Phase-plane analysis of driven multi-lane exclusion models

We show how a fixed point based boundary-layer analysis technique can be used to obtain the steady-state particle density profiles of driven exclusion processes on two-lane systems with open boundaries. We have considered two distinct two-lane systems. In the first, particles hop on the lanes in one direction obeying exclusion principle and there is no exchange of particles between the lanes. The hopping on one lane is affected by the particle occupancies on the other, which thereby introduces an indirect interaction among the lanes. Through a phase plane analysis of the boundary layer equation, we show why the bulk density undergoes a sharp change as the interaction between the lanes is increased. The second system involves one lane with driven exclusion process and the other with biased diffusion of particles. In contrast to the previous model, here there is a direct interaction between the lanes due to particle exchange between them. In this model, we have looked at two possible scenarios with constant (flat) and non-constant bulk profiles. The fixed point based boundary layer method provides a new perspective on several aspects including those related to maximal/minimal current phases, possibilities of shocks under very restricted boundary conditions for the flat profile but over a wide range of boundary conditions for the non-constant profile.Comment: 13 pages, 17 figure

Hierarchy of boundary driven phase transitions in multi-species particle systems

Interacting systems with $K$ driven particle species on a open chain or chains which are coupled at the ends to boundary reservoirs with fixed particle densities are considered. We classify discontinuous and continuous phase transitions which are driven by adiabatic change of boundary conditions. We build minimal paths along which any given boundary driven phase transition (BDPT) is observed and reveal kinetic mechanisms governing these transitions. Combining minimal paths, we can drive the system from a stationary state with all positive characteristic speeds to a state with all negative characteristic speeds, by means of adiabatic changes of the boundary conditions. We show that along such composite paths one generically encounters $Z$ discontinuous and $2(K-Z)$ continuous BDPTs with $Z$ taking values $0\leq Z\leq K$ depending on the path. As model examples we consider solvable exclusion processes with product measure states and $K=1,2,3$ particle species and a non-solvable two-way traffic model. Our findings are confirmed by numerical integration of hydrodynamic limit equations and by Monte Carlo simulations. Results extend straightforwardly to a wide class of driven diffusive systems with several conserved particle species.Comment: 12 pages, 11 figure

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

Analysis of segmental residual growth after progressive bone lengthening in congenital lower limb deformity

SummaryIntroductionThe issue of prognosis in limb length discrepancy in children affected by congenital abnormality remains a subject of concern. Therapeutic strategy must take length prediction into account, to adapt equalization techniques and the timing of treatment. Initial prognosis, however, may need revising after completion of one or several surgical interventions on the pathologic limb. The aim of this study was to determine the different types of growth response that a bone segment can present after progressive lengthening in case of congenital limb length discrepancy.Materials and methodsA series of 114 bone lengthenings with external fixator, performed in 36 girls and 50 boys with congenital lower limb length discrepancy, was retrospectively analyzed. Bone segment growth rates were measured before lengthening, during the first year after frame removal and finally over long-term follow-up, calculating the ratios of radiological bone length to the number of months between two measurements. Mean follow-up was 4.54±0.2 years.ResultsChanges in short- and long-term growth rate distinguished five patterns of bone behavior after lengthening, ranging from growth acceleration to total inhibition.DiscussionThese five residual growth patterns depended on certain factors causing acceleration or, on the contrary, slowing down of growth: age at the lengthening operation, percentage lengthening, and minimal period between two lengthenings. These criteria help optimize conditions for resumed growth after progressive segmental lengthening, avoiding conditions liable to induce slowing down or inhibition, and providing a planning aid in multi-step lengthening programs.Level of evidenceLevel IV. Retrospective study

Actualization of the concept of social cleavages St. Rokkana and S. Lipseate in the context of secession threats

У статті здійснено огляд ключових засад теорії соціальних розмежувань Ліпсета-Роккана з урахуванням основних напрямків сучасного дискурсу в цій сфері. Оцінено можливість застосування цієї концепції у дослідженні проблематики сецесійних загроз цілісності держави. Запропоновано з наведенням обґрунтування низку коригувальних застережень для підвищення наукової та практичної цінності теорії розмежувань поза межами дослідження партійної системи держави.The article reviews the key provisions of the theory of social cleavages of Lipset – Rokkana, taking into account the main directions of modern discourse in this field. The possibility of applying this concept in the study of the problems of secession threats to the integrity of the state is assessed. A set of corrective clauses is proposed to outline the rationale for increasing the scientific and practical value of the theory of cleavages beyond the boundaries of the studies of the party system of the state.В статье осуществлен обзор ключевых положений теории социальных размежеваний Липсета – Роккана с учетом основных направлений современного дискурса в этой сфере. Оценена возможность применения этой концепции в исследовании проблематики сецессионных угроз целостности государства. Предложен с изложением обоснования ряд корректирующих оговорок для повышения научной и практической ценности теории размежеваний вне границ исследований партийной системы государства

Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure