Cole-Hopf Like Transformation for Schr\"odinger Equations Containing Complex Nonlinearities

We consider systems, which conserve the particle number and are described by Schr\"odinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z, 03.65.-w, 05.45.-a, 11.30.Na, 11.40.DwComment: 26 pages, no figures, to be appear in J. Phys. A: Math. Gen. (2002

The NuMI Neutrino Beam and Potential for an Off-Axis Experiment

The Neutrinos at the Main Injector (NuMI) facility at Fermilab is under construction and due to begin operations in late 2004. NuMI will deliver an intense $\nu_{\mu}$ beam of variable energy 2-20 GeV directed into the Earth at 58 mrad. Several aspects of the design are reviewed, and potential limitations to the ultimate neutrino flux are described. In addition, potential measurements of neutrino mixing properties are described.Comment: talk given at NuFact '02, Imperial College London, proceedings to appear in J. Phys. G, revised to add a referenc

АНАЛИЗ ЭНЕРГОЭФФЕКТИВНОСТИ РЕЖИМОВ РАБОТЫ ЭЛЕКТРИЧЕСКИХ СИСТЕМ С ТЯГОВЫМИ НАГРУЗКАМИ

Innovative scenarios of reliable energy supply of transportation process aimed at reducing the specific energy consumption and increase energy efficiency of the systems of electric traction. The paper suggests innovative energy saving directions in traction networks of railways and new circuit solutions accessing traction substations in energy systems networks, ensure energy security of the transportation process. To ensure the energy security of rail transport special schemes were developed to propose the concept of external power traction substations, which would increase the number of connections to the networks of 220 – 330 kV, as well as the creation of transport and energy corridors, development of its own supply of electric networks of 110 kV substations and mobile RP-110 kV of next generation. Therefore, the investment program of the structures owned by the Ukrainian Railways (Ukrzaliznytsia) need to be synchronized in their technological characteristics, as well as the criteria of reliability and quality of power supply with the same external energy investment programs. It is found that without any load on left or right supplying arm one of two less loaded phases of traction transformer begins generating specific modes in the supplying three-phase line. Thus, modes of mobile substation cause leakage in one of the phases of the supply line of traction transformers of active-capacitive current, and as a result generating energy in the main power line of 154 kV, which is fixed and calculated by electricity meters. For these three phase mode supply network is necessary to use 1st algorithm, i.e. taking into account the amount of electricity as the energy in all phases. For effective application of reactive power compensation devices in the AC traction power supply systems it is proposed to develop regulatory documentation on necessity of application and the order of choice of parameters and placement of compensation systems taking into account operation mode of power systems and the use of software systems with imitation of instantaneous interrelated schemes of transport loads.В статье предложены инновационные направления энергосбережения в тяговых сетях железных дорог и новые схемотехнические решения присоединения тяговых подстанций к сетям энергосистем, обеспечивающие энергобезопасность перевозочного процесса. Дано обоснование необходимости расчета тяговых подстанций по векторному методу трехфазного потребления энергии от подстанций НЭК «Укрэнерго».В статье предложены инновационные направления энергосбережения в тяговых сетях железных дорог и новые схемотехнические решения присоединения тяговых подстанций к сетям энергосистем, обеспечивающие энергобезопасность перевозочного процесса. Дано обоснование необходимости расчета тяговых подстанций по векторному методу трехфазного потребления энергии от подстанций НЭК «Укрэнерго»

Monitoring of the content of manganese in soils and agricultural plants of the central Chernozem Region of Russia

The paper deals with the analysis of long-term observations of the manganese distribution in the soils of the south-western part of the Central Chernozem region of Russia in the Belgorod regio

Nonlinear Quantum Mechanics at the Planck Scale

I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear effects can be of comparable magnitude to the linear ones and still be highly suppressed at low energies. This can offer alternative approaches to quantum gravity and to the evolution of the early universe.Comment: Talk given at the International Quantum Structures 2004 meeting, 16 pages LaTe

Hernia or hernia Defect? Experimental herniology Models in Laboratory Animals

Hernias of the anterior abdominal wall remain one of the most common surgery pathologies. There is no unified approach to modeling anterior abdominal wall hernias in the world scientific community. In order to systematize the available knowledge in this field and to contribute to the formation of a unified idea of how to create a hernia model in a laboratory animal, it seems logical to study the accumulated experience of researchers in the field of experimental herniology. We found out that hernia defects generally modeled on male laboratory rats. To understand the tissue reaction to the prosthetic material a fenestration was performed in the anterior abdominal wall (including peritoneum) except for the skin and subcutaneous fat. A replacement or prosthetic material tailored to the fenestration was sutured end-to-end into the abdominal wall. We chose laboratory rats because they are easy to take care of and cheaper than larger laboratory animals

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Assessment of fatigue damage to aircraft glass using digital holography methods

The purpose of this work is to test the digital holography method for determining the depth of fatigue surface defects of the "silver" type of aviation organic glass caused by cyclic mechanical overloads, as well as the impact of aggressive substances. To study the fatigue defects of aviation organic glass, a digital holographic camera was used, the configuration of which is an axial scheme for recording digital Gabor holograms. During the experiment, the possibility of using the digital holography method to determine the characteristic transverse dimensions of surface defects in aircraft glazing parts and longitudinal dimensions was shown. The work carried out and the created model of the digital holographic camera show the potential possibility of creating a method for checking with a given accuracy the elements of the aircraft glazing for the presence of surface damage and assessing their impact on flight safety