Filippov Type Research Articles

Dynamic Faraday cup signal analysis and the measurement of energetic ions emitted by plasma focus

A theoretical model is developed to study the signals from a typical dynamic Faraday cup, and using this model the output signals from this structure are obtained. A detailed discussion on the signal structure, using different experimental conditions, is also given. It is argued that there is a possibility of determining the total charge of the generated ion pulse, the maximum velocity of the ions, ion velocity distribution, and the number of ion species for mixed working gases, under certain conditions. In addition, the number of different ionization stages, the number of different pinches in one shot, and the number of different existing acceleration mechanisms can also be determined provided that the mentioned conditions being satisfied. An experiment is carried out on the Filippov type 90 kJ Sahand plasma focus using Ar as the working gas at the pressure of 0.25 Torr. The data from a typical shot are fitted to a signal from the model and the total charge of the related energetic ion pulse is deduced using the values of the obtained fit parameters. Good agreement between the obtained amount of the total charge and the values obtained during other experiments on the same plasma focus device is observed.

Investigation of the Plasma Behavior in Filippov-Type Plasma Focus Using the State Space of Sing Lee’s Model

The state space of Lee’s model (SSL model) is a model developed for plasma behavior in Filippov-type plasma focus facilities which has been described and used. This model is attractive because it provides a practical approach for analysis of a plasma focus device. In this article, we turn to an alternative method of system analysis using time-domain methods. We will reconsider the differential equations describing the Filippov-type plasma focus device and select a certain form of differential equations. We will use a set of variables that can be used to establish a set of first-order differential equations. Using matrix methods, we will be able to determine the transient response of the Filippov-type plasma focus device and examine the performance of this system. This model is a derivation of modified Lee’s model and is based on the so-called slug model. Using the SSL model, the discharged current and its derivative as a function of time, pinch time, and maximum discharge current; as functions of pressure, have been predicted. The experimental data obtained by using the UIPFF1 facility with a maximum energy of 20 kJ is compared with the simulated data obtained through SSL model. This investigation shows that the SSL model is capable of predicting the plasma behavior in the Filippov type plasma focus.

On a fractional differential inclusion with nonlocal Riemann-Liouville type integral boundary conditions

We study the existence of solutions for fractional differential inclusions of order q ∈ (1; 2] with four-point nonlocal Riemann-Liouville integral boundary conditions. We establish Filippov type existence results in the case of nonconvex set-valued maps. Key words: fractional differential inclusion, Caputo fractional derivative, boundary value problem, integral boundary conditions.

Concurrent homoclinic bifurcation and Hopf bifurcation for a class of planar Filippov systems

This paper investigates both homoclinic bifurcation and Hopf bifurcation which occur concurrently in a class of planar perturbed discontinuous systems of Filippov type. Firstly, based on a geometrical interpretation and a new analysis of the so-called successive function, sufficient conditions are proposed for the existence and stability of homoclinic orbit of unperturbed systems. Then, with the discussion about Poincaré map, bifurcation analyses of homoclinic orbit and parabolic–parabolic (PP) type pseudo-focus are presented. It is shown that two limit cycles can appear from the two different kinds of bifurcation in planar Filippov systems.

Functional differential inclusions and dynamic behaviors for memristor-based BAM neural networks with time-varying delays

In this paper, we formulate and investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, the viability and dissipativity of solutions for functional differential inclusions and memristive BAM neural networks can be guaranteed by the matrix measure approach and generalized Halanay inequalities. Then, a new method involving the application of set-valued version of Krasnoselskii’ fixed point theorem in a cone is successfully employed to derive the existence of the positive periodic solution. The dynamic analysis in this paper utilizes the theory of set-valued maps and functional differential equations with discontinuous right-hand sides of Filippov type. The obtained results extend and improve some previous works on conventional BAM neural networks. Finally, numerical examples are given to demonstrate the theoretical results via computer simulations.

Energy spectrum of argon ions emitted from Filippov type Sahand plasma focus

The energy and flux of the argon ions produced in Sahand plasma focus have been measured by employing a well-designed Faraday cup. The secondary electron emission effects on the ion signals are simulated and the dimensions of Faraday cup are optimized to minimize these effects. The measured ion energy spectrum is corrected for the ion energy loss and charge exchange in the background gas. The effects of the capacitor bank voltage and working gas pressure on the ion energy spectrum are also investigated. It has been shown that the emitted ion number per energy increases as the capacitor bank voltage increases. Decreasing the working gas pressure leads to the increase in the number of emitted ion per energy.

Effect of hinge friction on the steady-state response of base-excited shallow arches

The focus in this paper is on investigating the influence of hinge friction on the steady-state dynamic response of a transversally base-excited shallow arch. Two semi-analytical models are derived by applying an assumed-modes approach based on sinusoidal modes and Craig–Bampton modes respectively. It is shown that both models give qualitatively and also to a great extent quantitatively similar response results. Hinge friction induces the presence of equilibrium sets rather than static equilibria. Furthermore, the influence of friction on the load-path for a quasi-static acceleration loading is illustrated. In the steady-state analysis of the semi-analytical models, amplitude–frequency diagrams are presented. These plots are obtained by solving two-point boundary value problems in combination with a path-following technique. Local stability and bifurcation analysis of periodic solutions is carried out using Floquet theory for systems of Filippov type. Especially for low excitation amplitudes, the responses dramatically change due to hinge friction, since these responses are dominated by hinge stick. Near resonances and in the case of high-amplitude excitation, the frictional hinge will only slip and the influence of hinge friction is significantly reduced. When hinge friction is relevant, the Craig–Bampton model is expected to predict responses more accurately.

Some Remarks on a Multi Point Boundary Value Problem for a Fractional Order Differential Inclusion

We study a multi point boundary value problem for a fractional order differential inclusion involving a nonconvex set-valued map. We establish a Filippov type existence theorem and we prove the arcwise connectedness of the solution set of the problem considered.

On an Integro-differential Inclusion of Fractional Order

We establish some Filippov type existence theorems for solutions of certain nonconvex fractional hyperbolic integro-differential inclusions involving Caputo’s fractional derivative.

PIECEWISE SMOOTH REVERSIBLE DYNAMICAL SYSTEMS AT A TWO-FOLD SINGULARITY

This paper focuses on the existence of closed orbits around a two-fold singularity of 3D discontinuous systems of the Filippov type in the presence of symmetries.

Attractors near grazing–sliding bifurcations

In this paper we prove, for the first time, that multistability can occur in three-dimensional Fillipov type flows due to grazing–sliding bifurcations. We do this by reducing the study of the dynamics of Filippov type flows around a grazing–sliding bifurcation to the study of appropriately defined one-dimensional maps. In particular, we prove the presence of three qualitatively different types of multiple attractors born in grazing–sliding bifurcations. Namely, a period-two orbit with a sliding segment may coexist with a chaotic attractor, two stable, period-two and period-three orbits with a segment of sliding each may coexist, or a non-sliding and period-three orbit with two sliding segments may coexist.

A note on the existence of solutions for some boundary value problems of fractional differential inclusions

Abstract We study the existence of solutions for fractional differential inclusions of order q ∈ (1, 2] with families of mixed and closed boundary conditions. We establish Filippov type existence results in the case of nonconvex setvalued maps.

Measurement of the Energy of Nitrogen Ions Produced in Filippov Type Plasma Focus Used for the Nitriding of Titanium

In this paper the nitrogen ion properties (maximum energy, current density and the most probable energy) are investigated by using Faraday cup in a time of flight method. These ions are produced in a Filippov type plasma focus (Sahand Facility) device and the Faraday cup was placed in a distance range of 18–24 cm from the top of the anode. Maximum and minimum most probable ion energies are 76 and 8.5 keV for the distance range of 18 and 24 cm, respectively. The displacement from 18 to 24 cm at top of the anode the ion current density varies from 4.5 × 106 to 3.2 × 105 (A m−2). For the investigation of the effect of ions bombardment of materials at different positions, at the optimum working conditions of 14 kV as a working voltage, and 0.25 Torr as a gas pressure, titanium samples are placed in a distance of 21, 22, 23 and 24 cm from the top of the anode (θ = 0) and each sample is put under irradiation for 30 plasma shots. The structure of the nitrided surfaces and their morphologies are characterized by X-ray diffractometry and by scanning electron microscopy, respectively. The average crystallite size deduced for (200) and (222) planes of TiN deposited with 30 shots in different distances are estimate to be from ~13 to ~38 nm.

On the existence of mild solutions for nonconvex fractional semilinear differential inclusions

We establish some Filippov type existence theorems for solutions of fractional semilinear differential inclusions involving Caputo’s fractional derivative in Banach spaces.

Neutron production with mixture of deuterium and krypton in Sahand Filippov type plasma focus facility

This Letter reports the order of magnitude enhancement in neutron yield from Sahand plasma focus device with krypton seeded deuterium operation. The highest average neutron yield of 2.2×109 neutrons per shot was achieved at 1.00 Torr deuterium with 3% krypton which is higher than the best average neutron yield of 3.18×108 neutrons per shot for pure deuterium operation. Estimation of average neutron energy showed that the maximum and minimum average energies are 2.98±0.6 MeV at 16 kV in 0.25 Torr deuterium with 3% Kr and 2.07±0.2 MeV at 18 kV operation in 0.5 Torr deuterium with 3% Kr, respectively. The anisotropy of neutron emission from Sahand DPF showed that the neutrons are produced mainly by beam–target mechanisms.

Increasing of Hardness of Titanium Using Energetic Nitrogen Ions from Sahand as a Filippov Type Plasma Focus Facility

In this paper a 90 kJ plasma focus facility was used to the bombardment of the titanium substrate using nitrogen ion beams. From x-ray diffraction patterns, we investigated the structure properties of titanium nitride layer has been successfully deposited on the titanium substrate such as grain size microstrain and dislocation density. In this work we observed the growth of in grain size with increasing a number of deposition shots. Decrease in dislocation density and microstrain at higher deposition is the another results we observed in this work. The topography and morphology of TiN samples was studied by scanning electron microscopy (SEM) and optical microscopy images. From SEM micrograph, damage of surface and creation of pits and cracks was reported. The goniometric test indicate increasing in contact angle of water drop for irradiated samples in respect to the unirradiated samples. The Knoop microhardness of the samples is increased about 500%. With increasing of nitrogen ion flux, the microhardness increases.

Design and Construction of the 5 kJ Filippov-Type Plasma Focus with Brass Anode

The paper reports on the design and construction of the first Iranian Filippov type plasma focus device (IFFT-PF). The main stages of the design, construction and the preliminary neutron detection tests on the IFFT are mentioned concisely. Some of the characteristics of the IFFT are the brass-made anode with a changeable effective length. Experimental results on the device represent the number of 1.6 × 107 fusion neutrons per shot, with deuterium operating gas including some percentage of krypton.

Some remarks on a fractional differential inclusion with non-separated boundary conditions

We study a boundary value problem for a fractional differential inclusion of order � 2 (1,2] with non-separated boundary conditions involving a nonconvex set-valued map. We establish a Filippov type existence theorem and we prove the arcwise connectedness of the solution set of the problem considered.

Fundamental matrix solutions of piecewise smooth differential systems

Abstract We consider the fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces. We review the cases of transversal intersection and of sliding motion on one surface. We also consider the case when sliding motion takes place on the intersection of two or more surfaces. Numerical results are also given.

Pointwise estimates for retractions on the solution set to Lipschitz differential inclusions

Denote by the set of derivatives of all absolutely continuous solutions of a Lipschitz differential inclusion It is known that the set is an absolute retract. We show the following: Theorem. For every there exists a continuous mapping such that for every the map r is a retraction of onto and for all and almost all we have a Filippov type pointwise estimate where and the functions and are related with the Lipschitz condition.