ON KPP EQUATIONS WITH VARIOUS WAVE FRONT SPEEDS, THE LARSON RESULT VIA LARGE DEVIATIONS

The influence of different bend curvatures on the detonation wave propagation was analyzed by an advanced numerical simulation system. The mechanism of propagation properties is revealed by cellular structure, internal and external boundary pressure distribution, propagation process of detonation wave and chemical reaction. The cellular structure and detonation wave front of bend with different curvature are very different. The simulation results show that the detonation wave with regular cell structure propagating through the curved parts induces detonation cell size increased by diffraction near the inner wall while detonation reflected on the bottom surface resulting in decrease of cell size. Detonation wave was affected by the rarefaction wave and compression wave in the bent pipe. The pressure distribution of the bend shows that the peak pressure in the 450 curvature is the largest, which should be paid more attention in industrial design. The chemical reaction could indicate the propagation characteristics of detonation wave, and different propagation characteristics have different profiles of chemical components.

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Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model

Acta Mathematicae Applicatae Sinica English Series ◽

10.1007/s10255-021-1030-z ◽

2021 ◽

Vol 37 (3) ◽

pp. 539-547

Author(s):

Ke-ang Fu ◽

Xin-mei Shen ◽

Hui-jie Li

Keyword(s):

Large Deviations ◽

Risk Model ◽

Claim Size ◽

Two Dimensional ◽

Precise Large Deviations ◽

Renewal Risk Model ◽

Size Dependent ◽

Renewal Risk

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Run-and-Tumble Motion: The Role of Reversibility

Journal of Statistical Physics ◽

10.1007/s10955-021-02787-1 ◽

2021 ◽

Vol 183 (3) ◽

Author(s):

Bart van Ginkel ◽

Bart van Gisbergen ◽

Frank Redig

Keyword(s):

Free Energy ◽

Diffusion Coefficient ◽

Large Deviations ◽

Energy Function ◽

Internal State ◽

Rate Function ◽

Free Energy Function ◽

Large Deviations Principle ◽

Preferred Direction ◽

State Process

AbstractWe study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

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