The Particle-In-Cell (PIC) method has been developed in order to investigate microscopic phenomena, and with the advances of computing power, newly developed codes have been used for several fields such as astrophysical, magnetospheric, and solar plasmas. PIC applications have grown extensively with large computing powers available on supercomputers such as Pleiades and Blue Waters in the US. For astrophysical plasma research PIC methods have been utilized for several topics such as reconnection, pulsar dynamics, non-relativistic shocks, relativistic shocks, relativistic jets, etc. PIC simulations of relativistic jets have been reviewed with the emphasis on the physics involved in the simulations. This review summarizes PIC simulations, starting with the Weibel instability in slab models of jets, and then focuses on global jet evolution in helical magnetic field geometry. In particular we address kinetic Kelvin-Helmholtz instabilities and mushroom instabilities.

Current-voltage characteristics curves of NFinFET are presented and are fitted with the modi-fied current-voltage (I-V) formulas, where the modified term in the triode region is demon-strated to be indispensable. In the as-known I-V formula, important parameters need determin-ing to make both the measured data and the fitting data as close as possible. Those parameters include kN (associated with the sizes of the transistor and mobility), (associated with Early Voltage), and Vth (the threshold voltage). The differences between the measured data and the fit-ting data vary as the applied source-drain bias, proving that the mobility of the carriers is not consistently constant. On the other hand, a modified formula, called kink effect factor, is nega-tively or positively added simulating solitary heat waves, which disturb the propagation of car-riers and thus influence the Source-Drain current (IDS). The new statistical standard deviations () are then found to be effectively suppressed as the kink effect is taken into account.

Insulated Gate Bipolar Transistor (IGBT) may convey high current and sustain high breakdown voltages; it may provide high power control. In a sense, how IGBT demonstrates the capability of power control was not specifically described, and the equivalent bipolar junction transistors (BJT) activated by an applied bias to the insulated gate is intriguing. As seen in Figure 1, IGBT shows an equivalent circuit structure containing two types of BJT, (NPN-type Bipolar transistor and PNP-type Bipolar transistor), which can be modeled as diode-associated transistor. Apparently, as a bias applies to the controlling gate, the channel beneath the gate oxide gets strongly inversed and turns out to be conductive just like what happens on metal-oxide-silicon field effect transistor (MOSFET), which provides necessary igniting currents to both BJTs and thus causes high current gain flowing through them-selves from the bottom. A proposed and renewed formula provides addressing the above scenario and successfully fitting the measured data that forms the characteristic curves. Some parameters in the proposed formula, which includes size and mobility associated constant, threshold voltage, and Early-Voltage-related lambda for MOSFET, explain and explore the underlying physics. IGBT thus enjoy high input impedance and high current gain due to MOSFET (Insulated Gate) and BJT, respectively. This formula combines both merits of MOSFET and BJT in order to fit the measured data. Indeed, the formula intimately fits IGBT electrical characteristic curves, and thus may be qualified and served as a model. The new model is then advisable for designing power integrated circuit to exactly achieve power saving, power control, and power efficiency.

This paper investigates the relationship between public debt and economic growth in the context of a panel kink regression with latent group structures. The proposed model allows us to explore the heterogeneous threshold effects of public debt on economic growth based on unknown group patterns. We propose a least squares estimator and demonstrate the consistency of estimating group structures. The finite sample performance of the proposed estimator is evaluated by simulations. Our findings reveal that the nonlinear relationship between public debt and economic growth is characterized by a heterogeneous threshold level, which varies among different groups, and highlight that the mixed results found in previous studies may stem from the assumption of a homogeneous threshold effect.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

In the study of relativistic jets one of the key open questions is their interaction with the environment on the microscopic level. Here, we study the initial evolution of both electron–proton (e^- - p⁺) and electron–positron (e^±) relativistic jets containing helical magnetic fields, focusing on their interaction with an ambient plasma. We have performed simulations of "global" jets containing helical magnetic fields in order to examine how helical magnetic fields affect kinetic instabilities such as the Weibel instability, the kinetic Kelvin-Helmholtz instability (kKHI) and the Mushroom instability (MI). In our initial simulation study these kinetic instabilities are suppressed and new types of instabilities can grow. In the e^- - p⁺ jet simulation recollimation-like instability occurs and jet electrons are strongly perturbed. In the e^± jet simulation a recollimation-like instability occurs at early times followed by a kinetic instability and the general structure is similar to a simulation without helical magnetic field. Simulations using much larger systems are required in order to thoroughly follow the evolution of global jets containing helical magnetic fields.