Heterogeneous information phase space reconstruction and stability prediction of filling body–surrounding rock combination

Traditional research believes that the filling body can effectively control stress concentration while ignoring the problems of unknown stability and the complex and changeable stress distribution of the filling body–surrounding rock combination under high-stress conditions.Current monitoring data processing methods cannot fully consider the complexity of monitoring objects,the diversity of monitoring methods,and the dynamics of monitoring data.To solve this problem,this paper proposes a phase space reconstruction and stability prediction method to process heterogeneous information of backfill–surrounding rock combinations.The three-dimensional monitoring system of a large-area filling body–surrounding rock combination in Longshou Mine was constructed by using drilling stress,multipoint displacement meter,and inclinometer.Varied information,such as the stress and displacement of the filling body–surrounding rock combination,was continuously obtained.Combined with the average mutual information method and the false nearest neighbor point method,the phase space of the heterogeneous information of the filling body–surrounding rock combination was then constructed.In this paper,the distance between the phase point and its nearest point was used as the index evaluation distance to evaluate the stability of the filling body–surrounding rock combination.The evaluated distances(ED)revealed a high sensitivity to the stability of the filling body–surrounding rock combination.The new method was then applied to calculate the time series of historically ED for 12 measuring points located at Longshou Mine.The moments of mutation in these time series were at least 3 months ahead of the roadway return dates.In the ED prediction experiments,the autoregressive integrated moving average model showed a higher prediction accuracy than the deep learning models(long short-term memory and Transformer).Furthermore,the root-mean-square error distribution of the prediction results peaked at 0.26,thus outperforming the no-prediction method in 70%of the cases.

Effects of phonon bandgap on phonon-phonon scattering in ultrahigh thermal conductivityθ-phase TaN

Phonon bandgap typically has a significant effect on phonon-phonon scattering process.In this work,the effects of mass modified phonon bandgap inθ-phase Ta N are systemically investigated by the means of first-principles calculations with linearized Boltzmann transport equation.Through detailed calculations,we find that phonon bandgap has a significant effect on three-phonon process while exhibits a much weaker effect on four-phonon process.The reason for the ultrahigh thermal conductivity ofθ-phase Ta N is the long lifetime of phonons including both three-phonon and four-phonon processes,which originates from the weak phonon anharmonicity and large phonon bandgap-induced small phonon-phonon scattering phase space.This work advances the understanding of phonon bandgap effects on phonon transport.

Prediction of seawater pH by bidirectional gated recurrent neural network with attention under phase space reconstruction:case study of the coastal waters of Beihai,China

Marine life is very sensitive to changes in pH.Even slight changes can cause ecosystems to collapse.Therefore,understanding the future pH of seawater is of great significance for the protection of the marine environment.At present,the monitoring method of seawater pH has been matured.However,how to accurately predict future changes has been lacking effective solutions.Based on this,the model of bidirectional gated recurrent neural network with multi-headed self-attention based on improved complete ensemble empirical mode decomposition with adaptive noise combined with phase space reconstruction(ICPBGA)is proposed to achieve seawater pH prediction.To verify the validity of this model,pH data of two monitoring sites in the coastal sea area of Beihai,China are selected to verify the effect.At the same time,the ICPBGA model is compared with other excellent models for predicting chaotic time series,and root mean square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE),and coefficient of determination(R2)are used as performance evaluation indicators.The R2 of the ICPBGA model at Sites 1 and 2 are above 0.9,and the prediction errors are also the smallest.The results show that the ICPBGA model has a wide range of applicability and the most satisfactory prediction effect.The prediction method in this paper can be further expanded and used to predict other marine environmental indicators.

Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space

The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics.

Enhancing Precision in Radiotherapy Delivery: Validating Monte Carlo Simulation Models for 6 MV Elekta Synergy Agility LINAC Photon Beam Using Two Models of the GAMOS Code

The most crucial requirement in radiation therapy treatment planning is a fast and accurate treatment planning system that minimizes damage to healthy tissues surrounding cancer cells. The use of Monte Carlo toolkits has become indispensable for research aimed at precisely determining the dose in radiotherapy. Among the numerous algorithms developed in recent years, the GAMOS code, which utilizes the Geant4 toolkit for Monte Carlo simula-tions, incorporates various electromagnetic physics models and multiple scattering models for simulating particle interactions with matter. This makes it a valuable tool for dose calculations in medical applications and throughout the patient’s volume. The aim of this present work aims to vali-date the GAMOS code for the simulation of a 6 MV photon-beam output from the Elekta Synergy Agility linear accelerator. The simulation involves mod-eling the major components of the accelerator head and the interactions of the radiation beam with a homogeneous water phantom and particle information was collected following the modeling of the phase space. This space was po-sitioned under the X and Y jaws, utilizing three electromagnetic physics mod-els of the GAMOS code: Standard, Penelope, and Low-Energy, along with three multiple scattering models: Goudsmit-Saunderson, Urban, and Wentzel-VI. The obtained phase space file was used as a particle source to simulate dose distributions (depth-dose and dose profile) for field sizes of 5 × 5 cm2 and 10 × 10 cm2 at depths of 10 cm and 20 cm in a water phantom, with a source-surface distance (SSD) of 90 cm from the target. We compared the three electromagnetic physics models and the three multiple scattering mod-els of the GAMOS code to experimental results. Validation of our results was performed using the gamma index, with an acceptability criterion of 3% for the dose difference (DD) and 3 mm for the distance-to-agreement (DTA). We achieved agreements of 94% and 96%, respectively, between simulation and experimentation for the three electromagnetic physics models and three mul-tiple scattering models, for field sizes of 5 × 5 cm2 and 10 × 10 cm2 for depth-dose curves. For dose profile curves, a good agreement of 100% was found between simulation and experimentation for the three electromagnetic physics models, as well as for the three multiple scattering models for a field size of 5 × 5 cm2 at 10 cm and 20 cm depths. For a field size of 10 × 10 cm2, the Penelope model dominated with 98% for 10 cm, along with the three multiple scattering models. The Penelope model and the Standard model, along with the three multiple scattering models, dominated with 100% for 20 cm. Our study, which compared these different GAMOS code models, can be crucial for enhancing the accuracy and quality of radiotherapy, contributing to more effective patient treatment. Our research compares various electro-magnetic physics models and multiple scattering models with experimental measurements, enabling us to choose the models that produce the most reli-able results, thereby directly impacting the quality of simulations. This en-hances confidence in using these models for treatment planning. Our re-search consistently contributes to the progress of Monte Carlo simulation techniques in radiation therapy, enriching the scientific literature.

New conserved quantities of Noether-Mei symmetry of mechanical system in phase space

This paper studies two new types of conserved quantities deduced by Noether Mei symmetry of mechanical system in phase space. The definition and criterion of Noether Mei symmetry for the system are given. A coordination function is introduced, and the conditions under which the Noether- Mei symmetry leads to the two types of conserved quantities and the forms of the two types of conserved quantities are obtained. An illustrative example is given. The coordination function can be selected according to the demand for finding the gauge function, and the choice of the coordination function has multiformity, so more conserved quantities deduced from Noether Mei symmetry of mechanical system can be obtained.

Prediction of elevator traffic flow based on SVM and phase space reconstruction

To make elevator group control system better follow the change of elevator traffic flow (ETF) in order to adjust the control strategy,the prediction method of support vector machine (SVM) in combination with phase space reconstruction has been proposed for ETF.Firstly,the phase space reconstruction for elevator traffic flow time series (ETFTS) is processed.Secondly,the small data set method is applied to calculate the largest Lyapunov exponent to judge the chaotic property of ETF.Then prediction model of ETFTS based on SVM is founded.Finally,the method is applied to predict the time series for the incoming and outgoing passenger flow respectively using ETF data collected in some building.Meanwhile,it is compared with RBF neural network model.Simulation results show that the trend of factual traffic flow is better followed by predictive traffic flow.SVM algorithm has much better prediction performance.The fitting and prediction of ETF with better effect are realized.

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method, this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors, which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens. The experimental results show that, the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system, and the nonlinear invariants such as correlation dimension, Lyapunov exponent and Kolmogorov entropy are still reserved. It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.

Deep learning approach to detect seizure using reconstructed phase space images

Epilepsy is a chronic neurological disorder that affects the function of the brain in people of all ages.It manifests in the electroencephalogram(EEG) signal which records the electrical activity of the brain.Various image processing,signal processing,and machine-learning based techniques are employed to analyze epilepsy,using spatial and temporal features.The nervous system that generates the EEG signal is considered nonlinear and the EEG signals exhibit chaotic behavior.In order to capture these nonlinear dynamics,we use reconstructed phase space(RPS) representation of the signal.Earlier studies have primarily addressed seizure detection as a binary classification(normal vs.ictal) problem and rarely as a ternary class(normal vs.interictal vs.ictal)problem.We employ transfer learning on a pre-trained deep neural network model and retrain it using RPS images of the EEG signal.The classification accuracy of the model for the binary classes is(98.5±1.5)% and(95±2)% for the ternary classes.The performance of the convolution neural network(CNN) model is better than the other existing statistical approach for all performance indicators such as accuracy,sensitivity,and specificity.The result of the proposed approach shows the prospect of employing RPS images with CNN for predicting epileptic seizures.

A Forecasting Model of Vector Similarity in Phase Space for Flood and Drought over the Huanghe-Huaihe-Haihe Plain in China

To represent well the characteristics of temporal and spatial distributions, chart of 3-dekad moving total precipitation is proposed in this paper first. Then this kind of chart is expanded in terms of Chebyshev polynomial at irregular grids, and the quantitative representation of precipitation is got. Finally the Chebyshev coefficients are forecasted by using the forecasting method of vector similarity in phase space proposed by Zhou (1992). Using above mentioned procedures temporal and spatial distributions of precipitation over the Huanghe-- Huaihe-- H aihe Plain in China are forecasted.

A Relation of the Noncommutative Parameters in Generalized Noncommutative Phase Space

We introduce the deformed boson operators which satisfy a deformed boson algebra in some special types of generalized noncommutative phase space. Based on the deformed boson algebra, we construct coherent state representations. We calculate the variances of the coordinate operators on the coherent states and investigate the corresponding Heisenberg uncertainty relations. It is found that there are some restriction relations of the noncommutative parameters in these special types of noncommutative phase space.

THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS NONHOLONOMIC SYSTEM OF NON-CHETAEV'S TYPE IN PHASE SPACE

The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.

A unified symmetry of nonholonomic mechanical systems in phase space

In this paper, we have studied the unified symmetry of a nonholonomic mechanical system in phase space. The definition and the criterion of a unified symmetry of the nonholonomic mechanical system in phase space are given under general infinitesimal transformations of groups in which time is variable. The Noether conserved quantity, the generalized Hojman conserved quantity and the Mei conserved quantity are obtained from the unified symmetry. An example is given to illustrate the application of the results.

Noether-Lie symmetry and conserved quantities of mechanical system in phase space

In this paper, a new kind of symmetry and its conserved quantities of a mechanical system in phase space are studied. The definition of this new symmetry, i.e. a Noether-Lie symmetry, is presented, and the criterion of this symmetry is also given. The Noether conserved quantity and the generalized Hojman conserved quantity of the Noether Lie symmetry of the system are obtained. The Noether-Lie symmetry contains the Noether symmetry and the Lie symmetry, and has more generalized significance.

New non-Noether conserved quantities of mechanical system in phase space

This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new nonNoether conserved quantity of Lie symmetry of the system, and Hojman and Mei＇s results are of special cases of our con-clusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformed invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformed invariance for general holonomic systems in phase space are provided. The conformed factor expression is deduced from conformed invariance and Lie symmetry. The relationship between the conformed invariance and the Lie symmetry is discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper,we study the Noether-form invariance of nonholonomic mechanical controllable systems inphase space.Equations of motion of the controllable mechanical systems in phase space are presented.The definitionand the criterion for this system are presented.A new conserved quantity and the Noether conserved quantity deducedfrom the Noether-form invariance are obtained.An example is given to illustrate the application of the results.

A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.

Validation of Transverse Phase Space Tomography at TRIUMF

Knowledge of the phase space density distribution in details is useful to understand subsequent evolution of the charged particle beam in a transport line.This makes the beam tomography very useful in the application for beam diagnostics.This application is not limited by the beam energy,as opposed to the emittance scanner.This paper presented the simulations and measurements we undertook in TRIUMF beam-lines to validate the maximum entropy(MENT)technique for the tomographic reconstruction of beam density distribution in the 2-dimensional transverse phase space.Beam profiles were taken with a single wire scanner while changing an upstream quadrupole’s strength.Moreover,the phase space plots were directly measured with emittance scanner.A close comparison was made on the resulting phase space density distribution and the emittance value at the same location of the beam-line.They show good agreement.

Form Invariance, Noether and Lie Symmetry of Non-conservative Hamiltonian Systems in Phase Space

For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results.