Temperature and entropy in molecular system

The irreversibility, temperature, and entropy are identified for an atomic system of solid material. Thermodynamics second law is automatically satisfied in the time evolution of molecular dynamics (MD). The irreversibility caused by an atom spontaneously moves from a non-stable equilibrium position to a stable equilibrium position. The process is dynamic in nature associated with the conversion of potential energy to kinetic energy and the dissipation of kinetic energy to the entire system. The forward process is less sensitive to small variation of boundary condition than reverse process, causing the time symmetry to break. Different methods to define temperature in molecular system are revisited with paradox examples. It is seen that the temperature can only be rigorously defined on an atom knowing its time history of velocity vector. The velocity vector of an atom is the summation of the mechanical part and the thermal part, the mechanical velocity is related to the global motion (translation, rotation, acceleration, vibration, etc.), the thermal velocity is related to temperature and is assumed to follow the identical random Gaussian distribution for all of its [Formula: see text], [Formula: see text] and [Formula: see text] component. The [Formula: see text]-velocity (same for [Formula: see text] or [Formula: see text]) versus time obtained from MD simulation is treated as a signal (mechanical motion) corrupted with random Gaussian distribution noise (thermal motion). The noise is separated from signal with wavelet filter and used as the randomness measurement. The temperature is thus defined as the variance of the thermal velocity multiply the atom mass and divided by Boltzmann constant. The new definition is equivalent to the Nose–Hover thermostat for a stationary system. For system with macroscopic acceleration, rotation, vibration, etc., the new definition can predict the same temperature as the stationary system, while Nose–Hover thermostat predicts a much higher temperature. It is seen that the new definition of temperature is not influenced by the global motion, i.e., translation, rotation, acceleration, vibration, etc., of the system. The Gibbs entropy is calculated for each atom by knowing normal distribution as the probability density function. The relationship between entropy and temperature is established for solid material.

Earthquake slip vectors in the Himalayan thrust Zone and their tectonic implications

Slip vectors of thirty-nine thrust events occurring along the Himalayan collision zone have been compared with the velocity vectors between the Indian-Eurasian plates derived from the RM 2 and NUVEL 1 models, The observed deviations of the slip vector from the velocity vector have been interpreted in terms of a simple kinematic model according to which the eastern and western blocks of south Tibet are separating from each other, From the model it is estimated that the western and eastern blocks of Tibet are moving at the rate of 3.6 cm/year westwards at 76°Eand 2.6 cm/year eastwards at 94°E with respect to Eurasia respectively, resulting in an east-west extension, projected to the trend at 85°E, at the rate of 5, 5 cm/year. This would correspond to a strain rate of about 6.9 x 10-8year in central Tibetan region.

Geometric models of the run method

This article discusses models of the run method in the pursuit problem. The considered models are based on the correction of the direction vector. Let’s assume that the intended direction on a plane is the line of sight between the pursuer and the target. The direction correction consists in the rotation of the velocity vector until it coincides with the line of sight. When constructing trajectories on the surface, a line of sight is built on the horizontal projection plane. After calculating horizontal projections, all points are projected back onto the surface. On the basis of the research carried out proposed a mathematical model, proposed mathematical models of the method of pursuit on a plane and on a surface given in an explicit form. Mathematical models are the development of chase and parallel approach methods. A modification of these methods is that the speed of the pursuer and the target are directed at random. These models can be in demand by developers of autonomous unmanned vehicles equipped with artificial intelligence systems.

Development of the method of laser Doppler anemometry for diagnostics of turbulent flows at high speed

The aim of the work was to develop a laser Doppler anemometry method for high-speed turbulent aerodynamic flow diagnostic. As a result, this allowed us to measure two projections of the velocity vector in the range of 0.1 - 400 m/s with a relative error not exceeding 0.5%. The measurement area was 0.1x0.1x0.5mm. The positioning device moved the measuring unit in the area of 250 x 250 x 250 mm with an accuracy of 0.1 mm. This method also provides the ability to measure local flow rate fluctuations.

Simulation of temperature distribution in refrigerated container 40 feet

This study shows the method for predicting the temperature distribution and air flow in the box of a refrigerated container 40 feet, for two configurations (open and closed) of the rear door. Computational Fluid Dynamics – CFD (Computational Fluid Dynamics) is decoupled and used when the truck door is fully closed. The temperature, velocity vector and heat flow are simulated based on the finite element method. The simulation results are compared with the experimental data.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

Development of an Instantaneous Velocity-Vector-Profile Method Using Conventional Ultrasonic Transducers

The velocity vector profile technique based on an ultrasound pulsed Doppler method can enrich the information of a flow field, however, it has shown a low availability because a new design of special transducers is required for each measurement case. This study proposes a new method of profiling the velocity vectors using conventional ultrasound transducers that are widely supplied to UVP (Ultrasound velocity profile) users. We constructed a configuration of the transducers to minimize the uncertainty of the detection points at the receivers, and a measurable distance was theoretically determined by the configuration. Two feasibility tests were carried out. One was a test for the assessment of the measurable distance, which agreed well with the theoretical distance. The other was the evaluation of the measurement of two-dimensional velocity vectors by the new method and it was performed in a towing tank facility without the velocity fluctuation. From the evaluation, it was confirmed that the measured vectors showed good agreement to the reference values, and their accuracy and precision were competitive compared to previous studies. The developed method was applied to two unsteady flows for demonstrations. The results clarified that the proposed method guarantees high availability and accuracy for the velocity vector profiles.

Reconstruction of the flow structure in a matrix channel based on two-component LDA data

The work is aimed at creating a technique for reconstructing the three-dimensional structure of turbulent flows using data of a two-component laser-Doppler anemometer at the example of a flow in flat coplanar channels. Data of paired measurements by a two-component LDA at two different angles relative to the measurement point are used to obtain information about the three-dimensional structure of the flow. Further, all three components of the velocity vector were calculated using transformations. The developed method is used to measure the velocity field in a coplanar channel.