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1.
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual. 相似文献
2.
The dependence of the beam propagation factor (M
2 parameter) with the absorbed pump power in the case of monolithic microchip laser under face-cooled configuration is extensively
studied. Our investigations show that the M
2 parameter is related to the absorbed pump power through two parameters (α and β) whose values depend on the laser material properties and laser configuration. We have shown that one parameter arises due
to the oscillation of higher order modes in the microchip cavity and the other parameter accounts for the spherical aberration
associated with the thermal lens induced by the pump beam. Such dependency of M
2 parameter with the absorbed pump power is experimentally verified for a face-cooled monolithic microchip laser based on Nd3+ -doped GdVO4 crystal and the values of α and β parameters were estimated from the experimentally measured data points. 相似文献
3.
The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated. 相似文献
4.
In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices). 相似文献
5.
G. A. Watson 《Advances in Computational Mathematics》1994,2(4):393-405
The orthogonal Procrustes problem involves finding an orthogonal matrix which transforms one given matrix into another in
the least-squares sense, and thus it requires the minimization of the Frobenius matrix norm. We consider, the solution of
this problem for a family of orthogonally invariant norms which includes the Frobenius norm as a special case. 相似文献
6.
7.
Endoscopic illumination systems conduct light down a built-in fibre-optic bundle to illuminate the object. Many modern endoscopes employ wide-field imaging optical systems and therefore require an illuminating beam of large divergence. This is commonly provided by placing a strong diverging lens at the far end of the fibre bundle, but it results in a poor uniformity of illumination in the object space. This paper describes the design of a telescopic illumination system to overcome this problem. 相似文献
8.
9.
Heavy ion irradiation in the electronic stopping power region induces macroscopic dimensional change in metallic glasses and introduces magnetic anisotropy in some magnetic materials. The present work is on the irradiation study of ferromagnetic metallic glasses, where both dimensional change and modification of magnetic anisotropy are expected. Magnetic anisotropy was measured using Mössbauer spectroscopy of virgin and irradiated Fe40Ni40B20 and Fe40Ni38Mo4B18 metallic glass ribbons. 90 MeV 127I beam was used for the irradiations. Irradiation doses were 5×1013 and 7.5×1013 ions/cm2. The relative intensity ratios D 23 of the second and third lines of the Mössbauer spectra were measured to determine the magnetic anisotropy. The virgin samples of both the materials display in-plane magnetic anisotropy, i.e., the spins are oriented parallel to the ribbon plane. Irradiation is found to cause reduction in magnetic anisotropy. Near-complete randomization of magnetic moments is observed at high irradiation doses. Correlation is found between the residual stresses introduced by ion irradiation and the change in magnetic anisotropy. 相似文献
10.
It was shown by G. A. Jones and the first author in [8] that underlying any map on a compact orientable surface S there is a natural complex structure making S into a Riemann surface. In this paper we consider regular maps and enquire about the Weierstrass points on the underlying Riemann surface. We are particularly interested to know when these are geometric, i.e. whether they lie at vertices, face-centres or edge-centres of the map. 相似文献