Searcharxiv⌕ Search

arXiv subjects

Eliot Fried

Publications and source records attributed to Eliot Fried.

At least 37 records · Page 2Linked to original sources
arXiv2016

Crystallization kinetics of binary colloidal monolayers

Experiments and simulations are used to study the kinetics of crystal growth in a mixture of magnetic and nonmagnetic particles suspended in ferrofluid. The growth process is quantified using both a bond order parameter and a mean domain size parameter. The largest single crystals obtained in experiments consist of approximately 1000 particles and form if the area fraction is held between 65-70% and the field strength is kept in the range of 8.5-10.5 Oe. Simulations indicate that much larger single crystals containing as many as 5000 particles can be obtained in impurity-free conditions within a few hours. If our simulations are modified to include impurity concentrations as small as 1-2%, then the results agree quantitatively with the experiments. These findings provide an important step toward developing strategies for growing single crystals that are large enough to enable follow-on investigations across many subdisciplines in condensed matter physics.

cond-mat.soft↗
arXiv2015

Influence of material stretchability on the equilibrium shape of a Möbius band

We use a discrete, lattice-based model for two-dimensional materials to show that Möbius bands made with stretchable materials are less likely to crease or tear. This stems a delocalization of twisting strain that occurs if stretching is allowed. The associated low-energy configurations provide strategic target shapes for the guided assembly of nanometer and micron scale Möbius bands. To predict macroscopic band shapes for a given material, we establish a connection between stretchability and relevant continuum moduli, leading to insight regarding the practical feasibility of synthesizing Möbius bands from materials with continuum parameters that can be measured experimentally or estimated by upscale averaging. To take advantage of stretchability in the case of Möbius bands made of graphene, DNA, and other effectively unstretchable materials, we develop and explore a novel architecture that uses the Chinese finger trap as a fundamental building block and imparts notable stretchability to otherwise unstretchable materials.

cond-mat.soft↗
arXiv2015

Theoretical and experimental study of the stability of a soap film spanning a flexible loop

A variational model is used to study the stability of a soap film spanning a flexible loop. The film is modeled as a fluid surface endowed with constant tension and the loop is modeled as an elastic rod resistant to both bending and twist. The first and second energy variations of the underlying energy functional are derived, leading to governing equilibrium equations and stability criteria. The latter criteria are employed to explore the stability of flat circular configurations with respect to planar and transverse perturbations. Experiments are performed to study post-buckled configurations and to explore the validity of the theoretical predictions. Imparting a twist to the bounding loop destabilizes flat circular loops which are short-enough to be stable when twist-free. Nevertheless, when the circular disk is perturbed merely radially or merely transversely, the stability condition is indifferent to twist. By the equilibrium equations, the twisting angle of a planar equilibrium configuration should be distributed uniformly along the loop. The stability criteria guarantee that this uniformity is preserved after buckling. The stability with respect to increasing the surface tension of the film or the length of the loop is sensitive to the cross-sectional thickness of the bounding loop. However, stability with respect to increasing the total twist is indifferent to that thickness.

cond-mat.soft↗
arXiv2014

Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"

This article is a translation of Michael Sadowsky's original paper "Ein elementarer Beweis für die Existenz eines abwickelbaren Möbiusschen Bandes und die Zurückführung des geometrischen Problems auf ein Variationsproblem." which appeared in Sitzungsberichte der Preussischen Akademie der Wissenschaften, physikalisch-mathematische Klasse, 17. Juli 1930, Mitteilung vom 26. Juni, 412-415. Published on September 12, 1930.

math.HO↗
arXiv2014

Translation of Michael Sadowsky's paper "The differential equations of the Möbius band"

This article is a translation of Michael Sadowsky's original paper "Die Differentialgleichungen des Möbiusschen Bandes." in Jahresbericht der Deutschen Mathematiker-Vereinigung 39 (2. Abt. Heft 5/8, Jahresversammlung vom 16. bis 23. September), 49-51 (1929), which is a short version of his paper "Theorie der elastisch biegsamen undehnbaren Bänder mit Anwendungen auf das Möbiussche Band" in 3. internationaler Kongress für technische Mechanik, Stockholm, 1930.

math.HO↗
arXiv2014

Translation and interpretation of Michael Sadowsky's paper "Theory of elastically bendable inextensible bands with applications to the Möbius band"

This article is a translation of Michael Sadowsky's original paper "Theorie der elastisch biegsamen undehnbaren Bänder mit Anwendungen auf das Möbiussche Band" in 3. internationaler Kongress für technische Mechanik, Stockholm, 1930. The translation is augmented by an Appendix containing an interpretation of the last section of Sadowsky's original paper including figures generated from recent numerical simulations.

math.HO↗
arXiv2014

Motility versus fluctuations in mixtures of self-propelled and passive agents

Many biological systems consist of self-motile and passive agents both of which contribute to overall functionality. However, there are very few studies of the properties of such mixtures. Here we formulate a model for mixtures of self-motile and passive agents and show that the model gives rise to three different dynamical phases: a disordered mesoturbulent phase, a polar flocking phase, and a vortical phase characterized by large-scale counterrotating vortices. We use numerical simulations to construct a phase diagram and compare the statistical properties of the different phases of the model with self-motile bacterial suspensions. Our findings afford specific insights regarding the interaction of microorganisms and passive particles and provide novel strategic guidance for efficient technological realizations of artificial active matter.

cond-mat.soft↗
arXiv2014

Calculating the bending moduli of the Canham--Helfrich free-energy density from a particular potential

The Canham--Helfrich free-energy density for a lipid bilayer involves the mean and Gaussian curvatures of the midsurface of the bilayer. The splay and saddle-splay moduli $κ$ and $\barκ$ regulate the sensitivity of the free-energy density to changes of these curvatures. Seguin and Fried derived the Canham--Helfrich energy by taking into account the interactions between the molecules comprising the bilayer, giving rise to integral representations for the moduli in terms of the interaction potential. In the present work, two potentials are chosen and the integrals are evaluated to yield expressions for the moduli, which are found to depend on parameters associated with each potential. These results are compared with values of the moduli found in the current literature.

physics.bio-ph↗
arXiv2014

Euler-Plateau, with a twist

A generalization of the Euler-Plateau problem to account for the energy contribution due to twisting of the bounding loop is proposed. Euler-Lagrange equations are derived in a parameterized setting and a bifurcation analysis is performed. A pair of dimensionless parameters govern bifurcations from a flat, circular ground state. While one of these is familiar from the Euler-Plateau problem, the other encompasses information about the ratio of the twisting to bending rigidities, twist, and size of the loop. For sufficiently small values of the latter parameter, two separate groups of bifurcation modes are identified. On the other hand, for values greater than the critical twist arising in Michell's problem of the bifurcation of a twisted annular ring, only one bifurcation mode exists. Bifurcation diagrams indicate that a loop with greater twisting rigidity shows more resistance to transverse buckling. However, a twisted and closed filament spanned by a surface endowed with uniform surface tension buckles at a twist less than the critical value for an elastic ring.

cond-mat.soft↗
arXiv2014

Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization

A new slender-body theory for viscous flow, based on the concepts of dimensional reduction and hyperviscous regularization, is presented. The geometry of flat, elongated, or point-like rigid bodies immersed in a viscous fluid is approximated by lower-dimensional objects, and a hyperviscous term is added to the flow equation. The hyperviscosity is given by the product of the ordinary viscosity with the square of a length that is shown to play the role of effective thickness of any lower-dimensional object. Explicit solutions of simple problems illustrate how the proposed method is able to represent with good approximation both the velocity field and the drag forces generated by rigid motions of the immersed bodies, in analogy with classical slender-body theories. This approach has the potential to open up the way to more effective computational techniques, since the complexity of the geometry can be significantly reduced. This, however, is achieved at the expense of involving higher-order derivatives of the velocity field. Importantly, both the dimensional reduction and the hyperviscous regularization, combined with suitable numerical schemes, can be used also in situations where inertia is not negligible.

physics.flu-dyn↗
arXiv2013

Stable and unstable helices: Soap films in cylindrical tubes

Cox & Jones recently devised and studied an interesting variant of the classical Plateau problem, a variant in which a helical soap film is confined to a cylindrical tube with circular cross-section. Through experiments, numerics, and some analysis, they found that the length and (inner) radius of the tube strongly influence the equilibrium shape of the confined soap film. In this paper, an area minimization problem associated with determining the shape of the film is formulated and analyzed to determine which surfaces are local minima. The connection between a functional inequality and the associated eigenvalue problem plays an important role in the analysis. For helical films, a more detailed analysis is carried out and stability conditions consistent with the experimental and numerical results of Cox & Jones are obtained.

math.CA↗
arXiv2013

Particle-based simulations of self-motile suspensions

A simple model for simulating flows of active suspensions is investigated. The approach is based on dissipative particle dynamics. While the model is potentially applicable to a wide range of self-propelled particle systems, the specific class of self-motile bacterial suspensions is considered as a modeling scenario. To mimic the rod-like geometry of a bacterium, two dissipative particle dynamics particles are connected by a stiff harmonic spring to form an aggregate dissipative particle dynamics molecule. Bacterial motility is modeled through a constant self-propulsion force applied along the axis of each such aggregate molecule. The model accounts for hydrodynamic interactions between self-propelled agents through the pairwise dissipative interactions conventional to dissipative particle dynamics. Numerical simulations are performed using a customized version of the open-source LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) software package. Detailed studies of the influence of agent concentration, pairwise dissipative interactions, and Stokes friction on the statistics of the system are provided. The simulations are used to explore the influence of hydrodynamic interactions in active suspensions. For high agent concentrations in combination with dominating pairwise dissipative forces, strongly correlated motion patterns and a fluid-like spectral distributions of kinetic energy are found. In contrast, systems dominated by Stokes friction exhibit weaker spatial correlations of the velocity field. These results indicate that hydrodynamic interactions may play an important role in the formation of spatially extended structures in active suspensions.

physics.flu-dyn↗
arXiv2013

Statistics of the Navier-Stokes-alpha-beta regularization model for fluid turbulence

We explore one-point and two-point statistics of the Navier-Stokes-alpha-beta regularization model at moderate Reynolds number in homogeneous isotropic turbulence. The results are compared to the limit cases of the Navier-Stokes-alpha model and the Navier-Stokes-alpha-beta model without subgrid-scale stress, as well as with high resolution direct numerical simulation. After reviewing spectra of different energy norms of the Navier-Stokes-alpha-beta model, the Navier-Stokes-alpha model, and Navier-Stokes-alpha-beta model without subrid-scale stress, we present probability density functions and normalized probability density functions of the filtered and unfiltered velocity increments along with longitudinal velocity structure functions of the regularization models and direct numerical simulation results. We highlight differences in the statistical properties of the unfiltered and filtered velocity fields entering the governing equations of the Navier-Stokes-alpha and Navier-Stokes-alpha-beta models and discuss the usability of both velocity fields for realistic flow predictions. The influence of the modified viscous term in the Navier-Stokes-alpha-beta model is studied through comparison to the case where the underlying subgrid-scale stress tensor is neglected. The filtered velocity field is found to have physically more viable probability density functions and structure functions for the approximation of direct numerical simulation results, whereas the unfiltered velocity field is found to have flatness factors close to direct numerical simulation results.

physics.flu-dyn↗
arXiv2013

Stability of discoidal high-density lipoprotein particles

Motivated by experimental and numerical studies revealing that discoidal high-density lipoprotein (HDL) particles may adopt flat elliptical and nonplanar saddle-like configurations, it is hypothesized that these might represent stabilized configurations of initially unstable flat circular particles. A variational description is developed to explore the stability of a flat circular discoidal HDL particle. While the lipid bilayer is modeled as two-dimensional fluid film endowed with surface tension and bending elasticity, the apoA-I belt is modeled as one-dimensional inextensible twist-free chain endowed with bending elasticity. Stability is investigated using the second variation of the underlying energy functional. Various planar and nonplanar instability modes are predicted and corresponding nondimensional critical values of salient dimensionless parameters are obtained. The results predict that the first planar and nonplanar unstable modes occur due to in-plane elliptical and transverse saddle-like perturbations. Based on available data, detailed stability diagrams indicate the range of input parameters for which a flat circular discoidal HDL particle is linearly stable or unstable.

cond-mat.soft↗
arXiv2013

Stability and bifurcation of a soap film spanning an elastic loop

The Euler--Plateau problem, proposed by \cite{gm}, concerns a soap film spanning a flexible loop. The shapes of the film and the loop are determined by the interactions between the two components. In the present work, the Euler--Plateau problem is reformulated to yield a boundary-value problem for a vector field that parameterizes both the spanning surface and the bounding loop. Using the first and second variations of the relevant free-energy functional, detailed bifurcation and stability analyses are performed. For spanning surface with energy density $σ$ and a bounding loop with length $2πR$ and bending rigidity $a$, the first bifurcation, during which the spanning surface remains flat but the bounding loop becomes noncircular, occurs at $σR^3/a=3$, confirming a result obtained previously via an energy comparison. Other bifurcation solution branches, including those emanating from the flat circular solution branch to nonplanar solution branches, are also shown to be unstable.

cond-mat.soft↗
arXiv2013

Gamma-limit of a model for the elastic energy of an inextensible ribbon

A Γ-convergence result involving the elastic energy of a narrow inextensible ribbon is established. A non-dimensional form of the elastic energy is reduced to a one-dimensional integral over the centerline of the ribbon with the aspect ratio of the ribbon being a small parameter. That integral is observed to increase monotonically with the aspect ratio. The Γ-limit of the family of non-dimensional elastic energies is taken in a Sobolev space of centerlines with non-vanishing curvature. In that space, it is shown that the Γ-limit is a functional first proposed by Sadowsky in the context of narrow ribbons that form Möbius bands. The results obtained here do not apply to such ribbons, since the centerline of a Möbius band must have at least one inflection point. As a first step toward dealing with such inflection points, a result is presented on the lower semicontinuity of the Sadowsky functional with inflection points comprising a set of measure zero within the domain of an arclength parameterization.

math.AP↗
arXiv2013

Microphysical derivation of the Canham--Helfrich free-energy density

The Canham--Helfrich free-energy density for a lipid bilayer has drawn considerable attention. Aside from the mean and Gaussian curvatures, this free-energy density involves a spontaneous mean-curvature that encompasses information regarding the preferred, natural shape of the lipid bilayer. We use a straightforward microphysical argument to derive the Canham--Helfrich free-energy density. Our derivation (i) provides a justification for the common assertion that spontaneous curvature originates primarily from asymmetry between the leaflets comprising a bilayer and (ii) furnishes expressions for the splay and saddle-splay moduli in terms of derivatives of the underlying potential.

physics.bio-ph↗