The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to simulate non-stationary ...compressible multicomponent reactive flows. The multicomponent composition of the reacting medium and the reactions occurring in it were described by expanding the original system of Euler equations by a system of non-stationary convection–reaction equations. The use of this method to simulate high stiff problems associated with reactions occurring in a multicomponent medium requires the use of the adaptive change in the time step. The solution of the classical problem related to the formation and propagation of a ZND detonation wave is carried out. It was shown that the space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter can be used to simulate flows without using of splitting in directions and fractional step methods.
The influence of poly(titanium oxide) obtained using the sol-gel method in 2-hydroxyethyl methacrylate medium on the viscoelastic and thermophysical properties of interpenetrating polymer networks ...(IPNs) based on cross-linked polyurethane (PU) and poly(hydroxyethyl methacrylate) (PHEMA) was studied. It was found that both the initial (IPNs) and organo-inorganic interpenetrating polymer networks (OI IPNs) have a two-phase structure by using methods of dynamic mechanical analysis (DMA) and differential scanning calorimetry (DSC). The differential scanning calorimetry methods and scanning electron microscopy (SEM) showed that the presence of poly(titanium oxide) increases the compatibility of the components of IPNs. It was found that an increase in poly(titanium oxide) content leads to a decrease in the intensity of the relaxation maximum for PHEMA phase and an increase in the effective crosslinking density due to the partial grafting of the inorganic component to acrylate. It was shown that the topology of poly(titanium oxide) structure has a significant effect on the relaxation behavior of OI IPNs samples. According to SEM, a uniform distribution of the inorganic component in the polymer matrix is observed without significant aggregation.
Crystallite size values were determined by X-ray diffraction methods for 210 TiO
2 (anatase) nanocrystalline powders with crystallite size from 3 nm to 35 nm. Each X-ray diffraction pattern was ...processed using different free and commercial software. The crystallite size calculations were performed using Scherrer equation and Warren–Averbach method. Statistical treatment and comparative assessment of the obtained results were performed for the purpose of an ascertainment of statistical significance of the obtained differences. The average absolute divergence between results obtained with using Scherrer equation does not exceed 0.36 nm for the crystallites smaller than 10 nm, 0.54 nm for the range 10–15 nm and 2.4 nm for the range >
15 nm. We have also found that increasing the analysis time improves statistics, however does not affect the calculated crystallite sizes. The values of crystallite size determined from X-ray data were in good agreement with those obtained by imaging in a transmission electron microscope.
It is assumed that an electric charge moving along a circular path, i.e., with centripetal acceleration, necessarily emits photons. The purpose of this work is to establish the conditions for the ...radiation of an electric charge proceeding from significant differences between its tangential and centripetal accelerations. Materials and methods. The starting point is a credible statement. A number of mathematically correct transformations are performed with it. Therefore, the result is necessarily reliable. Since electromagnetic radiation carries away energy, the energy of the radiating system changes during radiation. Associated with this is the following well-known rule: change in energy is equal to the work performed. The research results can be used in the construction of theoretical models of phenomena and processes, as well as considered in technical applications.
The defect of the angular momentum of an electron under cyclotron (synchrotron) radiation, including in terms of its spatial orientation, as well as the spatial orientation of the emitted photon, is ...considered. The possibility of the compatibility of the idea of the photon as a gauge boson, which can exist only in two spin states, ±1, with a linearly polarized photon, i.e., having no spin, has been studied. It is established that photons have no spin. The angular momentum defect can carry away a spinless photon. As applied to the angular momentum defect, the photon momentum arm is equal to its reduced wavelength.
Relevance and formulation of the problem. The number of areas of scientific and practical activity in which it is necessary to consider relativistic corrections is steadily growing. In many cases, ...two objects under study move towards one another. This takes place both in relation to astronomical objects and in relation to quantum particles, including in colliders—accelerators of charged particles in colliding beams. With counter relativistic motions, the relative velocity does not coincide with the approach velocity. However, considering relative velocity alone limits the arsenal of research tools and methods. As opposed to relative velocity, which is determined in accordance with the relativistic formula for velocity addition, the approach velocity of unaccelerated objects is defined as the ratio of the distance between them to the time it takes to cover it. The purpose of this work is to analyze the variety of the relativistic approach velocity of objects depending on the choice of inertial reference frames based on the data of the Large Hadron Collider. Results. At the Large Hadron Collider, the approach velocity of protons is almost twice as high as the speed of light in the laboratory reference frame. In frames of reference associated with moving protons, depending on the options of relativistic transformation of segments of lengths and time intervals, the maximum approach velocity of protons is 1.1 × 10
8
с
, and the minimum is 1.2 m/s. In accordance with the technique based on the relativistic velocity addition formula, the approach velocity in reference systems associated with moving protons is almost equal to the speed of light. In this case, the approach velocity becomes equal to the relative velocity, which should not be considered as a generalization of the classical mechanics rule on the indistinguishability of these velocities to relativistic mechanics. Practical significance. The results obtained may be of interest in assessing the approach velocities of astronomical objects, including the Earth and asteroids, as well as significantly expand the variability of hypotheses when processing experimental data arrays obtained at elementary particle accelerators, including the Large Hadron Collider.
A numerical model of wave packets on the surface of the reservoir was built with slowly changing depth, concentrated in the vicinity of moving points along space-time rays with group velocity (such ...wave packets are called quasiphotons). At the bottom, profile of the reservoir was taken as the bottom profile of the Gulf of Finland in the coastal zone of the Sestroretsk approach fairway.
This paper presents a technique for determining the types of discontinuities in the numerical solution of various problems of gas dynamics. The relevance of the topic is determined by the fact that ...in complex gas-dynamic formulations, the correct definition of the regions occupied by rarefaction waves (RWs), contact discontinuities, and shock waves (SWs) is required. The choice of the scheme for the numerical solution of the problem depends on the correct definition of such regions. In this paper, we present a technique that makes it possible to determine in a unified way the boundaries of regions containing discontinuities and waves of various types. To do this, in terms of the required gas-dynamic functions, inequalities are derived that single out such regions. This information is used when modifying known or constructing new difference schemes in order to increase their stability and/or monotonicity. For example, the resulting inequalities allow us to single out numerical schemes whose solutions satisfy the requirement of a nondecreasing entropy. The main consideration is given in the one-dimensional case. The technique is generalized to the multidimensional case. Examples are given of applying the technique to solving a number of well-known test problems in gas dynamics.
A mechanical counterpart of cyclotron motion is found. The configuration of the corresponding device is determined; it may be called a stabilized rotor. The natural rotational frequency (speed) of ...the rotor is fixed. (It does not depend on the moment of inertia or the angular momentum.) Remarkably, it is the same as the natural oscillation frequency of a pendulum with identical parameters.
We analyze conductivity of polymerized ionic liquids with focus on fundamental limitations hindering faster charge transport in polymer electrolytes. We emphasize that to achieve the required ionic ...conductivity ∼10−3 S/cm in dry polymer electrolytes, a decoupling of ion transport from segmental dynamics is required. We demonstrate that two competing mechanisms control decoupling of ion transport: electrostatic interactions that dominates for small ions such Li, and elastic force that dominates for large ions. Our experimental results indeed confirm significant contribution of the elastic force to the energy barrier controlling transport of large ions. We also emphasize importance of ion-ion correlations that strongly affect charge transport (conductivity) even at the same ion diffusivity. Our analysis suggests that these correlations suppress ion conductivity in polymer electrolytes by about ten times. At the end, we formulate some ideas on design of polymer electrolytes with high ion conductivity.
•Electrostatic and elastic forces control decoupled ion conductivity.•Increase in shear modulus increases energy barrier for ion conductivity.•Ion-ion correlations decrease conductivity in polymer electrolytes by ∼10 times.
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