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J. D. Gunton

Publications and source records attributed to J. D. Gunton.

At least 19 recordsLinked to original sources
arXiv2014

Phase Transition in a Model of Y-Shaped Molecules

In recent years the statistical mechanics of non-spherical molecules, such as polypeptide chains and protein molecules, has garnered considerable attention as their phase behavior has important scientific and health implications. One example is provided by immunoglobulin, which has a "Y"-shape. In this work, we determine the phase diagram of Y-shaped molecules on a hexagonal lattice through Monte Carlo Grand Canonical ensemble simulation, using histogram reweighting, multicanonical sampling, and finite-size scaling. We show that (as expected) this model is a member of the Ising universality class. For low temperatures, we implemented multicanonical sampling to induce faster phase transitions in the simulation. By studying several system sizes, we use finite-size scaling to determine the two phase coexistence curve, including the bulk critical temperature, critical chemical potential, and critical density.

cond-mat.stat-mech↗
arXiv2011

Self Assembly of Janus Ellipsoids

We propose a primitive model of Janus ellipsoids that represent particles with an ellipsoidal core and two semi-surfaces coded with dissimilar properties, for example, hydrophobicity and hydrophilicity, respectively. We investigate the effects of the aspect ratio on the self-assembly morphology and dynamical aggregation processes using Monte Carlo simulations. We also discuss certain differences between our results and those of earlier results for Janus spheres. In particular, we find that the size and structure of the aggregate can be controlled by the aspect ratio.

cond-mat.soft↗
arXiv2011

Kinetics of microribbon formation in a simplified model of amelogenin biomacromolecules

We show that the kinetics of microribbon formation of amelogenin molecules is well described by a combination of translational and rotational diffusion of a simplified anisotropic bipolar model consisting of hydrophobic spherical colloid particles and a point charge located on each particle surface. The colloid particles interact via a standard depletion attraction while the point charges interact through a screened Coulomb repulsion. We study the kinetics via a Brownian dynamics simulation of both translational and rotational motions and show that the anisotropy brought in by the charge dramatically affects the kinetic pathway of cluster formation and our simple model captures the main features of the experimental observations.

cond-mat.soft↗
arXiv2010

Some topics in the kinetics of protein aggregation

Preliminary results are presented for the kinetics of phase separation in three distinct models of protein aggregation. The first is a model of the formation of spherical microcrystals of insulin via an initial formation of fractal clusters of insulin. The results of our Brownian dynamics study of this model are in qualitative agreement with a recent experimental study (Biophys. Jour. 89 (2005) 3424-3433) of microcrystal formation from aqueous mixtures of insulin. A second work involves a theory for the formation of metastable bundles of sickle hemoglobin from fibers, based on a recent generic theory of bundle formation (Phy. Rev. Lett. 99 (2007) 098101). We also discuss a model for the microscopic formation of these fibers. Finally, we discuss preliminary results for the kinetics of cluster formation for a six patch model of protein crystallization.

physics.bio-ph↗
arXiv2010

The constructive role of diversity on the global response of coupled neuron systems

We study the effect that the heterogeneity present among the elements of an ensemble of coupled excitable neurons have on the collective response of the system to an external signal. We have considered two different interaction scenarios, one in which the neurons are diffusively coupled and another in which the neurons interact via pulse-like signals. We found that the type of interaction between the neurons has a crucial role in determining the response of the system to the external modulation. We develop a mean-field theory based on an order parameter expansion that quantitatively reproduces the numerical results in the case of diffusive coupling.

physics.bio-ph↗
arXiv2009

Ion specific effects on phase transitions in protein solutions

A recent Monte Carlo simulation determined the potential of mean force between two lysozyme molecules in various aqueous solutions [M. Lund et al. Phys. Rev. Lett. 100, 258105 (2008)]. The study involved a combination of explicit solvent and continuum model simulations and showed that there are significant ion-specific protein-protein interactions due to hydrophobic patches on the protein surfaces. In this paper we use the results of their study to determine the phase diagram for lysozyme for aqueous solutions of NaCl and NaI. Two of the three phase diagrams have a stable fluid-fluid critical point, while the third has a slightly metastable critical point. This results from a secondary extremum in the potential associated with a repulsive interaction. This repulsive interaction reduces the effective range of the attractive interaction and produces a metastable critical point. We compare the results of one of these phase diagrams with that for a model that includes ion-dispersion forces, but does not contain solvent structural effects.

physics.chem-ph↗
arXiv2006

Simple Model of Membrane Proteins Including Solvent

We report a numerical simulation for the phase diagram of a simple two dimensional model, similar to one proposed by Noro and Frenkel [J. Chem. Phys. \textbf{114}, 2477 (2001)] for membrane proteins, but one that includes the role of the solvent. We first use Gibbs ensemble Monte Caro simulations to determine the phase behavior of particles interacting via a square-well potential in two dimensions for various values of the interaction range. A phenomenological model for the solute-solvent interactions is then studied to understand how the fluid-fluid coexistence curve is modified by solute-solvent interactions. It is shown that such a model can yield systems with liquid-liquid phase separation curves that have both upper and lower critical points, as well as closed loop phase diagrams, as is the case with the corresponding three dimensional model.

cond-mat.soft↗
arXiv2005

Role of solvent for globular proteins in solution

The properties of the solvent affect the behavior of the solution. We propose a model that accounts for the contribution of the solvent free energy to the free energy of globular proteins in solution. For the case of an attractive square well potential, we obtain an exact mapping of the phase diagram of this model without solvent to the model that includes the solute-solvent contribution. In particular we find for appropriate choices of parameters upper critical points, lower critical points and even closed loops with both upper and lower critical points, similar to one found before [Macromolecules, 36, 5845 (2003)]. In the general case of systems whose interactions are not attractive square wells, this mapping procedure can be a first approximation to understand the phase diagram in the presence of solvent. We also present simulation results for both the square well model and a modified Lennard-Jones model.

cond-mat.soft↗
arXiv2004

Phase Behavior of Short Range Square Well Model

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square well model for the attractive ranges $λ= 1.15$ and $λ= 1.25$. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for $λ= 1.15$ are new. We find that the fluid-fluid critical point is metastable for both cases, with the case $λ= 1.25$ being just below the threshold value for metastability. We compare our results with prior studies and with experimental results for the gamma-II crystallin.

cond-mat.stat-mech↗
arXiv2004

A Finite-Size Scaling Study of a Model of Globular Proteins

Grand canonical Monte Carlo simulations are used to explore the metastable fluid-fluid coexistence curve of the modified Lennard-Jones model of globular proteins of ten Wolde and Frenkel (Science, v277, 1975 (1997)). Using both mixed-field finite-size scaling and histogram reweighting methods, the joint distribution of density and energy fluctuations is analyzed at coexistence to accurately determine the critical-point parameters. The subcritical coexistence region is explored using the recently developed hyper-parallel tempering Monte Carlo simulation method along with histogram reweighting to obtain the density distributions. The phase diagram for the metastable fluid-fluid coexistence curve is calculated in close proximity to the critical point, a region previously unattained by simulation.

cond-mat.soft↗
arXiv2001

Intercellular Communication Via Intracellular Calcium Oscillations

In this letter we present the results of a simple model for intercellular communication via calcium oscillations, motivated in part by a recent experimental study. The model describes two cells (a "donor" and "sensor") whose intracellular dynamics involve a calcium-induced, calcium release process. The cells are coupled by assuming that the the input of the sensor cell is proportional to the output of the donor cell. As one varies the frequency of calcium oscillations of the donor cell, the sensor cell passes through a sequence of N:M phase locked regimes and exhibits a "Devil's staircase" behavior. Such a phase locked response has been seen experimentally in pulsatile stimulation of single cells. We also study a stochastic version of the coupled two cell model. We find that phase locking holds for realistic choices for the cell volume.

physics.bio-ph↗
arXiv2001

Space and Scale Localization in a Model of a Direct Transition to Spatiotemporal Chaos

We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wavenumber). A projection onto a Daubechies basis yields a good separation of scales, as shown by an examination of the contribution of different wavelet levels to the power spectrum. At most scales, including the most energetic ones, we find essentially Gaussian dynamics. We also show that removal of certain wavelet modes can be made without altering the dynamics of the system as described by the Lyapunov spectrum.

nlin.CD↗
arXiv2000

Coherence Resonance in Chaotic Systems

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua system

cond-mat↗
arXiv2000

Phenomenological Theory for Phase Turbulence in Rayleigh-Bénard Convection

We present a phenomenological theory for phase turbulence (PT) in Rayleigh-Bénard convection, based on the generalized Swift-Hohenberg model. We apply a Hartree-Fock approximation to PT and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $ξ_2$. We hence obtain {\it analytical} results for the time-averaged convective current $J$ and the time-averaged mean square vorticity $Ω$. We also define power-law behaviors such as $J \sim ε^μ$, $Ω\sim ε^λ$ and $ξ_2 \sim ε^{-ν}$, where $ε$ is the control parameter. We find from our theory that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ ν$. These predictions, together with the scaling conjecture for $S(k)$, are confirmed by our numerical results.

cond-mat.stat-mech↗
arXiv2000

Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $ε$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.

cond-mat↗
arXiv1997

Nature of Roll to Spiral-Defect-Chaos Transition

We investigate the nature of the parallel-roll to spiral-defect-chaos (SDC) transition in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We carry out extensive, systematic numerical studies by, on one branch, increasing the control parameter gradually from the parallel roll regime to the SDC regime and, on the other branch, decreasing it in the opposite manner. We find that the data of several time-averaged global quantities all form hysteretic loops from the two branches. We also discuss several possible scenarios for the transition and analyze our data for SDC accordingly. We conclude that the roll-to-SDC transition is first-order in character and that the correlation length diverges at the conduction to convection onset. We further postulate that this transition can be understood somewhat similar to the hexagon-to-roll transition in non-Boussinesq fluids. Finally we comment on the differences between our conclusion and those in two experiments.

patt-sol↗
arXiv1997

Phenomenological Theory for Spatiotemporal Chaos in Rayleigh-Benard Convection

We present a phenomenological theory for spatiotemporal chaos (STC) in Rayleigh-Benard convection, based on the generalized Swift-Hohenberg model. We apply a random phase approximation to STC and conjecture a scaling form for the structure factor $S(k)$ with respect to the correlation length $ξ_2$. We hence obtain analytical results for the time-averaged convective current $J$ and the time-averaged vorticity current $Ω$. We also define power-law behaviors such as $J \sim ε^μ$, $Ω\sim ε^λ$ and $ξ_2 \sim ε^{-ν}$, where $ε$ is the control parameter. We find from our theory that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ ν$ for phase turbulence and that $μ= 1$, $ν\ge 1/2$ and $λ= 2 μ+ 2 ν$ for spiral-defect chaos. These predictions, together with the scaling conjecture for $S(k)$, are confirmed by our numerical results. Finally we suggest that Porod's law, $S(k) \sim 1/ξ_2 k^3$ for large $k$, might be valid in STC.

patt-sol↗