CONSIDERING THE SCOPE OF DEPRECIATION IN SHEET ROLLING MILLS IN DEVELOPING THE TECHNOLOGY OF THEIR RENOVATION

Consideration of the scope of depreciation in sheet rolling mills in developing the technology of their renovation

Robustness of delocalization to the inclusion of soft constraints in long-range random models

Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with the Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models, is numerically observed and confirmed by the analytical calculations. First, the matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases, a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and the previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum to the inclusion of soft constraints is generally discussed for single-particle and many-body systems

Ecological foresight in the nuclear power of XXI century

The access to reliable sources of energy is the key to sustainable development of mankind. The major part of the energy consumed by people is generated with a chemical reaction of fossil fuel burning. This leads to quick depletion of natural resources and progressing environmental pollution. The contribution of the renewable energy sources to the general energy production remains insignificant. A modern 1,000 MW coal-fired thermal power plant (TPP) burns 2.5 million tons of coal per year and produces significant amount of solid and gaseous waste. TPPs are the largest consumers of atmospheric oxygen and sources of carbon dioxide. A nuclear power plant (NPP) of the same power consumes less than 50 tons of fuel per year. Environmentally significant NPP’s waste (liquid, solid and gaseous) is carefully collected, reduced in volume (evaporation, filtering, compaction, incineration, etc.) and securely isolated from the environment at the plant. The annual volume of waste for storage is less than 100 m3. The waste is under the control of a special NPP’s service and regulatory authorities. The energy of fission reaction millions of times exceeding the energy of burning has an enormous potential that mankind can receive. Four hundred and thirty-three nuclear power units with a total capacity of about 400 GW exist in the world. The accident at the Fukushima Daiichi NPP in Japan in March 2011 caused anxiety about nuclear safety throughout the world and raised questions about the future of nuclear power. Now, it is clear that the use of nuclear power will continue to grow in the coming decades, although the growth will be slower than was anticipated before the accident. Many countries with existing nuclear power programmes plan to expand them. Many new countries, both developed and developing, plan to introduce nuclear power. Some countries, such as Germany, plan to abandon nuclear energy. The IAEA’s latest projections show a steady rise in the number of NPPs in the world in the next 20 years. They project a growth in nuclear power capacity by 23% by 2030 in the low projection and by 100% in the high projection [1,2]. The basis of modern nuclear power comprises water-cooled nuclear reactors which use the energy potential of natural uranium inefficiently (thermal reactors). The thermal reactors use isotope U-235 in which the content of natural uranium is <1%. Breeder reactors are capable of using the significant part of energy potential, which is unavailable to thermal light water reactors. As a result, the same starting quantity of uranium can produce 50 times more energy. These reactors can transform U-238 into fissile Pu-239 in larger amounts than they consume fissile material. This feature is called ‘breeding’ [3]. The key problem of using the basic benefitsv of nuclear power is to ensure the safety of its use, as well as decommissioning and reliable isolation of process waste from the biosphere. The long-term large-scale nuclear power should possess guaranteed safety, economic stability and competitiveness, absence of the raw material base restrictions for a long period of time and environmental sustainability (low waste). The nuclear power systems with fast neutron reactors and liquid metal coolant can satisfy these conditions. More than 40 years of Russian experience in the field of construction and operation of sodium fast reactors makes it possible to summarize and analyze the ecological features of reactors of this type, the possibility of their use for sustainable energy supply of mankind and solving environmental problems

Correlation-induced localization

A new paradigm of Anderson localization caused by correlations in the long-range hopping along with uncorrelated on-site disorder is considered which requires a more precise formulation of the basic localization-delocalization principles. A new class of random Hamiltonians with translation-invariant hopping integrals is suggested and the localization properties of such models are established both in the coordinate and in the momentum spaces alongside with the corresponding level statistics. Duality of translation-invariant models in the momentum and coordinate space is uncovered and exploited to find a full localization-delocalization phase diagram for such models. The crucial role of the spectral properties of hopping matrix is established and a new matrix inversion trick is suggested to generate a one-parameter family of equivalent localization/delocalization problems. Optimization over the free parameter in such a transformation together with the localization/delocalization principles allows to establish exact bounds for the localized and ergodic states in long-range hopping models. When applied to the random matrix models with deterministic power-law hopping this transformation allows to confirm localization of states at all values of the exponent in power-law hopping and to prove analytically the symmetry of the exponent in the power-law localized wave functions.Comment: 14 pages, 8 figures + 5 pages, 2 figures in appendice