8,452 research outputs found
Schlesinger system, Einstein equations and hyperelliptic curves
We review recent developments in the method of algebro-geometric integration
of integrable systems related to deformations of algebraic curves. In
particular, we discuss the theta-functional solutions of Schlesinger system,
Ernst equation and self-dual SU(2)-invariant Einstein equations.Comment: dedicated to the memory of Moshe Flat
The Significance of Non-ergodicity Property of Statistical Mechanics Systems for Understanding Resting State of a Living Cell
A better grasp of the physical foundations of life is necessary before we can
understand the processes occurring inside a living cell. In his physical theory
of the cell, American physiologist Gilbert Ling introduced an important notion
of the resting state of the cell. He describes this state as an independent
stable thermodynamic state of a living substance in which it has stored all the
energy it needs to perform all kinds of biological work. This state is
characterised by lower entropy of the system than in an active state. However,
Ling's approach is primarily qualitative in terms of thermodynamics and it
needs to be characterised more specifically. To this end, we propose a new
thermodynamic approach to studying Ling's model of the living cell (Ling's
cell), the center piece of which is the non-ergodicity property which has
recently been proved for a wide range of systems in statistical mechanics [7].
These approach allowed us to develop general thermodynamic approaches to
explaining some of the well-known physiological phenomena, which can be used
for further physical analysis of these phenomena using specific physical
models
Quantum dynamics of a hydrogen-like atom in a time-dependent box: non-adiabatic regime
We consider a hydrogen atom confined in time-dependent trap created by a
spherical impenetrable box with time-dependent radius. For such model we study
the behavior of atomic electron under the (non-adiabatic) dynamical confinement
caused by the rapidly moving wall of the box. The expectation values of the
total and kinetic energy, average force, pressure and coordinate are analyzed
as a function of time for linearly expanding, contracting and harmonically
breathing boxes. It is shown that linearly extending box leads to de-excitation
of the atom, while the rapidly contracting box causes the creation of very high
pressure on the atom and transition of the atomic electron into the unbound
state. In harmonically breathing box diffusive excitation of atomic electron
may occur in analogy with that for atom in a microwave field
The Generalized Counting Rule and Oscillatory Scaling
We have studied the energy dependence of the elastic scattering data and
the pion-photoproduction data at 90 c.m. angle in light of the new
generalized counting rule derived for exclusive processes. We show that by
including the helicity flipping amplitudes (with energy dependence given by the
generalized counting rule) and their interference with the Landshoff amplitude,
we are able to reproduce the energy dependence of all cross-section and
spin-correlation (A) data available above the resonance region. The
pion-photoproduction data can also be described by this approach, but in this
case data with much finer energy spacing is needed to confirm the oscillations
about the scaling behavior.Comment: 5 pages, 4 figs, submitted to PRC rapid com
Vanishing Point Detection with Direct and Transposed Fast Hough Transform inside the neural network
In this paper, we suggest a new neural network architecture for vanishing
point detection in images. The key element is the use of the direct and
transposed Fast Hough Transforms separated by convolutional layer blocks with
standard activation functions. It allows us to get the answer in the
coordinates of the input image at the output of the network and thus to
calculate the coordinates of the vanishing point by simply selecting the
maximum. Besides, it was proved that calculation of the transposed Fast Hough
Transform can be performed using the direct one. The use of integral operators
enables the neural network to rely on global rectilinear features in the image,
and so it is ideal for detecting vanishing points. To demonstrate the
effectiveness of the proposed architecture, we use a set of images from a DVR
and show its superiority over existing methods. Note, in addition, that the
proposed neural network architecture essentially repeats the process of direct
and back projection used, for example, in computed tomography.Comment: 9 pages, 9 figures, submitted to "Computer Optics"; extra experiment
added, new theorem proof added, references added; typos correcte
Spontaneous Spin Polarization in Quantum Wires
A number of recent experiments report spin polarization in quantum wires in
the absence of magnetic fields. These observations are in apparent
contradiction with the Lieb-Mattis theorem, which forbids spontaneous spin
polarization in one dimension. We show that sufficiently strong interactions
between electrons induce deviations from the strictly one-dimensional geometry
and indeed give rise to a ferromagnetic ground state in a certain range of
electron densities.Comment: 4 pages, 4 figure
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