2,176 research outputs found
Probability Theory Compatible with the New Conception of Modern Thermodynamics. Economics and Crisis of Debts
We show that G\"odel's negative results concerning arithmetic, which date
back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites
paradox") pose the questions of the use of fuzzy sets and of the effect of a
measuring device on the experiment. The consideration of these facts led, in
thermodynamics, to a new one-parameter family of ideal gases. In turn, this
leads to a new approach to probability theory (including the new notion of
independent events). As applied to economics, this gives the correction, based
on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us
to consider the theory of debt crisis.Comment: 48p., 14 figs., 82 refs.; more precise mathematical explanations are
added. arXiv admin note: significant text overlap with arXiv:1111.610
On the superfluidity of classical liquid in nanotubes
In 2001, the author proposed the ultra second quantization method. The ultra
second quantization of the Schr\"odinger equation, as well as its ordinary
second quantization, is a representation of the N-particle Schr\"odinger
equation, and this means that basically the ultra second quantization of the
equation is the same as the original N-particle equation: they coincide in
3N-dimensional space.
We consider a short action pairwise potential V(x_i -x_j). This means that as
the number of particles tends to infinity, , interaction is
possible for only a finite number of particles. Therefore, the potential
depends on N in the following way: . If V(y) is finite
with support , then as the support engulfs a finite
number of particles, and this number does not depend on N.
As a result, it turns out that the superfluidity occurs for velocities less
than , where
is the critical Landau velocity and R is the radius of
the nanotube.Comment: Latex, 20p. The text is presented for the International Workshop
"Idempotent and tropical mathematics and problems of mathematical physics",
Independent University of Moscow, Moscow, August 25--30, 2007 and to be
published in the Russian Journal of Mathematical Physics, 2007, vol. 15, #
q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant
In this paper we construct a q-analogue of the Legendre transformation, where
q is a matrix of formal variables defining the phase space braidings between
the coordinates and momenta (the extensive and intensive thermodynamic
observables). Our approach is based on an analogy between the semiclassical
wave functions in quantum mechanics and the quasithermodynamic partition
functions in statistical physics. The basic idea is to go from the
q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in
thermodynamics. It is shown, that this requires a non-commutative analogue of
the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the
classical formulae. Being applied to statistical physics, this naturally leads
to an idea to go further and to replace the Boltzmann constant with an infinite
collection of generators of the so-called epoch\'e (bracketing) algebra. The
latter is an infinite dimensional noncommutative algebra recently introduced in
our previous work, which can be perceived as an infinite sequence of
"deformations of deformations" of the Weyl algebra. The generators mentioned
are naturally indexed by planar binary leaf-labelled trees in such a way, that
the trees with a single leaf correspond to the observables of the limiting
thermodynamic system
Expansion Around the Mean-Field Solution of the Bak-Sneppen Model
We study a recently proposed equation for the avalanche distribution in the
Bak-Sneppen model. We demonstrate that this equation indirectly relates
,the exponent for the power law distribution of avalanche sizes, to ,
the fractal dimension of an avalanche cluster.We compute this relation
numerically and approximate it analytically up to the second order of expansion
around the mean field exponents. Our results are consistent with Monte Carlo
simulations of Bak-Sneppen model in one and two dimensions.Comment: 5 pages, 2 ps-figures iclude
Automatic Geotagging of Russian Web Sites
The poster describes a fast, simple, yet accurate method to associate large amounts of web resources stored in a search engine database with geographic locations. The method uses location-by-IP data, domain names, and content-related features: ZIP and area codes. The novelty of the approach lies in building location-by-IP database by using continuous IP blocks method. Another contribution is domain name analysis. The method uses search engine infrastructure and makes it possible to effectively associate large amounts of search engine data with geography on a regular basis. Experiments ran on Yandex search engine index; evaluation has proved the efficacy of the approach.ACM Special Interest Group on Hypertext, Hypermedia, and We
Mathematical Conception of "Phenomenological" Equilibrium Thermodynamics
In the paper, the principal aspects of the mathematical theory of equilibrium
thermodynamics are distinguished. It is proved that the points of degeneration
of a Bose gas of fractal dimension in the momentum space coincide with critical
points or real gases, whereas the jumps of critical indices and the Maxwell
rule are related to the tunnel generalization of thermodynamics. Semiclassical
methods are considered for the tunnel generalization of thermodynamics and also
for the second and ultrasecond quantization (operators of creation and
annihilation of pairs). To every pure gas there corresponds a new critical
point of the limit negative pressure below which the liquid passes to a
dispersed state (a foam). Relations for critical points of a homogeneous
mixture of pure gases are given in dependence on the concentration of gases.Comment: 37 pages, 9 figure, more precise explanations, more references. arXiv
admin note: substantial text overlap with arXiv:1202.525
WKB Propagation of Gaussian Wavepackets
We analyze the semiclassical evolution of Gaussian wavepackets in chaotic
systems. We prove that after some short time a Gaussian wavepacket becomes a
primitive WKB state. From then on, the state can be propagated using the
standard TDWKB scheme. Complex trajectories are not necessary to account for
the long-time propagation. The Wigner function of the evolving state develops
the structure of a classical filament plus quantum oscillations, with phase and
amplitude being determined by geometric properties of a classical manifold.Comment: 4 pages, 4 figures; significant improvement
Critical exponents of the anisotropic Bak-Sneppen model
We analyze the behavior of spatially anisotropic Bak-Sneppen model. We
demonstrate that a nontrivial relation between critical exponents tau and
mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its
anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model
we derive a novel exact equation for the distribution of avalanche spatial
sizes, and extract the value gamma=2 for one of the critical exponents of the
model. Other critical exponents are then determined from previously known
exponent relations. Our results are in excellent agreement with Monte Carlo
simulations of the model as well as with direct numerical integration of the
new equation.Comment: 8 pages, three figures included with psfig, some rewriting, + extra
figure and table of exponent
Application of the informational reference system OZhUR to the automated processing of data from satellites of the Kosmos series
The structure and potential of the information reference system OZhUR designed for the automated data processing systems of scientific space vehicles (SV) is considered. The system OZhUR ensures control of the extraction phase of processing with respect to a concrete SV and the exchange of data between phases.The practical application of the system OZhUR is exemplified in the construction of a data processing system for satellites of the Cosmos series. As a result of automating the operations of exchange and control, the volume of manual preparation of data is significantly reduced, and there is no longer any need for individual logs which fix the status of data processing. The system Ozhur is included in the automated data processing system Nauka which is realized in language PL-1 in a binary one-address system one-state (BOS OS) electronic computer
Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
The leading semiclassical estimates of the electromagnetic Casimir stresses
on a spherical and a cylindrical metallic shell are within 1% of the field
theoretical values. The electromagnetic Casimir energy for both geometries is
given by two decoupled massless scalars that satisfy conformally covariant
boundary conditions. Surface contributions vanish for smooth metallic
boundaries and the finite electromagnetic Casimir energy in leading
semiclassical approximation is due to quadratic fluctuations about periodic
rays in the interior of the cavity only. Semiclassically the non-vanishing
Casimir energy of a metallic cylindrical shell is almost entirely due to
Fresnel diffraction.Comment: 12 pages, 2 figure
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