Self-consistent Problem Research Articles

Analysis of momentum characteristics of the miniengine of a microelectromechanical system operating on a solid mixed propellant

A self-consistent problem relating combustion parameters of a solid propellant in a miniengine of the microelectromechanical system to the engine’s structural characteristics is solved. The dependence of the pressure in the combustion chamber of this engine on the combustion rate of the propellant in it and the engine’s outlet diameter is determined. Recommendations are formulated for the choice of the composition of a mixed solid propellant based on glycidyl azide polymer doped with nitramines and for the geometry of the combustion chamber of the above miniengine, which provide the required values of its total momentum and the propulsive force.

Numerical modeling of the processes within the combustion chamber of a solid propellant rocket engine during the stabilization of the design operation mode

Comprehensive numerical modeling of the processes occurring in the combustion chamber of a solid propellant rocket engine during the stabilization of the design operation mode is performed. The self-consistent problem considered includes nonstationary operation of an ignition device, warmup and ignition of a solid propellant charge followed by its nonstationary burning, nonstationary threephase homogeneous-heterogeneous flow of the combustion products in the combustion chamber, in the nozzle, and behind the engine nozzle unit, engine depressurization, and nozzle unit plug blowing-out. The results of the calculations are presented.

Singularity/scattering alternative for a discrete family of static critical solutions with various numbers of unstable eigenmodes

This paper reports on the study of some solutions for a system of coupled nonlinear wave equations of a hyperbolic type, effectively dependent on one spatial (radial) variable and one time variable. This system of equations, which is a coupled system of the Yang-Mills equations with a scalar field, i.e., dilaton, belongs to the so-called class of supercritical systems, for which there exist solutions that inevitably lead to the formation of singularities at a point or even a whole region during a finite period of time at smooth initial distributions with finite energy. This system of equations has regular stationary solutions with finite energy. All such stationary solutions are unstable and can be parametrized by the number N, which is the number of their unstable eigenmodes in linear approximation, and N = 1, 2, 3, …, ∞. The self-consistent problem of the decay of such stationary solutions with N = 1, 2, 3, 4 on the independent excitation of their unstable eigenmodes was solved numerically in nonlinear regime. The corresponding initial-boundary problem was investigated numerically by means of an adaptive computation scheme based on a conservative finite-differential scheme with energy conservation. It has been found that for each considered stationary solution only the perturbation of its basic unstable eigenmode leads to the formation of the singularity/scattering alternative, the governing parameter in the choice of the alternative being the sign of the major unstable eigenmode. It is shown that the independent perturbation of all higher unstable eigenmodes necessarily leads to the formation of a singularity. It is also found that the nonlinear waves formed with the decay of the basic N = 1 solution on the perturbation of its single unstable mode may expose some properties peculiar to solitons.

Quantum ballistic transport in the junctionless nanowire pinch-off field effect transistor

In this work we investigate quantum ballistic transport in ultrasmall junctionless and inversion mode semiconducting nanowire transistors within the framework of the self-consistent Schrodinger-Poisson problem. The quantum transmitting boundary method is used to generate open boundary conditions between the active region and the electron reservoirs. We adopt a subband decomposition approach to make the problem numerically tractable and make a comparison of four different numerical approaches to solve the self-consistent Schrodinger-Poisson problem. Finally we discuss the IV-characteristics for small (r?5 nm) GaAs nanowire transistors. The novel junctionless pinch-off FET or junctionless nanowire transistor is extensively compared with the gate-all-around (GAA) nanowire MOSFET.

Self-Consistent Field and Polarizable Continuum Model: A New Strategy of Solution for the Coupled Equations.

We present a new strategy for the solution of the self-consistent field (SCF) equations when solvent effects are included by means of the polarizable continuum model (PCM). By exploiting the recently introduced variational formalism of the PCM (VPCM), we are able to recast the self-consistent reaction field problem as an energy functional of both electronic and polarization degrees of freedom. The variational minimization of such a functional leads to the free energy of the solvated molecule at a given geometry. In this contribution we describe an effective procedure and its implementation to achieve the solution of such a variational problem. Moreover, we present numerical evidence that the new approach is superior to the traditional one in terms of performance, especially when a relatively inexpensive semiempirical method is used to describe medium- and large-size solutes.

Equilibrium ion distribution modeling in RF ion traps and guides with regard to Coulomb effects

Considered is the problem of numerical simulation of the equilibrium ion distributions for ions with different m/z ratios in RF ion traps and guides, in which the ion confinement is due to the averaged RF pseudopotential field and collision cooling. The proposed algorithm takes into account the buffer gas temperature and Coulomb interaction between the particles.The original self-consistent problem for the Poisson equation is reduced to a variational problem for a thermodynamic potential, which is solved numerically basing on the smooth spline approximations and the conjugate gradients method. The algorithm is implemented as a separate program module of the MASIM 3D package and comprehensively tested. Some numerical results are discussed.

Application of partially coherent modes for studying generation of a Gaussian partially coherent laser beam

The problem of steady-state generation of a Gaussian partially coherent beam in a stable-cavity laser is considered within the framework of the method of expansion of the radiation coherence function in partially coherent modes. We discuss the conditions whose fulfilment makes it possible to neglect the intermode beatings of the radiation field and the effect of the gain dispersion on the steady-state generation of multimode partially coherent radiation. Based on the simplified model, we solve the self-consistent problem of generation of a Gaussian partially coherent beam for the given laser pump conditions and the resonator parameters. The dependence of the beam characteristics (power, radius, etc.) on the active medium properties and the resonator parameters is obtained.

The self-consistent dynamic problem of estimating the damage of a material by an acoustic method

An approach is proposed for formulating the self-consistent problem on the basis of equations that describe the dynamics of a material and the state of its defects. It is shown that the damage of the material gives rise to frequency-dependent attenuation and phase velocity dispersion of an ultrasonic wave propagating in it. This makes it possible to estimate the damage by means of the acoustic method. The applied deformation field leads to accumulation of defects. A kinetic equation is derived for describing the damage growth, which proves to be an exponential process. The parameters of the system for which the accumulation of defects can approximately be considered as linear are estimated.

Non-local model of hollow cathode and glow discharge

A general form of the non-local equation for an ionization source in glow discharge and hollow cathode 3D-simulation is formulated. It is a fundamental equation in hollow cathode theory, which allows formulation of a complete set of field equations for a self-consistent problem in a stationary glow discharge and hollow cathode. It enables us to describe the region of negative glow and the hollow cathode effect and compare calculation results of electrical dependencies (pressure-voltage) with experimental data, – under conditions of gradual appearance of the hollow cathode effect.

Determination of screened Coulomb repulsion energies in organic molecular crystals: A real space approach

We present a general method for determining screened Coulomb parameters in molecular assemblies, in particular organic molecular crystals. This allows us to calculate the interaction parameters used in a generalized Hubbard model description of correlated organic materials. In such a model only the electrons in levels close to the Fermi level are included explicitly, while the effect of all other electrons is included as a renormalization of the model parameters. For the Coulomb integrals this renormalization is mainly due to screening. For molecular materials we can split the screening into intra- and inter-molecular screening. Here we demonstrate how the inter-molecular screening can be calculated by modeling the molecules by distributed point-polarizabilities and solving the resulting self-consistent electrostatic screening problem in real space. For the example of the quasi one-dimensional molecular metal TTF–TCNQ we demonstrate that the method gives remarkably accurate results.

New theoretical approaches for correlated systems in nonequilibrium

We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a "prethermalized" intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensembles.

Simulation of multilayer injection lasers with internal emission leaking

A mathematical model of multilayer injection lasers, based on the self-consistent kinetic problem taking into account the correlation between optical and electrical characteristics of a device is presented. The light-current characteristic of such laser is measured. A fast algorithm for computing complex eigenvalues of the wave equation is proposed. The calculation results are compared with experimentally measured light-current characteristics of diode lasers (fabricated by the GNOptics Company) with emission leaking to an optical cavity. The optical field profiles are determined in subthreshold and above-threshold modes for structures of high-power injection lasers with internal emission leaking. Good agreement between experimental and calculated data is achieved.

Feshbach Resonances: The Branching of Quantum Mechanics into Hermitian and Non-Hermitian Formalisms

As has been shown long time ago by Feshbach, the exact energy spectrum of the full problem can be obtained by solving two different self-energy problems. In spite of the fact that the two effective Hamiltonians are derived in very similar ways in one case, the exact energy spectrum of the full problem can be either real or complex (depending on the boundary conditions), whereas the exact energy spectrum associated with the second effective Hamiltonian has to be complex (excluding bound states in the continuum). The focus of this paper is on the fact that in both cases the complex eigenvalues result from the same requirement of an out-going boundary condition. The branching of quantum mechanics to standard (Hermitian) formalism and non-Hermitian formalism is associated with the decision to express the exact energy spectrum with one of the two possible self-consistent like problems where the use of the Green operator imposes an outgoing boundary condition on the solutions of the time-independent Schrodinger equation. Our analysis is made for the case where an ABC molecule has sufficient energy to dissociate to A + BC but not to A + B + C and not to AB + C or to AC + B.

Self-consistent many-body perturbation theory in range-separated density-functional theory: A one-electron reduced-density-matrix-based formulation

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schr\"odinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this ``self-consistency problem'' and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order M\o{}ller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid G\"orling-Levy-type MBPT-DFT model.

Modelling the radiative electromagnetic field

The radiative electromagnetic field is generated during the experiments with a radiation and is of importance for spacecrafts under sun radiation and for the radio-electronic equipment of the nuclear reactor control systems. The paper presents the developed methods of modelling the multistage process of the radiative electromagnetic field excitation. The methods are based on both deterministic technique of solving the time-dependent self-consistent problems for the Maxwell equations and statistical algorithms for modelling the ionising radiation transport in dense materials.

The determination of the parameters of a thermal wave for solving self-consistent problems of electromagnetic heating

The wave process of the propagation of heat in electromagnetic heating devices is analyzed. The velocity of propagation of a thermal wave and its dispersion properties are determined. It is shown that it is possible to use this method to solve self-consistent problems.

Magnetic-field-induced phase transition in a two-dimensional quantum magnet with plaquette distortion

Magnetic field effect on the structure of the ground state of a two-dimensional quantum Heisenberg magnet is analyzed. A plaquette representation is used to solve the self-consistent problem and calculate the collective excitation spectrum in a magnetic field. Conditions are found for quantum transition between non-magnetic and oblique antiferromagnetic phases. The change in the ground state of the system is associated with disappearance of the gap in the spin excitation spectrum. Effects of frustration and magnetic field on the spectrum are analyzed. A phase diagram of stable singlet and magnetically ordered phases is presented.

Diffraction phenomena in ring gas lasers

The frequency and amplitude diffraction nonreciprocity of counterpropagating waves in a ring gas laser is studied. The self-consistent eigenmode problem is solved within the framework of the model of Gaussian beams for a ring optical resonator containing a nonlinear gaseous medium and a model aperture. The expressions for frequency-dependent losses, frequencies and intensities of counterpropagating waves are obtained and analysed. Experimental data on the influence of diffraction phenomena on the frequencies and intensities of counterpropagating waves reported in the literature are analysed. Nonreciprocal effects related to diffraction are classified by comparing the experimental data with theoretical results. The mechanisms of the asymmetry of the lasing region with respect to the central frequency of the transition and asymmetry of the laser line are explained.

Disorder effects in the quantum Heisenberg model: Extended dynamical mean-field theory analysis

We investigate a quantum Heisenberg model with both antiferromagnetic and disordered nearest-neighbor couplings. We use an extended dynamical mean-field approach, which reduces the lattice problem to a self-consistent local impurity problem that we solve by using a quantum Monte Carlo algorithm. We consider both two- and three-dimensional antiferromagnetic spin fluctuations and systematically analyze the effect of disorder. We find that in three dimensions for any small amount of disorder a spin-glass phase is realized. In two dimensions, while clean systems display the properties of a highly correlated spin liquid (where the local spin susceptibility has a noninteger power-law frequency and temperature dependence), in the present case this behavior is more elusive unless disorder is very small. In fact the spin-glass transition temperature leaves only a limited intermediate temperature regime, where the system displays the spin-liquid behavior.

Self-consistent analytical solution of a problem of charge-carrier injection at a conductor/insulator interface

We present a closed description of the charge-carrier injection process from a conductor into an insulator. Common injection models are based on single electron descriptions, being problematic especially once the amount of charge-carriers injected is large. Accordingly, we developed a model, which incorporates space-charge effects in the description of the injection process. The challenge of this task is the problem of self-consistency. The amount of charge carriers injected per unit time strongly depends on the energy barrier emerging at the contact, while at the same time the electrostatic potential generated by the injected charge carriers modifies the height of this injection barrier itself. In our model, self-consistency is obtained by assuming continuity of the electric displacement and the electrochemical potential all over the conductor/insulator system. The conductor and the insulator are properly taken into account by means of their respective density of state distributions. The electric-field distributions are obtained in a closed analytical form and the resulting current-voltage characteristics show that the theory embraces injection-limited as well as bulk-limited charge-carrier transports. Analytical approximations of these limits are given, revealing physical mechanisms responsible for the particular current-voltage behavior. In addition, the model exhibits the crossover between the two limiting cases and determines the validity of respective approximations. The consequences resulting from our exactly solvable model are discussed on the basis of a simplified indium tin oxide/organic semiconductor system.