Transition from Discrete to Continuous Media: The Impact of Symmetry Changes on Asymptotic Behavior of Waves

This paper is devoted to comparing the asymptotics of a solution, describing the wave motion of a discrete lattice and its continuous approximations. The transition from a discrete medium to a continuous one changes the symmetry of the system. The influence of this change on the asymptotic behavior of waves is of great interest. For the discrete case, Schrödinger’s analytical solution of the initial-value problem for the Lagrange lattice is used. Various continuous approximations are proposed to approximate the lattice. They are based on Debye’s concept of quasicontinuum. The asymptotics of the initial motion and the behavior of the systems in the vicinity of the quasifront and at large times are compared. The approximations of phase and group velocities is analyzed. The merits and limitations of the described approaches are discussed.

Research on vehicle critical condition prediction and optimal yaw moment intervention based on nonlinear dynamics and Monte Carlo simulation

Timely and effective yaw moment intervention is required to suppress the instability tendency of vehicle under critical conditions, which is mainly caused by the overshoot of state parameters. As the development of vehicle nonlinear dynamics, the prediction of vehicle critical condition enables the vehicle to stabilize in this condition by timely yaw moment intervention. The yaw moment intervention law based on the prediction of critical conditions cannot be solely investigated by the initial motion states, since the online iterative optimization is an indispensable part in the predictive control. In this paper, the combination of threshold model, quadratic optimal yaw moment prediction method and Monte Carlo simulation provides a new approach to investigate the optimal open loop yaw moment intervention law based on initial motion states, which can be used to maintain the stability of vehicle plane motion in critical situations and optimize the predictive control method. Specifically, a total of 480,000 samples of quadratic yaw moment intervention parameters and corresponding system responses are obtained and analysed. It is certified that the optimized quadratic yaw moment can effectively suppress the overshoot of system responses. Specifically, statistics indicate that the initial value of yaw moment intervention plays an important role in preventing instability, but with the increase of speed and steering angle, the final yaw moment will be the decisive factor to maintain the lateral stability.

Initial Moving Mechanism of Densely-Packed Particles Driven by a Planar Shock Wave

The initial moving mechanism of densely packed particles driven by shock waves is unclear but vital for the next accurate calculation of the problem. Here, the initial motion details are investigated experimentally and numerically. We found that before particles show notable motion, shock waves complete reflection and transmission, and stress waves propagate downstream on particle skeleton. Due to the particle stress wave, particles successively accelerate and obtain an axial velocity of 6–8 m/s. Then, the blocked gas pushes the upstream particles integrally to move downstream, while the gas flow in the pores drags the downstream particles to separate dramatically and accelerate to the velocity of 60–70 m/s. This gas push-drag dual mechanism transforms densely packed particles into a dense gas-particle cloud, which behaves as the expansion phenomena of the dense particles.

Motion of rain drops on a car side window

The present paper studies the initial motion of rain drops on a car side window. An explanation to the common observation of drops going up the window when a car reaches a given speed is provided, which takes into account the dimensions of the drops and the wind speed. We also discuss the importance of the actual window geometry, the state of the surface, and the drop size distribution. This work may thus be used as a basis for complete study of a population of drops against a car window.

Stopping power ,Z_1^3- Parameter, Bloch and shell corrections in Bethe formula for protons and Helium ions in DNA and liquid water.

The Barkas effect came because of target electrons due to responding to the approaching particle and slightly changing the orbits before occur from interaction of energy loss (denominate target polarization). At high energies (above 20 10 insignificant because the ion moving too fast to cause initial motion the target electrons where at low energies the Barkas effect is investigated.[1].In present work stopping power, Barkas effects, Bloch and shell corrections have been investigated for the interaction of protons and Helium ions in DNA and liquid water. Braggs rule has been used on each element in DNA and liquid water to determine the parameters correction in Bethe-Bloch formula using Ziegler’s semi-empirical formula [1].

Buoyant Motion of a Turbulent Thermal

By introducing an equivalence between magnetostatics and the equations governing buoyant motion, we derive analytical expressions for the acceleration of isolated density anomalies (thermals). In particular, we investigate buoyant acceleration, defined as the sum of the Archimedean buoyancy B and an associated perturbation pressure gradient. For the case of a uniform spherical thermal, the anomaly fluid accelerates at 2B/3, extending the textbook result for the induced mass of a solid sphere to the case of a fluid sphere. For a more general ellipsoidal thermal, we show that the buoyant acceleration is a simple analytical function of the ellipsoid’s aspect ratio. The relevance of these idealized uniform-density results to turbulent thermals is explored by analyzing direct numerical simulations of thermals at a Reynolds number (Re) of 6300. We find that our results fully characterize a thermal’s initial motion over a distance comparable to its length. Beyond this buoyancy-dominated regime, a thermal develops an ellipsoidal vortex circulation and begins to entrain environmental fluid. Our analytical expressions do not describe the total acceleration of this mature thermal, but they still accurately relate the buoyant acceleration to the thermal’s mean Archimedean buoyancy and aspect ratio. Thus, our analytical formulas provide a simple and direct means of estimating the buoyant acceleration of turbulent thermals.