Radial kinetic nonholonomic trajectories are Riemannian geodesics!

Nonholonomic mechanics describes the motion of systems constrained by nonintegrable constraints. One of its most remarkable properties is that the derivation of the nonholonomic equations is not variational in nature. However, in this paper, we prove (Theorem 1.1) that for kinetic nonholonomic systems, the solutions starting from a fixed point q are true geodesics for a family of Riemannian metrics on the image submanifold $${{\mathcal {M}}}^{nh}_q$$ M q nh of the nonholonomic exponential map. This implies a surprising result: the kinetic nonholonomic trajectories with starting point q, for sufficiently small times, minimize length in $${{\mathcal {M}}}^{nh}_q$$ M q nh !

MODELING PRESSURE FIELDS IN A PETROLEUM RESERVOIR TAKING INTO ACCOUNT THE CHANGE OF LIQUID LEVEL IN THE WELL

This article presents a numerical model of pressure fields during filtration of reservoir fluid, which accounts for the effect of the well. The mathematical formulation of the problem under consideration includes the equation of piezoconductivity in a cylindrical coordinate system and differs in a non-classical boundary condition obtained from the ratio of the balance of mass and momentum. The authors compare the numerical calculations and the analytical solution constructed in the Laplace — Carson image space. Den Iseger’s numerical algorithm is used to convert it to the original space. As a result of the comparison, the area of applicability of the computational experiment was determined. It is shown that in the case of a limited reservoir, the exact solution of the problem coincides with a numerical experiment over the entire domain of definition. In the case of an infinite reservoir, the numerical model is applicable only in the region of small times, the dimensions of which are determined by the values of the right boundary and the radial coordinate.

Identification of changes in the activity of Kambalny volcano (South Kamchatka) based on correlation of seismic noise

Using experimental data obtained from the network of stations installed on Kambalny volcano in the period from July 2018 to July 2019, a set of correlation functions was obtained and its preliminary interpretation was carried out. Works aimed at quality control of the obtained cross-correlation functions have been performed. We have identified considerable variations of the frequency-amplitude characteristics of the cross-correlation functions at small times, as well as significant shifts of the derived phases in large correlation times. Such variations of the cross-correlation patterns may indicate the existence of distinct time periods with different types of seismicity, as well as strong variations of mechanical properties of rocks. In turn, this might be an evidence for the ongoing activity of the magmatic system beneath the Kambalny volcano.

Mathematical modeling of (Cu−Al2O3) water based Maxwell hybrid nanofluids with Caputo-Fabrizio fractional derivative

In this article, a free convection flow of [Formula: see text] hybrid Maxwell nanofluids through a channel formed by two infinite vertical plates have been studied. Together with the the energy balance and heat source, a fractional model of Maxwell fluid is considered. To develop an analytical exact solution for velocity field, only the Caputo-Fabrizio definition of non-integral derivative together with application of Laplace transform method has been used. Some graphical presentation and discussion are made to see the effects of hybrid nanofluids and non-dimensional parameters on velocity boundary layer. As a result, a dual behavior of velocity was exposed due to fractional parameter for large and small times. A comparison between two kind of non-Newtonian fluids has been made and found that Brinkman fluid is more viscous than Maxwell fluid. Also, by letting Brinkman and Maxwell parameters zero, they coincides and the results obtained for Newtonian fluid showed graphically. The obtained results are realistic from the fractional model as by adjusting the values of fractional parameter can be compared with some experimental data.

Mixed-type stochastic differential equations driven by standard and fractional Brownian motions with Hurst indices greater than 1/3

In this paper we consider mixed-type stochastic differential equations driven by standard and fractional Brownian motions with Hurst indices greater than 1/3. There are proved theorems on the existence, uniqueness, and continuous dependence of solutions on the initial data. We provide an analog of the Ito formula to change variables. Asymptotic expansions of functionals on the solutions of mixed-type stochastic differential equations for small times are obtained. We receive analogs of the Kolmogorov equations for mathematical expectations and probability densities in the commutative case. Finally, we consider an application of mixed-type stochastic differential equations to solving the problem of macroeconomic variables extrapolation in credit risks models.

Optimization of sprint interplanetary trajectories with nuclear bimodal thermal propulsion

Interplanetary missions require fast and fuel-efficient transfers. Combining small times transfers of high-thrust and efficiency of low-thrust propulsion can provide a good compromise. Saving an amount of fuel from the initial high-thrust burn and using it to correct the trajectory could lead to an economy of fuel. We investigated the optimal way to take advantages of both high and low-thrust propulsion benefits in order to maximize the payload mass of the mission. Using a simple model of ideal engine of limited power and the transporting trajectory method, we determined the analytical expression of final payload mass. The solution of the optimization problem gave us the optimal repartition of fuel between high and low-thrust maneuvers for a given thrust of thermal propulsion and electrical power of low-thrust propulsion system. As the mass of the low-thrust propulsion system depends on the electrical power, we took it into account to determine the optimal electrical power for a sprint trajectory in a given time. As a result, we could obtain the interval of transfer time for which the combination of high and low thrust becomes optimal.

DIAGNOSTICS OF AMORPHOUS ALLOY MAGNETIC PROPERTIES AFTER THERMOMAGNETIC PROCESSING

Hysteresis magnetic properties formation and plasticity of Fe&Co-based amorphous alloy tapes (brand 30KCP, the Fe–Co–Si–B system) for improvement increase in its properties and ensuring its competitive application on the control basis have been investigated. In researches magnetomeasuring installation have been used. It is intended for automatic magnetic characteristics measurement of soft magnetic materials ring samples by GOST 8.377 techniques. Defined degree of a flexural tension relaxation when annealing tapes. It was established that even at five-minute annealing at a temperature of 360 °C processes of a relaxation manage to take place almost completely. Further change in time of parameter of a relaxation is insignificant. The received dependences of magnetic characteristics on time of thermomagnetic processing at the enclosed field of 10 A/m and their comparison with usual annealing showed that coercive force changes on the same types of curves with insignificant deviations. After thermomagnetic processing in the enclosed field of 21 A/m coercive force in big fields increased approximately by 30 %, in small Hc failure observed around 5 … 15 min of processing as well as Br values increased. This observed result is very interesting in terms of magnetic reversal processes. The lack of stabilization mobile 180° domains borders, at simultaneous course stabilization 90° borders, is reflected in the form of recession of residual induction and growth of magnetic permeability. It is shown that thermomagnetic processing of amorphous alloy of brand 30KCP in not sating longitudinal field with small times of endurance 5…15 min at 360 °C leads to the drawn hysteresis loops, the lowered squareness of hysteresis loops and high values of low-field magnetic permeability 10.

Determination of a time-dependent coefficient in awave equation with unusual boundary condition

In this paper, an initial boundary value problem for a wave equation with unusual boundary condition is considered. Giving an integral over-determination condition, a time-dependent potential is determined and existence and uniqueness theorem for small times is proved. We characterize the estimates of conditional stability of the solution of the inverse problem. Also, the numerical solution of the inverse problem is studied by using finite difference method.