scholarly journals Simulating Nonlinear Dynamics of a 3D Crystal Lattice of Metals

2021 ◽  
Vol 2131 (3) ◽  
pp. 032092
Author(s):  
A S Semenov ◽  
M N Semenova ◽  
Yu V Bebikhov ◽  
P V Zakharov ◽  
E A Korznikova
Keyword(s):  
Nonlinear Dynamics ◽  
Crystal Lattice ◽  
Mathematical Simulation ◽  
Piecewise Linear ◽  
Experimental Studies ◽  
Piecewise Linear Approximation ◽  
Calculation Error ◽  
Simulation Techniques ◽  
Welch Method ◽  
Computationally Intensive

Abstract Oscillations of crystal lattices determine important material properties such as thermal conductivity, heat capacity, thermal expansion, and many others; therefore, their study is an urgent and important problem. Along with experimental studies of the nonlinear dynamics of a crystal lattice, effective computer simulation techniques such as ab initio simulation and the molecular dynamics method are widely used. Mathematical simulation is less commonly used since the calculation error there can reach 10 %. Herewith, it is the least computationally intensive. This paper describes the process and results of mathematical simulation of the nonlinear dynamics of a 3D crystal lattice of metals using the Lennard-Jones potential in the MatLab software package, which is well-proven for solving technical computing problems. The following main results have been obtained: 3D distribution of atoms over the computational cell has been plotted, proving the possibility of displacement to up to five interatomic distances; the frequency response has been evaluated using the Welch method with a relative RMS error not exceeding 30 %; a graphical dependence between the model and the reference cohesive energy data for a metal HCP cell has been obtained with an error of slightly more than 3 %; an optimal model for piecewise-linear approximation has been calculated, and its 3D interpolation built. All studies performed show good applicability of mathematical simulation to the problems of studying dynamic processes in crystal physics.

scholarly journals CHANGE OF ENERGY CHARACTERISTICS OF LITHOSPHERE ELEMENTS DURING THEIR DEFORMATION

2021 ◽  
pp. 63-69
Author(s):  
Anatolii Kryuchkov ◽  
Anatolii Bakhtyn
Keyword(s):  
Rock Mass ◽  
Energy Density ◽  
Piecewise Linear ◽  
Experimental Studies ◽  
Analytical Description ◽  
Stress Change ◽  
Piecewise Linear Approximation ◽  
Complete Deformation ◽  
Experimental Researches ◽  
Destruction Of Rocks

Purpose. The purpose of this study is to establish analytical patterns for predicting changes in stress and energy density spent on the destruction of rocks according to experimental studies. To solve this purpose in the article were set the following scientific problems: 1) analytical description of the dependence of the stress σij on the main deformation εij; 2) establishment of calculation parameters that are included in the analytical patterns; 3) analytical description and study of fracture energy density curves. Methodology. In the course of analytical and experimental researches of full diagrams of deformation of rocks the mathematical model of dependence of the stress on the deformation is developed. Physico-mechanical processes of all characteristic sections of the complete deformation diagram were also analyzed and described. Analysis of the resulting curve showed that the rock mass and elements of the lithosphere are not perfectly elastic or plastic objects. Along with the elastic ones, plastic ones are always present to one degree or another. The integration of the obtained analytical expression σ11 = f(ε11) allowed to establish the volumetric energy density spent on the destruction of the rock sample under the action of external load. The maximum activation energy for the considered rock is 0.67 MJ/m3. A comparison of the experimental and calculated values of the energy dependence u(ε1) shows a coincidence over almost the entire range of deformation changes (ε11 = 0..0.04). Findings. The study of rock samples at hard stress allowed to obtain a complete deformation characteristics of the rock. The curve that surrounds the deformation cycles (1) combines pre-boundary, boundary, extremal modes of deformation and destruction of rocks. Equation (4) allows us to establish that the destruction can occur at different values of energy density U(ε). Originality. An analytical description of the energy diagram of deformation and a complete diagram of stress change in the form of a single dependence, which takes into account the boundary and extremal areas, was developed in the work. In contrast to the method of piecewise linear approximation, this approach corresponds to the physics of the process and reduces errors in calculations. Practical implications. Theoretical and experimental analysis of the obtained energy fracture diagrams and complete stress change diagrams in rocks allows to estimate the bearing capacity of a rock mass or other solid body. This allows you to predict critical values of stresses and external loads to prevent failure in a timely manner.

scholarly journals Exact simulation of multidimensional reflected Brownian motion

2018 ◽  
Vol 55 (1) ◽  
pp. 137-156
Author(s):  
Jose Blanchet ◽  
Karthyek Murthy
Keyword(s):  
Brownian Motion ◽  
Information Structure ◽  
Piecewise Linear ◽  
Simulation Method ◽  
Uniform Norm ◽  
Piecewise Linear Approximation ◽  
Reflected Brownian Motion ◽  
Proposal Distribution ◽  
Exact Simulation ◽  
Simulation Techniques

AbstractWe present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance–rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.

scholarly journals Improvement Dependability of Offshore Horizontal-Axis Wind Turbines by Applying New Mathematical Methods for Calculation the Excess Speed in Case of Wind Gusts

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3085
Author(s):  
Konstantin Osintsev ◽  
Seregei Aliukov ◽  
Alexander Shishkov
Keyword(s):  
Computer Simulation ◽  
Wind Turbines ◽  
Experimental Studies ◽  
Offshore Wind ◽  
Approximation Schemes ◽  
Calculation Error ◽  
Strong Wind ◽  
Mathematical Methods ◽  
Wind Gusts ◽  
Gas Dynamic

The problem of increasing the reliability of wind turbines exists in the development of new offshore oil and natural gas fields. Reducing emergency situations is necessary due to the autonomous operation of drilling rigs and bulk seaports in the subarctic and Arctic climate. The relevance of the topic is linked with the development of a methodology for theoretical and practical studies of gas dynamics when gas flows in a pipe, based on a mathematical model using new mathematical methods for calculation of excess speeds in case of wind gusts. Problems in the operation of offshore wind turbines arise with storm gusts of wind, which is comparable to the wave movement of the gas flow. Thus, the scientific problem of increasing the reliability of wind turbines in conditions of strong wind gusts is solved. The authors indicate a gross error in the calculations when approximating through the use of the Fourier series. The obtained results will allow us to solve one of the essential problems of modeling at this stage of its development, namely: to reduce the calculation time and the adequacy of the model built for similar installations and devices. Experimental studies of gas-dynamic flows are carried out on the example of a physical model of a wind turbine. In addition, a computer simulation of the gas-dynamic flow process was carried out. The use of new approximation schemes in processing the results of experiments and computer simulation can reduce the calculation error by 1.2 percent.

scholarly journals Actor-critic learning-based energy optimization for UAV access and backhaul networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yaxiong Yuan ◽  
Lei Lei ◽  
Thang X. Vu ◽  
Symeon Chatzinotas ◽  
Sumei Sun ◽  
...  
Keyword(s):  
Power Allocation ◽  
Heuristic Algorithms ◽  
Piecewise Linear ◽  
Access Network ◽  
Computation Time ◽  
Combinatorial Problem ◽  
Base Station ◽  
Piecewise Linear Approximation ◽  
Group Scheduling ◽  
User Group

AbstractIn unmanned aerial vehicle (UAV)-assisted networks, UAV acts as an aerial base station which acquires the requested data via backhaul link and then serves ground users (GUs) through an access network. In this paper, we investigate an energy minimization problem with a limited power supply for both backhaul and access links. The difficulties for solving such a non-convex and combinatorial problem lie at the high computational complexity/time. In solution development, we consider the approaches from both actor-critic deep reinforcement learning (AC-DRL) and optimization perspectives. First, two offline non-learning algorithms, i.e., an optimal and a heuristic algorithms, based on piecewise linear approximation and relaxation are developed as benchmarks. Second, toward real-time decision-making, we improve the conventional AC-DRL and propose two learning schemes: AC-based user group scheduling and backhaul power allocation (ACGP), and joint AC-based user group scheduling and optimization-based backhaul power allocation (ACGOP). Numerical results show that the computation time of both ACGP and ACGOP is reduced tenfold to hundredfold compared to the offline approaches, and ACGOP is better than ACGP in energy savings. The results also verify the superiority of proposed learning solutions in terms of guaranteeing the feasibility and minimizing the system energy compared to the conventional AC-DRL.

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