The note is concerned with the theory of many players differential games examined within the framework of mean field approach. The results presented in the note are as follows. First, we show that the solution to the deterministic mean field game can be nonunique. Second, we present a property of the multifunction of the mean field game that describes the value multifunction using its value in the intermediate time.
We consider a stochastic model of changes of prices in real estate markets. We suppose that in a book of prices the changes happen in points of jumps of a Poisson process with a random intensity, i.e. moments of changes sequently follow to a random process of the Cox process type. We calculate cumulative mathematical expectations and variances for the random intensity of this point process. In the case that the process of random intensity is a martingale the cumulative variance has a linear grows. We statistically process a number of observations of real estate prices and accept hypotheses of a linear grows for estimations as well for cumulative average, as for cumulative variance both for input and output prises that are writing in the book of prises.
In this note we deal with control of a quadrocopter in a horizontal plane under state constraints in the form of a labyrinth. An algorithm to construct the programmed motion of the quadrocopter in a flat labyrinth is proposed. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler angles is considered. For synthesis of the control the nonlinear dynamics inversion approach is used. Numerical simulation results are given.
This paper deals with trajectory tracking control of a quadcopter in a horizontal plane. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler angles is considered. For synthesis of the tracking control the nonlinear dynamics inversion approach is used. Three different control strategies with restrictions on the orientation of the quadrotor are studied.
Electronic spin polarization up to 100 % has been observed in type‐II narrow‐gap heterostructures with InSb quantum dots in an InAs matrix via investigation of circular‐polarized photoluminescence at external magnetic field applied in Faraday geometry. Energy spectrum of holes confined in monolayer scale InSb/InAs quantum well is calculated using tight‐binding approach. The observed effect is explained in terms of strong Zeeman splitting of electrons in InAs matrix due to their large intrinsic g‐factor and corresponding optical transition selection rules. Temperature dependence of polarization degree well fit obtained data providing its experimental verification of suggested model.
In the subasymptotic range of variation of parameters of combinatorial schemes, we consider a method of analysis based on explicit enumeration of their outputs in the following directions: enumeration of the output enumeration graph, determination of their number, solution of the numeration problems for outputs in the direct and inverse settings, evaluation of their probability distribution, and construction of an algorithm for their modeling.
Circular‐polarized magneto‐photoluminescence of InSb/InAs type‐II quantum dots has been investigated at a magnetic field applied in the Faraday geometry in the wide range of the excitation intensity. It was observed that under condition of the low excitation (∼1 mW in a spot of 1 mm diameter) luminescence from quantum dots is 100% polarized even at the moderate magnetic field of 4T. Increase of excitation results in diminishing polarization and even change of its sign at the power above ∼100 mW. The effect is explained in terms of full electronic spin polarization in the conduction band due to the Zeeman effect in InAs matrix and power‐dependent contribution into optical recombination of the pure heavy hole states or the combined heavy‐light hole states emerged in InSb/InAs quantum dots.
Although the high-pressure phase diagram of carbon at extreme temperatures and pressures is in focus of theoretical and experimental dynamic compression studies, there still exist outstanding problems including disagreement between theoretical predictions and experiments. Using first-principles molecular dynamics simulations at high temperatures and pressures and employing large unit cells, we construct an accurate phase diagram of carbon using two-phase and Z-methods. In accord with previous simulations, a large positive slope of the melting line is observed for pressures from 0 to 200 GPa, whereas at pressures above 500 GPa a very small negative slope exists, which is in contrast to most of previous simulations and experiment. Our accurate results demonstrate the necessity for future dynamic compression experiments to clarify behavior of carbon at extreme conditions including its melting line.
Graphene nanoribbons are attracting much attention as a platform for optoelectronics. Properties of graphene nanoribbons depend on the width, edge type, edge atoms, etc. and can be significantly changed. Inducing magnetism to graphene nanoribbons would open up a new field for applications. In this work we study optical and magnetic properties of graphene nanoribbons with cobalt incorporated atoms that were grown inside single-walled carbon nanotubes from cobalt phthalocyanine molecules.
This paper is devoted to the numerical simulation of stochastic system for inventory management products using controlled semi-Markov process. The results of a special software for the system’s research and finding the optimal control are presented.
We consider binary gas mixture flows with viscous compressible components in the absence of chemical reactions. We aggregate the previously derived regularized equations for inhomogeneous mixtures and thus derive new simpler regularized equations for homogeneous ones (i.e., with the common velocity and temperature). The entropy balance equation with the non-negative entropy production is stated for the new equations. They are constructed for numerical simulations of flows.
An attitude dynamics of a satellite with a variable properties of inertia under the central of gravity is analyzed. One assumes that the satellite is equipped by rotors with a variable kinetic moments. We suppose that the satellite mass center moves staying in a Keplerian elliptic orbit. We find special rules for the mass distribution change such that relative equilibria prescribed in advance exist. For these relative equilibria necessary conditions of stability are analysed.
We used technology of making high-efficiency superconducting single-photon detectors as a basis for improvement of photon-number-resolving devices. By adding optical cavity and using an improved NbN superconducting film, we enhanced previously reported system detection efficiency at telecom range for such detectors. Our results show that implementation of optical cavity helps to develop four-section device with quantum efficiency over 50% at 1.55μm. Performed experimental studies of detecting multi-photon optical pulses showed irregularities over defining multi-photon through single-photon quantum efficiency.
Measuring the thermal properties such as the heat capacity provide information about intrinsic mechanisms operated inside. In general, the ratio between electron and phonon specific heat Ce/Cp shows how the absorbed energy shared between electron and phonon subsystems. In this work we make estimations for amplitude-modulated absorption of THz radiation technique for investigation of the ratio Ce/Cp in superconducting Niobium Nitride (NbN) at T = Tc . Our results indicates that experimentally the frequency of modulation has to be extra large to extract the quantity. We perform a new technique allowed to work at low frequency with accurately measurement of absorbed power.
We present a new quantum accurate Spectral Neighbor Analysis Potential (SNAP) machine-learning potential for simulating carbon under extreme conditions of dynamic compression (pressures up to 1 TPa and temperatures up to 10,000 K). The development of SNAP potential involves (1) the generation of the training database comprised of the consistent and meaningful set of first-principles DFT (Density Functional Theory) data for carbon materials at high pressure and temperature; (2) the robust and physically guided training of the SNAP parameters on first-principles data involving statistical data analysis; and (3) the validation of the SNAP potential in MD simulations of carbon at high PT conditions. The excellent performance of quadratic SNAP potential is demonstrated by simulating the radial distribution functions at high pressure-temperature conditions and melt curve of diamond, which were found in good …
The present study is devoted to development of a technique for numerical simulation of the wave function dynamics the single Josephson qubits and arrays of noninteracting qubits controlled by ultra-short pulses. We wish to demonstrate the feasibility of a new principle of basic logical operations on the picosecond timescale. The influence of the unipolar pulse (“fluxon”) form on the evolution of the state during the execution of the quantum onequbit operations – “NOT”, “READ” and “ SQR-NOT” – is investigated in the presence of decoherence. In the array of non interacting qubits, the question of the influence of the spread of their energy parameters (tunnel constants) is studied. It is shown that a single unipolar pulse can control a huge array of artificial atoms with 10% spread of geometric parameters in the array.
In this work we discuss the emergence of p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic p-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological px + ipy superfluid of identical microwave-dressed polar molecules.
Microelectromechanical system (MEMS) oscillators are timing devices that generate highly stable frequencies. The stability of the MEMS resonator is widely studied in recent years for avoiding such pull in-instability event. In this letter, we found the MEMS resonator approach the pull in-instability via the emerging extreme event (EE) phenomenon. We analyze the EE with many statistical and numerical measures. The importance of the present work also discussed in this present study.
In this paper we deal with nonlinear control design for Parrot Mambo or Parrot Rolling Spider quadcopters using Simulink Support Package for Parrot Minidrones. A full rigid body model of the flying vehicle that doesn't assume smallness of the Euler angles is considered. For synthesis of the control the nonlinear dynamics inversion and integrator backstepping approaches are used. Block diagrams illustrate how the control laws are applied to Parrot Minidrone flight control. Exercises to design nonlinear Parrot Minidrone control algorithms as Simulink Subsystem blocks are suggested.