arXiv subjects

Michael P. Brenner

Publications and source records attributed to Michael P. Brenner.

At least 73 records · Page 4Linked to original sources

arXiv2018

Controlling polyelectrolyte adsorption onto carbon nanotubes by tuning ion-image interactions

Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamen- tal challenge in nanotechology. Polyelectrolytes have been shown to stabilise nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. The conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interac- tions. We develop a simple mean-field model and show that ion-image attraction is a significant effect for adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes based on their electronic structure which in turn modifies the ion-image attraction.

cond-mat.soft↗

arXiv2017

Optimal design of experiments by combining coarse and fine measurements

In many contexts it is extremely costly to perform enough high quality experimental measurements to accurately parameterize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.

physics.data-an↗

arXiv2017

Local pore size correlations determine flow distributions in porous media

The relationship between the microstructure of a porous medium and the observed flow distribution is still a puzzle. We resolve it with an analytical model, where the local correlations between adjacent pores, which determine the distribution of flows propagated from one pore downstream, predict the flow distribution. Numerical simulations of a two-dimensional porous medium verify the model and clearly show the transition of flow distributions from $δ$-function-like via Gaussians to exponential with increasing disorder. Comparison to experimental data further verifies our numerical approach.

physics.flu-dyn↗

arXiv2017

Physical and geometric constraints explain the labyrinth-like shape of the nasal cavity

The nasal cavity is a vital component of the respiratory system that heats and humidifies inhaled air in all vertebrates. Despite this common function, the shapes of nasal cavities vary widely across animals. To understand this variability, we here connect nasal geometry to its function by theoretically studying the airflow and the associated scalar exchange that describes heating and humidification. We find that optimal geometries, which have minimal resistance for a given exchange efficiency, have a constant gap width between their side walls, but their overall shape is restricted only by the geometry of the head. Our theory explains the geometric variations of natural nasal cavities quantitatively and we hypothesize that the trade-off between high exchange efficiency and low resistance to airflow is the main driving force shaping the nasal cavity. Our model further explains why humans, whose nasal cavities evolved to be smaller than expected for their size, become obligate oral breathers in aerobically challenging situations.

physics.bio-ph↗

arXiv2017

Hot Particles Attract in a Cold Bath

Controlling interactions out of thermodynamic equilibrium is crucial for designing addressable and functional self-organizing structures. These active interactions also underpin collective behavior in biological systems. Here we study a general setting of active particles in a bath of passive particles, and demonstrate a novel mechanism for long range attraction between active particles. The mechanism operates when the translational persistence length of the active particle motion is smaller than the particle diameter. In this limit, the system reduces to particles of higher diffusivity ("hot" particles) in a bath of particles with lower diffusivity ("cold" particles). This attractive interaction arises as a hot particle pushes cold particles away to create a large hole around itself, and the holes interact via a depletion-like attraction. Strikingly, the interaction range is more than an order of magnitude larger than the particle radius, well beyond the range of conventional depletion force. Although the mechanism occurs outside the parameter regime of typical biological swimmers, the mechanism could be realized in the laboratory.

cond-mat.soft↗

arXiv2016

Pruning to Increase Taylor Dispersion in Physarum polycephalum Networks

How do the topology and geometry of a tubular network affect the spread of particles within fluid flows? We investigate patterns of effective dispersion in the hierarchical, biological transport network formed by Physarum polycephalum. We demonstrate that a change in topology - pruning in the foraging state - causes a large increase in effective dispersion throughout the network. By comparison, changes in the hierarchy of tube radii result in smaller and more localized differences. Pruned networks capitalize on Taylor dispersion to increase the dispersion capability.

physics.bio-ph↗

arXiv2016

Mutation at Expanding Front of Self-Replicating Colloidal Clusters

We construct a scheme for self-replicating square clusters of particles in two spatial dimensions, and validate it with computer simulations in a finite-temperature heat bath. We find that the self-replication reactions propagate through the bath in the form of Fisher waves. Our model reflects existing colloidal systems, but is simple enough to allow simulation of many generations and thereby the first study of evolutionary dynamics in an artificial system. By introducing spatially localized mutations in the replication rules, we show that the mutated cluster population can survive and spread with the expanding front in circular sectors of the colony.

cond-mat.soft↗

arXiv2016

Designing steep, sharp patterns on uniformly ion-bombarded surfaces

We propose and experimentally test a method to fabricate patterns of steep, sharp features on surfaces, by exploiting the nonlinear dynamics of uniformly ion bombarded surfaces. We show via theory, simulation, and experiment, that the steepest parts of the surface evolve as one-dimensional curves which move in the normal direction at constant velocity. The curves are a special solution to the nonlinear equations that arises spontaneously whenever the initial patterning on the surface contains slopes larger than a critical value; mathematically they are traveling waves (shocks) that have the special property of being undercompressive. We derive the evolution equation for the curves by considering long-wavelength perturbations to the one-dimensional traveling wave, using the unusual boundary conditions required for an undercompressive shock, and we show this equation accurately describes the evolution of shapes on surfaces, both in simulations and in experiments. Because evolving a collection of one-dimensional curves is fast, this equation gives a computationally efficient and intuitive method for solving the inverse problem of finding the initial surface so the evolution leads to a desired target pattern. We illustrate this method by solving for the initial surface that will produce a lattice of diamonds connected by steep, sharp ridges, and experimentally demonstrating the evolution of the initial surface into the target pattern.

cond-mat.mtrl-sci↗

arXiv2016

The Information Capacity of Specific Interactions

Specific interactions are a hallmark feature of self-assembly and signal-processing systems in both synthetic and biological settings. Specificity between components may arise from a wide variety of physical and chemical mechanisms in diverse contexts, from DNA hybridization to shape-sensitive depletion interactions. Despite this diversity, all systems that rely on interaction specificity operate under the constraint that increasing the number of distinct components inevitably increases off-target binding. Here we introduce `capacity', the maximal information encodable using specific interactions, to compare specificity across diverse experimental systems, and to compute how specificity changes with physical parameters. Using this framework, we find that `shape'-coding of interactions has higher capacity than chemical (`color') coding because the strength of off-target binding is strongly sublinear in binding site size for shapes while being linear for colors. We also find that different specificity mechanisms, such as shape and color, can be combined in a synergistic manner, giving a capacity greater than the sum of the parts.

cond-mat.soft↗

arXiv2016

Receptor arrays optimized for natural odor statistics

Natural odors typically consist of many molecules at different concentrations. It is unclear how the numerous odorant molecules and their possible mixtures are discriminated by relatively few olfactory receptors. Using an information-theoretic model, we show that a receptor array is optimal for this task if it achieves two possibly conflicting goals: (i) each receptor should respond to half of all odors and (ii) the response of different receptors should be uncorrelated when averaged over odors presented with natural statistics. We use these design principles to predict statistics of the affinities between receptors and odorant molecules for a broad class of odor statistics. We also show that optimal receptor arrays can be tuned to either resolve concentrations well or distinguish mixtures reliably. Finally, we use our results to predict properties of experimentally measured receptor arrays. Our work can thus be used to better understand natural olfaction and it also suggests ways to improve artificial sensor arrays.

physics.bio-ph↗

arXiv2015

Two-Dimensional Clusters of Colloidal Spheres: Ground States, Excited States, and Structural Rearrangements

We study experimentally what is arguably the simplest yet non-trivial colloidal system: two-dimensional clusters of 6 spherical particles bound by depletion interactions. These clusters have multiple, degenerate ground states whose equilibrium distribution is determined by entropic factors, principally the symmetry. We observe the equilibrium rearrangements between ground states as well as all of the low-lying excited states. In contrast to the ground states, the excited states have soft modes and low symmetry, and their occupation probabilities depend on the size of the configuration space reached through internal degrees of freedom, as well as a single "sticky parameter" encapsulating the depth and curvature of the potential. Using a geometrical model that accounts for the entropy of the soft modes and the diffusion rates along them, we accurately reproduce the measured rearrangement rates. The success of this model, which requires no fitting parameters or measurements of the potential, shows that the free-energy landscape of colloidal systems and the dynamics it governs can be understood geometrically.

cond-mat.soft↗

arXiv2014

Multifarious Assembly Mixtures: Systems Allowing Retrieval of Diverse Stored Structures

Self-assembly materials are traditionally designed so that molecular or meso-scale components form a single kind of large structure. Here, we propose a scheme to create "multifarious assembly mixtures", which self-assemble many different large structures from a set of shared components. We show that the number of multifarious structures stored in the solution of components increases rapidly with the number of different types of components. Yet, each stored structure can be retrieved by tuning only a few parameters, the number of which is only weakly dependent on the size of the assembled structure. Implications for artificial and biological self-assembly are discussed.

cond-mat.dis-nn↗

arXiv2012

A geometrical approach to computing free energy landscapes from short-ranged potentials

Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such systems as the range of the potential goes to zero. In this limit, the landscape is entirely defined by geometrical manifolds, plus a single control parameter. These manifolds are fundamental objects that do not depend on the details of the interaction potential, and provide the starting point from which any quantity characterizing the system -- equilibrium or non-equilibrium -- can be computed for arbitrary potentials. To consider dynamical quantities we compute the asymptotic limit of the Fokker-Planck equation, and show that it becomes restricted to the low-dimensional manifolds connected by "sticky" boundary conditions. To illustrate our theory, we compute the low-dimensional manifolds for n<=8 identical particles, providing a complete description of the lowest-energy parts of the landscape including floppy modes with up to 2 internal degrees of freedom. The results can be directly tested on colloidal clusters. This limit is a novel approach for understanding energy landscapes, and our hope is that it can also provide insight into finite-range potentials.

math-ph↗

arXiv2012

Development of Knife-Edge Ridges on Ion-Bombarded Surfaces

We demonstrate in both laboratory and numerical experiments that ion bombardment of a modestly sloped surface can create knife-edge like ridges with extremely high slopes. Small pre-fabricated pits expand under ion bombardment, and the collision of two such pits creates knife-edge ridges. Both laboratory and numerical experiments show that the pit propagation speed and the precise shape of the knife edge ridges are universal, independent of initial conditions, as has been predicted theoretically. These observations suggest a novel method of fabrication in which a surface is pre-patterned so that it dynamically evolves to a desired target pattern made of knife-edge ridges.

cond-mat.mtrl-sci↗

arXiv2011

Deriving Finite Sphere Packings

Sphere packing problems have a rich history in both mathematics and physics; yet, relatively few analytical analyses of sphere packings exist, and answers to seemingly simple questions are unknown. Here, we present an analytical method for deriving all packings of n spheres in R^3 satisfying minimal rigidity constraints (>= 3 contacts per sphere and >= 3n-6 total contacts). We derive such packings for n <= 10, and provide a preliminary set of maximal contact packings for 10 < n <= 20. The resultant set of packings has some striking features, among them: (i) all minimally rigid packings for n <= 9 have 3n-6 contacts, (ii) non-rigid packings satisfying minimal rigidity constraints arise for n >= 9, (iii) the number of ground states (i.e. packings with the maximal number of contacts) oscillates with respect to n, (iv) for 10 <= n <= 20 there are only a small number of packings with the maximal number of contacts, and for 10 <= n < 13 these are all commensurate with the HCP lattice. The general method presented here may have applications to other related problems in mathematics, such as the Erdos repeated distance problem and Euclidean distance matrix completion problems.

cond-mat.soft↗

arXiv2011

Skating on a Film of Air: Drops Impacting on a Surface

Drops impacting on a surface are ubiquitous in our everyday experience. This impact is understood within a commonly accepted hydrodynamic picture: it is initiated by a rapid shock and a subsequent ejection of a sheet leading to beautiful splashing patterns. However, this picture ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air must break down as the fluid wets the surface. We suggest that this occurs in a spinodal-like fashion, and causes a very rapid spreading of a wetting front outwards; simultaneously the wetting fluid spreads inward much more slowly, trapping a bubble of air within the drop. Our results show that the dynamics of impacting drops are much more complex than previously thought and exhibit a rich array of unexpected phenomena that require rethinking classical paradigms.

physics.flu-dyn↗

arXiv2011

Algorithm for a microfluidic assembly line

Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical constituents. We illustrate the algorithm by showing that a modified Hele-Shaw cell with 7 controlled flowrates can be designed to construct the entire English alphabet from particles that irreversibly stick to each other.

physics.flu-dyn↗

arXiv2010

MD-Predicted Phase diagrams for Pattern Formation due to Ion Irradiation

Energetic particle irradiation of solids can cause surface ultra-smoothening, self-organized nanoscale pattern formation, or degradation of the structural integrity of nuclear reactor components. Periodic patterns including high-aspect ratio quantum dots, with occasional long-range order and characteristic spacing as small as 7 nm, have stimulated interest in this method as a means of sub-lithographic nanofabrication. Despite intensive research there is little fundamental understanding of the mechanisms governing the selection of smooth or patterned surfaces, and precisely which physical effects cause observed transitions between different regimes has remained a matter of speculation. Here we report the first prediction of the mechanism governing the transition from corrugated surfaces to flatness, using only parameter-free molecular dynamics simulations of single-ion impact induced crater formation as input into a multi-scale analysis, and showing good agreement with experiment. Our results overturn the paradigm attributing these phenomena to the removal of target atoms via sputter erosion. Instead, the mechanism dominating both stability and instability is shown to be the impact-induced redistribution of target atoms that are not sputtered away, with erosive effects being essentially irrelevant. The predictions are relevant in the context of tungsten plasma-facing fusion reactor walls which, despite a sputter erosion rate that is essentially zero, develop, under some conditions, a mysterious nanoscale topography leading to surface degradation. Our results suggest that degradation processes originating in impact-induced target atom redistribution effects may be important, and hence that an extremely low sputter erosion rate is an insufficient design criterion for morphologically stable solid surfaces under energetic particle irradiation.

cond-mat.mtrl-sci↗