and grows linearly and exponentially times power law prefactor at the critical density and above, respectively. The scaled second cumulant per site, i.e. the diffusion coefficient or the scaled variance of the associated interface height, shows the O(N-1⁄2) decay expected for models in the Kardar-Parisi-Zhang universality class below the critical density, while it is growing as O(N3⁄2) and exponentially times power law prefactor at the critical point and above. Also, we identify the crossover regime and obtain the scaling functions for the uniform asymptotics unifying the three regimes. These functions are compared to the scaling functions describing crossover of the cumulants of the avalanche size, obtained as statistics of the first return area under the time space trajectory of the Vasicek random process.

RECONSTRUCTION OF THE TWO VARIABLES DISCONTINUOUS FUNCTION BY DIFFERENT INFORMATION OPERATORS USING TRIANGULAR ELEMENTS

The paper examines methods for constructing mathematical models of two variables discontinuous functions using various information about them: one-sided values at points and one-sided traces along a given system of lines. The case is considered when the domain of the required function is triangulated by right-angled triangles. If interpolation or approximation methods are used, then for their construction the values of the function at given points must be given; if we use interlination methods, then traces of the desired function along a given system of lines. In this work, we construct a discontinuous interpolation and approximation splines for approximating a discontinuous function of two variables with given one-sided values in a given system of points (in our case, at the vertices of right-angled triangles), and prove theorems on the estimation of the approximation error by constructed discontinuous structures. In the paper a discontinuous interlination spline, which uses completely different information about the discontinuous function, namely one-sided traces along a given system of lines (in our case, along the sides of right-angled triangles) is also built. Interlination of functions can find wide application in the aircraft and automobile body design automation; when receiving and processing the results of sonar and radar, when solving problems of computed tomography, in digital signal processing and in many other areas. In the paper theorems on the integral form and an estimate of the approximation error by the constructed discontinuous interlination operator are also proved. Computational experiments that compare the results of the approximation of a discontinuous function of two variables by different information operators using triangular elements are presented. In the future, it is planned to apply the constructed operators of discontinuous approximation and interlination to solve a two-dimensional problem of computed tomography with a significant use of the inhomogeneity of the internal structure of the body, which must be reconstructed.

Mesh filtration problems with a two-flow structure of phase velocities

This paper deals with the problem of filtration of a two-phase incompressible fluid within the Buckley-Leverett model. From a general point of view, a two-flow structure of conservation laws is investigated. In addition, since the solution in the Buckley-Leverett model is discontinuous, conservation laws are presented in the generalized integral form. A good illustration of the approach presented is the problem of gravitational segregation of oil and water in a porous medium. For this problem, a two-flow mesh structure of conservation laws is described.