Asymmetric Coupling in Two-Channel Simple Exclusion Processes

Simple exclusion processes for particles moving along two parallel lattices and jumping between them are theoretically investigated for asymmetric rates of transition between the channels. An approximate theoretical approach, that describes the particle dynamics exactly in any vertical cluster of two parallel sites and neglects the correlations between the different vertical clusters, is applied to calculate stationary-state density profiles, currents and phase diagrams. Surprisingly, it is found that asymmetry in the coupling between the channels leads to a very complex phase behavior that is very different from two-channel simple exclusion processes with symmetric coupling. There are seven stationary-state phases in the simple exclusion processes with asymmetric transition rates between the channels, in contrast to three phases found for the systems with symmetric coupling. In addition, a new maximal-current phase with a domain wall in the middle of the lattices, that has no analogs in other exclusion processes, is observed. Although the explicit calculations are presented only for the case of full asymmetry, when the particles can only jump between the channels in one direction, the properties of two-channel simple exclusion systems with general asymmetry are also discussed. Theoretical predictions are in excellent agreement with extensive computer Monte Carlo simulations.Comment: 12 pages, 6 figure

Ethno-confessional immigrant ghettos as a national security problem in Denmark’s social and political discourse

The ghettoisation of immigrant areas in Denmark is a lengthy and objective process of the emergence of ethno-religious ‘parallel societies’ in the state. Cultural and religious principles that are often at odds with the democratic values of Danish society guide the actions of ghetto residents. Danish social and political discourse pictures this ideological difference between the host society and Muslim immigrant minorities as a potential threat to Denmark’s national security caused by a combination of political, social, and economic factors. The ensuing social disunity and violation of the country’s territorial integrity take the problem to a regional and international level. Through analysing public speeches of Danish social and political actors, this article reconstructs key stages in the development of parallel societies in Denmark. Another focus is official government strategies to prevent isolated immigrant areas from turning into ghettoes: the Government’s Strategy against Ghettoisation (2004), Return of the Ghetto to Society: Confronting Parallel Societies in Denmark (2010), and One Denmark without Parallel Societies: No Ghettos in 2030 (2018). The escalation of the social conflict calls for the Danish authorities to take decisive action against the enclavisation of segregated immigrant communities. This study employs discourse analysis to evaluate the efficiency and identify the shortcomings of government action to integrate ethno-confessional minorities into society. Particular attention is paid to analysing public reaction to the criteria for identifying ghettoes as well as to annual publications of official ghetto lists

Swedish Islamism as a social and political aspect in the formation of an ethno-confessional parallel society

A new actor in the European geopolitical space - an ethno-religious "parallel society" - is transforming the social and political fabric of Sweden. An institutionalised Muslim parallel society is emerging in vulnerable areas, such as marginalised immigrant districts of Swedish cities, through the efforts of Islamist political, social, and economic structures adhering to the religious and political doctrine of the Muslim Brotherhood (this organization is banned in the Russian Federation). Committed to maintaining the Muslim identity, these organisations seek gradual Islamisation of the Swedish population through ideological influence on immigrants with a Muslim background. These efforts thwart cultural assimilation attempts and hinder the implementation of Swedish integration policy. The lack of research into the peaceful Islamisation of Swedish society and the related problems of Islamophobia, anti-Muslim racism, and radicalisation of Muslim youth lends urgency to investigating the influence of Islamist organisations on the Swedish Muslim immigrant community. This study analyses the literature, sources, and statistics on the essential aspects of Swedish Islamisation to provide a holistic picture of the formation of an ethno-religious parallel society in Sweden. The findings help evaluate the effectiveness of the national policy on confronting parallel societies, as well as of measures to promote democratic values as the foundation of a united Swedish society

Spontaneous Symmetry Breaking in Two-Channel Asymmetric Exclusion Processes with Narrow Entrances

Multi-particle non-equilibrium dynamics in two-channel asymmetric exclusion processes with narrow entrances is investigated theoretically. Particles move on two parallel lattices in opposite directions without changing them, while the channels are coupled only at the boundaries. A particle cannot enter the corresponding lane if the exit site of the other lane is occupied. Stationary phase diagrams, particle currents and densities are calculated in a mean-field approximation. It is shown that there are four stationary phases in the system, with two of them exhibiting spontaneous symmetry breaking phenomena. Extensive Monte Carlo computer simulations confirm qualitatively our predictions, although the phase boundaries and stationary properties deviate from the mean-field results. Computer simulations indicate that several dynamic and phase properties of the system have a strong size dependency, and one of the stationary phases predicted by the mean-field theory disappears in the thermodynamic limit.Comment: 13 page

Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branch. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain-wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions.Comment: 16 pages, 7 figure

Dynamic Properties of Molecular Motors in Burnt-Bridge Models

Dynamic properties of molecular motors that fuel their motion by actively interacting with underlying molecular tracks are studied theoretically via discrete-state stochastic ``burnt-bridge'' models. The transport of the particles is viewed as an effective diffusion along one-dimensional lattices with periodically distributed weak links. When an unbiased random walker passes the weak link it can be destroyed (``burned'') with probability p, providing a bias in the motion of the molecular motor. A new theoretical approach that allows one to calculate exactly all dynamic properties of motor proteins, such as velocity and dispersion, at general conditions is presented. It is found that dispersion is a decreasing function of the concentration of bridges, while the dependence of dispersion on the burning probability is more complex. Our calculations also show a gap in dispersion for very low concentrations of weak links which indicates a dynamic phase transition between unbiased and biased diffusion regimes. Theoretical findings are supported by Monte Carlo computer simulations.Comment: 14 pages. Submitted to J. Stat. Mec

Two-Channel Totally Asymmetric Simple Exclusion Processes

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.Comment: 13 pages, 10 figure

Differential Expression of CHL1 Gene during Development of Major Human Cancers

CHL1 gene (also known as CALL) on 3p26.3 encodes a one-pass trans-membrane cell adhesion molecule (CAM). Previously CAMs of this type, including L1, were shown to be involved in cancer growth and metastasis.We used Clontech Cancer Profiling Arrays (19 different types of cancers, 395 samples) to analyze expression of the CHL1 gene. The results were further validated by RT-qPCR for breast, renal and lung cancer. Cancer Profiling Arrays revealed differential expression of the gene: down-regulation/silencing in a majority of primary tumors and up-regulation associated with invasive/metastatic growth. Frequent down-regulation (>40% of cases) was detected in 11 types of cancer (breast, kidney, rectum, colon, thyroid, stomach, skin, small intestine, bladder, vulva and pancreatic cancer) and frequent up-regulation (>40% of cases)--in 5 types (lung, ovary, uterus, liver and trachea) of cancer. Using real-time quantitative PCR (RT-qPCR) we found that CHL1 expression was decreased in 61% of breast, 60% of lung, 87% of clear cell and 89% papillary renal cancer specimens (P<0.03 for all the cases). There was a higher frequency of CHL1 mRNA decrease in lung squamous cell carcinoma compared to adenocarcinoma (81% vs. 38%, P = 0.02) without association with tumor progression.Our results suggested that CHL1 is involved in the development of different human cancers. Initially, during the primary tumor growth CHL1 could act as a putative tumor suppressor and is silenced to facilitate in situ tumor growth for 11 cancer types. We also suggested that re-expression of the gene on the edge of tumor mass might promote local invasive growth and enable further metastatic spread in ovary, colon and breast cancer. Our data also supported the role of CHL1 as a potentially novel specific biomarker in the early pathogenesis of two major histological types of renal cancer

Theoretical investigation of biological transport: Asymmetric simple exclusion processes in two-channel systems

Multi-particle non-equilibrium dynamics in two-channel biological transport systems is investigated theoretically within the framework of asymmetric simple exclusion processes (ASEP). In exclusion processes particles move along the lattice by hopping between neighboring sites that are vacant. We consider the systems with open boundaries, where particles enter the lattice on the entrance site and leave from the exit site with given rates. Four different ASEP models are studied. The first two models investigate interchannel coupling between parallel channels in a one-way transport system. The third model considers junction of two parallel tracks, while the last model investigates two-way transport system with narrow entrances with coupling on the boundaries. Theoretical investigation of these non-equilibrium systems reveal many interesting phenomena, such as unusual phase diagrams that contain up to seven stationary-state phases, localization of the domain wall in the bulk of the system, symmetry-breaking and strong interparticle correlation. Stationary phase diagrams, particle currents and bulk values of densities are calculated in a mean-field approximation for the systems in the thermodynamic limit. In addition, exact matrix product ansatz method and phenomenological domain-wall theory are applied to analyze dynamic properties. For several systems nearest-neighbour correlation and density distribution functions are computed and size-scaling effects are analyzed. Extensive Monte Carlo computer simulations are carried out for all systems to test predictions and they verify our theoretical results