An improved result of exponential stability of stochastic semilinear evolution equations

Sufficient conditions for the exponential stability of a class ofnonlinear, non-autonomous stochastic differential equations in infinitedimensions are studied. The analysis consists of introducing a suitableapproximating solution systems and using a limiting argument to pass onstability of strong solutions to mild ones. As a consequence, the classicalcriteriaof stability in A. Ichikawa [8] are improved and extended to cover a class ofnon-autonomous stochastic evolution equations.Two examples are investigated to illustrate our theory.

Ergodicity and stability of generalised Markov branching processes with resurrection

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

Assessment of the origin and stability of Nifedipine polymorph IV by differential scanning calorimetry (DSC)

Purpose. To examine the thermal transition(s) between different polymorphic forms of Nifedipine and to define experimental conditions that lead to the generation of polymorph IV. Methods. Experiments were performed using a DSC 823e (Mettler Toledo). Nifedipine exists in four polymorphic forms, as well as an amorphous state. Examination of Nifedipine was conducted using the following method(s): cycle 1: 25ºC to 190ºC, 190ºC to 25ºC (formation of amorphous Nifedipine); cycle 2: 25ºC to X (60,70,80...150ºC), X to 25ºC; cycle 3: 25ºC to 190ºC and holding isothermally for 5 min between cycles (heating/cooling rate of 10ºC/min). Results. The amorphous state Nifedipine can sustain heating up to 90ºC without significant changes in its composition. Cycle 2 of amorphous material heated up to 90ºC shows only the glass transition at ~44ºC. In cycle 3 of the same material, a glass transition has been recorded at ~44ºC, followed by two exotherms (~100 and ~115ºC (crystallisation of polymorph III and II, respectively) and an endotherm (169ºC (melting of polymorphs I/II)). Samples that have been heated to temperatures between 100ºC and 120ºC in the second cycle showed a glass transition at ~44ºC and an additional exotherm at ~95ºC (crystallisation of polymorph III) on cooling a exotherm was observed at ~40ºC (crystallisation of polymorph IV). The same material showed no glass transition in cycle 3 but an endotherm at around 62ºC (melting of polymorph IV) an exotherm (~98ºC) and an endotherm (169ºC) melting of polymorph I/II. Heating the sample to a temperatures greater than 130ºC in cycle two results in a glass transition at ~44ºC, and two exotherms at ~102 and 125ºC (crystallisation of polymorphs III and I, respectively). Conclusions. DSC data suggests that polymorph IV can only be produced from amorphous or polymorph III samples. The presence of polymorph I or II drives the conversion of the less stable polymorphic form IV into the most stable form, I. Although form IV of Nifedipine can easily be created, following defined experimental conditions, it may only coexist with amorphous or polymorph III states. When polymorphs I and II are present in the sample polymorph IV cannot be etected.