High-frequency dynamics of wave localisation

We study the effect of localisation on the propagation of a pulse through a multi-mode disordered waveguide. The correlator of the transmitted wave amplitude u at two frequencies differing by delta_omega has for large delta_omega the stretched exponential tail ~exp(-sqrt{tau_D delta_omega/2}). The time constant tau_D=L^2/D is given by the diffusion coefficient D, even if the length L of the waveguide is much greater than the localisation length xi. Localisation has the effect of multiplying the correlator by a frequency-independent factor exp(-L/2xi), which disappears upon breaking time-reversal symmetry.Comment: 3 pages, 1 figur

Localization fom conductance in few-channel disordered wires

We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic boundary conditions between the chains. The finite disordered wires are connected to ideal leads and the localization length is defined from the Landauer conductance in terms of the transmission coefficients matrix. The transmission- and reflection amplitudes in properly defined quantum channels are obtained from S-matrices constructed from transfer matrices in Bloch wave bases for the various quasi-1D systems. Our exact analytic expressions for localization lengths for weak disorder reduce to the Thouless expression for 1D systems in the limit of vanishing interchain hopping. For weak interchain hopping the localization length decreases with respect to the 1D value in all three cases. In the three-channel cases it increases with interchain hopping over restricted domains of large hopping

Current Helicity and Twist as Two Indicators of The Mirror Asymmetry of solar Magnetic Fields

A comparison between the two tracers of magnetic field mirror asymmetry in solar active regions, twist and current helicity, is presented. It is shown that for individual active regions these tracers do not possess visible similarity while averaging by time over the solar cycle, or by latitude, reveals similarities in their behaviour. The main property of the dataset is anti-symmetry over the solar equator. Considering the evolution of helical properties over the solar cycle we find signatures of a possible sign change at the beginning of the cycle, though more systematic observational data are required for a definite confirmation. We discuss the role of both tracers in the context of the solar dynamo theory.Comment: 14 pages, 6 figure

Solar Grand Minima and random fluctuations in dynamo parameters

We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.Comment: Solar Physics, in prin

Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functionsComment: 36 pages, LaTeX, 4 separated Postscript figures, submitted to Nucl. Phys. B [PM

ВЛИЯНИЕ РЕНТГЕНОКОНТРАСТНОГО ВЕЩЕСТВА НА ФУНКЦИЮ ПОЧЕЧНОГО ТРАНСПЛАНТАТА ПРИ ЭНДОВАСКУЛЯРНОЙ РЕВАСКУЛЯРИЗАЦИИ МИОКАРДА

Ballon angioplasty with coronary arteries stenting was performed in 56 renal allograft recipients (75 procedures). The influence of contrast media on renal graft function was investigated. Renal graft function was estimated by creatinine level 24 hour before and 48 hours after the intervention. Risk factors of contrast induced nephropathy (CIN) development at renal graft recipients are discussed. Mathematical approaches for calculation of risk of CIN development are analyzed. Выполнена ангиопластика со стентированием коронарных артерий у 56 реципиентов почечного транс- плантата (75 процедур). В данной работе исследуется влияние рентгеноконтрастного вещества (РКВ) на функцию почечного трансплантата. Функция почечного трансплантата оценивалась по уровню креати- нина за 24 часа до и в первые 48 часов после вмешательства. Рассмотрено влияние и значимость факто- ров риска развития контрастинуцированной нефропатии (КИН) у реципиентов почечного трансплантата. Проанализированы математические подходы для расчета риска развития КИН.

Fokker-Planck description of the transfer matrix limiting distribution in the scattering approach to quantum transport

The scattering approach to quantum transport through a disordered quasi-one-dimensional conductor in the insulating regime is discussed in terms of its transfer matrix \bbox{T}. A model of $N$ one-dimensional wires which are coupled by random hopping matrix elements is compared with the transfer matrix model of Mello and Tomsovic. We derive and discuss the complete Fokker-Planck equation which describes the evolution of the probability distribution of \bbox{TT}^{\dagger} with system length in the insulating regime. It is demonstrated that the eigenvalues of \ln\bbox{TT}^{\dagger} have a multivariate Gaussian limiting probability distribution. The parameters of the distribution are expressed in terms of averages over the stationary distribution of the eigenvectors of \bbox{TT}^{\dagger}. We compare the general form of the limiting distribution with results of random matrix theory and the Dorokhov-Mello-Pereyra-Kumar equation.Comment: 25 pages, revtex, no figure