Random walks in Euclidean space

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove a local limit theorem under a suitable moment condition and a necessary non-degeneracy condition. Under stronger hypothesis, we prove a limit theorem on a wide range of scales: between e^(-cl^(1/4)) and l^(1/2), where l is the number of steps.Comment: 62 pages, 1 figure, revision based on referee's report, proofs and results unchange

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

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

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

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

Evolutionary methods in modelling behaviour of complex system

In this paper, a recursive-regression approach is formulated in the formation of a functioning model of a complex system. The complex system consist of the object of study represented by a set of related signs. The proposed sub-course combines the method of group accounting of arguments with standard regression analysis adapted to fast dynamic processes. As an example, recursive-regression modelling of the functioning of an industrial enterprise was performed

Status of creation of hardware-software complex of automatic control of the insulin delivery

The article discusses issues related to the prospects for the implementation of the idea of creating a hardware-software complex for automated regulation of insulin delivery. Today, there are drugs that allow people to live relatively comfortably even with the most severe types of diabetes. The main difficulty of insulin therapy is that it is necessary to constantly (at any time, day or night) to carry out the procedure of control and regulation of the introduction of the drug into the patient's body. Unfortunately, not all patients are able to perform it properly. The ideal solution could be a system that performs all these actions automatically, without the participation of the patient. Therefore, the implementation of the idea of creating a hardware and software system for automatic regulation of insulin delivery using the program-adaptive control scheme is relevant. The article forms the general requirements for an approach capable of providing safe medical care for people with type 1 diabetes. The requirements to which the hardware-software complexes of automatic regulation of insulin delivery must correspond are formulated, their block diagram is presented

Model of analysis of sustainable management of information security of a distributed information system

The article presents a model of stability analysis of a distributed information system in the sense of sustainable provision of its information security with some means of protection. It is assumed that the information system in question is operating in real time. On the basis of the proposed model, the area of functional security of a distributed information system under the influence of information attacks of the enemy is constructed, while this task is solved from the condition of specified allowed intervals: the probability of ensuring the information security of the system under consideration, as well as the criterion of deterioration of the main indicator of its effectiveness from enemy interference in process of its functioning. In the form of a strict sequence of actions, an algorithm is formulated to implement the proposed model in practice, provided that the information security of a distributed information system is managed reliably