M. Forest - Academia.edu (original) (raw)

Papers by M. Forest

Bulletin of Mathematical Biology

Liquid-liquid phase separation is an emerging mechanism for intracellular organization. This work... more Liquid-liquid phase separation is an emerging mechanism for intracellular organization. This work presents a mathematical model to examine molecular mechanisms that yield phase-separated droplets composed of different RNA-protein complexes. Using a Cahn-Hilliard diffuse interface model with a Flory-Huggins free energy scheme, we explore how multiple (here two, for simplicity) protein-RNA complexes (species) can establish a heterogeneous droplet field where droplets with single or multiple species phase separate and evolve during coarsening. We show that the complex-complex de-mixing energy tunes whether the complexes co-exist or form distinct droplets, while the transient binding kinetics dictate both the timescale of droplet formation and whether distinct species phase separate into droplets simultaneously or sequentially. For specific energetics and kinetics, a field of droplets driven by the formation of only one protein-RNA complex will emerge. Slowly, the other droplet species will accumulate inside the preformed droplets of the other species, allowing them to occupy the same droplet space. Alternatively, unfavorable species mixing creates a parasitic relationship: the slow-to-form protein-RNA complex will accumulate at the surface of a competing droplet species, siphoning off the free protein as it is released. Once this competing protein-RNA complex has sufficiently accumulated on the droplet surface, it can form a new droplet that is capable of sharing an interface with the first complex droplet but is not capable of mixing. These results give insights into a wide range of phase-separation scenarios and heterogeneous droplets that coexist but do not mix within the nucleus and the cytoplasm of cells.

ABSTRACT This contract has led to a design and control capability for high performance, nano-comp... more ABSTRACT This contract has led to a design and control capability for high performance, nano-composite materials. Results obtained explicitly link material performance properties to detailed modeling of flow processing. The target materials are nematic polymer nano-composites in which nano-elements are high-aspect-ratio rods or platelets with extreme property contrasts relative to the matrix. Benchmark prototype materials yield striking enhancements in multi-functional properties. A suite of modeling tools for design engineering, which did not exist previously, have been developed. We have developed key theoretical, modeling, and numerical tools for modeling nano-composite permeability to gases or liquids, high electrical conductivity, high and low thermal conductivity, and elastic moduli, and have developed an integrated model and simulation package, capable of direct predictions as well as inverse characterization tools. In this 9 month period, we have arrived at the key ingredients for a property control strategy.

ABSTRACT This project targets mathematical and computational underpinnings of a predictive capabi... more ABSTRACT This project targets mathematical and computational underpinnings of a predictive capability for high performance, nano-composite (HPNC) materials. The overall goal is two-fold: 1st we develop theory, models, and numerical algorithms for the HPNC processing pipeline, starting with composite information, through flow processing, and finally to multi-functional property characterization, 2nd we implement these mathematical tools to predict measurable and significant features of HPNC materials.

This note, following my lecture, is a summary of the current state of practical application of pe... more This note, following my lecture, is a summary of the current state of practical application of periodic, N-phase modulation equations. First, I sketched interesting bifurcation phenomena that have been documented in [1] through extensive direct numerical investigations. These long-lived “attractors” of the damped, driven periodic sine-Gordon equation consist of various flows among coherent spatial structures. The temporal behavior ranges from periodic to quasiperiodic to chaotic, quantified in terms of several diagnostics. The spatial resolution during each flow is coherent and low-dimensional. In addition to Fourier projections, we use the sine-Gordon spectral transform to independently measure the “N-phase integrable mode approximations” of the perturbed field at each time step. The upshot is that the attractors are well-approximated, at least locally, by modulated N-phase periodic waves, where N remains small into the chaotic regime.

Physica D: Nonlinear Phenomena, 1990

In this paper the homoclinic geometric structure of the integrable sine-Gordon equation under per... more In this paper the homoclinic geometric structure of the integrable sine-Gordon equation under periodic boundary conditions is developed. Specifically, focus is given to orbits homoclinic to N-tori. Simple examples of such homoclinic orbits are constructed and a physical interpretation of these states is given. A labeling is provided which identifies and catalogues all such orbits. These orbits are related in a one-to-one manner to linearized instabilities. Explicit formulas for all homoclinic orbits are given in terms of Backlund transformations.

Nonlinearity, 2009

The modulation equations for the amplitude and the phase of the defocusing nonlinear Schrödinger ... more The modulation equations for the amplitude and the phase of the defocusing nonlinear Schrödinger (NLS) equation in the semi-classical limit are solved exactly for smooth pulse initial data using an implicit hodograph representation of Tsarev (1985 Sov. Math.—Dokl.31 448) combined with an extension of Riemann's method on multi-sheeted characteristic planes developed by Ludford (1952 Proc. Camb. Phil. Soc.48 499–510, 1954 J. Ration. Mech.3 77–88). Our results extend previous exact solutions of the modulation equations for piecewise step function data (Biondini and Kodama 2006 J. Nonlinear Sci.16 435–81, Kodama and Wabnitz 1995 Opt. Lett.20 2291–3, Kodama 1999 SIAM J. Appl. Math.59 2162–92) and for smooth monotone data (Wright et al 1999 Phys. Lett. A 257 170–4) to more physically relevant smooth pulse data (a finite number of pulses). Our results also provide an exact characterization of the estimates for smooth pulse data of first breaking time and location, previously based on analysis of the modulation equations as hyperbolic conservation laws (Forest and McLaughlin 1998 J. Nonlinear Sci.7 43–62). Extensions to other integrable nonlinear equations of NLS-type are also discussed in the appendix.

Journal of Rheology, 1997

We have constructed an apparatus which provides enhanced resolution in the measurement of the fre... more We have constructed an apparatus which provides enhanced resolution in the measurement of the free surface profile and the axial force exiting the die during spinning of a liquid filament. In this paper we demonstrate how this information can be exploited to give quantitative information about rheological material properties in isothermal elongational flows. The fiber spinning experiments are coupled with mathematical models that serve as inverse problems to deduce material properties when the fiber profile and upstream axial force are experimentally known. We first develop integral and differential forms of the fiber spinning momentum balance which describe how stress varies down the length of the filament for an incompressible material, independent of rheology. These forms are then combined with experiments to deduce the evolution of the elongational viscosity along the spinline and verify the accuracy of free surface measurements. A fiber spinning model specialized to the Giesekus constitutive equation...

Journal of Rheology, 2013

ABSTRACT

Journal of Nonlinear Science, 1998

We study the modulation equations for the amplitude and phase of smoothed rectangular pulse initi... more We study the modulation equations for the amplitude and phase of smoothed rectangular pulse initial data for the defocusing nonlinear Schrodinger (NLS) equation in the semiclassical limit, and show that these equations exhibit shock formation. In this way we identify and explain one source for the onset of pulse oscillations in nonlinear fibers whose transmission is modeled by the semiclassical NLS equation. The onset of pulse ripples predicted here develops on the leading and trailing slopes of a smooth pulse, as a consequence of shock formation in the modulation equations. This mechanism for the onset of pulse ripples is distinct, both in the location and timescale, from the scenario pursued by Kodama and Wabnitz [11]: A piecewise linear pulse evolves for distances O(1) down the fiber, beyond which oscillations develop associated with the vanishing of the upper step of the pulse [10]. Here we show that the scenario in [11] is correct, but specific to pure rectangular pulses; any smoothing of this data fails to obey their scenario, but rather is described by the results presented here. That is, the semiclassical limit of the NLS equation is highly unstable with respect to smooth regularizations of rectangular data. In our analysis, the onset of oscillations is associated with the location of the maximum gradient of the pulse slopes, and onset occurs on the pulse slopes, at short distances down the fiber proportional to the inverse of this maximum gradient. Explicit upper and lower bounds on the initial shock location are derived. We thereby deduce the onset for this source of pulse degradation scales linearly with the pulse width, and scales with the reciprocal square root of the fiber nonlinear coefficient, the pulse power, and the fiber dispersion coefficient.

Journal of Nonlinear Science, 1993

Summary The purpose of this paper is the derivation of reduced, finite-dimensional dynamical sys... more Summary The purpose of this paper is the derivation of reduced, finite-dimensional dynamical systems that govern the near-integrable modulations ofN-phase, spatially periodic, integrable wavetrains. The small parameter in this perturbation theory is the size of the nonintegrable perturbation in the equation, rather than the amplitude of the solution, which is arbitrary. Therefore, these reduced equations locally approximate strongly nonlinear behavior of

Journal of Nonlinear Science, 1998

Summary. We study the modulation equations for the amplitude and phase of smoothed rectangular... more Summary. We study the modulation equations for the amplitude and phase of smoothed rectangular pulse initial data for the defocusing nonlinear Schrodinger (NLS) equation in the semiclassical limit, and show that these equations exhibit shock formation. In this way we identify and explain one source for the onset of pulse oscillations in nonlinear fibers whose transmission is modeled by

Communications on Pure and Applied Mathematics, 1980

Inverse spectral theory is used to prescribe and study equations for the slow modulations of N-ph... more Inverse spectral theory is used to prescribe and study equations for the slow modulations of N-phase wave trains for the Korteweg-de Vries (KdV) equation. An invariant representation of the modulational equations is deduced. This representation depends upon certain ...

… on Pure and Applied …, 1980

Physica D: Nonlinear …, 1990

Advanced Functional Materials, 2005

Forest and co-workers report on p. 2029 that nematic polymer nanocomposite (NPNC) films can be pr... more Forest and co-workers report on p. 2029 that nematic polymer nanocomposite (NPNC) films can be processed in steady shear flows, which generate complex orientational distributions of the nanorod inclusions. Distribution functions for a benchmark NPNC (11 vol.-% of 1 nm × 200 nm rods) are computed for a range of shear rates, yielding a bifurcation diagram with steady states at very low (logrolling) and high (flow-aligning) shear rates, and limit cycles (tumbling, wagging, kayaking) at intermediate shear rates. The orientational distributions dictate the effective conductivity tensor of the NPNC film, which is computed for all distribution functions, and extract the maximum principal conductivity enhancement (Emax, averaged in time for periodic distributions) relative to the matrix. The result is a “property bifurcation diagram” for NPNC films, which predicts an optimal shear rate that maximizes Emax. Nematic, or liquid-crystalline, polymer nanocomposites (NPNCs) are composed of large aspect ratio, rod-like or platelet, rigid macromolecules in a matrix or solvent, which itself may be aqueous or polymeric. NPNCs are engineered for high-performance material applications, ranging across mechanical, electrical, piezoelectric, thermal, and barrier properties. The rods or platelets possess enormous property contrasts relative to the solvent, yet the composite properties are strongly affected by the orientational distribution of the nanophase. Nematic polymer film processing flows are shear-dominated, for which orientational distributions are well known to be highly sensitive to shear rate and volume fraction of the nematogens, with unsteady response being the most expected outcome at typical low shear rates and volume fractions. The focus of this article is a determination of the ranges of anisotropy and dynamic fluctuations in effective properties arising from orientational probability distribution functions generated by steady shear of NPNC monodomains. We combine numerical databases for sheared monodomain distributions[1,2] of thin rod or platelet dispersions together with homogenization theory for low-volume-fraction spheroidal inclusions[3] to calculate effective conductivity tensors of steady and oscillatory sheared mesophases. We then extract maximum scalar conductivity enhancement and anisotropy for each type of sheared monodomain (flow-aligned, tumbling, kayaking, and chaotic).

Physica D: Nonlinear Phenomena, 1986

Abstract Pattern formation and transitions to chaos are described for the damped, ac-driven, one-... more Abstract Pattern formation and transitions to chaos are described for the damped, ac-driven, one-dimensional, periodic sine-Gordon equation. In a nonlinear Schrödinger regime, a generic quasi-periodic route to intermittent chaos is exhibited in detail using a range of ...

Discrete and Continuous Dynamical Systems - Series B, 2010

ABSTRACT Liquid crystalline polymers have been extensively studied in shear starting from an equi... more ABSTRACT Liquid crystalline polymers have been extensively studied in shear starting from an equilibrium nematic phase. In this study, we explore the transient and long-time behavior as a steady shear cell experiment commences during an isotropic-nematic (I-N) phase transition. We initialize a localized Gaussian nematic droplet within an unstable isotropic phase with nematic, vorticity-aligned equilibrium at the walls. In the absence of flow, the simulation converges to a homogeneous nematic phase, but not before passing through quite intricate defect arrays and patterns due to physical anchoring, the dimensions of the shear cell, and transient backflow generated around the defect arrays during the I-N transition. Snapshots of this numerical experiment are then used as initial data for shear cell experiments at controlled shear rates. For homogeneous stable nematic equilibrium initial data, the Leal group [4, 5, 6] and the authors [12] confirm the Larson-Mead experimental observations [7, 8]: stationary 2-D roll cells and defect-free 2-D orientational structure at low shear rates, followed at higher shear rates by an unstable transition to an unsteady 2-D cellular flow and defect-laden attractor. We show at low shear rates that the memory of defect-laden data lasts forever; 2-D steady attractors of [4, 5, 12] emerge for defect free initial data, whereas 1-D unsteady attractors arise for defect-laden initial data.

Bulletin of Mathematical Biology

Physica D: Nonlinear Phenomena, 1990

Nonlinearity, 2009

Journal of Rheology, 1997

Journal of Rheology, 2013

ABSTRACT

Journal of Nonlinear Science, 1998

Journal of Nonlinear Science, 1993

Journal of Nonlinear Science, 1998

Communications on Pure and Applied Mathematics, 1980

… on Pure and Applied …, 1980

Physica D: Nonlinear …, 1990

Advanced Functional Materials, 2005

Physica D: Nonlinear Phenomena, 1986

Discrete and Continuous Dynamical Systems - Series B, 2010