Coarsening of "clouds" and dynamic scaling in a far-from-equilibrium model system

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams ("clouds"), as the system approaches a non-equilibrium steady state from a disordered initial state. We monitor the dynamic structure factor $S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of the form $S(0,k_y;t)=t^\beta \tilde{S}(k_yt^\alpha)$. Over a significant range of times, we observe excellent data collapse with $\alpha=1/2$ and $\beta=1$. The effects of varying filling fraction and driving force are discussed

Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change

Power Spectra of the Total Occupancy in the Totally Asymmetric Simple Exclusion Process

As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a 1-dimensional open lattice, and its power spectrum. Using both Monte Carlo simulations and analytic methods, we explore its behavior in different characteristic regimes. In the maximal current phase and on the coexistence line (between high/low density phases), the power spectrum displays algebraic decay, with exponents -1.62 and -2.00, respectively. Deep within the high/low density phases, we find pronounced \emph{oscillations}, which damp into power laws. This behavior can be understood in terms of driven biased diffusion with conserved noise in the bulk.Comment: 4 pages, 4 figure

Far-from-equilibrium transport with constrained resources

The totally asymmetric simple exclusion process (TASEP) is a well studied example of far-from-equilibrium dynamics. Here, we consider a TASEP with open boundaries but impose a global constraint on the total number of particles. In other words, the boundary reservoirs and the system must share a finite supply of particles. Using simulations and analytic arguments, we obtain the average particle density and current of the system, as a function of the boundary rates and the total number of particles. Our findings are relevant to biological transport problems if the availability of molecular motors becomes a rate-limiting factor.Comment: 14 pages, 7 figures, uses iopart12.clo and iopart.cl

Power Spectra of a Constrained Totally Asymmetric Simple Exclusion Process

To synthesize proteins in a cell, an mRNA has to work with a finite pool of ribosomes. When this constraint is included in the modeling by a totally asymmetric simple exclusion process (TASEP), non-trivial consequences emerge. Here, we consider its effects on the power spectrum of the total occupancy, through Monte Carlo simulations and analytical methods. New features, such as dramatic suppressions at low frequencies, are discovered. We formulate a theory based on a linearized Langevin equation with discrete space and time. The good agreement between its predictions and simulation results provides some insight into the effects of finite resoures on a TASEP.Comment: 4 pages, 2 figures v2: formatting change

Competition for finite resources

The resources in a cell are finite, which implies that the various components of the cell must compete for resources. One such resource is the ribosomes used during translation to create proteins. Motivated by this example, we explore this competition by connecting two totally asymmetric simple exclusion processes (TASEPs) to a finite pool of particles. Expanding on our previous work, we focus on the effects on the density and current of having different entry and exit rates.Comment: 15 pages, 9 figures, v2: minor revisions, v3: additional reference & minor correction

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

Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.Comment: 25 pages, 7 figure

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figuresMajor update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figuresThe preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure