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We study the three-dimensional compressible elastic Navier--Stokes--Poisson equations induced by a new bipolar viscoelastic model derived here, which model the motion of the compressible electrically conducting fluids. The various boundary conditions for the electrostatic potential including the Dirichlet and Neumann boundary conditions are considered. By using a unified energy method, we obtain the unique global H² solution near a constant equilibrium state in the half-space or exterior of an obstacle. The elasticity plays a crucial role in establishing the L² estimate for the electrostatic field. [ABSTRACT FROM AUTHOR]

Canonical equations play a pivotal role in various sub-fields of physics and mathematics. However, for complex systems and systems without first principles, deriving canonical equations analytically is quite laborious or might even be impossible. This work is devoted to automatedly distilling the canonical equations solely from random state data. The random state data are collected from stochastically excited, dissipative dynamical systems either experimentally or numerically, while other information, such as the system characterization itself and the excitations, is not needed. The identification procedure comes down to a nested optimization problem, and the explicit expressions of the momentum (density) functions and energy (density) functions are identified simultaneously. Three representative examples are investigated to illustrate its high accuracy of identification, the small requirement for data amount, and high robustness to excitations and dissipation. The identification procedure serves as a filter, filtering out nonconservative information while retaining conservative information, which is especially suitable for systems with unobtainable excitations. [ABSTRACT FROM AUTHOR]

Criteria for guaranteeing the existence, uniqueness and asymptotic stability (in the sense of Liapunov) of periodic solutions of a forced Liénard-type equation under certain assumptions are presented. These criteria are obtained by application of the Manásevich–Mawhin continuation theorem, Floquet theory, Liapunov stability theory and some analysis techniques. An example is provided to demonstrate the applicability of our results. [ABSTRACT FROM AUTHOR]

In this work, we prove the existence and uniqueness of periodic solutions for a Liénard equation with two deviating arguments. Our main tools are the Mawhin's continuation theorem and the Schwarz inequality. We obtain our results under weaker conditions than those in, as shown by an example in the last section of this artticle. [ABSTRACT FROM AUTHOR]

Data-driven equation identification for dynamical systems has achieved great progress, which for static systems, however, has not kept pace. Unlike dynamical systems, static systems are time invariant, so we cannot capture discrete data along the time stream, which requires identifying governing equations only from scarce data. This work is devoted to this topic, building a data-driven method for extracting the differential-variational equations that govern static behaviors only from scarce, noisy data of responses, loads, as well as the values of system attributes if available. Compared to the differential framework typically adopted in equation identification, the differential-variational framework, due to its spatial integration and variation arbitrariness, brings some advantages, such as high robustness to data noise and low requirements on data amounts. The application, efficacy, and all the aforementioned advantages of this method are demonstrated by four numerical examples, including three continuous systems and one discrete system. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports on A-harmonic equations including the A-harmonic equations and Dirac operator, the global estimation of the singular integrals of maximal operator and Green's operator's composition, and the harmonic quasiconformal quasiisometrics.

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [ABSTRACT FROM AUTHOR]

The simplified governing equations of applied mechanics play a pivotal role and were derived based on ingenious assumptions or hypotheses regarding the displacement fields for specific problems. In this paper, we introduce a data-driven method by the name AI-Timoshenko in honor of Timoshenko, father of applied solid mechanics, to automatically discover simplified governing equations for applied mechanics problems directly from discrete data simulated by the three-dimensional (3D) finite element method. The simplified governing equations are in variational form, which is compact and advantageous for data-driven discovery. AI-Timoshenko liberates applied mechanicians from burdensome labor, including assumptions, derivation, and trial and error. The simplified governing equations for Euler-Bernoulli and Timoshenko beam theories are successfully rediscovered using the present AI-Timoshenko method, which shows that this method is capable of discovering simplified governing equations for applied mechanics problems. [ABSTRACT FROM AUTHOR]

A novel model was developed to evaluate gap coupling coefficient considering ac-space-charge effects due to the bunching in the interaction gap. The formulation was derived based on Webster's debunching theory and the electron-stream oscillation equation with arbitrary gap field distribution on the gridless gap. The coupling coefficient with ac-space-charge effects was investigated through both analysis and particle-in-cell simulation. The calculation results are in reasonable agreement with the simulation results. With the ac-space-charge effects, the coupling coefficient is lower than that calculated by ballistic theory. It is found that the plasma gap transit angle is a key factor in the effects of ac space charge on the coupling coefficient. Large beam current or gap length and, hence, mean large plasma transit angle indicate strong ac-space-charge effects on the coupling coefficient. [ABSTRACT FROM PUBLISHER]

An approach to the enhancement of Cherenkov radiation source driven by two electron beams (TEBs) is presented in this paper. The Cherenkov radiation source is composed of a cylindrical grating, and TEBs with a velocity separation are concentric and separated. By a field matched method, the dispersion equation is derived with a linearized fluid theory and solved by numerical calculation. The numerical results show that a considerable enhancement of growth rate is realized at an optimized voltage ratio due to two stream instability. Moreover, with a help of 2-D particle-in-cell simulations, the improvement of output power induced by the two stream instability is demonstrated, and the decreased of output power is observed as the increased distance of two electron beams. [ABSTRACT FROM PUBLISHER]

In this paper, we shall study a fourth-order stochastic heat equation driven by a fractional noise, which is fractional in time and white in space. We will discuss the existence and uniqueness of the solution to the equation. Furthermore, the regularity of the solution will be obtained. On the other hand, the large deviation principle for the equation with a small perturbation will be established through developing a classical method. [ABSTRACT FROM AUTHOR]

Calculation of the liquid-liquid equilibrium (LLE) based on an activity coefficient model is a common and significant problem in chemical thermodynamics. This is usually carried out by either minimizing the Gibbs free energy of the system coupled with the stability test (tangent plane distance criterion) or solving the isoactivity equations. While established, the stability test requires a very robust algorithm. By contrast, it is easy to solve the isoactivity equations; nevertheless, the solution strongly depends on the initial estimate. This study aims to investigate the structure of the solutions of the isoactivity equations for LLE systems in order to provide a calculation strategy that is not so dependent on the initial estimates while still maintaining its simplicity. A systematic study covering one- and two-phase ternary, quaternary, and quinary LLE systems and three-phase ternary systems has been carried out using the nonrandom two-liquid model, and it has been found that the equation-solving approach can be applied to multiphase systems. [ABSTRACT FROM AUTHOR]