THE EXTREMES OF DEPENDENT CHI-PROCESSES ATTRACTED BY THE BROWN-RESNICK PROCESS

Motivated by some recent works on the topic of the Brown-Resnick process, we study the functional limit theorem for normalized pointwise maxima of dependent chi-processes. It is proven that the properly normalized pointwise maxima of those processes are attracted by the Brown-Resnick process.

Quantification of CO_(2) Emissions from Three Power Plants in China Using OCO-3 Satellite Measurements

Coal-fired power plants are a major carbon source in China. In order to assess the evaluation of China's carbon reduction progress with the promise made on the Paris Agreement, it is crucial to monitor the carbon flux intensity from coal-fired power plants. Previous studies have calculated CO_(2) emissions from point sources based on Orbiting Carbon Observatory-2 and-3(OCO-2 and OCO-3) satellite measurements, but the factors affecting CO_(2) flux estimations are uncertain. In this study, we employ a Gaussian Plume Model to estimate CO_(2) emissions from three power plants in China based on OCO-3 XCO_(2) measurements. Moreover, flux uncertainties resulting from wind information, background values,satellite CO_(2) measurements, and atmospheric stability are discussed. This study highlights the CO_(2) flux uncertainty derived from the satellite measurements. Finally, satellite-based CO_(2) emission estimates are compared to bottom-up inventories.The satellite-based CO_(2) emission estimates at the Tuoketuo and Nongliushi power plants are ~30 and ~10 kt d^(-1) smaller than the Open-Data Inventory for Anthropogenic Carbon dioxide(ODIAC) respectively, but ~10 kt d^(-1) larger than the ODIAC at Baotou.

Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.

Global Well-Posedness of the Fractional Tropical Climate Model

In this paper, we consider the Cauchy problem of 3-dimensional tropical climate model. This model reflects the interaction and coupling among the barotropic mode u, the first baroclinic mode v of the velocity and the temperature θ. The systems with fractional dissipation studied here may arise in the modeling of geophysical circumstances. Mathematically these systems allow simultaneous examination of a family of systems with various levels of regularization. The aim here is the global strong solution with the least dissipation. By energy estimate and delicate analysis, we prove the existence of global solution under three different cases: first, with the help of damping terms, the global strong solution of the system with Λ2au, Λ2βv and Λ2γ θ for;and second, the global strong solution of the system for with damping terms;finally, the global strong solution of the system for without any damping terms, which improve the known existence theory for this system.

The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences

In this paper,we study the asymptotic relation between the first crossing point and the last exit time for Gaussian order statistics which are generated by stationary weakly and strongly dependent Gaussian sequences.It is shown that the first crossing point and the last exit time are asymptotically independent and dependent for weakly and strongly dependent cases,respectively.The asymptotic relations between the first crossing point and the last exit time for stationary weakly and strongly dependent Gaussian sequences are also obtained.

Classification and structural characteristics of amorphous materials based on interpretable deep learning

Defining the structure characteristics of amorphous materials is one of the fundamental problems that need to be solved urgently in complex materials because of their complex structure and long-range disorder.In this study,we develop an interpretable deep learning model capable of accurately classifying amorphous configurations and characterizing their structural properties.The results demonstrate that the multi-dimensional hybrid convolutional neural network can classify the two-dimensional(2D)liquids and amorphous solids of molecular dynamics simulation.The classification process does not make a priori assumptions on the amorphous particle environment,and the accuracy is 92.75%,which is better than other convolutional neural networks.Moreover,our model utilizes the gradient-weighted activation-like mapping method,which generates activation-like heat maps that can precisely identify important structures in the amorphous configuration maps.We obtain an order parameter from the heatmap and conduct finite scale analysis of this parameter.Our findings demonstrate that the order parameter effectively captures the amorphous phase transition process across various systems.These results hold significant scientific implications for the study of amorphous structural characteristics via deep learning.

Spatial distribution order parameter prediction of collective system using graph network

In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a new order parameter φ to quantify the degree of order in the spatial distribution of particles. The results show that the spatial distribution order parameter can effectively describe the transition from a disorderly moving phase to a phase with a coherent motion of the particle distribution and the same conclusion could be obtained for systems with different sizes. Furthermore, we develop a powerful molecular dynamic graph network(MDGNet) model to realize the long-term prediction of the self-propelled collective system solely from the initial particle positions and movement angles. Employing this model, we successfully predict the order parameters of the specified time step. And the model can also be applied to analyze other types of complex systems with local interactions.

Quantum correlation enhanced bound of the information exclusion principle

We investigate the information exclusion principle for multiple measurements with assistance of multiple quantum memories that are well bounded by the upper and lower bounds.The lower bound depends on the observables'complementarity and the complementarity of uncertainty whilst the upper bound includes the complementarity of the observables,quantum discord,and quantum condition entropy.In quantum measurement processing,there exists a relationship between the complementarity of uncertainty and the complementarity of information.In addition,based on the information exclusion principle the complementarity of uncertainty and the shareability of quantum discord can exist as an essential factor to enhance the bounds of each other in the presence of quantum memory.

Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

Physical information-enhanced graph neural network for predicting phase separation

Although phase separation is a ubiquitous phenomenon, the interactions between multiple components make it difficult to accurately model and predict. In recent years, machine learning has been widely used in physics simulations. Here,we present a physical information-enhanced graph neural network(PIENet) to simulate and predict the evolution of phase separation. The accuracy of our model in predicting particle positions is improved by 40.3% and 51.77% compared with CNN and SVM respectively. Moreover, we design an order parameter based on local density to measure the evolution of phase separation and analyze the systematic changes with different repulsion coefficients and different Schmidt numbers.The results demonstrate that our model can achieve long-term accurate predictions of order parameters without requiring complex handcrafted features. These results prove that graph neural networks can become new tools and methods for predicting the structure and properties of complex physical systems.

Nonexistence of Global Solutions for a Semilinear Double-Wave Equation with Nonlinearity of Derivative Type

In this paper,we study the blow-up of solutions to a semilinear double-wave equation with nonlinearity of derivative type.By using the iteration method and the differential inequality techniques,we can get the estimates of the lifespan and the blow-up of solutions in the subcritical case under some assumptions.

Effects of short-range attraction on Jamming transition

Enormous progresses to understand the jamming transition have been driven via simulating purely repulsive particles which were somehow idealized in the past two decades. While the attractive systems are both theoretical and practical compared with repulsive systems. By studying the statistics of rigid clusters, we find that the critical packing fraction φ_(c) varies linearly with attraction μ for different system sizes when the range of attraction is short. While for systems with long-range attractions, however, the slope of φ_(c) appears significantly different, which means that there are two distinct jamming scenarios. In this paper, we focus our main attention on short-range attractions scenario and define a new quantity named "short-range attraction susceptibility" χ_(p), which describes the degree of response of the probability of finding jammed states pjto short-range attraction strength μ. Our central results are that χ_(p) diverges in the thermodynamic limit as χ_(p) ∝|φ-φ_(c)^(∞)|^(-γ_(p)), where φ_(c)^(∞) is the packing fraction at the jamming transition for the infinite system in the absence of attraction. χ_(p) obeys scaling collapse with a scaling function in both two and three dimensions, illuminating that the jamming transition can be considered as a phase transition as proposed in previous work.

Blow-Up Result for a Semi-Linear Wave Equation with a Nonlinear Memory Term of Derivative Type

In this paper,we study the blow-up of solutions to a semi-linear wave equation with a nonlinear memory term of derivative type.By using methods of an iteration argument and di erential inequalities,we obtain the blow-up result for the semi-linear wave equation when the exponent of p is under certain conditions.Meanwhile,we derive an upper bound of the lifespan of solutions to the Cauchy problem for the semi-linear wave equation.

Stochastic responses of tumor-immune system with periodic treatment

We investigate the stochastic responses of a tumor–immune system competition model with environmental noise and periodic treatment. Firstly, a mathematical model describing the interaction between tumor cells and immune system under external fluctuations and periodic treatment is established based on the stochastic differential equation. Then, sufficient conditions for extinction and persistence of the tumor cells are derived by constructing Lyapunov functions and Ito＇s formula. Finally, numerical simulations are introduced to illustrate and verify the results. The results of this work provide the theoretical basis for designing more effective and precise therapeutic strategies to eliminate cancer cells, especially for combining the immunotherapy and the traditional tools.

New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

Stamping Reliability of Rocket Engine Cover Based on Finite Element Anglysis and Experiments

This paper mainly focuses on the simulation and experimental study of the reliability of the solid rocket nozzle cover.The test-bed is designed according to the technical requirements in order to provide different stamping rates and tests for different sizes of covers.The gas source,the four valves and the installation container structure are used to realize the stamping.The installation container is a multistage flange stacking structure to achieve the installation of different sizes of plugging covers,and then the opening process of the plugging cover is recorded by the high speed pressure sensor and the automatic control system.The fluid solid coupling method is used to simulate the impact state of plugging cover in the flow field at 10,20,30 and 35 ms,and the maximum pressure at 35 ms is 1.244 MPa.Then the deformation of aluminum alloy plugging cover is observed by stress analysis and display dynamic method.The maximum value of Von Mises Stress of the simulation result is 277.600 MPa.In the experimental test,the performance of the system is tested with a high strength plugging cover.In the opening state of the two large flux control valves,the pressure in the installation container reaches 1.000 MPa at 35 ms.And then we modify the experimental system with the knowledge of aerodynamic theory.Finally,the plugging cover is installed to carry out the experiment,so as to obtain the reliable stamping rate of the plugging cover.Simulations,blind measurements and measurement results provide strong data for reliability of the plugging cover opening,and provide reliable reference data for rocket engine charge structure and nozzle shape optimization.

Graph dynamical networks for forecasting collective behavior of active matter

After decades of theoretical studies,the rich phase states of active matter and cluster kinetic processes are still of research interest.How to efficiently calculate the dynamical processes under their complex conditions becomes an open problem.Recently,machine learning methods have been proposed to predict the degree of coherence of active matter systems.In this way,the phase transition process of the system is quantified and studied.In this paper,we use graph network as a powerful model to determine the evolution of active matter with variable individual velocities solely based on the initial position and state of the particles.The graph network accurately predicts the order parameters of the system in different scale models with different individual velocities,noise and density to effectively evaluate the effect of diverse condition.Compared with the classical physical deduction method,we demonstrate that graph network prediction is excellent,which could save significantly computing resources and time.In addition to active matter,our method can be applied widely to other large-scale physical systems.

Symmetry Classification of Partial Differential Equations Based on Wu's Method

Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.

The No-Ellipsoidal Bound of Reachable Sets for Neutral Markovian Jump Systems with Disturbances

This paper is concerned with the reachable set estimation problem for neutral Markovian jump systems with bounded peak disturbances, which was rarely proposed for neutral Markovian jump systems. The main consideration is to find a proper method to obtain the no-ellipsoidal bound of the reachable set for neutral Markovian jump system as small as possible. By applying Lyapunov functional method, some derived conditions are obtained in the form of matrix inequalities. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

An Alternative Algorithm for the Symmetry Classification of Ordinary Differential Equations

This is the first paper on symmetry classification for ordinary differential equations(ODEs)based on Wu’s method.We carry out symmetry classification of two ODEs,named the generalizations of the Kummer-Schwarz equations which involving arbitrary function.First,Lie algorithm is used to give the determining equations of symmetry for the given equations,which involving arbitrary functions.Next,differential form Wu’s method is used to decompose determining equations into a union of a series of zero sets of differential characteristic sets,which are easy to be solved relatively.Each branch of the decomposition yields a class of symmetries and associated parameters.The algorithm makes the classification become direct and systematic.Yuri Dimitrov Bozhkov,and Pammela Ramos da Conceição have used the Lie algorithm to give the symmetry classifications of the equations talked in this paper in 2020.From this paper,we can find that the differential form Wu’s method for symmetry classification of ODEs with arbitrary function(parameter)is effective,and is an alternative method.