A deterministic model for one-dimensional excluded flow with local interactions.
ABSTRACT: Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a "soft" simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.
Project description:Environmental dust particles repelling from a hydrophobic surface under the electrostatic influence are considered and the dynamics of the dust particles are analyzed incorporating the high speed camera. The velocity of the repelled dust particles are formulated using the force balance incorporating the forces associated with the electrostatic repulsion, particle adhesion, particle drag, and the inflight particles interaction under the charge influence. The functionalized silica particles are deposited on the glass surface towards achieving a hydrophobic wetting state on the surface. An electronic circuitry is designed and built while generating the electrostatic effect, in the pulse form, on the dust particles located on the surface of the hydrophobic plate. Findings revealed that functionalized silica particles deposited surface results in hydrophobic wetting state with contact angle in the order of 158°?±?2° and contact angle hysteresis of 2°?±?1°. The electrostatic impulsive force generated on the plate surface enables to repel most of the sizes of the dust particles; however, some of the small dust particles remain as the residues on the surface after the electrostatic influence. The dust particle velocity predicted from the analytical formulation agrees with that obtained from the high speed camera data. The pinning force of the small size particles (0.6?µm?), due to adhesion on the surface, is found to be larger than the average size particles (?1.2?µm), which in turn, suppresses these particles repelling from the surface under the electrostatic influence. The residues of the dust particles on the as received glass surface after dust repelling are more than those residues on the hydrophobic surface. This behavior is associated with the dust particles adhesion on the surface. Consequently, hydrophobic wetting state on the plate surface improves the dust particle repelling from the surface.
Project description:BACKGROUND:Spiral waves are considered to be one of the potential mechanisms that maintain complex arrhythmias such as atrial and ventricular fibrillation. The aim of the present study was to quantify the complex dynamics of spiral waves as the organizing manifolds of information flow at multiple scales. METHOD:We simulated spiral waves using a numerical model of cardiac excitation in a two-dimensional (2-D) lattice. We created a renormalization group by coarse graining and re-scaling the original time series in multiple spatiotemporal scales, and quantified the Lagrangian coherent structures (LCS) of the information flow underlying the spiral waves. To quantify the scale-invariant structures, we compared the value of the finite-time Lyapunov exponent between the corresponding components of the 2-D lattice in each spatiotemporal scale of the renormalization group with that of the original scale. RESULTS:Both the repelling and the attracting LCS changed across the different spatial and temporal scales of the renormalization group. However, despite the change across the scales, some LCS were scale-invariant. The patterns of those scale-invariant structures were not obvious from the trajectory of the spiral waves based on voltage mapping of the lattice. CONCLUSIONS:Some Lagrangian coherent structures of information flow underlying spiral waves are preserved across multiple spatiotemporal scales.
Project description:Spatial patterning of coral reef sessile benthic organisms can constrain competitive and demographic rates, with implications for dynamics over a range of time scales. However, techniques for quantifying and analysing reefscape behaviour, particularly at short to intermediate time scales (weeks to decades), are lacking. An analysis of the dynamics of coral reefscapes simulated with a lattice model shows consistent trends that can be categorized into four stages: a repelling stage that moves rapidly away from an unstable initial condition, a transient stage where spatial rearrangements bring key competitors into contact, an attracting stage where the reefscape decays to a steady-state attractor, and an attractor stage. The transient stage exhibits nonlinear dynamics, whereas the other stages are linear. The relative durations of the stages are affected by the initial spatial configuration as characterized by coral aggregation-a measure of spatial clumpiness, which together with coral and macroalgae fractional cover, more completely describe modelled reefscape dynamics. Incorporating diffusional processes results in aggregated patterns persisting in the attractor. Our quantitative characterization of reefscape dynamics has possible applications to other spatio-temporal systems and implications for reef restoration: high initial aggregation patterns slow losses in herbivore-limited systems and low initial aggregation configurations accelerate growth in herbivore-dominated systems.
Project description:In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.
Project description:A new lattice Boltzmann method to simulate open channel flows with complex geometry described by a conservative form of Saint-Venant equations is developed. The Saint-Venant equations include an original treatment of the momentum equation source term. Concrete hydrostatic pressure thrust expressions are provided for rectangular, trapezoidal and irregular cross-section shapes. A D1Q3 lattice arrangement is adopted. External forces, such as bed friction and the static term, are discretized with a centred scheme. Bounce back and imposed boundary conditions are considered. To verify the proposed model, four cases are carried out: tidal flow over a regular bed in a rectangular cross-section, steady flow in a channel with horizontal and vertical contractions, steady flow over a bump in a trapezoidal channel and steady flow in a non-prismatic channel with friction. Results indicate that the proposed scheme is simple and can provide accurate predictions for open channel flows.
Project description:Magnetic forces and curvature-induced hydrodynamic drag have both been studied and employed in continuous microfluidic particle separation and enrichment schemes. Here we combine the two. We investigate consequences of applying an outwardly directed magnetic force to a dilute suspension of magnetic microspheres circulating in a spiral microfluidic channel. This force is realized with an array of permanent magnets arranged to produce a magnetic field with octupolar symmetry about the spiral axis. At low flow rates particles cluster around an apparent streamline of the flow near the outer wall of the turn. At high flow rates this equilibrium is disrupted by the induced secondary (Dean) flow and a new equilibrium is established near the inner wall of the turn. A model incorporating key forces involved in establishing these equilibria is described, and is used to extract quantitative information about the magnitude of local Dean drag forces from experimental data. Steady-state fractionation of suspensions by particle size under the combined influence of magnetic and hydrodynamic forces is demonstrated. Extensions of this work could lead to new continuous microscale particle sorting and enrichment processes with improved fidelity and specificity.
Project description:Mitigation of environmental dust from surfaces becomes one of the challenges for maintaining the optical characteristics of surfaces. Dust repelling from hydrophobic and hydrophilic surfaces under vibrational excitation is investigated and the percentage of dust repelled from surfaces is evaluated. The characteristics of the dust particles are examined and dust adhesion on surfaces under molecular forces (van der Walls) is explored. High speed recording system is utilized to monitor dust repelling from the surfaces. The dust residues, which are not repelled from the sample surfaces, are analyzed and the percentage of area coverage of the dust repelled from the surfaces is assessed. The repelling height of the dust is predicted analytically, and the findings are compared with the experimental data. Findings revealed that the analytical predictions of dust repelling height are in good agreement with the experimental data. Due to none-stoichiometric elemental compositions in the dust compounds, ionic forces are created while forming the cluster-like structures because of particle adhesion. The vibrational excitation repels dust from sample surfaces in the form of cluster-like structures. Dust repelled from hydrophobic surface results in a larger clean area on the hydrophobic surface (80% of total surface area) than that of the hydrophilic surface (20% of total surface area).
Project description:The ribosome flow model with input and output (RFMIO) is a deterministic dynamical system that has been used to study the flow of ribosomes during mRNA translation. The input of the RFMIO controls its initiation rate and the output represents the ribosome exit rate (and thus the protein production rate) at the 3' end of the mRNA molecule. The RFMIO and its variants encapsulate important properties that are relevant to modeling ribosome flow such as the possible evolution of "traffic jams" and non-homogeneous elongation rates along the mRNA molecule, and can also be used for studying additional intracellular processes such as transcription, transport, and more. Here we consider networks of interconnected RFMIOs as a fundamental tool for modeling, analyzing and re-engineering the complex mechanisms of protein production. In these networks, the output of each RFMIO may be divided, using connection weights, between several inputs of other RFMIOs. We show that under quite general feedback connections the network has two important properties: (1) it admits a unique steady-state and every trajectory converges to this steady-state; and (2) the problem of how to determine the connection weights so that the network steady-state output is maximized is a convex optimization problem. These mathematical properties make these networks highly suitable as models of various phenomena: property (1) means that the behavior is predictable and ordered, and property (2) means that determining the optimal weights is numerically tractable even for large-scale networks. For the specific case of a feed-forward network of RFMIOs we prove an additional useful property, namely, that there exists a spectral representation for the network steady-state, and thus it can be determined without any numerical simulations of the dynamics. We describe the implications of these results to several fundamental biological phenomena and biotechnological objectives.
Project description:We study the motility behavior of the unicellular protozoan Paramecium tetraurelia in a microfluidic device that can be prepared with a landscape of attracting or repelling chemicals. We investigate the spatial distribution of the positions of the individuals at different time points with methods from spatial statistics and Poisson random point fields. This makes quantitative the informal notion of "uniform distribution" (or lack thereof). Our device is characterized by the absence of large systematic biases due to gravitation and fluid flow. It has the potential to be applied to the study of other aquatic chemosensitive organisms as well. This may result in better diagnostic devices for environmental pollutants.
Project description:The particle-in-cell method is generally considered a flexible and robust method to model the geodynamic problems with chemical heterogeneity. However, velocity interpolation from grid points to particle locations is often performed without considering the divergence of the velocity field, which can lead to significant particle dispersion or clustering if those particles move through regions of strong velocity gradients. This may ultimately result in cells void of particles, which, if left untreated, may, in turn, lead to numerical inaccuracies. Here we apply a two-dimensional conservative velocity interpolation (CVI) scheme to steady state and time-dependent flow fields with strong velocity gradients (e.g., due to large local viscosity variation) and derive and apply the three-dimensional equivalent. We show that the introduction of CVI significantly reduces the dispersion and clustering of particles in both steady state and time-dependent flow problems and maintains a locally steady number of particles, without the need for ad hoc remedies such as very high initial particle densities or reseeding during the calculation. We illustrate that this method provides a significant improvement to particle distributions in common geodynamic modeling problems such as subduction zones or lithosphere-asthenosphere boundary dynamics.