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Search Results: 1 - 10 of 2816 matches for " Herbert Levine "
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Mean Field Theory of the Morphology Transition in Stochastic Diffusion Limited Growth
Yuhai Tu,Herbert Levine
Physics , 1995, DOI: 10.1103/PhysRevE.52.5134
Abstract: We propose a mean-field model for describing the averaged properties of a class of stochastic diffusion-limited growth systems. We then show that this model exhibits a morphology transition from a dense-branching structure with a convex envelope to a dendritic one with an overall concave morphology. We have also constructed an order parameter which describes the transition quantitatively. The transition is shown to be continuous, which can be verified by noting the non-existence of any hysteresis.
A Phase-Field Model of Spiral Dendritic Growth
Royce Kam,Herbert Levine
Physics , 1996, DOI: 10.1103/PhysRevE.54.2797
Abstract: Domains of condensed-phase monolayers of chiral molecules exhibit a variety of interesting nonequilibrium structures when formed via pressurization. To model these domain patterns, we add a complex field describing the tilt degree of freedom to an (anisotropic) complex-phase-field solidification model. The resulting formalism allows for the inclusion of (in general, non-reflection symmetric) interactions between the tilt, the solid-liquid interface, and the bond orientation. Simulations demonstrate the ability of the model to exhibit spiral dendritic growth.
Wave nucleation rate in excitable systems in the low noise limit
Herve Henry,Herbert Levine
Physics , 2003, DOI: 10.1103/PhysRevE.68.031914
Abstract: Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes.
Dynamic instabilities of fracture under biaxial strain using a phase field model
Herve Henry,Herbert Levine
Physics , 2004, DOI: 10.1103/PhysRevLett.93.105504
Abstract: We present a phase field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under bi-axial load. Our model again reproduces well observed supercritical Hopf bifurcation, and is therefore the first simulation which does so.
Interfacial Velocity Corrections due to Multiplicative Noise
Leonid Pechenik,Herbert Levine
Physics , 1998, DOI: 10.1103/PhysRevE.59.3893
Abstract: The problem of velocity selection for reaction fronts has been intensively investigated, leading to the successful marginal stability approach for propagation into an unstable state. Because the front velocity is controlled by the leading edge which perforce has low density, it is interesting to study the role that finite particle number fluctuations have on this picture. Here, we use the well-known mapping of discrete Markov processes to stochastic differential equations and focus on the front velocity in the simple $A+A \stackrel{\leftarrow}{\to} A$ system. Our results are consistent with a recent (heuristic) proposal that $v_{MS} - v \sim {1\over \ln^2 {N}}$.
Unicellular algal growth: A biomechanical approach to cell wall dynamics
Royce Kam,Herbert Levine
Physics , 1997, DOI: 10.1103/PhysRevLett.79.4290
Abstract: We present a model for unicellular algal growth as motivated by several experiments implicating the importance of calcium ions and ``loosening'' enzymes in morphogenesis. A growing cell at rest in a diffusive calcium solution is viewed as an elastic shell on short timescales. For a given turgor pressure, we calculate the stressed shapes of the wall elements whose elastic properties are determined by Young's modulus and the thickness of the wall. The local enzyme concentration then determines the rate at which the unstressed shape of a wall element relaxes toward its stressed shape. The local wall thickness is calculated from the calcium-mediated addition of material and thinning due to elongation. We use this model to calculate growth rates for small perturbations to a circular cell. We find an instability related to modulations of the wall thickness, leading to growth rates which peak at a finite wave number.
A Thermodynamic Model for Receptor Clustering
Chinlin Guo,Herbert Levine
Physics , 1999, DOI: 10.1016/S0006-3495(99)77073-6
Abstract: Intracellular signaling often arises from ligand-induced oligomerization of cell surface receptors. This oligomerization or clustering process is fundamentally a cooperative behavior between near-neighbor receptor molecules; the properties of this cooperative process clearly affects the signal transduction. Recent investigations have revealed the molecular basis of receptor-receptor interactions, but a simple theoretical framework for using this data to predict cluster formation has been lacking. Here, we propose a simple, coarse-grained, phenomenological model for ligand-modulated receptor interactions and discuss its equilibrium properties via mean-field theory. The existence of a first-order transition for this model has immediate implications regarding the robustness of the cellular signaling response.
Signal processing in local neuronal circuits based on activity-dependent noise and competition
Vladislav Volman,Herbert Levine
Quantitative Biology , 2009, DOI: 10.1063/1.3184806
Abstract: We study the characteristics of weak signal detection by a recurrent neuronal network with plastic synaptic coupling. It is shown that in the presence of an asynchronous component in synaptic transmission, the network acquires selectivity with respect to the frequency of weak periodic stimuli. For non-periodic frequency-modulated stimuli, the response is quantified by the mutual information between input (signal) and output (network's activity), and is optimized by synaptic depression. Introducing correlations in signal structure resulted in the decrease of input-output mutual information. Our results suggest that in neural systems with plastic connectivity, information is not merely carried passively by the signal; rather, the information content of the signal itself might determine the mode of its processing by a local neuronal circuit.
Activity-dependent stochastic resonance in recurrent neuronal networks
Vladislav Volman,Herbert Levine
Quantitative Biology , 2008, DOI: 10.1103/PhysRevE.77.060903
Abstract: We use a biophysical model of a local neuronal circuit to study the implications of synaptic plasticity for the detection of weak sensory stimuli. Networks with fast plastic coupling show behavior consistent with stochastic resonance. Addition of an additional slow coupling that accounts for the asynchronous release of neurotransmitter results in qualitatively different properties of signal detection, and also leads to the appearance of transient post-stimulus bistability. Our results suggest testable hypothesis with regard to the self-organization and dynamics of local neuronal circuits.
Small Regulatory RNAs May Sharpen Spatial Expression Patterns
Erel Levine ,Peter McHale ,Herbert Levine
PLOS Computational Biology , 2007, DOI: 10.1371/journal.pcbi.0030233
Abstract: The precise establishment of gene expression patterns is a crucial step in development. Formation of a sharp boundary between high and low spatial expression domains requires a genetic mechanism that exhibits sensitivity, yet is robust to fluctuations, a demand that may not be easily achieved by morphogens alone. Recently, it has been demonstrated that small RNAs (and, in particular, microRNAs) play many roles in embryonic development. Whereas some RNAs are essential for embryogenesis, others are limited to fine-tuning a predetermined gene expression pattern. Here, we explore the possibility that small RNAs participate in sharpening a gene expression profile that was crudely established by a morphogen. To this end, we study a model in which small RNAs interact with a target gene and diffusively move from cell to cell. Though diffusion generally smoothens spatial expression patterns, we find that intercellular mobility of small RNAs is actually critical in sharpening the interface between target expression domains in a robust manner. This sharpening occurs as small RNAs diffuse into regions of low mRNA expression and eliminate target molecules therein, but cannot affect regions of high mRNA levels. We discuss the applicability of our results, as examples, to the case of leaf polarity establishment in maize and Hox patterning in the early Drosophila embryo. Our findings point out the functional significance of some mechanistic properties, such as mobility of small RNAs and the irreversibility of their interactions. These properties are yet to be established directly for most classes of small RNAs. An indirect yet simple experimental test of the proposed mechanism is suggested in some detail.
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