One-dimensional Scheme Research Articles

Total Approximation Method for an Equation Describing Droplet Breakup and Freezing in Convective Clouds

A locally one-dimensional scheme for a general parabolic equation in a $$p$$ -dimensional parallelepiped is considered. A special nonlocal integral source is added to the considered equation to describe droplet breakup and freezing in convective clouds. An a priori estimate for the solution of the locally one-dimensional scheme is obtained, and its convergence is proved.

Theoretical and experimental investigations of vertical hole transport through unipolar AlGaN structures: Impacts of random alloy disorder

We report on the vertical hole transport through unipolar unintentionally doped (UID) and p-type doped AlGaN heterostructures to evaluate the effectiveness of the UID and doped AlGaN as barriers to the hole transport. Band diagram and current density–voltage (J–V) simulations are conducted in one-dimensional and three-dimensional schemes, with the latter including compositional fluctuations within the alloy AlGaN barrier layer. The simulation results using a self-consistent Poisson-drift diffusion scheme, incorporating the Localization Landscape theory, indicate a large asymmetric barrier to the hole transport by UID AlGaN. The asymmetric J–V characteristics are attributed to the asymmetric band diagrams calculated for the unipolar structure. The simulation results are verified by experiments using unipolar vertical hole transport structures enabled by n-to-p tunnel junctions (TJs) grown by ammonia molecular-beam epitaxy. The TJ structures are utilized to minimize the issues with the high spreading resistance of p-regions and to eliminate the need for its dry etching, which normally results in degraded p-contacts. The experimental results show that even a thin UID AlxGa1−xN (x = 14%, 13 nm) introduces an asymmetric barrier to the hole transport; a nearly 100% increase in the voltage drop induced by a thin UID AlGaN at 50 A/cm2 in the reverse direction is observed compared to an only 25% corresponding increase in the forward direction. Furthermore, p-type doping of the AlGaN layer results in a drastic drop in the potential barrier to hole transport in both directions. The results are beneficial for understanding the behavior of various structure designs within optoelectronics and power electronics.

A notion of non-negativity preserving relaxation for a mono-dimensional three velocities scheme with relative velocity

In this contribution, we study a stability notion for a fundamental linear one-dimensional lattice Boltzmann scheme, this notion being related to the maximum principle. We seek to characterize the parameters of the scheme that guarantee the preservation of the non-negativity of the particle distribution functions. In the context of the relative velocity schemes, we derive necessary and sufficient conditions for the non-negativity preserving property. These conditions are then expressed in a simple way when the relative velocity is reduced to zero. For the general case, we propose some simple necessary conditions on the relaxation parameters and we put in evidence numerically the non-negativity preserving regions. Numerical experiments show finally that no oscillations occur for the propagation of a non-smooth profile if the non-negativity preserving property is satisfied.

Parallel finite-difference algorithms for three-dimensional space-fractional diffusion equation with $$\psi $$-Caputo derivatives

The paper deals with the issues of parallel computations’ organization while solving three-dimensional space-fractional diffusion equation with the $$\psi $$ -Caputo derivatives using finite difference schemes. For an implicit scheme and locally one-dimensional splitting scheme, we present parallel algorithms for distributed memory systems that use one-dimensional block and red–black data partitioning. To reduce the order of algorithms’ computational complexity, we use an approach based on the expansion of integral operator’s kernel into series. We present the theoretical estimates of parallel algorithms’ performance and the results of computational experiments conducted on a testing problem that has an analytical solution for the case of the Caputo–Katugampola derivative. The results of the experiments show close-to-linear parallelization efficiency of one-dimensional splitting scheme with block partitioning and inefficiency of red–black partitioning in this case. For the implicit scheme, the scalability of parallel algorithms is weak and the use of red–black partitioning is more efficient than the use of block partitioning when running on a small number of computational resources.

Simulating Real Atmospheric Boundary Layers at Gray-Zone Resolutions: How Do Currently Available Turbulence Parameterizations Perform?

Recent computational and modeling advances have led a diverse modeling community to experiment with atmospheric boundary layer (ABL) simulations at subkilometer horizontal scales. Accurately parameterizing turbulence at these scales is a complex problem. The modeling solutions proposed to date are still in the development phase and remain largely unvalidated. This work assesses the performance of methods currently available in the Weather Research and Forecasting (WRF) model to represent ABL turbulence at a gray-zone grid spacing of 333 m. We consider three one-dimensional boundary layer parameterizations (MYNN, YSU and Shin-Hong) and coarse large-eddy simulations (LES). The reference dataset consists of five real-case simulations performed with WRF-LES nested down to 25 m. Results reveal that users should refrain from coarse LES and favor the scale-aware, Shin-Hong parameterization over traditional one-dimensional schemes. Overall, the spread in model performance is large for the cellular convection regime corresponding to the majority of our cases, with coarse LES overestimating turbulent energy across scales and YSU underestimating it and failing to reproduce its horizontal structure. Despite yielding the best results, the Shin-Hong scheme overestimates the effect of grid dependence on turbulent transport, highlighting the outstanding need for improved solutions to seamlessly parameterize turbulence across scales.

Application of compact grid-characteristic schemes for acoustic problems

This work is devoted to the numerical solution of the acoustic problem. It has a lot of important applications, for example, direct and inverse problems of the seismic survey process. The grid-characteristic approach was used to transform the problem into a set of independent linear transport equations. In one-dimensional case explicit numerical schemes for continuous and discontinuous materials were derived. Using differential sequences of initial equations, the new compact scheme on the two-point spatial stencil was proposed. A set of numerical experiments with different initial conditions and materials were carried out. Direct numerical simulations proved the third order of the approximation.

Locally One-Dimensional Difference Scheme for a Nonlocal Boundary Value Problem for a Parabolic Equation in a Multidimensional Domain

We study a nonlocal boundary value problem for a parabolic equation in the multidimensional case. A locally one-dimensional difference scheme is constructed to solve this problem numerically. A priori estimates are derived by the method of energy inequalities in the differential and difference settings. The uniform convergence of the locally one-dimensional scheme is proved.

Modeling and control of a Fischer-Tropsch synthesis fixed-bed reactor with a novel mechanistic kinetic approach

A modeling and dynamic control study for a Fischer-Tropsch synthesis fixed-bed reactor under the one-dimensional pseudohomogeneous scheme representation with integration of the cooling jacket dynamic approach has been developed. The proposed reactor model contemplates the use of a novel mechanistic kinetic model based on the Langmuir theory recently reported in the literature. To ensure a good thermal behavior and an improvement reactor performance a proportional-integral controller is implemented in the cooling jacket. The robustness of the controller, the dynamic model and the mechanistic kinetic approach are evaluated and validated against the use of four different sets of initial operating conditions of temperature, pressure and gas hourly space-velocity. The results indicate the reactor model potential under the proportional-integral controller action, since it allows to completely attenuate the typical hot-spot formation in fixed-bed reactors in which highly exothermic reactions are carried out. In addition, the mechanistic kinetic model represents to a great extent the Fischer-Tropsch synthesis reaction network in terms of the syngas conversion and the light gases and heavy liquid hydrocarbons selectivity.

Machine Learning-Based Energy-Spectrum Two-Dimensional Cognition in Energy Harvesting CRNs

Energy harvesting cognitive radio network (EH-CRN) is a promising approach to address the shortage of spectrum resources and the increase of energy consumption simultaneously in wireless networks. In this article, we propose a novel machine learning (ML)-based energy-spectrum two-dimensional (2D) cognition technology to improve the sensing accuracy as well as the network throughput in EH-CRNs, which consists of sensing, prediction and decision modules. More specifically, we first study the 2D sensing module which is achieved by a carefully constructed dynamic Bayesian network (DBN) to effectively exploit the coupling between spectrum usage and energy harvesting in EH-CRNs. Then we propose a deep neural network (DNN) based 2D transmission decision module to optimize the transmission energy of secondary users (SUs). With our proposed novel 2D cognition scheme, SUs can characterize the energy-spectrum correlation and transmit data with optimal transmission energy. The proposed ML-based 2D cognition is evaluated via extensive simulations in terms of sensing accuracy, prediction accuracy, and network throughput, and simulation results indicate that our proposed scheme significantly outperforms the conventional one-dimensional (1D) cognition scheme working in spectrum or energy dimension only.

LDPC-Coded Modulation Performance Analysis and System Design

In this work, the low-density parity-check (LDPC)-coded modulation scheme which has been selected for inclusion in the next generation of International Telecommunication Union (ITU) broadband standard is investigated. The multi-level mapping of this scheme offers excellent performance along with a straightforward modulation which is separable into simple one-dimensional schemes. A subset of modulated bit positions are protected by the LDPC code, while the remaining positions benefit from improved Euclidean distance through assignment to distinct constellation regions. To date, there has been a lack of analytical treatment of the scheme. This is problematic given the number of tunable scheme and code parameters, necessitating time-consuming Monte Carlo simulation. This motivates the novel analytical work of this article, which derives overall error-rate and threshold performances through considering separately the effects of the channel on the coded and uncoded bits. First, new closed-form expressions are derived for the hard-decision performance of the bit mapping of the multi-level modulation scheme, for both coded and uncoded bits. Extrinsic information transfer (EXIT) analysis is then applied to the coded bits in the scheme. The derived theoretical performance of the uncoded bit positions is used in combination with the derived EXIT threshold to provide for the first time for this modulation scheme a method to evaluate analytically whether a designed system will offer capacity-approaching performance. Following this, an approximation to the capacity curve for the coded modulation scheme is produced, again based on the derived analytical performance. Finally, through the relationship between mutual information and error rate performance for error control codes, the derived analytical expressions are used to produce a semi-analytical finite-length performance predictor, whereby error rate results for a given code on the binary input additive white Gaussian noise (AWGN) channel can be mapped to the coded modulation scheme under consideration for any coded system parameters.

AGROSKETCHINESS VS HISTORISM: THE AUDIT EXPERIENCE OF THE SECTORAL INTERPRETATION OF THE STATE LEGAL EVOLUTION OF EARLY-MEDIEVAL EUROPE

The principal aim of the paper is a comparative analysis of revisionist and traditional views on the history of the Early Middle Ages. The results of the research show many variants of state-legal evolution and it’s impossible to make the one-line and one-dimensional scheme proposed by a specialist in the field of agrarian law. In each of the variants there is a unique combination of German and Roman agrarian and legal structures but there is no total reception of Roman law, agrarian system. The gap of cultural and historical continuity was very common both for Pax Romana and Barbaricum. It was especially great in the territory of «Albion», the evolution of which is characterized by the singularity. This allowed for identifying the complete failure of agrosketchiness aimed at ignoring the diversity of the real historical process, the regional and country specific of state-legal evolution.

Evolution of Gaussian wave packets in capillary jets.

A temporal analysis of the evolution of Gaussian wave packets in cylindrical capillary jets is presented through both a linear two-mode formulation and a one-dimensional nonlinear numerical scheme. These analyses are normally applicable to arbitrary initial conditions but our study focuses on pure-impulsive ones. Linear and nonlinear findings give consistent results in the stages for which the linear theory is valid. The inverse Fourier transforms representing the formal linear solution for the jet shape is both numerically evaluated and approximated by closed formulas. After a transient, these formulas predict an almost Gaussian-shape deformation with (i) a progressive drift of the carrier wave number to that given by the maximum of the Rayleigh dispersion relation, (ii) a progressive increase of its bell width, and (iii) a quasiexponential growth of its amplitude. These parameters agree with those extracted from the fittings of Gaussian wave packets to the numerical simulations. Experimental results are also reported on near-Gaussian pulses perturbing the exit velocity of a 2-mm diameter water jet. The possibility of controlling the breakup location along the jet and other features, such as pinch-off simultaneity, are demonstrated.

Unconditionally stable meshless method for solving 3D transient electromagnetic problems based on LOD scheme

One of the main problems of the conventional meshless methods in the time domain is their conditional stability. Up to now, some algorithms have been introduced to remove the stability condition, like alternating-direction-implicit (ADI) and locally one-dimensional (LOD) schemes. ADI meshless method has been investigated completely, but there is no report to exploit the full efficiency of the LOD meshless method. So, in this study, LOD scheme is employed to a meshless method for solving three-dimensional transient electromagnetic problems. The initial form of the proposed meshless method solves time-domain Maxwell's equations in three sub-steps, so it is called LOD3. LOD3 meshless method has first-order temporal accuracy. Moreover, LOD5 meshless method is introduced to upgrade temporal accuracy. Also, the results show that LOD5 meshless method is more accurate than ADI and LOD3 meshless methods. The accuracy of the proposed method is due to two main factors; Crank–Nicolson scheme and solving the equation in five sub-steps instead of one sub-step. Stability and accuracy of the proposed method are assessed through numerical experiment. Also, the unconditional stability of the proposed method is proved, analytically.

Quantifying the bias of radiative heating rates in numerical weather prediction models for shallow cumulus clouds

Abstract. The interaction between radiation and clouds represents a source of uncertainty in numerical weather prediction (NWP) due to both intrinsic problems of one-dimensional radiation schemes and poor representation of clouds. The underlying question addressed in this study is how large the NWP radiative bias is for shallow cumulus clouds and how it scales with various input parameters of radiation schemes, such as solar zenith angle, surface albedo, cloud cover and liquid water path. A set of radiative transfer calculations was carried out for a realistically evolving shallow cumulus cloud field stemming from a large-eddy simulation (LES). The benchmark experiments were performed on the highly resolved LES cloud scenes (25 m grid spacing) using a three-dimensional Monte Carlo radiation model. An absence of middle and high clouds is assumed above the shallow cumulus cloud layer. In order to imitate the poor representation of shallow cumulus in NWP models, cloud optical properties were horizontally averaged over the cloudy part of the boxes with dimensions comparable to NWP horizontal grid spacing (several kilometers), and the common δ-Eddington two-stream method with maximum-random overlap assumption for partial cloudiness was applied (denoted as the “1-D” experiment). The bias of the 1-D experiment relative to the benchmark was investigated in the solar and thermal parts of the spectrum, examining the vertical profile of heating rate within the cloud layer and the net surface flux. It is found that, during daytime and nighttime, the destabilization of the cloud layer in the benchmark experiment is artificially enhanced by an overestimation of the cooling at cloud top and an overestimation of the warming at cloud bottom in the 1-D experiment (a bias of about −15 K d−1 is observed locally for stratocumulus scenarios). This destabilization, driven by the thermal radiation, is maximized during nighttime, since during daytime the solar radiation has a stabilizing tendency. The daytime bias at the surface is governed by the solar fluxes, where the 1-D solar net flux overestimates (underestimates) the corresponding benchmark at low (high) Sun. The overestimation at low Sun (bias up to 80 % over land and ocean) is largest at intermediate cloud cover, while the underestimation at high Sun (bias up to −40 % over land and ocean) peaks at larger cloud cover (80 % and beyond). At nighttime, the 1-D experiment overestimates the amount of benchmark surface cooling with the maximal bias of about 50 % peaked at intermediate cloud cover. Moreover, an additional experiment was carried out by running the Monte Carlo radiation model in the independent column mode on cloud scenes preserving their LES structure (denoted as the “ICA” experiment). The ICA is clearly more accurate than the 1-D experiment (with respect to the same benchmark). This highlights the importance of an improved representation of clouds even at the resolution of today's regional (limited-area) numerical models, which needs to be considered if NWP radiative biases are to be efficiently reduced. All in all, this paper provides a systematic documentation of NWP radiative biases, which is a necessary first step towards an improved treatment of radiation–cloud interaction in atmospheric models.

Research on Self Calibration Technology for Precision Workpiece Measurement Based on Laser Doppler Vibrometer

This article introduces the present development status at home and abroad of laser Doppler vibrometer, and analyses the basic principle of self-calibration technique. The one-dimensional self-calibration measurement scheme is designed by laser Doppler vibrometer. Taking gear vibration measurement as an example, four laser Doppler vibrometer are used to construct the self-calibration measurement system. Based on the principle of self-calibration, the system of paraboloid measurement and modification of large satellite antenna and its measurement and modification process are designed.

The solution of the Riemann problem in rectangular channels with constrictions and obstructions

Usually, the rapid geometric transitions that are of negligible length with respect to the channel are treated in one-dimensional Saint Venant models as internal boundary conditions, assuming that an instantaneous equilibrium is attained between the flow characteristics through the structure and the flow characteristics in the channel. In the present paper, a different point of view is assumed by considering rapid transients at channel constrictions and obstructions that are caused by the lack of instantaneous equilibrium between the flow conditions immediately upstream and downstream of the structure. These transients are modelled as a Riemann problem, assuming that the flow through the geometric transition is described by a stationary weak solution of the Saint Venant equations without friction. For this case, it is demonstrated that the solution of the Riemann problem exists and it is unique for a wide class of initial flow conditions, including supercritical flows. The solutions of the Riemann problem supplied by the one-dimensional mathematical model compare well with the results of a two-dimensional Shallow Water Equations numerical model when the head loss through the structure is negligible. The inspection of the exact solutions structure shows that the flow conditions immediately to the left and to the right of the geometric discontinuity may be very different from the initial conditions, and this contributes to explain the numerical issues that are reported in the literature for the rapid transients at internal boundary conditions in finite difference models. The solution of the Riemann problem has been coded, and the corresponding exact fluxes have been used as numerical fluxes in a one-dimensional Finite Volume scheme for the solution of the Shallow water Equations. The results demonstrate that spurious oscillations and instability phenomena are completely eliminated, ensuring the robustness of the approach. In the case that the energy loss is not negligible, the exact solutions capture the essential features of the two-dimensional model numerical results, ensuring that the mathematical procedure is generalizable to realistic conditions. This generalization is presented in the final part of the paper.

Improving backtracking search algorithm with variable search strategies for continuous optimization

The backtracking search algorithm (BSA), a relatively new evolutionary algorithm (EA), has been shown to be a competitive alternative to other population-based algorithms. To effectively solve a variety of optimization problems, this paper suggests ten mutation strategies and compares the performance of selection mechanisms in employing these strategies. Moreover, following the original BSA design, new parameters of historical mean and best positions are proposed in order to implement several additional mutation strategies. In addition, as recommended in the literature, a one-dimensional crossover scheme is enacted for greedy strategies in order to prevent premature convergence. Furthermore, three settings for search factors of mutation strategies are proposed. As a result, improved BSA versions that employed, respectively, ten and four mutation strategies were found to significantly facilitate the ability of BSA to handle optimization tasks of different characteristics. The experimental results show that the proposed versions outperformed the basic BSA in terms of achieving high convergence speed in the early stage, reaching the convergence precision and plateau with better scores, and performing perfectly on tests of composition functions. In addition, the improved BSA versions outperformed five popular, nature-inspired algorithms in terms of achieving the best convergence precision and performing perfectly on six composition functions.

Modeling of acetylene detonation in a shock tube by the large particle method with TVD correction

A one-dimensional TVD correction scheme is described, which can be successfully applied not only in 1D calculations, but also in 2D - 3D modeling [1-2]. The advantage of the proposed scheme is the lack of solving matrix equations. The implementation of the scheme in conjunction with the large particle method was tested on the problems of arbitrary discontinuity breakup and strong point explosion. The modeling of acetylene combustion in a shock tube and its transition to detonation was performed depending on the conditions set on the surface of the tube, and the parameters of the problem.

Efficient Iterative Method for Solving Optimal Control Problem Governed by Diffusion Equation with Time Fractional Derivative

We solve finite-difference approximations of a linear-quadratic optimal control problem governed by Dirichlet boundary value problem with fractional time derivative. The state equation of the problem is approximated using locally one-dimensional difference schemes. The stability estimates of discrete state equations necessary for studying the convergence of iterative solution methods for the constructed discrete optimal control problems are proved. The rate of convergence of the proposed iterative method is obtained and the optimal iterative parameter is found. The results of numerical tests for a model problem are presented.

Design of Secure and Reliable MU-MIMO Transceiver System for Vehicular Networks

MU-MIMO (Multi-User MIMO) has been a promising technique for vehicular networks to achieve faster communication. Conventional MU-MIMO transceiver is designed with One-dimensional (1-D) improper modulation schemes such as Binary Phase Shift Keying (BPSK) and Multilevel Amplitude Shift Keying (MASK) failed to yield standard ABER (average bit error rate). To achieve high reliability, a novel MUMIMO uplink transceiver system is designed under PAPC (Per-Antenna Power Constraint) by assuming perfect and imperfect channel state information (CSI). MIMO communication channels are perceptible. Hence, security of the proposed system is improved by novel pseudorandom key generation technique using randomized synthetic colour image. Analytical design for proposed systems is carried and simulated for various p-norm constraints. Simulation results show higher reliability and security than the existing system. It also satisfies the linearity constraint of a power amplifier, which makes the system more suitable for practical applications.