Self-consistent Analytical Model Research Articles

Asymmetric sound scattering by gratings of monopolar and dipolar resonators in a viscoelastic materiala).

A self-consistent analytical model of a locally resonant coating exhibiting strong asymmetric wave scattering is presented. Gratings of resonant inclusions composed of cavities and hard particles embedded in a soft matrix are translated to the problem of sound scattering by monopolar and dipolar type resonators in a one-dimensional waveguide. Equations of motion for gratings of cavities and hard particles are developed that incorporate added mass, damping, and restoration forces to take into account multiple scattering effects. Expressions for the impedances of the resonators are derived from which the particle velocity fields are obtained. Monopole and dipole strengths are also calculated in terms of polarizability tensor components, which in turn are obtained from a retrieval method. Sound scattering by monopolar and dipolar resonators of different size and distribution within the waveguide are examined. Using detailed understanding of the interaction between groups of resonators, optimized solutions for a new class of acoustic materials can be designed by selecting layers of resonators to produce a given response.

Integrated modelling and simulation of NiTi alloy by powder bed fusion: Single track study

In-depth understanding of the layer-by-layer process is critical for the quality control of additive manufactured (AM) components. Besides the development of experimental techniques, computational modelling is another important way to study the AM mechanisms in detail. However, currently there is still lack of a modelling platform that integrates all the necessary physics involved in the AM process. In the present study, we develop a modelling framework that integrates a phase field method for microstructure evolution, a lattice Boltzmann method for melt pool dynamics, a modified ray-tracing method for laser-material interaction, and a minimum gravity energy algorithm for powder bed generation to simulate the single-track, powder bed fusion (PBF) process of NiTi shape memory alloy. Our simulation shows that different from keyhole depth, melt pool size does not obey the scaling law with line energy density, the keyhole depth and the overlapping ratio of laser spot vs. keyhole opening together determine the laser absorptivity. Based on the simulation finding, we also develop a self-consistent analytical model to predict the keyhole depth and the absorptivity for given scanning parameters. The present work lays a solid foundation towards quantitative understanding of multi-layer AM process.

Black Hole Images as Tests of General Relativity: Effects of Plasma Physics

The horizon-scale images of black holes obtained with the Event Horizon Telescope have provided new probes of their metrics and tests of general relativity. The images are characterized by a bright, near-circular ring from the gravitationally lensed emission from the hot plasma and a deep central depression cast by the black hole. The metric tests rely on the fact that the bright ring closely traces the boundary of the black hole shadow with a small displacement that has been quantified using simulations. In this paper we develop a self-consistent covariant analytic model of the accretion flow that spans a broad range of plasma conditions and black hole properties to explore the general validity of this result. We show that, for any physical model of the accretion flow, the ring always encompasses the outline of the shadow and is not displaced by it by more than half the ring width. This result is a consequence of conservation laws and basic thermodynamic considerations and does not depend on the microphysics of the plasma or the details of the numerical simulations. We also present a quantitative measurement of the bias between the bright ring and the shadow radius based on the analytical models.

The thermodynamics of stellar multiplicity: an analytic model for the dynamical evolution of binary star populations in dense stellar environments due to single–binary interactions

ABSTRACT We recently derived, using the density-of-states approximation, analytic distribution functions for the outcomes of direct single-binary scatterings. Using these outcome distribution functions, we present in this paper a self-consistent statistical mechanics-based analytic model obtained using the Fokker–Planck limit of the Boltzmann equation. Our model quantifies the dominant gravitational physics, combining both strong and weak single–binary interactions, which drives the time evolution of binary orbital parameter distributions in dense stellar environments. We focus in particular the distributions of binary orbital energies and eccentricities. We find a novel steady-state distribution of binary eccentricities, featuring strong depletions of both the highest and the lowest eccentricity binaries. In energy space, we compare the predictions of our analytic model to the results of numerical N-body simulations, and find that the agreement is good for the initial conditions considered here. This work is a first step towards the development of a fully self-consistent semi-analytic model for dynamically evolving binary star populations in dense stellar environments due to direct few-body interactions.

Atmospheric propagation of space-fractional Gaussian-beam waves in a FSO communication system.

We present a novel, self-consistent analytical model of Gaussian-beam propagation through the atmospheric turbulence by solving the paraxial wave equation in a fractional-dimension space of dimension D, in the range 2 < D ≤ 3, corresponding to the effective spatial dimension experienced by the beam under given turbulent conditions in a free space optical (FSO) communication system. The well-known refractive index structure parameter (C n2) has been mapped from D = 2.668 (C n2≈10-13, strong fluctuations) to D = 2.999 (C n2≈10-16, weak fluctuations) in our simple analytical model, whereas D = 3 corresponds to the ideal case of free-space propagation under zero turbulence. Finally, an optimization problem is developed to mitigate the effects of atmospheric turbulence, leading to efficient transceiver design for the FSO communication system to ensure the reliability of links under varying atmospheric turbulence.

A thermodynamic analytical model based on entropy production for predicting the grain size and yield strength of the joint formed by continuous drive friction welding

A self-consistent analytical model for predicting qualities of a joint welded by continuous drive friction welding (CDFW) was developed based on the Onsager-Ziegler maximum entropy production principle (OZ-MEPP), dislocation kinetics, and the CDFW analytical model developed in our previous work. The microstructure and mechanical properties of the friction-welded joint can be predicted by the model requiring only the geometric, thermal, and physical parameters of the specimens without any assumed or premeasured response parameters. The accuracy of the model was verified by the microstructure and properties of the joints fabricated by CDFW of 304 stainless steel. The results indicated that the model is feasible and effective for forecasting the grain size and yield strength of the joints, which means it is possible to use a single thermodynamic state function, i.e., entropy production, for predicting the qualities of a CDFW joint, especially when the joined alloy has a simple phase composition.

Understanding the electrostatics of top-electrode vertical quantized Si nanowire metal–insulator–semiconductor (MIS) structures for future nanoelectronic applications

In this paper, a comprehensive analysis of the electrostatics of top-electrode vertically aligned quantized Si nanowire metal–insulator–semiconductor (MIS) structure is performed by formulating a self-consistent analytical model with simultaneous solution of Schrodinger and Poisson equations. The impact of high-k dielectrics on the electrostatic control of such quantized nanowire MIS devices is studied in detail. The electrostatic control is observed to degrade significantly for such high-k insulators with identical equivalent oxide thickness (EOT) due to the nonlinear dependence between dielectric constant and EOT in quantized nanowire MIS devices. The distribution of 3D confined charges along the nanowire is primarily governed by the generated quantum states which are a nonlinear function of the applied voltage. The electrostatic integrity of such device is investigated in terms of simultaneously maintaining the electrostatic control and reduction in carrier tunneling probability. In this context, the impact of several controlling parameters such as applied voltage, barrier height of the insulator/semiconductor junction, carrier effective mass of the insulator and nanowire diameter on tunneling probability is examined. The results suggest insulator effective mass (high-m*) to be the more significant parameter for maintaining electrostatic integrity than its dielectric constant (high-k) in quantized nanowire top-electrode MIS devices.

Modeling and Simulation of Quasi-Ballistic III-Nitride Transistors for RF and Digital Applications

This paper presents a self-consistent analytic model to describe the current-voltage (I-V) and charge-voltage (Q-V) behavior of quasi-ballistic III-nitride transistors. We focus on two types of transistor geometries: (i) high electron mobility transistors (HEMTs) suitable for radio frequency (RF) applications and (ii) nanowire field-effect transistors (FETs) for digital applications. Our core model is based on Landauer transport theory which is combined with the calculation of charge density and velocity of charges at the top-of-the-barrier in the transistor. The effect of extrinsic device features, such as the nonlinearity of access regions and Joule heating at high currents, are included in the static I-V model. In the case of the dynamic Q-V model, we calculate intrinsic terminal charges by approximating the solution of the 2D Poisson equation in the channel over a broad bias range. The effect of fringing capacitances, prominently inner-fringing capacitance that varies nonlinearly with the gate bias, is included in our Q-V model. We amend the model electrostatics and the description of source/drain rectifying contacts in our core model to represent the I-V characteristics of III-nitride nanowire FETs. The model shows excellent match against experimentally and numerically measured characteristics of GaN transistors with gate lengths ranging from 42 nm to 274 nm. With only 38 input parameters, most of which are extracted based on straightforward device characterization, our model can be used for device-circuit co-design and optimization using a standard hierarchical circuit simulator.

A self-consistent first order analytical model of plasma jets: A two fluids approach

Laser ablation processes have applications from thin film deposition to isotope separation, through plasma plume generation, which suggests mass and charge separation of species as the plume evolves. However, they do not have a theoretical model that takes into account equilibrium configurations. The present work is dedicated to build a simplified non-neutral self-consistent two fluid model, based on a few parameters for the first and fast analysis of morphological and statistical features for typical experimental plasma plumes. The velocity field, density profiles, and normalized histograms for the velocity module associated with the species were determined. The electrostatic potential field was also depicted. The model was validated for laser-ablated plasma plumes and found to be in good agreement with the experimental molybdenum plasma jet generated by the interaction of the Nd:YAG nanosecond pulsed laser with the solid target expanding in air at atmospheric pressure.

Investigation of the short argon arc with hot anode. II. Analytical model

Short atmospheric pressure argon arc is studied numerically and analytically. In a short arc with inter-electrode gap of several millimeters non-equilibrium effects in plasma play important role in operation of the arc. High anode temperature leads to electron emission and intensive radiation from its surface. Complete self-consistent analytical model of the whole arc comprising of models for near-electrode regions, arc column and a model of heat transfer in cylindrical electrodes was developed. The model predicts width of non-equilibrium layers and arc column, voltages and plasma profiles in these regions, heat and ion fluxes to the electrodes. Parametric studies of the arc have been performed for a range of the arc current densities, inter-electrode gap widths and gas pressures. The model was validated against experimental data and verified by comparison with numerical solution. Good agreement between the analytical model and simulations and reasonable agreement with experimental data were obtained.

A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks

A theoretical and numerical analysis is carried out for turbulent collisionless shocks mediated by the ion-Weibel instability during high-velocity plasma collisions. We develop a simple model based on the coalescence dynamics of the ion current filaments, which predicts the spatio-temporal evolution of the magnetic fluctuations formed in the upstream plasma region. From comparison with particle-in-cell simulations, our model is shown to correctly capture the magnetic-field and ion-beam properties during the early-time shock propagation.

IONIZATION AND DUST CHARGING IN PROTOPLANETARY DISKS

ABSTRACT Ionization–recombination balance in dense interstellar and circumstellar environments is a key factor for a variety of important physical processes, such as chemical reactions, dust charging and coagulation, coupling of the gas with magnetic field, and development of instabilities in protoplanetary disks. We determine a critical gas density above which the recombination of electrons and ions on the grain surface dominates over the gas-phase recombination. For this regime, we present a self-consistent analytical model, which allows us to calculate exactly the abundances of charged species in dusty gas, without making assumptions on the grain charge distribution. To demonstrate the importance of the proposed approach, we check whether the conventional approximation of low grain charges is valid for typical protoplanetary disks, and discuss the implications for dust coagulation and development of the “dead zone” in the disk. The presented model is applicable for arbitrary grain-size distributions and, for given dust properties and conditions of the disk, has only one free parameter—the effective mass of the ions, shown to have a small effect on the results. The model can be easily included in numerical simulations following the dust evolution in dense molecular clouds and protoplanetary disks.

Self-consistent analytical model of the radial temperature profile of a high-powered He–SrBr2 laser

There is significant practical interest in the determining of the thermal parameters of metal vapor and metal vapor halide lasers. This study develops a self-consistent analytical model determining the radial temperature profile of a high-powered strontium bromide (SrBr2) vapor laser, emitting in the infrared spectrum. The model is built under the assumption of arbitrary distribution of power density for the internal heat source without any given specific experiment measurements. It makes it possible to evaluate the nature of the main physical processes of the transfer of heat from the center of the tube to its interaction with the ambient environment. An exact solution of a heat conduction equation with first- and second-order boundary conditions is applied for the active laser medium. New boundary conditions are proposed, including third and fourth order ones, taking into account the various heat transfer processes through the layers of the gas discharge tube. Structural materials, the thermal conductivity of the helium layer between the ceramic and quartz tubes, the transmittance of heat in the outer quartz tube and suitable boundary conditions for the thermal insulation and the ambient environment are taken into consideration. The model is applied to calculate the temperature distribution within the laser tube of an existing high-powered SrBr2 laser in the case of natural convection. Very good fit is achieved with the experiment. The model is applicable for preliminary evaluation of the temperature profile of both existing and new metal vapor and other similar laser devices.

A self-consistent analytical magnetar model: the luminosity of γ-ray burst supernovae is powered by radioactivity

We present an analytical model that considers energy arising from a magnetar central engine. The results of fitting this model to the optical and X-ray light curves (LCs) of five long-duration $\gamma$-ray bursts (LGRBs) and two ultra-long GRBs (ULGRBs), including their associated supernovae (SNe), show that emission from a magnetar central engine cannot be solely responsible for powering an LGRB-SN. While the early AG-dominated phase can be well described with our model, the predicted SN luminosity is underluminous by a factor of $3-17$. We use this as compelling evidence that additional sources of heating must be present to power an LGRB-SN, which we argue must be radioactive heating. Our self-consistent modelling approach was able to successfully describe all phases of ULGRB 111209A / SN 2011kl, from the early afterglow to the later SN, where we determined for the magnetar central engine a magnetic field strength of $1.1-1.3\times10^{15}$ G, an initial spin period of $11.5-13.0$ ms, a spin-down time of $4.8-6.5$ d, and an initial energy of $1.2-1.6\times10^{50}$ erg. These values are entirely consistent with those determined by other authors. The luminosity of a magnetar-powered SN is directly related to how long the central engine is active, where central engines with longer durations give rise to brighter SNe. The spin-down timescales of superluminous supernovae (SLSNe) are of order months to years, which provides a natural explanation as to why SN 2011kl was less luminous than SLSNe that are also powered by emission from magnetar central engines.

Incoherent synchrotron emission of laser-driven plasma edge

When a relativistically intense linearly polarized laser pulse is incident on an overdense plasma, a dense electron layer is formed on the plasma edge which relativistic motion results in high harmonic generation, ion acceleration, and incoherent synchrotron emission of gamma-photons. Here we present a self-consistent analytical model that describes the edge motion and apply it to the problem of incoherent synchrotron emission by ultrarelativistic plasma electrons. The model takes into account both coherent radiation reaction from high harmonics and incoherent radiation reaction in the Landau–Lifshitz form. The analytical results are in agreement with 3D particle-in-cell simulations in a certain parameter region that corresponds to the relativistic electronic spring interaction regime.

RECOMBINATION CLUMPING FACTOR DURING COSMIC REIONIZATION

We discuss the role of recombinations in the IGM, and the related concept of the clumping factor, during cosmic reionization. The clumping factor is, in general, a local quantity that depends on the local over-density and the scale below which the baryon density field can be assumed smooth. That scale, called the filtering scale, is itself depended on over-density and local thermal history. We present a method for building a self-consistent analytical model of inhomogeneous reionization assuming the linear growth rate of the density fluctuation, which accounts for these effects simultaneously. We show that taking into account the local clumping factor introduces significant corrections to the total recombination rate, comparing to the model with a globally uniform clumping factor.

Analytical Determination of Collisional Sheath Properties for Triple Frequency Capacitively Coupled Plasma

A self-consistent analytical model for a time-independent collisional capacitively coupled plasma (CCP) sheath driven by a triple frequency (TF) RF current source is proposed. Sheath parameters are calculated using this model for some standard plasma parameters and are compared with those of a single frequency (SF) and a dual frequency (DF) capacitively coupled collisional sheath. This model estimates higher values of sheath width and potential with more oscillating behavior compared with SF and DF sheaths. By proper choice of source frequencies or phase differences in the source currents, it is possible to adjust the ion energy hitting the electrode. Use of TF source is found to facilitate better control upon sheath parameters for collisional CCP.

Plasma heating by discontinuous MHD flows in the vicinity of a magnetic reconnection region

An expression that explicitly describes variations in the internal energy of the plasma that flows through a discontinuity is derived based on the complete system of boundary conditions for the MHD equations on the discontinuity surface. The dependence of the plasma heating on the magnetic field density and configuration in the vicinity of the discontinuity surface (i.e., on the MHD flow type) is studied. The conditions of plasma heating at discontinuities in a self-consistent analytical model of magnetic reconnection are discussed.

Quasistatic magnetic fields generated by a nonrelativistic intense laser pulse in uniform underdense plasma

Quasistatic magnetic fields generated by nonrelativistic intense linearly polarized (LP) and circularly polarized (CP) laser pulses in an initially uniform underdense plasma in the collision-dominated limit are investigated analytically. Using a selfconsistent analytical model, we perform a detailed derivation of quasistatic magnetic fields in the laser pulse envelope in the collision-dominated limit to obtain exact analytical expressions for magnetic fields and discuss the dependence of magnetic fields on laser and plasma parameters. Equations for quasistatic magnetic fields including both axial component Bz and the azimuthal one Bθ are derived simultaneously from such a selfconsistent model. The dependence of quasistatic magnetic field on incident laser intensity, transverse focused radius of laser pulse, electron density and electron temperature is discussed.

Power Relations and a Consistent Analytical Model for Receiving Wire Antennas

The main objective of this paper is to provide a self-consistent analytical model for the approximate current distribution induced on an arbitrarily loaded wire antenna of moderate length operating in its receiving mode. The results of our analysis shed light on a debated issue regarding the circuit model of a receiving antenna and show that currently available simplified analytical models for receiving dipoles fail to satisfy basic power conservation requirements. These general findings are applied to the proper homogenization of composite materials and surfaces, and to minimum-scattering receivers and absorbers.