Inhomogeneous Conditions Research Articles

Synthetic Next Generation Very Large Array line observations of a massive star-forming cloud

Context. Studies of the interstellar medium and the pre-stellar cloud evolution require spectral line observations that have a high sensitivity and high angular and velocity resolution. Regions of high-mass star formation are particularly challenging because of line-of-sight confusion, inhomogeneous physical conditions, and potentially very high optical depths. Aims. We wish to quantify to what accuracy the physical conditions within a massive star-forming cloud can be determined from observations. We are particularly interested in the possibilities offered by the Next Generation Very Large Array (ngVLA) interferometer. Methods. We used data from a magnetohydrodynamic simulation of star formation in a high-density environment. We concentrated on the study of a filamentary structure that has physical properties similar to a small infrared-dark cloud. We produced synthetic observations for spectral lines observable with the ngVLA and analysed these to measure column density, gas temperature, and kinematics. Results were compared to ideal line observations and the actual 3D model. Results. For a nominal cloud distance of 4kpc, ngVLA provides a resolution of ~0.01 pc even in its most compact configuration. For abundant molecules, such as HCO+, NH3, N2H+, and CO isotopomers, cloud kinematics and structure can be mapped down to subarcsecond scales in just a few hours. For NH3, a reliable column density map could be obtained for the entire 15″ × 40″ cloud, even without the help of additional single-dish data, and kinetic temperatures are recovered to a precision of ~1 K. At higher frequencies, the loss of large-scale emission becomes noticeable. The line observations are seen to accurately trace the cloud kinematics, except for the largest scales, where some artefacts appear due to the filtering of low spatial frequencies. The line-of-sight confusion complicates the interpretation of the kinematics, and the usefulness of collapse indicators based on the expected blue asymmetry of optically thick lines is limited. Conclusions. The ngVLA will be able to provide accurate data on the small-scale structure and the physical and chemical state of star-forming clouds, even in high-mass star-forming regions at kiloparsec distances. Complementary single-dish data are still essential for estimates of the total column density and the large-scale kinematics.

The Effect of Heat Accumulation on the Local Grain Structure in Laser-Directed Energy Deposition of Aluminium

The energy used to melt the material at each layer during laser-directed energy deposition (L-DED) accumulates in the solidified layers upon layer deposition and leads to an increase in the temperature of the part with an increasing number of layers. This heat accumulation can lead to inhomogeneous solidification conditions, increasing residual stresses and potentially anisotropic mechanical properties due to columnar grain structures. In this work, infrared imaging is applied during the directed energy deposition process to capture the evolution of the temperature field in high spatial and temporal evolutions. Image processing algorithms determined the solidification rate and the temperature gradient in the spatial and temporal evolutions and evidenced their change with the proceeding deposition process. Metallographic analysis proves that these changes significantly affect the local grain structure of the L-DED fabricated parts. The study provides comprehensive quantitative measurements of the change in the solidification variables in local and temporal resolutions. The comprehensive comparison of different parameter combinations reveals that applied power, and especially the frequency of the consecutive deposition of the individual layers, are the key parameters to adjusting heat accumulation. These findings provide a methodology for optimising L-DED manufacturing processes and tailoring the local microstructure development by controlling heat accumulation.

The Hollow Porous Sphere Cell Carrier for the Dynamic Three-Dimensional Cell Culture.

Large-scale mammalian cell culture is essential in cell therapy, vaccine production, and the manufacturing of therapeutic protein drugs. Due to the adherent growth characteristic of most mammalian cell types, the combination of cell carrier and bioreactor is a common choice in large-scale mammalian cell culture. Current cell carriers developed by polymer crosslinking, lithography, or emulsion drops are unable to obtain a structure with uniformed porous structure and porous interior design, which results in an inhomogeneous culture condition for cells and therefore cannot ensure an optimal dynamic culture condition for cell proliferation, matrix production, and cell differentiation. In addition, the fluidic shear stress (a standard mechanical stimulation in bioreactor culture) and inner-carrier velocity (to ensure nutrient transport and waste exchange), which influence cell viability and growth, are not well-controlled/analyzed due to an irregular porous structure with these traditionally synthesized cell carriers. To solve these problems, we designed four types of hollow porous spheres (HPS, 1.0 cm diameter) with different porous structures. To investigate the impacts of porous structure on surface shear stress and inner velocity, computational fluid dynamics (CFD) simulations were conducted to analyze the liquid flow behavior in HPSs, based on which an optimal structure with minimal surface shear stress and best inner velocity was obtained and fabricated using fused deposition modeling three-dimensional (3D) printing technology. Inspired by the industrial large-scale culture system, a novel 3D dynamic culture system was then established using HPSs to seed the cells, which were then placed in a mini bioreactor on a tube roller. CFD analysis showed that under 0.1 m/s water flow, the shear stress at most surface areas from four HPSs was lower than 20 dynes/cm2, which suggests that the HPSs should provide protection against physical stress to the cells living on the scaffold surface. A dynamic cell seeding was developed and refined using the 3D culture system, which increased the 32% seeding efficiency of MC3T3 cells compared to the traditional static cell seeding method. The cell proliferation analysis demonstrated that HPSs could speed up cell growth in dynamic cell culture. The HPS with a honeycomb-like structure showed the highest inner pore velocity (CFD analysis) and achieved the fastest cell proliferation and the highest cell viability. Overall, our study, for the first time, developed a 3D printed HPS cell culture device with a uniformed porous structure, which can effectively facilitate cell adhesion and proliferation in the dynamic cultural environment, thereby could be considered an ideal carrier candidate.

Advanced design of MRI inversion pulses for inhomogeneous field conditions by optimal control.

Non-selective inversion pulses find widespread use in MRI applications, where requirements on them are increasingly demanding. With the use of high and ultra-high field strength systems, robustness to and inhomogeneities, while tackling SAR and hardware limitations, has rapidly become important. In this work, we propose a time-optimal control framework for the optimization of - and -robust inversion pulses. Robustness is addressed by means of ensemble formulations, while allowing inclusion of hardware and energy limitations. The framework is flexible and performs excellently for various optimization goals. The optimization results are analyzed extensively in numerical experiments. Furthermore, they are validated, and compared with adiabatic RF pulses, in various phantom and in vivo measurements on a 3 T MRI system.

Enhanced energy output from a PV system under partial shaded conditions through grey wolf optimizer

Due to its several powerful characteristics, the Grey Wolf Optimization (GWO) algorithm has recently become widely used in numerous optimization problems. In photovoltaic (PV) systems, power-voltage (P–V) curves present multiple maxima in case of partial shadow or modules mismatch which can be viewed as an optimization problem. In this paper, a GWO-based maximum power tracking (MPPT) algorithm for PV systems operating under partial shading conditions (PSCs) is proposed. With a direct control method, the proposed GWO-based MPPT allows successfully catching the global maximum power point (GMPP) of the PV array in case of uniform and non-uniform solar irradiation. To evaluate the effectiveness of the proposed MPPT scheme, a co-simulation combining Matlab/Simulink™ and Cadence/Pspice™ software environments is carried out and tested under various static and dynamic shading conditions. Furthermore, the tracking performance is compared with that of the particle swarm optimization (PSO) and classical perturb and observe (P&O) based MPPT methods under transient PSCs and also under inhomogeneous real conditions of Algerian sky. The simulation results have demonstrated the satisfactory performances of the proposed approach in terms of tracking efficiency and tracking speed over the other MPPT methods.

Thermal emission in the successive orders of scattering (SOS) radiative transfer approach

The Successive Orders of Scattering (SOS) approach [1] is one of the well known methods for solving the Radiative Transfer (RT) problem. Its efficiency in terms of speed and accuracy of computation was already demonstrated for scattering and absorbing atmospheres in Solar spectrum. Although there are no principle limitations to account for the emission processes, the application of the SOS method for atmospheres with thermal emission is not widely used yet. In this paper we present a SOS-based RT approach accounting for the full source function, which enables its application from the UV (UltraViolet) to the TIR (Thermal InfraRed) parts of the electromagnetic spectrum. The atmospheric vertical discretization in this extended SOS scheme is a key point in order to properly retain the scattering and emission processes. An analysis of different methodologies to perform this vertical discretization is presented. The numerical implementation has been included in GRASP (Generalized retrieval of Atmosphere and Surface Properties) RT code [2]. In comparison with the widely used code DISORT (DIScrete-ORdinatemethod for Radiative Transfer) [3], the developed SOS scheme achieves a mean accuracy of radiance calculation of −0.005 K (−0.003%) expressed in terms of brightness temperature. Under the same configuration and vertically inhomogeneous atmospheric conditions, GRASP SOS RT is approximately eight times faster than DISORT. The analysis of the sensitivity of GRASP TIR SOS scheme to the number of layers and the effect of polarization are also investigated in the paper.

Gravitational dynamics in Higgs inflation: Preinflation and preheating with an auxiliary field

The dynamics of both the preinflationary and the preheating epochs for a model consisting of a Higgs inflaton plus an additional auxiliary field are studied in full General Relativity. The minimally coupled auxiliary field allows for parametric-type resonances that successfully transfer energy from the inflaton condensate to particle excitations in both fields. Depending on the interaction strengths of the fields, the broad resonance periods lead to structure formation consisting of large under/over-densities, and possibly the formation of compact objects. Moreover, when confronting the same model to multi-field inhomogeneous preinflation, the onset of inflation is shown to be a robust outcome. At relatively large Higgs values, the non-minimal coupling acts as a stabilizer, protecting the dynamics of the inflaton, and significantly reducing the impact of perturbations in other fields and matter sectors. These investigations further confirm the robustness of Higgs inflation to multi-field inhomogeneous initial conditions, while putting in evidence the formation of complex structures during the reheating.

Checking of the condition of transformers and the efficiency of oil regeneration with RVM (return voltage measurement)

Up to now the insulation in HV power transformers has been made from oil/paper therefore the diagnosis of this kind of insulation will be also important in the next forty-fifty years. The lifetime of this equipment strongly depends on the condition of the insulation system. The ageing process of oil/paper insulating systems is a very complex and complicated phenomenon. In order to get a well-supported decision on the further operation of aged transformers, relevant information would be necessary on the condition of the oil-paper insulation. We also know that the oil-paper insulation has almost always inhomogeneous condition considering the temperature, moistening and ageing processes. The classical methods (insulation resistance, loss tangent, etc.) characterise the insulation by single measured value. This single value is not sufficient for relevant characterisation and diagnosis of such a complex system with lots of tons of insulation and with almost always inhomogeneous distribution of temperature, moisture and ageing product. If we measure the polarization spectra in three states (new insulation in equilibrium and uniform polarization spectrum, new insulation with not uniform distribution of polarization spectrum, later reaching again the uniform distributions) the shape of three polarization spectra will be different. Comparing the polarization and classical methods of this three case we can realize that sometimes the “classical single values” are almost the same but the polarization spectra are different. The three response methods provide very practical information about the insulation system (e.g. moisture, ageing). The moistening and accumulation of ageing by-products change the distribution of interfacial polarisation in the range of long time-constants. These promising response methods measure the polarisation distribution in the range of long time-constant (with other words, in the low frequency range). The three test methods were: Return Voltage measurement (RVM), the C and tgδ measurement in range of some tens of mHz to 50 Hz (FDS=Frequency Domain Spectroscopy), and the measurement of DC charging and discharging currents (PDC=polarisation and depolarization currents) up to some thousands of sec. These equivalent methods (RVM, FDS and PDC) are able to follow the changing of condition of insulation contrary to classical methods. Therefore a little bit surprising that until now the convenient standards is missing considering the polarization methods. In an earlier Hungarian research work (Budapest University of Technology) almost all the necessary measurements have been realized, consequently we are in possession of fundamental data considering the polarization methods. This paper would like to show a short review about the RVM technique, the correct interpretation of RVM data and a case study for the checking of the efficiency of the oil reclamation with RVM technique.

Model tests of a hydroelastic truncated floating bridge

Literature on tank tests of floating bridges is extremely rare, while a very limited number of publications covering tests of other types of very large floating structures exist. Here, the authors share their experience in designing and carrying out a model test campaign aimed at providing empirical data to aid the process of validating and calibrating a numerically based design of a generic floating bridge. The tested model represents a truncated segment of a full straight bridge at a fjord crossing supported by floating pontoons with 4 mooring clusters providing additional lateral stiffness. The tested environmental conditions comprise combinations of regular and irregular waves, current and wind, including a spectral amplitude inhomogeneous condition realization. The setup of the objectives, strategy adopted for the truncation, experimental setup and relevant system identification and control procedures carried out, are explained thoroughly. Noteworthy is a novel approach for carrying out static pull-outs and decays using a set of actuator winches, also used for applying prescribed wind forces on the model, allowing for inhomogeneous dynamic prescribed forces to be accurately applied.A dataset of time series and selected video recordings is publicly shared for selected measurements and test runs. It is expected that this paper and the accompanying dataset become a valuable resource for researchers and engineers addressing model testing or experimental validation of numerical models of floating bridges within the functional design process of these structures. Specifically, the dataset should provide important empirical data for benchmarking numerical predictions of hydrodynamic interaction, and hydroelasticity models in general. Recommendations for testing of floating bridges in a basin are also given, based on the experience gathered in the project.

A Hybrid Particle Swarm Optimization and Single-Objective Slap Swarm Optimization Algorithm Based MPPT Strategy

Under inhomogeneous irradiance conditions, multiple peak characteristic of P-V curve reduces the efficiency of conventional trackers like incremental conductance control. A hybrid particle swarm optimization and single-objective slap swarm optimization algorithm (PSO-SOSSOA) based which is applied to maximum power point tracking (MPPT) strategy is presented. The PSO-SOSSOA adopts the particle swarm optimization algorithm in the early period of the algorithm operation and a modified single-objective slap swarm optimization algorithm (SOSSOA) in the remaining period. The simulation results reveal that the PSO-SOSSOA can successfully deal with global MPPT and exhibits performance advantages in terms of efficiency, search speed, and power oscillation compared with the SOSSOA.

Application of agent-based approach for heat conduction processes simulation

Heat transfer processes are the basis of the most technological processes of the energy sector. Thus, the development of modern approaches for computer simulation and visualization of the phenomena of thermal energy transfer in various objects are of great importance and is relevant. Classical models in the form of differential equations of various types describe processes in continuous space and time. So, it is difficult to apply classical models to study nonlinear phenomena, and processes in inhomogeneous media in the presence of discontinuous solutions at the boundaries. In these cases, simplifying assumptions are used, thus, the adequacy of the models is reduced. It is of great interest to apply fundamentally different approaches to describe transfer processes, which include discrete dynamic models. The purpose of this project is to study the possibilities to apply discrete approaches to simulate nonlinear heat transfer processes under conditions of material inhomogeneity and the presence of volume sources of variable power. The paper studies the possibilities to apply the agent-based approach to simulate models of complex systems. This approach allows us to consider a continuum as a set of interacting elements (agents). The behavior of the elements is completely described by local dependencies. At the same time, the laws of functioning of individual elements are accepted as deterministic and they correspond to the fundamental principles of the theory of heat transfer. The possibility to apply a discrete approach for simulating the process of heat transfer by the molecular mechanism has been studied. The general methodology to develop an agent-based deterministic model is described. Its applicability to describe quasi-linear and nonlinear heat conduction processes is considered. The examples of simulation of combustion processes complicated by exothermic and endothermic effects are considered. The advantages and disadvantages of the proposed method are indicated. The results of the study have shown that discrete agent models are a good alternative to classical continuum approaches to study heat transfer processes in inhomogeneous media. The results obtained do not contradict modern approaches to the description of thermal processes. It has also been found that the simulation algorithms used in the agent-based approach are quite universal and easily adapt to changes under the conditions of problem setting. The analysis of the results makes it possible to recommend a discrete agent-based approach to develop simulation models of complex technological processes and systems.

Bifurcations of Solutions to Equations with Deviating Spatial Arguments

A periodic boundary-value problem for an equation with deviating spatial argument is considered. This equation describes the phase of a light wave in light resonators with distributed feedback. Optical systems of this type are used in computer technologies and in the study of laser beams. The boundary-value problem was considered for two values of spatial deviations. In the work, bifurcation problems of codimensions 1 and 2 were analyzed by various methods of studying dynamical systems, for example, the method of normal Poincaré–Dulac forms, the method of integral manifolds, and asymptotic formulas. The problem on the stability of certain homogeneous equilibrium states is examined. Asymptotic formulas for spatially inhomogeneous solutions and conditions for their stability are obtained.

Microfluidic Reproduction of Dynamic Bioreactor Environment Based on Computational Lifelines

The biotechnological production of fine chemicals, proteins and pharmaceuticals is usually hampered by loss of microbial performance during scale-up. This challenge is mainly caused by discrepancies between homogeneous environmental conditions at laboratory scale, where bioprocesses are optimized, and inhomogeneous conditions in large-scale bioreactors, where production takes place. Therefore, to improve strain selection and process development, it is of great interest to characterize these fluctuating conditions at large-scale and to study their effects on microbial cells. In this paper, we demonstrate the potential of computational fluid dynamics (CFD) simulation of large-scale bioreactors combined with dynamic microfluidic single-cell cultivation (dMSCC). Environmental conditions in a 200 L bioreactor were characterized with CFD simulations. Computational lifelines were determined by combining simulated turbulent multiphase flow, mass transport and particle tracing. Glucose availability for Corynebacterium glutamicum cells was determined. The reactor was simulated with average glucose concentrations of 6 g m−3, 10 g m−3 and 16 g m−3. The resulting computational lifelines, discretized into starvation and abundance regimes, were used as feed profiles for the dMSCC to investigate how varying glucose concentration affects cell physiology and growth rate. In this study, each colony in the dMSCC device represents a single cell as it travels through the reactor. Under oscillating conditions reproduced in the dMSCC device, a decrease in growth rate of about 40% was observed compared to continuous supply with the same average glucose availability. The presented approach provides insights into environmental conditions observed by microorganisms in large-scale bioreactors. It also paves the way for an improved understanding of how inhomogeneous environmental conditions influence cellular physiology, growth and production.

Network Inefficiency: Empirical Findings for Six European Cities

When planning road networks, inhomogeneous traffic conditions and the effects of multimodal interactions are often neglected. This can lead to a substantial overestimation of network capacities. Empirical macroscopic fundamental diagrams (MFDs) or volume delay relationships show considerable scatter, reflecting a reduction in network performance and an inefficient use of infrastructure. The implication is that the external costs of vehicular (car) traffic get underestimated, when planning traffic capacities and speeds based on optimal rather than on real estimates. In this paper, we contribute with an explorative and empirical approach to analyze network inefficiency and quantify its drivers. We propose to measure network efficiency by introducing the idea of excess delays for the MFD. We define excess delays as the difference between the observed speed and the optimal network speed at a given density. We apply the concept to traffic data sets of six European cities that differ in the data collection method and we use quantile regression methods for analysis. We find that excess delays are present in every data set and increase with the road network’s traffic load. We further confirm the intuition that traffic signal control, network loading, and multimodality influence the level of network inefficiency. The excess delay formula allows quantifying this information in a simple way and provides additional insights apart from the standard MFD model. The approach supports planners to obtain better real-world and less optimistic speed predictions for traffic analyses and suggests shifting urban transport to more spatially and temporally efficient modes.

The final Kasner regime inside black holes with scalar or vector hair

The final (close to the singularity) dynamical behavior of the metric inside black holes with massive charged scalar or vector hair is analyzed for general anisotropic and inhomogeneous initial conditions. These solutions are relevant to a holographic realization of superconductivity. It is shown that the dynamics falls within the scope of the “cosmological billiard” description and that in both cases, the corresponding hyperbolic billiard region has infinite volume so that the system ultimately settles down to a final Kasner regime. For massive vector hair, the conclusion holds because the longitudinal mode plays the same role as a scalar field. There exists, however, a measure-zero subset of solutions characterized by vanishing longitudinal modes that exhibit a chaotic behavior with an infinite number of BKL oscillations as one goes to the singularity.

Continuous observation of twinning and dynamic recrystallization in ZM21 magnesium alloy tubes during locally heated dieless drawing

Compared to cold drawing, dieless drawing has shown great potential for manufacturing biodegradable Mg alloy microtubes due to the large reduction in area acquired in a single pass. However, owing to the local heating and local deformation, the deformation mechanism during dieless drawing is not clear, and thus causing difficulties in controlling the microstructure of dieless drawn tubes. For the purpose of acquiring a desired microstructure, in this study the deformation mechanism of ZM21 Mg alloy tube was clarified by conducting continuous observation of the microstructural evolution during dieless drawing. The results show that both SRX and DRX occurred during dieless drawing. SRX occurred before the plastic deformation to soften dieless drawn tubes. With increase of feeding speed, the deformation mechanism changed accordingly: (1) At the low-speed of 0.02 mm/s, the deformation mechanism was dominated by twin-slip sliding, during which {10–12} tension twins were generated inside grains to accommodate the plastic deformation by changing the crystal orientation. (2) At the intermediate-speed of 2 mm/s, a twin-DRX process related to {10–12} tension twin was observed, which was characterized by the generation of abundant {10–12} tension twins and the evolution of misorientation angle of {10–12} tension twins. Moreover, the transformation from twin-DRX to CDRX can be observed at the late stage of plastic deformation, which was attributed to the inhomogeneous conditions of dieless drawing. (3) At the high-speed of 5 mm/s, a CDRX process was observed, during which grain boundary sliding and grain tilting were observed, in addition to the gradual rotation of subgrains. These results show that during dieless drawing, DRX is not only a temperature-dependent phenomenon, but also influenced by the variation of feeding speed.

Discrete orthogonal polynomials reduced models based on shift-transformation and discrete Walsh functions

This paper investigates model order reduction (MOR) methods of discrete-time systems via discrete orthogonal polynomials in the time domain. First, this system is expanded under discrete orthogonal polynomials, and the expansion coefficients are computed from a linear equation. Then the reduced-order system is produced by using the orthogonal projection matrix that is defined in terms of the expansion coefficients, which can match the first several expansion coefficients of the original output, and preserve the asymptotic stability and bounded-input/bounded-output (BIBO) stability. We also study the output error between the original system and its reduced-order system. Besides, the MOR method using discrete Walsh functions is proposed for discrete-time systems with inhomogeneous initial conditions. Finally, three numerical examples are given to illustrate the feasibility of the proposed methods.

Model order reduction of port-Hamiltonian systems with inhomogeneous initial conditions via approximate finite-time Gramians

Based on the approximate finite-time Gramians, this paper studies model order reduction method of port-Hamiltonian systems with inhomogeneous initial conditions. The approximate controllability and observability Gramians on the finite-time interval [T1,T2](0≤T1<T2<∞) can be obtained by the shifted Legendre polynomials and the reduced port-Hamiltonian system is constructed by the union of dominant eigenspaces. Since the port-Hamiltonian system is square, the cross Gramian on the time interval [T1,T2] can also be approximated by using the shifted Legendre polynomials. Then, the truncated singular value decomposition of the approximate finite-time cross Gramian is carried out to obtain the projection matrix. Finally, the proposed methods are verified by two numerical examples.

High-resolution diffusion-order NMR spectroscopy in inhomogeneous magnetic fields via intermolecular zero-quantum coherences

Diffusion-order NMR spectroscopy (DOSY) presents a powerful tool for studying solution mixtures by recording diffusion coefficients of individual components and separating their signals into respective 1D NMR spectra. Existing DOSY experiments, however, are generally unsuitable for measurements under adverse magnetic field conditions, because calculations for diffusion coefficients strictly rely on resolved resonances in the 1D NMR spectral domain. Herein, we propose a general DOSY method by introducing intermolecular zero-quantum coherence mechanism into molecular diffusion evolution to overcome the challenge of magnetic field inhomogeneity and to record high-resolution DOSY spectra free of magnetic field inhomogeneity. Our experimental results and theoretical interpretation suggest that the proposed method allows to diffusion analysis and component discrimination on solution mixtures under externally inhomogeneous magnetic field conditions and on intact biological tissues with field inhomogeneity internally caused by magnetic susceptibility variations. This study provides a previously unreported NMR protocol for high-resolution DOSY measurements in inhomogeneous magnetic fields, thus broadening the scope of DOSY applications and showing the promising prospect for studies on chemical and biological mixture samples.

Control of the chirality of a vortex in a ferroelectric nanodot by uniform electric fields mediated by inhomogeneous surface screening

The manipulation of a ferroelectric vortex under the boundary condition of inhomogeneous screening is simulated by phase-field calculations. It is revealed that the vortex chirality can be tuned by utilizing uniform electric fields under inhomogeneous screening boundary conditions in which the switching mechanism is distinct from that under boundary conditions of asymmetric screening previously reported. The influence of the screening inhomogeneity and the ambient temperature on the vortex switching is further studied. The results indicate that inhomogeneous screening conditions are of vital importance to the switching behaviors of vortex chirality in a ferroelectric nanodot under the influence of a uniform electric field. Furthermore, the critical electric field is inextricably linked to the screening inhomogeneity and the ambient temperature.