Experimental Study of a Sphere Bouncing on the Water

In this paper, the flow physics and impact dynamics of a sphere bouncing on a water surface are studied experimentally. During the experiments, high-speed camera photography techniques are used to capture the cavity and free surface evolution when the sphere impacts and skips on the water surface. The influences of the impact velocity (v1) and impact angle (θ1) of the sphere on the bouncing flow physics are also investigated, including the cavitation evolution, motion characteristics, and bounding law. Regulations for the relationship between v1 and θ1 to judge whether the sphere can bounce on the water surface are presented and analyzed by summarizing a large amount of experimental data. In addition, the effect of θ1 on the energy loss of the sphere is also analyzed and discussed. The experiment results show that there is a fitted curve of $${v}_{1}=17.5{\theta }_{1}-45.5$$ v 1 = 17.5 θ 1 - 45.5 determining the relationship between the critical initial velocity and angle whether the sphere bounces on the water surface.

Devising a method for improving the efficiency of artillery shooting based on the Markov model

This paper reports a method for improving the firing efficiency of an artillery unit that results in enhanced effectiveness. Given the modern use of artillery for counter-battery warfare, the effectiveness of shooting is not enough assessed by accuracy only. It is also necessary to take into consideration and minimize the time spent by the unit in the firing position and the consumption of shells to hit the target. It has been shown that in order to assess the effectiveness of an artillery shot due to the initial velocity of the projectile, the most rapid and simple means is to classify the quality of the shot by the acoustic field. A procedure for categorizing the shot has been improved by applying an automatic classifier with training based on a machine of support vectors with the least squares. It is established that the error in the classification of the effectiveness of the second shot does not exceed 0.05. The concept of the effectiveness of a single artillery shot was introduced. Under the conditions of intense shooting, there may be accidental disturbances in each shot due to the wear of the charging chamber of the gun, its barrel, and incomplete information about the powder charge. When firing involves disturbances, the firing of an artillery unit can be described by a model of a discrete Markov chain. Based on the Markov model, a method for improving the efficiency of artillery fire has been devised. The method is based on the identification of guns that produce ineffective shots. The fire control phase of the unit has been introduced. In the process of controlling the fire of the unit, such guns are excluded from further firing. A generalized criterion for the effectiveness of artillery firing of a unit, based on the convolution of criteria, has been introduced. It is shown that the devised method significantly improves the effectiveness of shooting according to the generalized criterion.

Expansion of Rindler Coordinate Theory and Light’s Doppler Effect

In the general theory of relativity the Rindler coordinate theory has been extended to the Rindler coordinate theory of accelerated observer that has already some initial velocity. In this paper, we present this extended theory that uses the tetrad as the new method, and discover the new inverse-coordinate transformation. Specially, if, a0 < 0 , this theory treats the observer with the initial velocity that does slowdown by the constant negative acceleration in the Rindler’s time-space. We consider the light’s Doppler Effect in the accelerated system as well as the decelerated system.

Kinetic Analysis Misinterpretations Due to the Occurrence of Enzyme Inhibition by Reaction Product: Comparison between Initial Velocities and Reaction Time Course Methodologies

The Michaelis–Menten equation (MME) has been extensively used in biochemical reactions, but it is not appropriate when the reaction product inhibits the enzyme. Under these circumstances, each determined initial velocity, v0, is one experimental point that actually belongs to a different MME because enzymatic product inhibition occurs as the reaction starts. Furthermore, the inhibition effect is not constant, since the concentration of the product inhibitor rises as time increases. To unveil the hidden enzyme inhibition and to simultaneously demonstrate the superiority of an integrated Michaelis–Menten equation (IMME), the same range of data points, assuming product inhibition and the presence of a second different inhibitor, was used for kinetic analysis with both methodologies. This study highlights the superiority of the IMME methodology for when the enzyme is inhibited by the reaction product, giving a more coherent inhibition model and more accurate kinetic constants than the classical MME methodology.

Mathematical model of the influence of the time of start reaction in 100 m sprint run

The purpose of this study is to explain the influence of the time of start reaction tR to the results of sprinters in a 100 m run, using a new simple mathematical model based on the measured values for distance s, corresponding time t, and tR. The research is based on IAAF data obtained by measuring the segment length, the time of start reaction, transient times in 100 m run, and final times for the top sprinters C. Lewis (1988); M. Green (2011), and U. Bolt (2009) (men) and F. Griffith-Joyner (1988); E. Ashford (1988), and H. Drechsler (1988) (women). The values of the start reaction tR for both male and female top sprinters indicate that there appear no substantial differences in the values of tR based on gender which would directly favor male or female sprinters in achieving the top results in the 100m run. The influence of the time of start reaction tR decreases exponentially with the time t during the run (t>tR) and ends up at about 30 m, influencing the initial velocity vR although it is not directly related to the result of the run. Due to its applicative simplicity, the presented mathematical model and related conclusions can represent a solid basis for future studies concerning sprint running.

Movement of the particle on the surface of the conveyor belt, arbitrarily oriented in space

The movement of the material on the inclined belt of the conveyor takes place during transportation or its frictional cleaning. For an inclined moving plane (slide), the angle of its inclination to the horizontal plane is decisive. The absolute motion of a particle is the sum of two motions - the portable belt and the relative particle along the belt, so it is affected by the angle between the vectors of the greatest inclination of the plane and the transfer velocity of the plane (tape). The purpose of the study is to determine the motion of a material particle on the conveyor belt for the case when the angle between the vector of the line of greatest inclination of the conveyor plane and the direction of its transfer speed is arbitrary. To do this, the conveyor belt element was depicted as a rectangle with an axis of symmetry drawn along the direction of translational movement. In the initial position, the plane was placed horizontally, so the angle of greatest inclination is absent. In the future, the plane was given an arbitrary location in space due to alternate rotation around the sides bounding its compartment or around the axes of symmetry of the compartment, which is equivalent. The relative and absolute motions of the material particle along the moving web of the conveyor are considered for the case when the line of the greatest inclination of the web plane makes an arbitrary angle with the direction of the portable motion of the web. A system of differential equations of motion is compiled and solved. The obtained results are illustrated graphically. It is established that the nature of the relative motion of a particle on an inclined plane moving rectilinearly and uniformly depends on the direction of the vector of the line of the greatest inclination and the value of the angle of inclination of this plane. If the angle of inclination is less than the angle of friction, then the lateral feed of the particle will eventually stop either on the curved section of the trajectory or on a straight line that is parallel to the line of greatest inclination. The stopping place of the particle depends on the value of the initial velocity. At an angle of inclination of the plane equal to the angle of friction, the particle during the movement along the curved section of the trajectory reduces its initial velocity by half and then moves in a straight line and evenly. If the angle of inclination of the plane is greater than the angle of friction, the particle in relative motion along the curvilinear section of the trajectory first reduces the velocity, and when approaching a rectilinear section, its velocity increases and continues to increase on a rectilinear section of the trajectory. Key words: material particle, conveyor, inclined plane, plane inclination angle, particle velocity

The effective mass problem for the Landau-Pekar equations

We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar.

The Well Posedness for Nonhomogeneous Boussinesq Equations

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces (θ,u)∈LT∞(B˙p,1N/p)×LT∞(B˙p,1N/p−1)⋂LT1(B˙p,1N/p+1) with 1<p<2N. We proved the global existence of the solution when the initial velocity is small with respect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, we proved the uniqueness for 1<p≤N. Our results can been seen as a version of symmetry in Besov space for the Boussinesq equations.

Recurrent coronal jets observed by SDO/AIA

In this paper, we carried out multiwavelength observations of three recurring jets on 2014 November 7. The jets originated from the same region at the edge of AR 12205 and propagated along the same coronal loop. The eruptions were generated by magnetic reconnection, which is evidenced by continuous magnetic cancellation at the jet base. The projected initial velocity of jet2 is ∼402 km s−1. The accelerations in the ascending and descending phases of jet2 are not consistent, the former is considerably larger than the value of g ⊙ at the solar surface, while the latter is lower than g ⊙. There are two possible candidates of extra forces acting on jet2 during its propagation. One is the downward gas pressure from jet1 when it falls back and meets with jet2. The other is the viscous drag from the surrounding plasma during the fast propagation of jet2. As a contrast, the accelerations of jet3 in the rising and falling phases are constant, implying that the propagation of jet3 is not significantly influenced by extra forces.