CALCULATION OF FLOWS IN AN ACCELERATOR OF ELEMENTARY PARTICLES

The Schrödinger and Klein-Gordon equations have a finite velocity solution using the Navier-Stokes equation. But the Dirac equation did not lend itself to solving with the help of a finite formula for an arbitrary vector and scalar potential. Finally, the transition from the derivative of the function to the derivative of the logarithm of the function worked. Then we managed to solve a linear equation with respect to the derivative of the logarithm of the function, which can be integrated. Moreover, it turned out that it is possible to describe many particles. At accelerators, the trajectories of particles with an error are described, i.e. complex trajectories. In this article, the task is to calculate the accelerator in the complex plane, where the imaginary part is the error of the mean — the real part.

Gravitational Fields and Gravitational Waves

For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession?

Temperature Dependent Entropy Driven Water Uptake in Phase Separated Aerosol from Steered Molecular Dynamics and Intrinsic Surface Analysis

<p>Dynamic water uptake by aerosol is a major driver of cloud droplet activation and growth. Interfacial mass transfer— that governs water uptake if the mean free path of molecules in the vapour phase is comparable to particle size — is represented in models by the mass accommodation coefficient. Although widely used, this approach neglects <em>i</em>) other internal interfaces (e.g., liquid-liquid that may be important for water uptake), and, <em>ii</em>) fluctuations of the liquid surface from capillary waves that modulate the surface and induce ambiguity in the estimation of mass accommodation coefficients. These issues can be addressed if the full path of the water molecule – from vapour to the bulk aqueous phase - is considered.<span> </span></p><p>We demonstrate, using steered molecular simulations, that a full treatment of the water uptake process reveals important details of the mechanism. The simulations are used to reconstruct the free energy profile of water transport across a vapour/hydroxy cis-pinonic acid/water double interface at 300 K and 200 K. In steered molecular dynamics the transferred molecule is pulled with a finite velocity along an aptly chosen reaction coordinate and the work exerted is used to reconstruct the free energy profile. Due to the finite velocity pulling, this method takes the effect of friction on the transport mechanism into account, which is important for phases of considerably different friction coefficients and is neglected by<span>  </span>quasi equilibrium free energy methods. Free energy profiles are used to estimate surface and bulk uptake coefficients and are decomposed into entropic and enthalpic contributions.<span> </span></p><p>Surface accommodation coefficients are unity at both temperatures, while bulk uptake at 300 K from the internal interface is strongly hindered (k<sub>b</sub>=0.05) by the increased density and molecular order in the first layer of the aqueous phase, which results in decreased orientational entropy. The difference between bulk and surface uptake coefficients also implies that water accumulates in the organic shell, which cannot be predicted using a single uptake coefficient for the whole particle. The minimum of the free energy profile at the organic/water interface, rationalised by increased conformational entropy due to local mixing and the depleted system density, results in a concentration gradient which helps maintain low surface tension and phase separation. Low surface tensions may explain increased CCN activity. These entropic features of the free energy profiles diminish at low temperature, which invokes a completely different mechanism of water uptake. Our results point out the need to describe water uptake in aerosol growth models using a temperature dependent parametrisation.</p>

Transmission of Trading Orders through Communication Line with Relativistic Delay

The notion of “relativistic finance” became ingrained in the public imagination and has been asserted in many mass-media reports. However, despite an observed drive of the most reputable Wall Street firms to establish their servers ever closer to the trading hubs, there is surprisingly little concrete information related to the relativistic delay of the trading orders. There is an underlying assumption that faster electronics are always beneficial to the stability of the network. In this paper, the author proposes a modified M/M/G queue theory to describe the propagation of the trading signal with finite velocity. Based on this theory, we demonstrate that, even if the reaction time of the system is negligible, the propagating signal is distorted by simple acts of trading along the transmission line.

Modelling of Nonlinear Thermodiffusion for a Spherically Symmetric Case

The paper discusses the properties of the nonlinear thermodiffusion equation corresponding to the heat transfer processes occurring with a finite velocity in gas from a high intensity source. In the previous papers A. J. Janavičius proposed the nonlinear diffusion equation which provided a more exact description of impurities diffusion by fast moving vacancies generated by X-rays in Si crystals. This is similar to the heat transfer in gas with constant pressure by molecules carrying a greater average kinetic energy based on the nonlinear thermodiffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. Heat transfer in gas must be compatible with the Maxwell distribution function. Heat transfer in gas described by using nonlinear thermodiffusion equation with heat transfer coefficients directly proportional to temperature . The solution of the thermodiffusion equation in gas was obtained by using similarity variables. The equation is solved by separating the linear part of the equation that coincides with Fick's second law. The obtained results coincide with Ya.B. Zeldovich’s previously published solutions of nonlinear equations by changing the respective coefficients.

PROBLEM OF THE COSMIC GRAVITY MEASUREMENT

Based on Newton's adapted law of universal gravitation in the case of moving masses, taking into account the finite velocity of gravity, differential equations of motion of celestial bodies are obtained. The transient process of the precession of the planet's perihelion was simulated for the first time. A new physical interpretation of the celestial phenomenon due to the discovered new component of force in addition to the Newtonian and Lorentz (gravitomagnetic) is given. The problem of measuring a new force has been formed. The results of computer simulation of the precessing perihelion of the planet considering a new force component are discussed.

Law of universal gravitation with finite velocity of gravity and mathematical model of motion of a finite number of material points

The law of universal gravitation is intro- duced taking into account the finiteness of the gravi- tational velocity. Based on this law, a mathematical model of the motion of a finite number of material points is constructed, a separate case of which is the classical model of the motion of points, which is de- scribed by a system of ordinary differential equations. The constructed model is a system of nonlinear dif- ferential equations with deviating argument and func- tional equations. It more accurately describes the dy- namics of a finite number of material points than the corresponding classical model. A mathematical model of the motion of two material points is also considered.