Parallel Coupling of Symmetric and Asymmetric Exclusion Processes

A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions.Comment: 16 page

Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes

Asymmetric exclusion processes for particles moving on parallel channels with inhomogeneous coupling are investigated theoretically. Particles interact with hard-core exclusion and move in the same direction on both lattices, while transitions between the channels is allowed at one specific location in the bulk of the system. An approximate theoretical approach that describes the dynamics in the vertical link and horizontal lattice segments exactly but neglects the correlation between the horizontal and vertical transport is developed. It allows us to calculate stationary phase diagrams, particle currents and densities for symmetric and asymmetric transitions between the channels. It is shown that in the case of the symmetric coupling there are three stationary phases, similarly to the case of single-channel totally asymmetric exclusion processes with local inhomogeneity. However, the asymmetric coupling between the lattices lead to a very complex phase diagram with ten stationary-state regimes. Extensive Monte Carlo computer simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation, suggesting the importance of correlations in the system. Dynamic properties and phase diagrams are discussed by analyzing constraints on the particle currents across the channels

Generalized entropy arising from a distribution of q-indices

It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics determines, given classes of initial conditions, the occupation of the accessible phase space (or of a symmetry-determined nonzero-measure part of it), which in turn appears to determine the entropic form to be used. This occupation might be a uniform one (the usual {\it equal probability hypothesis} of BG statistical mechanics), which corresponds to $q=1$; it might be a free-scale occupancy, which appears to correspond to $q \ne 1$. Since occupancies of phase space more complex than these are surely possible in both natural and artificial systems, the task of further generalizing the entropy appears as a desirable one, and has in fact been already undertaken in the literature. To illustrate the approach, we introduce here a quite general entropy based on a distribution of $q$-indices thus generalizing $S_q$. We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the $q$-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.Comment: 14 pages including 3 figure

Phase diagram of two-lane driven diffusive systems

We consider a large class of two-lane driven diffusive systems in contact with reservoirs at their boundaries and develop a stability analysis as a method to derive the phase diagrams of such systems. We illustrate the method by deriving phase diagrams for the asymmetric exclusion process coupled to various second lanes: a diffusive lane; an asymmetric exclusion process with advection in the same direction as the first lane, and an asymmetric exclusion process with advection in the opposite direction. The competing currents on the two lanes naturally lead to a very rich phenomenology and we find a variety of phase diagrams. It is shown that the stability analysis is equivalent to an `extremal current principle' for the total current in the two lanes. We also point to classes of models where both the stability analysis and the extremal current principle fail

Dynamics at barriers in bidirectional two-lane exclusion processes

A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an extended subsystem (either by appropriate boundary conditions or by the embedding environment) where, in the absence of the constraint, the current would be negative. We have found two qualitatively different types of steady states and formulated the conditions of them in terms of the transition rates. In the first type of steady state, a localized cluster of particles forms with an anti-shock located in the subsystem and the current vanishes exponentially with the extension of the subsystem. This behavior is analogous to that of the one-lane partially asymmetric simple exclusion process, and can be realized e.g. when the local drive is induced by making the jump rates in two lanes unequal. In the second type of steady state, which is realized e.g. if the local drive is induced purely by the bias in the lane change rates, and which has thus no counterpart in the one-lane model, a delocalized cluster of particles forms which performs a diffusive motion as a whole and, as a consequence, the current vanishes inversely proportionally to the extension of the subsystem. The model is also studied in the presence of quenched disordered, where, in case of delocalization, phenomenological considerations predict anomalously slow, logarithmic decay of the current with the system size in contrast with the usual power-law.Comment: 24 pages, 13 figure

Modelling Students’ Thematically Associated Knowledge : Networked Knowledge from Affinity Statistics

Peer reviewe

Lipidomics Analysis Reveals Efficient Storage of Hepatic Triacylglycerides Enriched in Unsaturated Fatty Acids after One Bout of Exercise in Mice

Background: Endurance exercise induces lipolysis, increases circulating concentrations of free fatty acids (FFA) and the uptake and oxidation of fatty acids in the working muscle. Less is known about the regulation of lipid metabolism in the liver during and post-exercise

Pediatric trauma and emergency surgery: an international cross-sectional survey among WSES members

Background: In contrast to adults, the situation for pediatric trauma care from an international point of view and the global management of severely injured children remain rather unclear. The current study investigates structural management of pediatric trauma in centers of different trauma levels as well as experiences with pediatric trauma management around the world. Methods: A web-survey had been distributed to the global mailing list of the World Society of Emergency Surgery from 10/2021-03/2022, investigating characteristics of respondents and affiliated hospitals, case-load of pediatric trauma patients, capacities and infrastructure for critical care in children, trauma team composition, clinical work-up and individual experiences with pediatric trauma management in response to patients´ age. The collaboration group was subdivided regarding sizes of affiliated hospitals to allow comparisons concerning hospital volumes. Comparable results were conducted to statistical analysis. Results: A total of 133 participants from 34 countries, i.e. 5 continents responded to the survey. They were most commonly affiliated with larger hospitals (> 500 beds in 72.9%) and with level I or II trauma centers (82.0%), respectively. 74.4% of hospitals offer unrestricted pediatric medical care, but only 63.2% and 42.9% of the participants had sufficient experiences with trauma care in children ≤ 10 and ≤ 5 years of age (p = 0.0014). This situation is aggravated in participants from smaller hospitals (p < 0.01). With regard to hospital size (≤ 500 versus > 500 in-hospital beds), larger hospitals were more likely affiliated with advanced trauma centers, more elaborated pediatric intensive care infrastructure (p < 0.0001), treated children at all ages more frequently (p = 0.0938) and have higher case-loads of severely injured children < 12 years of age (p = 0.0009). Therefore, the majority of larger hospitals reserve either pediatric surgery departments or board-certified pediatric surgeons (p < 0.0001) and in-hospital trauma management is conducted more multi-disciplinarily. However, the majority of respondents does not feel prepared for treatment of severe pediatric trauma and call for special educational and practical training courses (overall: 80.2% and 64.3%, respectively). Conclusions: Multi-professional management of pediatric trauma and individual experiences with severely injured children depend on volumes, level of trauma centers and infrastructure of the hospital. However, respondents from hospitals at all levels of trauma care complain about an alarming lack of knowledge on pediatric trauma management

Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport

Unlike equilibrium statistical mechanics, with its well-established foundations, a similar widely-accepted framework for non-equilibrium statistical mechanics (NESM) remains elusive. Here, we review some of the many recent activities on NESM, focusing on some of the fundamental issues and general aspects. Using the language of stochastic Markov processes, we emphasize general properties of the evolution of configurational probabilities, as described by master equations. Of particular interest are systems in which the dynamics violate detailed balance, since such systems serve to model a wide variety of phenomena in nature. We next review two distinct approaches for investigating such problems. One approach focuses on models sufficiently simple to allow us to find exact, analytic, non-trivial results. We provide detailed mathematical analyses of a one-dimensional continuous-time lattice gas, the totally asymmetric exclusion process (TASEP). It is regarded as a paradigmatic model for NESM, much like the role the Ising model played for equilibrium statistical mechanics. It is also the starting point for the second approach, which attempts to include more realistic ingredients in order to be more applicable to systems in nature. Restricting ourselves to the area of biophysics and cellular biology, we review a number of models that are relevant for transport phenomena. Successes and limitations of these simple models are also highlighted.Comment: 72 pages, 18 figures, Accepted to: Reports on Progress in Physic