A novel method for simulating nuclear explosion with chemical explosion to form an approximate plane wave: Field test and numerical simulation

A nuclear explosion in the rock mass medium can produce strong shock waves,seismic shocks,and other destructive effects,which can cause extreme damage to the underground protection infrastructures.With the increase in nuclear explosion power,underground protection engineering enabled by explosion-proof impact theory and technology ushered in a new challenge.This paper proposes to simulate nuclear explosion tests with on-site chemical explosion tests in the form of multi-hole explosions.First,the mechanism of using multi-hole simultaneous blasting to simulate a nuclear explosion to generate approximate plane waves was analyzed.The plane pressure curve at the vault of the underground protective tunnel under the action of the multi-hole simultaneous blasting was then obtained using the impact test in the rock mass at the site.According to the peak pressure at the vault plane,it was divided into three regions:the stress superposition region,the superposition region after surface reflection,and the approximate plane stress wave zone.A numerical simulation approach was developed using PFC and FLAC to study the peak particle velocity in the surrounding rock of the underground protective cave under the action of multi-hole blasting.The time-history curves of pressure and peak pressure partition obtained by the on-site multi-hole simultaneous blasting test and numerical simulation were compared and analyzed,to verify the correctness and rationality of the formation of an approximate plane wave in the simulated nuclear explosion.This comparison and analysis also provided a theoretical foundation and some research ideas for the ensuing study on the impact of a nuclear explosion.

Gaussian Mixture-Learned Approximate Message Passing(GM-LAMP)Based Hybrid Precoders for mmWave Massive MIMO Systems

Hybrid precoder design is a key technique providing better antenna gain and reduced hardware complexity in millimeter-wave(mmWave)massive multiple-input multiple-output(MIMO)systems.In this paper,Gaussian Mixture learned approximate message passing(GM-LAMP)network is presented for the design of optimal hybrid precoders suitable for mmWave Massive MIMO systems.Optimal hybrid precoder designs using a compressive sensing scheme such as orthogonal matching pursuit(OMP)and its derivatives results in high computational complexity when the dimensionality of the sparse signal is high.This drawback can be addressed using classical iterative algorithms such as approximate message passing(AMP),which has comparatively low computational complexity.The drawbacks of AMP algorithm are fixed shrinkage parameter and non-consideration of prior distribution of the hybrid precoders.In this paper,the fixed shrinkage parameter problem of the AMP algorithm is addressed using learned AMP(LAMP)network,and is further enhanced as GMLAMP network using the concept of Gaussian Mixture distribution of the hybrid precoders.The simula-tion results show that the proposed GM-LAMP network achieves optimal hybrid precoder design with enhanced achievable rates,better accuracy and low computational complexity compared to the existing algorithms.

Approximately Bi-Similar Symbolic Model for Discretetime Interconnected Switched System

Dear Editor,This letter concerns the development of approximately bi-similar symbolic models for a discrete-time interconnected switched system(DT-ISS).The DT-ISS under consideration is formed by connecting multiple switched systems known as component switched systems(CSSs).Although the problem of constructing approximately bi-similar symbolic models for DT-ISS has been addressed in some literature,the previous works have relied on the assumption that all the subsystems of CSSs are incrementally input-state stable.

Embedding-based approximate query for knowledge graph

To solve the low efficiency of approximate queries caused by the large sizes of the knowledge graphs in the real world,an embedding-based approximate query method is proposed.First,the nodes in the query graph are classified according to the degrees of approximation required for different types of nodes.This classification transforms the query problem into three constraints,from which approximate information is extracted.Second,candidates are generated by calculating the similarity between embeddings.Finally,a deep neural network model is designed,incorporating a loss function based on the high-dimensional ellipsoidal diffusion distance.This model identifies the distance between nodes using their embeddings and constructs a score function.k nodes are returned as the query results.The results show that the proposed method can return both exact results and approximate matching results.On datasets DBLP(DataBase systems and Logic Programming)and FUA-S(Flight USA Airports-Sparse),this method exhibits superior performance in terms of precision and recall,returning results in 0.10 and 0.03 s,respectively.This indicates greater efficiency compared to PathSim and other comparative methods.

A signal coordination algorithm for two adjacent intersections based on approximate dynamic programming

To reduce vehicle emissions in road networks, a new signal coordination algorithm based on approximate dynamic programming （ADP） is developed for two intersections. Taking the Jetta car as an experimental vehicle, field tests are conducted in Changchun Street of Changchun city and vehicle emission factors in complete stop and uniform speed states are collected. Queue lengths and signal light colors of approach lanes are selected as state variables, and green switch plans are selected as decision variables of the system. Then the calculation model of the optimization index during the planning horizon is developed based on the basis function method of the ADP. The temporal-difference algorithm is employed to update the weighting factor vector of the approximate function. Simulations are conducted in Matlab and the results show that the established algorithm outperforms the conventional coordination algorithm in reducing vehicle emissions by 8.2%. Sensitive analysis of the planning horizon length on the evaluation index is also conducted and the statistical results show that the optimal length of the planning horizon is directly proportional to the traffic load.

APPROXIMATE QUERY AND CALCULATION OF RNN_k BASED ON VORONOI CELL

Reverse k nearest neighbor （RNNk） is a generalization of the reverse nearest neighbor problem and receives increasing attention recently in the spatial data index and query. RNNk query is to retrieve all the data points which use a query point as one of their k nearest neighbors. To answer the RNNk of queries efficiently, the properties of the Voronoi cell and the space-dividing regions are applied. The RNNk of the given point can be found without computing its nearest neighbors every time by using the rank Voronoi cell. With the elementary RNNk query result, the candidate data points of reverse nearest neighbors can he further limited by the approximation with sweepline and the partial extension of query region Q. The approximate minimum average distance （AMAD） can be calculated by the approximate RNNk without the restriction of k. Experimental results indicate the efficiency and the effectiveness of the algorithm and the approximate method in three varied data distribution spaces. The approximate query and the calculation method with the high precision and the accurate recall are obtained by filtrating data and pruning the search space.

Global Piecewise Analysis of HIV Model with Bi-Infectious Categories under Ordinary Derivative and Non-Singular Operator with Neural Network Approach

This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.

Statistical analysis on the validity of the cold plasma approximation for chorus waves based on Van Allen Probe observations and their effects on radiation belt electrons

Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.

An Approximation Method for Singular Trudinger-Moser Inequality

In this paper,we construct a power type functional which is the approximation functional of the Singular Trudinger-Moser functional.Moreover,we obtain the concentration level of the functional and show it converges to the concentration level of singular Trudinger-Moser functional on the unit ball.

Comparison of two kinds of approximate proximal point algorithms for monotone variational inequalities

This paper proposes two kinds of approximate proximal point algorithms （APPA） for monotone variational inequalities, both of which can be viewed as two extended versions of Solodov and Svaiter＇s APPA in the paper ＂Error bounds for proximal point subproblems and associated inexact proximal point algorithms＂ published in 2000. They are both prediction- correction methods which use the same inexactness restriction; the only difference is that they use different search directions in the correction steps. This paper also chooses an optimal step size in the two versions of the APPA to improve the profit at each iteration. Analysis also shows that the two APPAs are globally convergent under appropriate assumptions, and we can expect algorithm 2 to get more progress in every iteration than algorithm 1. Numerical experiments indicate that algorithm 2 is more efficient than algorithm 1 with the same correction step size,

Effect of orbital symmetry on atomic ionization in near-infrared laser fields

We have performed a comparative study of the photoelectron spectra adopting different initial states(2s or 2_(p0))of hydrogen atoms in a near-infrared laser pulse by using the full three-dimensional time-dependent Schr?dinger equation.It is demonstrated that the atomic photoelectron spectra oscillate out of step as a function of electron kinetic energies for different initial states(2s or 2_(p0)),which is well reproduced by the simulations based on strong field approximation,and the above distinct feature is ascribed to the different interferences from the partial electron wave packets detached by positive and negative electric fields for different initial states of 2s and 2_(p0).

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

An Approximate Analytical Propagation Formula for Gaussian Beams through a Cat-Eye Optical Lens under Large Incidence Angle Condition

Based on the generalized diffraction integral formula and the idea that the angle misalignment of the cat-eye optical lens can be transformed into the displacement misalignment,an approximate analytical propagation formula for Gaussian beams through a cat-eye optical lens under large incidence angle condition is derived.Numerical results show that the diffraction effect of the apertures of the cat-eye optical lens becomes stronger along with the increase in incidence angle.The results are also compared with those from using an angular spectrum diffraction integral and experiment to illustrate the applicability and validity of our theoretical formula.It is shown that the approximate extent is good enough for the application of a cat-eye optical lens with a radius of 20 mm and a propagation distance of 100 m,and the approximate extent becomes better along with the increase in the radius of the cat-eye optical lens and the propagation distance.

Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm

This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.

Application of approximate entropy on dynamic characteristics of epileptic absence seizure

Electroencephalogram signals are time-varying complex electrophysiological signals. Existing studies show that approximate entropy, which is a nonlinear dynamics index, is not an ideal method for electroencephalogram analysis. Clinical electroencephalogram measurements usually contain electrical interference signals, creating additional challenges in terms of maintaining robustness of the analytic methods. There is an urgent need for a novel method of nonlinear dynamical analysis of the electroencephalogram that can characterize seizure-related changes in cerebral dynamics. The aim of this paper was to study the fluctuations of approximate entropy in preictal, ictal, and postictal electroencephalogram signals from a patient with absence seizures, and to improve the algorithm used to calculate the approximate entropy. The approximate entropy algorithm, especially our modified version, could accurately describe the dynamical changes of the brain during absence seizures. We could also demonstrate that the complexity of the brain was greater in the normal state than in the ictal state. The fluctuations of the approximate entropy before epileptic seizures observed in this study can form a good basis for further study on the prediction of seizures with nonlinear dynamics.

A simplified approximate model of compressible hypervelocity penetration

A simplified approximate model considering rod/target material's compressibility is proposed for hypervelocity penetration.We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger,analogously,and much less than that of the target,respectively.The results show that the effect of shockwaves is insignificant up to 12 km/s,so the shockwave is neglected in the present approximate model.The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved.The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved.The solution of the approximate model is in agreement with the result of the complete compressible model.In addition,the effect of shockwaves on hypervelocity penetration is shown to weaken material's compressibility and reduce the interface pressure of the rod/target,and thus the striking/protective performance of the rod/target is weakened,respectively.We also conduct an error analysis of the interface pressure and penetration efficiency.With a velocity change of 1.6 times the initial sound speed for the rod or target,the error of the approximate model is very small.For metallic rod-target combinations,the approximate model is applicable even at an impact velocity of 12 km/s.

Using approximate dynamic programming for multi-ESM scheduling to track ground moving targets

This paper researches the adaptive scheduling problem of multiple electronic support measures(multi-ESM) in a ground moving radar targets tracking application. It is a sequential decision-making problem in uncertain environment. For adaptive selection of appropriate ESMs, we generalize an approximate dynamic programming(ADP) framework to the dynamic case. We define the environment model and agent model, respectively. To handle the partially observable challenge, we apply the unsented Kalman filter(UKF) algorithm for belief state estimation. To reduce the computational burden, a simulation-based approach rollout with a redesigned base policy is proposed to approximate the long-term cumulative reward. Meanwhile, Monte Carlo sampling is combined into the rollout to estimate the expectation of the rewards. The experiments indicate that our method outperforms other strategies due to its better performance in larger-scale problems.

Approximate solutions of the Alekseevskii–Tate model of long-rod penetration

The Alekseevskii–Tate model is the most successful semi-hydrodynamic model applied to long-rod penetration into semi-infinite targets. However, due to the nonlinear nature of the equations, the rod(tail) velocity, penetration velocity, rod length, and penetration depth were obtained implicitly as a function of time and solved numerically By employing a linear approximation to the logarithmic relative rod length, we obtain two sets of explicit approximate algebraic solutions based on the implicit theoretica solution deduced from primitive equations. It is very convenient in the theoretical prediction of the Alekseevskii–Tate model to apply these simple algebraic solutions. In particular, approximate solution 1 shows good agreement with the theoretical(exact) solution, and the first-order perturbation solution obtained by Walters et al.(Int. J. Impac Eng. 33:837–846, 2006) can be deemed as a special form of approximate solution 1 in high-speed penetration. Meanwhile, with constant tail velocity and penetration velocity approximate solution 2 has very simple expressions, which is applicable for the qualitative analysis of long-rod penetration. Differences among these two approximate solutions and the theoretical(exact) solution and their respective scopes of application have been discussed, and the inferences with clear physical basis have been drawn. In addition, these two solutions and the first-order perturbation solution are applied to two cases with different initial impact velocity and different penetrator/target combinations to compare with the theoretical(exact) solution. Approximate solution 1 is much closer to the theoretical solution of the Alekseevskii–Tate model than the first-order perturbation solution in both cases, whilst approximate solution 2 brings us a more intuitive understanding of quasi-steady-state penetration.

Approximate Solution for Mechanism of Thermally and Wind-driven Ocean Circulation

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

In this paper, the approximate expressions of the solitary wave solutions for a class of nonlinear disturbed long-wave system are constructed using the homotopie mapping method.