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David A. Kessler

Publications and source records attributed to David A. Kessler.

126 records · Page 7Linked to original sources
arXiv2002

Non-native beta-sheet formation: insights into protein amyloidosis

Protein amyloidosis is a cytopathological process characterized by the formation of highly beta-sheet-rich fibrils. How this process occurs and how to prevent/treat the associated diseases are not completely understood. Here, we carry out a theoretical investigation of sequence-independent beta-sheet formation, based on recent findings regarding the cooperativity of hydrogen-bond network formation. Our results strongly suggest that in vivo beta-sheet aggregation is induced by inter-sheet stacking dynamics. This leads to a prediction for the minimal length of susceptible polymer needed to form such an aggregate. Remarkably, the prediction corresponds quite well with the critical lengths detected in poly-glutamine-related diseases. Our work therefore provides a theoretical framework capable of understanding the underlying mechanism and shedding light on therapy strategies of protein amyloidosis.

cond-mat.soft↗
arXiv2001

Mode I fracture in a nonlinear lattice with viscoelastic forces

We study Mode I fracture in a viscoelastic lattice model with a nonlinear force law, with a focus on the velocity and linear stability of the steady-state propagating solution. This study is a continuation both of the study of the piece-wise linear model in Mode I, and the study of more general nonlinear force laws in Mode III fracture. At small driving, there is a strong dependency of the velocity curve on the dissipation and a strong sensitivity to the smoothness of the force law at large dissipation. At large driving we calculate, via a linear stability analysis, the critical velocity for the onset of instability as a function of the smoothness, the dissipation and the ratio of lattice spacing to critical extension. This critical velocity is seen to be very sensitive to these parameters. We confirm our calculations via direct numerical simulations of the initial value problem.

cond-mat.mtrl-sci↗
arXiv2001

Frenet algorithm for simulations of fluctuating continuous elastic filaments

We present a new algorithm for generating the equilibrium configurations of fluctuating continuous elastic filaments, based on a combination of statistical mechanics and differential geometry. We use this to calculate the distribution function of the end-to-end distance of filaments with nonvanishing spontaneous curvature and show that for small twist and large bending rigidities, there is an intermediate temperature range in which the filament becomes nearly completely stretched. We show that volume interactions can be incorporated into our algorithm, demonstrating this through the calculation of the effect of excluded volume on the end-to-end distance of the filament.

cond-mat.soft↗
arXiv2001

Mechanisms underlying sequence-independent beta-sheet formation

We investigate the formation of beta-sheet structures in proteins without taking into account specific sequence-dependent hydrophobic interactions. To accomplish this, we introduce a model which explicitly incorporates both solvation effects and the angular dependence (on the protein backbone) of hydrogen bond formation. The thermodynamics of this model is studied by comparing the restricted partition functions obtained by "unfreezing" successively larger segments of the native beta-sheet structure. Our results suggest that solvation dynamics together with the aforementioned angular dependence gives rise to a generic cooperativity in this class of systems; this result explains why pathological aggregates involving beta-sheet cores can form from many different proteins. Our work provides the foundation for the construction of phenomenological models to investigate the competition between native folding and non-specific aggregation.

cond-mat.soft↗
arXiv2001

Phase-Field Model of Mode III Dynamic Fracture

We introduce a phenomenological continuum model for mode III dynamic fracture that is based on the phase-field methodology used extensively to model interfacial pattern formation. We couple a scalar field, which distinguishes between ``broken'' and ``unbroken'' states of the system, to the displacement field in a way that consistently includes both macroscopic elasticity and a simple rotationally invariant short scale description of breaking. We report two-dimensional simulations that yield steady-state crack motion in a strip geometry above the Griffith threshold.

cond-mat.soft↗
arXiv2001

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.

nlin.PS↗
arXiv2000

Nonlinear lattice model of viscoelastic Mode III fracture

We study the effect of general nonlinear force laws in viscoelastic lattice models of fracture, focusing on the existence and stability of steady-state Mode III cracks. We show that the hysteretic behavior at small driving is very sensitive to the smoothness of the force law. At large driving, we find a Hopf bifurcation to a straight crack whose velocity is periodic in time. The frequency of the unstable bifurcating mode depends on the smoothness of the potential, but is very close to an exact period-doubling instability. Slightly above the onset of the instability, the system settles into a exactly period-doubled state, presumably connected to the aforementioned bifurcation structure. We explicitly solve for this new state and map out its velocity-driving relation.

cond-mat.mtrl-sci↗
arXiv2000

Steady-state mode III cracks in a viscoelastic lattice model

We extend the Slepyan solution of the problem of a steady-state crack in an infinite ideally brittle lattice model to include dissipation in the form of Kelvin viscosity. As a demonstration of this technique, based on the Wiener-Hopf method, we apply the method to mode III cracks in a square lattice. We use this solution to find the critical velocity at which the steady-state solution becomes inconsistent due to additional bond-breaking; this point signaling the onset of complex dynamical behavior.

cond-mat.mtrl-sci↗
arXiv2000

Steady-state mode I cracks in a viscoelastic triangular lattice

We continue our study of the exact solutions for steady-state cracks in ideally brittle viscoelastic lattice models by focusing on mode I in a triangular system. The issues we address include the crack velocity versus driving curve as well as the onset of additional bond-breaking, signaling the emergence of complex spatio-temporal behavior. Somewhat surprisingly, the critical velocity for this transition becomes a decreasing function of the dissipation for sufficiently large values thereof. At the end, we briefly discuss the possible relevance of our findings for experiments on mode I crack instabilities.

cond-mat.mtrl-sci↗
arXiv1999

Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.

cond-mat.mtrl-sci↗
arXiv1999

Arrested Cracks in Nonlinear Lattice Models of Brittle Fracture

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement for which these arrested cracks exist is very small. Also, our results indicate that small changes in the vicinity of the crack tip can have an extremely large effect on arrested cracks. Finally, we briefly discuss the possible relevance of our findings to recent experiments.

cond-mat.soft↗
arXiv1998

Steady-State Cracks in Viscoelastic Lattice Models

We study the steady-state motion of mode III cracks propagating on a lattice exhibiting viscoelastic dynamics. The introduction of a Kelvin viscosity $η$ allows for a direct comparison between lattice results and continuum treatments. Utilizing both numerical and analytical (Wiener-Hopf) techniques, we explore this comparison as a function of the driving displacement $Δ$ and the number of transverse sites $N$. At any $N$, the continuum theory misses the lattice-trapping phenomenon; this is well-known, but the introduction of $η$ introduces some new twists. More importantly, for large $N$ even at large $Δ$, the standard two-dimensional elastodynamics approach completely misses the $η$-dependent velocity selection, as this selection disappears completely in the leading order naive continuum limit of the lattice problem.

cond-mat.soft↗
arXiv1998

The Universal Gaussian in Soliton Tails

We show that in a large class of equations, solitons formed from generic initial conditions do not have infinitely long exponential tails, but are truncated by a region of Gaussian decay. This phenomenon makes it possible to treat solitons as localized, individual objects. For the case of the KdV equation, we show how the Gaussian decay emerges in the inverse scattering formalism.

patt-sol↗
arXiv1998

Front Propagation: Precursors, Cutoffs and Structural Stability

We discuss the problem of fronts propagating into metastable and unstable states. We examine the time development of the leading edge, discovering a precursor which in the metastable case propagates out ahead of the front at a velocity more than double that of the front and establishes the characteristic exponential behavior of the steady-state leading edge. We also study the dependence of the velocity on the imposition of a cutoff in the reaction term. These studies shed new light on the problem of velocity selection in the case of propagation into an unstable state. We also examine how discreteness in a particle simulation acts as an effective cutoff in this case.

patt-sol↗
arXiv1997

Mutator Dynamics on a Smooth Evolutionary Landscape

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness is steadily increasing in time, is governed solely by the transition rates into and out of the mutator state. This results is a much faster rate of fitness increase than would be the case without the mutator allele. Near the fitness equilibrium, however, the mutators are severely suppressed, due to the detrimental effects of a large mutation rate near the fitness maximum. We discuss the results of a recent experiment on natural selection of E. coli in the light of our model.

patt-sol↗
arXiv1997

Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral

Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to one involving the motion of a free surface separating the excited and quiescent phases. In this work, we study the free surface problem in the limit of small diffusivity for the slow field variable. Specifically, we show that a previously found spiral solution in the diffusionless limit can be extended to finite diffusivity, without significant alteration. This extension involves the creation of a variety of boundary layers which cure all the undesirable singularities of the aforementioned solution. The implications of our results for the study of spiral stability are briefly discussed.

patt-sol↗
arXiv1996

Evolution on a smooth landscape

We study in detail a recently proposed simple discrete model for evolution on smooth landscapes. An asymptotic solution of this model for long times is constructed. We find that the dynamics of the population are governed by correlation functions that although being formally down by powers of $N$ (the population size) nonetheless control the evolution process after a very short transient. The long-time behavior can be found analytically since only one of these higher-order correlators (the two-point function) is relevant. We compare and contrast the exact findings derived herein with a previously proposed phenomenological treatment employing mean field theory supplemented with a cutoff at small population density. Finally, we relate our results to the recently studied case of mutation on a totally flat landscape.

cond-mat↗