scholarly journals The Dynamic State of a Pseudo-Crystalline Structure of B42 Molecules

Crystals ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 510 ◽  
Author(s):  
Alexey Bubenchikov ◽  
Mikhail Bubenchikov ◽  
Dmitriy Mamontov
Keyword(s):  
Mathematical Model ◽  
Intermolecular Interactions ◽  
Crystalline Structure ◽  
Rotation Frequency ◽  
Molecular Structures ◽  
Dynamic State ◽  
Characteristic Vibration ◽  
Individual Molecule ◽  
Centers Of Mass ◽  
Stable Structures

In this paper, we have developed a mathematical model of the dynamics of molecular structures arising from an approach using B42 molecules. The model is based on equations that determine the motion of the centers of mass of the molecules in question, and equations for the projections of the moments of quantities of motion of these particles on the axes associated with them. The thermal motions of boron atoms within each individual molecule are calculated using a bond-ordered potential. The intermolecular interactions of atoms have a potential that appears to coincide with that of free atoms. However, the interaction parameters differ. The obtained columns of molecular disks for B42 are stable structures. We determine the characteristic vibration amplitudes and rotation frequency of the molecules in question.

ROTATIONS AND VIBRATIONS OF FULLERENES IN THE MOLECULAR COMPLEX C20@C80

2021 ◽  
pp. 35-48
Author(s):  
M.A. Bubenchikov ◽  
◽  
A.M. Bubenchikov ◽  
D.V. Mamontov ◽  
◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Rotation Frequency ◽  
Dynamic State ◽  
Large Molecules ◽  
Rotational Degrees Of Freedom ◽  
Rotational Motions ◽  
Centers Of Mass ◽  
The Moment

The aim of this work is to apply classical mechanics to a description of the dynamic state of C20@C80 diamond complex. Endohedral rotations of fullerenes are of great interest due to the ability of the materials created on the basis of onion complexes to accumulate energy at rotational degrees of freedom. For such systems, a concept of temperature is not specified. In this paper, a closed description of the rotation of large molecules arranged in diamond shells is obtained in the framework of the classical approach. This description is used for C20@C80 diamond complex. Two different problems of molecular dynamics, distinguished by a fixing method for an outer shell of the considered bimolecular complex, are solved. In all the cases, the fullerene rotation frequency is calculated. Since a class of possible motions for a single carbon body (molecule) consists of rotations and translational displacements, the paper presents the equations determining each of these groups of motions. Dynamic equations for rotational motions of molecules are obtained employing the moment of momentum theorem for relative motions of the system near the fullerenes’ centers of mass. These equations specify the operation of the complex as a molecular pendulum. The equations of motion of the fullerenes’ centers of mass determine vibrations in the system, i.e. the operation of the complex as a molecular oscillator.

scholarly journals Steady-State Steering Characteristics of Mathematical Model for Semitrailer Based on Variations in Camber Parameters

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yi Wei ◽  
Shuilong He ◽  
Enyong Xu ◽  
Genge Zhang ◽  
Rongjiang Tang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Test Data ◽  
Dynamic State ◽  
Model Parameters ◽  
Stability Factor ◽  
Camber Angle ◽  
Body Roll ◽  
Vehicle Test ◽  
Real Vehicle

To master the basic characteristics of steady-state cornering for a semitrailer, this paper summarises the current modelling methods for handling and stability and discusses their limitations. The classical linear mathematical model for a two-degree-of-freedom (DOF) handling and stability system is used to develop a new model. Analysis methods are proposed to introduce the influence of the camber angle and body roll into the model parameters. Thus, a mathematical model for the lateral stability of semitrailer with five DOFs is established. At the same time, a modified formula to calculate the stability factor of the semitrailer is developed with a MATLAB model to solve the dynamic state equation. The mathematical model, which considers the body roll and the changes in the camber angle caused by roll, compares the turning radius ratio and yaw rate as the evaluation index with the classical linear mathematical model of a two-DOF system. The vehicle parameters for three different types of semi-tractor trailers are used to calculate and compare two mathematical models for handling and stability using real vehicle test data. The results show that the new modelling and analysis method proposed in this paper has a high calculation accuracy and fast calculation speed, is clear and concise, and is consistent with the real vehicle test data. In addition, the accuracy of the new mathematical model for handling and stability and the improved stability factor are verified.

scholarly journals Mathematical model of pantograph cooperation with two degrees of freedom with a catenary system

2019 ◽  
Vol 294 ◽  
pp. 05005
Author(s):  
Marek Kaniewski ◽  
Michał Cichoński
Keyword(s):  
Mathematical Model ◽  
Discrete Model ◽  
Degrees Of Freedom ◽  
Variable Stiffness ◽  
System Model ◽  
Dynamic State ◽  
Rolling Stock ◽  
Two Degrees Of Freedom ◽  
Technical Specifications ◽  
Catenary System

The authors present a method of modeling pantograph cooperation with a catenary system by means of a computer program based on a pantograph discrete model with two degrees of freedom and a catenary system model as a focused mass that in the dynamic state has variable stiffness along the span. After performing the appropriate tests, the validation was carried out according to the proposed method in the PN EN 50318:2019-02 standard required in the Technical Specifications for the interoperability of the subsystem “Energy” and “Rolling stock -locomotives and passenger rolling stock” of the trans-European rail system in Europe.

Conformational differences and intermolecular C—H...N interactions in three polymorphs of a bis(pyridinyl)-substituted benzimidazole

2016 ◽  
Vol 72 (11) ◽  
pp. 867-874 ◽  
Author(s):  
David K. Geiger ◽  
Matthew R. DeStefano
Keyword(s):  
Dft Calculations ◽  
Intermolecular Interactions ◽  
Crystal Engineering ◽  
Density Functional ◽  
Molecular Conformation ◽  
Molecular Structures ◽  
Acta Cryst ◽  
Space Groups ◽  
Polymorphic Forms

The structural characterization of several polymorphic forms of a compound allow the interplay between molecular conformation and intermolecular interactions to be studied, which can contribute to the development of strategies for the rational preparation of materials with desirable properties and the tailoring of intermolecular interactions to produce solids with predictable characteristics of interest in crystal engineering. The crystal structures of two new polymorphs of 5,6-dimethyl-2-(pyridin-2-yl)-1-[(pyridin-2-yl)methyl]-1H-benzimidazole, C20H18N4, are reported. The previously reported polymorph, (1) [Geiger & DeStefano (2014).Acta Cryst.E70, o365], exhibits the space groupC2/c, whereas polymorphs (2) and (3) presented here are in thePnmaandP\overline{1} space groups, respectively. The molecular structures of the three forms differ in their orientations of the 2-(pyridin-2-yl)- and 1-[(pyridin-2-yl)methyl]- substituents. Density functional theory (DFT) calculations show that the relative energies of the molecule in the three conformations follows the order (1) < (2) < (3), with a spread of 10.6 kJ mol−1. An analysis of the Hirshfeld surfaces shows that the three polymorphs exhibit intermolecular C—H...N interactions, which can be classified into six types. Based on DFT calculations involving pairs of molecules having the observed interactions, the C—H...N energy in the systems explored is approximately −11.2 to −14.4 kJ mol−1.

scholarly journals BLDC Motor Speed Control using Fuzzy Logic PID Controller and Comparing It with PI Controller

2019 ◽  
Vol 9 (2) ◽  
pp. 4917-4922
Keyword(s):  
Mathematical Model ◽  
Pid Controller ◽  
High Performance ◽  
Pi Controller ◽  
Dynamic State ◽  
Bldc Motor ◽  
Fuzzy Pid ◽  
Motor Speed ◽  
Brushless Dc ◽  
Fuzzy Pid Controller

In this project, mathematical model of the Brushless DC motor (BLDC) is developed and the closed-loop Fuzzy PID controller has been simulated in MATLAB-Simulink environment. The three-phase (BLDC) is developed and the DC power is supplied to this machine though six step inverter whose switching state is controlled by the hall signal. The hall effect sensor senses the rotor posit ion of the motor and it generates binary digit number which is decoded and given to the six-step inverter. The mathematical model is developed using the back emf equations and torque equation of the BLDC motor. The PI controller doesn’t operate properly during dynamic state and hence the fuzzy-PID-controller is better option to control and regulate the speed of the BLDC motor which has high performance in comparison to the PI controller. And, we can get the smooth speed-torque characteristics using Fuzzy PID controller.

scholarly journals VIBRATION MODULATION CAUSES AT ROTATION FREQUENCY IN ROTARY MACHINES

Akustika ◽  
2019 ◽  
Vol 32 ◽  
pp. 151-157
Author(s):  
Sergey Alekseevich Rykov ◽  
Irina Kudryavtseva ◽  
Sergey Vladimirovich Rykov
Keyword(s):  
Mathematical Model ◽  
Experimental Studies ◽  
Rotation Frequency ◽  
Diagnostic Methods ◽  
Bearing Unit ◽  
Rotary Machines ◽  
The Mathematical Model

The results of theoretical and experimental studies of the modulation of vibrations of rotary machines have been presented at rotation frequency. It has been shown that at the rotation frequency, the possible causes of the origin of the “side” spectral discrete components are the presence of a clearance and friction in bearing units. On the basis of the data obtained in the mathematical model, the diagnostic methods of the quality of functioning the bearing unit of rotary mechanisms are proposed.

scholarly journals Estimation Impact of Capital Development Projects on Adjacent Street and Road Network in Organization of Traffic by Means of Signal Controlled Intersections

2021 ◽  
Vol 20 (6) ◽  
pp. 506-513
Author(s):  
A. V. Zedgenizov ◽  
D. V. Kapskiy ◽  
R. Yu. Lagerev
Keyword(s):  
Mathematical Model ◽  
Traffic Flow ◽  
Flow Rate ◽  
Road Network ◽  
Signalized Intersections ◽  
Cycle Phase ◽  
Saturation Flow Rate ◽  
Centers Of Mass ◽  
Saturation Flow ◽  
Demand And Capacity

The paper discusses problems of assessing the impact of mass attraction centers on the adjacent street and road network in the process of their functioning, expansion or conversion. The choice of criteria for assessing the organization of traffic flow, given in the Russian and foreign literature, has been substantiated, in particular, it is proposed to use v/c ratio for adjacent junction and corresponding level of traffic service (LOS). The main models for estimating capacity of signalized intersections are presented. The procedures of forming a mathematical model for estimating the load factor of signalized intersections is shown. The concepts of lane group capacity, total lost time per cycle, phase coefficients, saturation flow rate, and coefficients taking into account the decrease in the ideal saturation flow rate are explained. A mathematical model for estimating transport demand is presented, which allows to calculate the intensity of traffic flow to and from the center of mass attraction on the basis of the total traffic flow of correspondence, share of visitors in individual transport, average filling of individual transport, and coefficient of daily irregularity upon arrival and departure of visitors on an individual transport. An integrated mathematical model of loaf factor is proposed which includes parameters for estimating transport demand for centers of mass embarrassment and parameters that determine the signalized intersections capacity. The uniqueness of the integrated model is that it simultaneously involves parameters reflecting the demand and capacity of loading intersection. Recommendations are made on assessing the level of traffic service flows and the v/s ratio, based on the data of transport demand and capacity, adjacent to the centers of mass attraction of the road network. The presented method of estimating the LOS based on the capacity of the signalized intersections allows us to estimate the influence degree of mass attraction centers on the adjacent urban road network.

scholarly journals MODELING THE WORK FLOW OF CUT-OUT SPHERICAL DISKS WITH HYDRAULIC DRIVE FOR FIRE-FIGHTING SOIL-THROWER

2020 ◽  
Vol 10 (1) ◽  
pp. 185-192
Author(s):  
Maksim Gnusov ◽  
Mikhail Drapalyuk ◽  
P. Popikov ◽  
N. Sherstyukov
Keyword(s):  
Mathematical Model ◽  
Forest Fire ◽  
Cutting Edge ◽  
Fire Fighting ◽  
Dynamic State ◽  
Soil Environment ◽  
Spherical Elements ◽  
Working Bodies ◽  
The Mathematical Model ◽  
The Relationship

In this article, considerable attention is paid to the method of mathematical creation of a structurally complex soil environment with vegetation. Structural and technological parameters of the interaction of the working bodies of the fire-fighting soil thrower with soil have been determined using a simulation-physical-mathematical model of the spherical disk relationship with the soil environment. The disk is equipped with a cutting edge with semicircular cuts. The mathematical model presents complex geometry of all forms of active work planes, as well as the relationship of the working bodies with soil elements. Surfaces of complex construction in the process of applying the finite element method have been transformed into a large number of simplified planar figures. The soil in the simulation physical-mathematical model is described as a complex system of a large number of spherical elements, determinately connecting with each other, as well as with the working planes of the machine. It has been determined that the relationship between the soil particles during deformation is viscoelastic in its nature. The calculation of forces is presented in the form of an algorithm for the interaction of elements on each other in relation to the distance of their location. The equations of motion are used that describe the change in the dynamic state of the soil over time. The movement of the working bodies of the unit, including spherical disk working bodies with cutouts in the framework of the mathematical model, has been considered in the simulated space, described as a parallelepiped. The ability to simulate the interaction of the working bodies of a forest fire soil-throwing machine with a working medium, including plant roots, which are located next to each other in the form of spherical elements in the geometric region. The task of increasing the efficiency of the forest fire-fighting soil-throwing machine when laying fire strips has been solved by improving the quality of preparing the soil shaft with spherical hydraulic disks equipped with a cutting edge with semicircular cuts, which are subsequently taken by thrower-cutters and feed the soil flow in a given direction

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