A QUASISTATIC FRICTIONAL CONTACT PROBLEM WITH NORMAL DAMPED RESPONSE FOR THERMO-ELECTRO-ELASTIC-VISCOPLASTIC BODIES

We consider a mathematical problem for quasistatic contact between a thermo-electro--elastic-viscoplastic body and an obstacle. The contact is modeled by a general normal damped response condition with friction law and heat exchange. We present a variational formulation of the problem and prove the existence and uniqueness of the weak solution. The proof is based on the formulation of four intermediate problems for the displacement field, the electric potential field and the temperature field, respectively. We prove the unique solvability of the intermediate problems, then we construct a contraction mapping whose unique fixed point is the solution of the original problem.

Study on Electroosmosis Consolidation of Punctiform Electrode Unit

In the electroosmosis method, when the distance between the opposite electrode and the same electrode is equal, the two-dimensional effect of electroosmotic consolidation is significant, and the use of one-dimensional model will overestimate the potential gradient, making the calculated pore pressure value too large. Aiming at this problem, according to the electrode arrangement rule and the minimum composition, a punctiform electrode unit model is proposed, and electroosmotic experiments are carried out on the symmetric and asymmetric unit models. The two-dimensional electroosmotic consolidation governing equation of the punctiform electrode unit is established. The electric potential field of the electrode unit and the finite element form of the electroosmotic consolidation equation are given by the Galerkin method. The PyEcFem finite-element numerical library is developed using Python programming to calculate. The research results show the following: (1) The two-dimensional effect of the potential field distribution of the punctiform electrode unit is significant. The reduction of spacing of the same nature electrode in the symmetrical unit can make the potential distribution close to a uniform electric field. The asymmetry prevents the electric potential field distribution from being reduced to a one-dimensional model. (2) The number of anodes will affect the electroosmosis effect of the soil. The more the anodes, the better the electroosmosis reinforcement effect of the soil, and the distribution of negative excess pore water pressure will be more uniform. (3) In the early stage of electroosmosis, the more the drainage boundaries, the faster the generation of negative pore pressure, but in the middle and late stages of electroosmosis, the potential value becomes the decisive factor, and the amplitude of negative pore water pressure in asymmetric units is higher than that in symmetric units. The potential distribution will not affect the degree of consolidation but will affect the extreme pore water pressure.

Optimal error estimates and recovery technique of a mixed finite element method for nonlinear thermistor equations

This paper is concerned with optimal error estimates and recovery technique of a classical mixed finite element method for the thermistor problem, which is governed by a parabolic/elliptic system with strong nonlinearity and coupling. The method is based on a popular combination of the lowest-order Raviart–Thomas mixed approximation for the electric potential/field $(\phi , \boldsymbol{\theta })$ and the linear Lagrange approximation for the temperature $u$. A common question is how the first-order approximation influences the accuracy of the second-order approximation to the temperature in such a strongly coupled system, while previous work only showed the first-order accuracy $O(h)$ for all three components in a traditional way. In this paper, we prove that the method produces the optimal second-order accuracy $O(h^2)$ for $u$ in the spatial direction, although the accuracy for the potential/field is in the order of $O(h)$. And more importantly, we propose a simple one-step recovery technique to obtain a new numerical electric potential/field of second-order accuracy. The analysis presented in this paper relies on an $H^{-1}$-norm estimate of the mixed finite element methods and analysis on a nonclassical elliptic map. We provide numerical experiments in both two- and three-dimensional spaces to confirm our theoretical analyses.

A model of so-called "Zebra" emissions in solar flare radio burst continua

A simple mechanism for the generation of electromagnetic "Zebra" pattern emissions is proposed. "Zebra" bursts are regularly spaced narrow-band radio emissions on the otherwise broadband radio continuum emitted by the active solar corona. The mechanism is based on the generation of an ion-ring distribution in a magnetic mirror geometry in the presence of a properly directed field-aligned electric potential field. Such ion-rings or ion-conics are well known from magnetospheric observations. Under coronal conditions they may become weakly relativistic. In this case the ion-cyclotron maser generates a number of electromagnetic ion-cyclotron harmonics which modulate the electron maser emission. The mechanism is capable of switching the emission on and off or amplifying it quasi-periodically which is a main feature of the observations.