Commodity and Financial Networks in Regional Economics

The article discusses the relationship between commodity-production and financial network structures in the regional economy as dual conjugate systems. Material flows (raw materials, goods and so on) circulate in the commodity network as shown by Leontiev’s input-output balance model. Nonmaterial flows of property rights, money, and so on circulate in the financial network and reflect the movement of material objects in commodity networks. A network structure comprises closed and open circuits, which have fundamentally different characteristics: locally closed circuits meet local demand by supplying locally produced goods, thus ensuring self-reproduction of the local economy; open (or transit) circuits provide export-import flows. The article describes the mechanism of ‘internal’ money generation in closed circuits of commodity-production networks. The results of the theoretical study are illustrated by the calculations of closed and open circuit flows in the municipal economy model. Mutual settlements between the population and manufacturing enterprises are given in matrix form. It was found that the volume of the turnover in closed circuits of the municipal economic network model is about 28.5 % of the total turnover and can be provided by ‘internal’ non-inflationary money. The remaining 71.5 % of the total turnover correspond to the flows in the network’s open circuits providing export and import. The conclusion is made that in the innovation-driven economy, main attention should be given to the projects oriented towards domestic consumption rather than export supplies. The economy is based on internal production cycles in closed circuits. Thus, it is necessary to find the chains in the inter-industrial and inter-production relations which could become the basis of the production cycle. Money investments will complete such commodity chains and ‘launch’ the production cycle.The work has been prepared with the supprot of the Ural Federal University within the UrFU Program for the winners of the competition “Young Scientists of UrFU” No. 2.1.1.1-14/43

Are Simple Real Pole Solutions Physical?

We consider exact solutions generated by the inverse scattering technique, also known as the soliton transformation. In particular, we study the class of simple real pole solutions. For quite some time, those solutions have been considered interesting as models of cosmological shock waves. A coordinate singularity on the wave fronts was removed by a transformation which induces a null fluid with negative energy density on the wave front. This null fluid is usually seen as another coordinate artifact, since there seems to be a general belief that that this kind of solution can be seen as the real pole limit of the smooth solution generated with a pair of complex conjugate poles in the transformation. We perform this limit explicitly, and find that the belief is unfounded: two coalescing complex conjugate poles cannot yield a solution with one real pole. Instead, the two complex conjugate poles go to a different limit, what we call a ``pole on a pole''. The limiting procedure is not unique; it is sensitive to how quickly some parameters approach zero. We also show that there exists no improved coordinate transformation which would remove the negative energy density. We conclude that negative energy is an intrinsic part of this class of solutions.Comment: 13 pages, 3 figure

The Approximating Hamiltonian Method for the Imperfect Boson Gas

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.Comment: 7 page

The Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page

Strong enhancement of spin fluctuations in the low-temperature-tetragonal phase of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4

Measurements of the static magnetization, susceptibility and ESR of Gd spin probes have been performed to study the properties of antiferromagnetically ordered La_{2-x-y}Eu_ySr_xCuO_4 (x less or equal 0.02) with the low temperature tetragonal structure. According to the static magnetic measurements the CuO_2 planes are magnetically decoupled in this structural phase. The ESR study reveals strong magnetic fluctuations at the ESR frequency which are not present in the orthorhombic phase. It is argued that this drastic enhancement of the spin fluctuations is due to a considerable weakening of the interlayer exchange and a pronounced influence of hole motion on the antiferromagnetic properties of lightly hole doped La_2CuO_4. No evidence for the stripe phase formation at small hole doping is obtained in the present study.Comment: 10 pages, LaTeX, 3 EPS figures; to be published in Journal of Physics: Condensed Matte

Theta dependence of CP^9 model

We apply to the $CP^9$ model two recently proposed numerical techniques for simulation of systems with a theta term. The algorithms, successfully tested in the strong coupling limit, are applied to the weak coupling region. The results agree and errors have been evaluated and are at % level. The results scale well with the renormalization group equation and show that, for $CP^9$ in presence of a theta term, CP symmetry is spontaneously broken at $\theta=\pi$ in the continuum limit.Comment: 4 pages, 4 figure

Large-scale Monte Carlo simulations of the isotropic three-dimensional Heisenberg spin glass

We study the Heisenberg spin glass by large-scale Monte Carlo simulations for sizes up to 32^3, down to temperatures below the transition temperature claimed in earlier work. The data for the larger sizes show more marginal behavior than that for the smaller sizes, indicating the lower critical dimension is close to, and possibly equal to three. We find that the spins and chiralities behave in a quite similar manner.Comment: 8 pages, 8 figures. Replaced with published versio

Thermodynamics of two lattice ice models in three dimensions

In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for groundstate configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.Comment: 5 pages, 7 figure

Gravitational diffraction radiation

We show that if the visible universe is a membrane embedded in a higher-dimensional space, particles in uniform motion radiate gravitational waves because of spacetime lumpiness. This phenomenon is analogous to the electromagnetic diffraction radiation of a charge moving near to a metallic grating. In the gravitational case, the role of the metallic grating is played by the inhomogeneities of the extra-dimensional space, such as a hidden brane. We derive a general formula for gravitational diffraction radiation and apply it to a higher-dimensional scenario with flat compact extra dimensions. Gravitational diffraction radiation may carry away a significant portion of the particle's initial energy. This allows to set stringent limits on the scale of brane perturbations. Physical effects of gravitational diffraction radiation are briefly discussed.Comment: 5 pages, 2 figures, RevTeX4. v2: References added. Version to appear in Phys. Rev.

Stacking Entropy of Hard Sphere Crystals

Classical hard spheres crystallize at equilibrium at high enough density. Crystals made up of stackings of 2-dimensional hexagonal close-packed layers (e.g. fcc, hcp, etc.) differ in entropy by only about $10^{-3}k_B$ per sphere (all configurations are degenerate in energy). To readily resolve and study these small entropy differences, we have implemented two different multicanonical Monte Carlo algorithms that allow direct equilibration between crystals with different stacking sequences. Recent work had demonstrated that the fcc stacking has higher entropy than the hcp stacking. We have studied other stackings to demonstrate that the fcc stacking does indeed have the highest entropy of ALL possible stackings. The entropic interactions we could detect involve three, four and (although with less statistical certainty) five consecutive layers of spheres. These interlayer entropic interactions fall off in strength with increasing distance, as expected; this fall-off appears to be much slower near the melting density than at the maximum (close-packing) density. At maximum density the entropy difference between fcc and hcp stackings is $0.00115 +/- 0.00004 k_B$ per sphere, which is roughly 30% higher than the same quantity measured near the melting transition.Comment: 15 page