123 research outputs found
Anomalous Microfluidic Phonons Induced by the Interplay of Hydrodynamic Screening and Incompressibility
We investigate the acoustic normal modes ("phonons") of a 1D microfluidic
droplet crystal at the crossover between 2D flow and confined 1D plug flow. The
unusual phonon spectra of the crystal, which arise from long-range hydrodynamic
interactions, change anomalously under confinement. The boundaries induce
weakening and screening of the interactions, but when approaching the 1D limit
we measure a marked increase in the crystal sound velocity, a sign of
interaction strengthening. This non-monotonous behavior of the phonon spectra
is explained theoretically by the interplay of screening and plug flow.Comment: http://link.aps.org/doi/10.1103/PhysRevLett.99.124502
http://www.weizmann.ac.il/complex/tlusty/papers/PhysRevLett2007.pd
Dynamic Fluctuation Phenomena in Double Membrane Films
Dynamics of double membrane films is investigated in the long-wavelength
limit including the overdamped squeezing mode. We demonstrate that thermal
fluctuations essentially modify the character of the mode due to its nonlinear
coupling to the transversal shear hydrodynamic mode. The corresponding Green
function acquires as a function of the frequency a cut along the imaginary
semi-axis. Fluctuations lead to increasing the attenuation of the squeezing
mode it becomes larger than the `bare' value.Comment: 7 pages, Revte
Numerical Observation of a Tubular Phase in Anisotropic Membranes
We provide the first numerical evidence for the existence of a tubular phase,
predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes
without self-avoidance. Incorporating anisotropy into the bending rigidity of a
simple model of a tethered membrane with free boundary conditions, we show that
the model indeed has two phase transitions corresponding to the flat-to-tubular
and tubular-to-crumpled transitions. For the tubular phase we measure the Flory
exponent and the roughness exponent . We find
and , which are in reasonable agreement with the theoretical
predictions of RT --- and .Comment: 8 pages, LaTeX, REVTEX, final published versio
Fluid-membrane tethers: minimal surfaces and elastic boundary layers
Thin cylindrical tethers are common lipid bilayer membrane structures,
arising in situations ranging from micromanipulation experiments on artificial
vesicles to the dynamic structure of the Golgi apparatus. We study the shape
and formation of a tether in terms of the classical soap-film problem, which is
applied to the case of a membrane disk under tension subject to a point force.
A tether forms from the elastic boundary layer near the point of application of
the force, for sufficiently large displacement. Analytic results for various
aspects of the membrane shape are given.Comment: 12 page
Instability of Myelin Tubes under Dehydration: deswelling of layered cylindrical structures
We report experimental observations of an undulational instability of myelin
figures. Motivated by this, we examine theoretically the deformation and
possible instability of concentric, cylindrical, multi-lamellar membrane
structures. Under conditions of osmotic stress (swelling or dehydration), we
find a stable, deformed state in which the layer deformation is given by \delta
R ~ r^{\sqrt{B_A/(hB)}}, where B_A is the area compression modulus, B is the
inter-layer compression modulus, and h is the repeat distance of layers. Also,
above a finite threshold of dehydration (or osmotic stress), we find that the
system becomes unstable to undulations, first with a characteristic wavelength
of order \sqrt{xi d_0}, where xi is the standard smectic penetration depth and
d_0 is the thickness of dehydrated region.Comment: 5 pages + 3 figures [revtex 4
Algorithms in nature: the convergence of systems biology and computational thinking
Biologists rely on computational methods to analyze and integrate large data sets, while several computational methods were inspired by the high-level design principles of biological systems. This Perspectives discusses the recent convergence of these two ways of thinking
Single Molecule Statistics and the Polynucleotide Unzipping Transition
We present an extensive theoretical investigation of the mechanical unzipping
of double-stranded DNA under the influence of an applied force. In the limit of
long polymers, there is a thermodynamic unzipping transition at a critical
force value of order 10 pN, with different critical behavior for homopolymers
and for random heteropolymers. We extend results on the disorder-averaged
behavior of DNA's with random sequences to the more experimentally accessible
problem of unzipping a single DNA molecule. As the applied force approaches the
critical value, the double-stranded DNA unravels in a series of discrete,
sequence-dependent steps that allow it to reach successively deeper energy
minima. Plots of extension versus force thus take the striking form of a series
of plateaus separated by sharp jumps. Similar qualitative features should
reappear in micromanipulation experiments on proteins and on folded RNA
molecules. Despite their unusual form, the extension versus force curves for
single molecules still reveal remnants of the disorder-averaged critical
behavior. Above the transition, the dynamics of the unzipping fork is related
to that of a particle diffusing in a random force field; anomalous,
disorder-dominated behavior is expected until the applied force exceeds the
critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure
Sublinear Algorithms for Approximating String Compressibility
We raise the question of approximating the compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and a variant of Lempel-Ziv (LZ77), and present sublinear algorithms for approximating compressibility with respect to both schemes. We also give several lower bounds that show that our algorithms for both schemes cannot be improved significantly.
Our investigation of LZ77 yields results whose interest goes beyond the initial questions we set out to study. In particular, we prove combinatorial structural lemmas that relate the compressibility of a string with respect to LZ77 to the number of distinct short substrings contained in it (its ℓth subword complexity , for small ℓ). In addition, we show that approximating the compressibility with respect to LZ77 is related to approximating the support size of a distribution.National Science Foundation (U.S.) (Award CCF-1065125)National Science Foundation (U.S.) (Award CCF-0728645)Marie Curie International Reintegration Grant PIRG03-GA-2008-231077Israel Science Foundation (Grant 1147/09)Israel Science Foundation (Grant 1675/09
Phonons in a one-dimensional microfluidic crystal
The development of a general theoretical framework for describing the
behaviour of a crystal driven far from equilibrium has proved difficult1.
Microfluidic crystals, formed by the introduction of droplets of immiscible
fluid into a liquid-filled channel, provide a convenient means to explore and
develop models to describe non-equilibrium dynamics2, 3, 4, 5, 6, 7, 8, 9, 10,
11. Owing to the fact that these systems operate at low Reynolds number (Re),
in which viscous dissipation of energy dominates inertial effects, vibrations
are expected to be over-damped and contribute little to their dynamics12, 13,
14. Against such expectations, we report the emergence of collective normal
vibrational modes (equivalent to acoustic 'phonons') in a one-dimensional
microfluidic crystal of water-in-oil droplets at Reapprox10-4. These phonons
propagate at an ultra-low sound velocity of approx100 mum s-1 and frequencies
of a few hertz, exhibit unusual dispersion relations markedly different to
those of harmonic crystals, and give rise to a variety of crystal instabilities
that could have implications for the design of commercial microfluidic systems.
First-principles theory shows that these phonons are an outcome of the
symmetry-breaking flow field that induces long-range inter-droplet
interactions, similar in nature to those observed in many other systems
including dusty plasma crystals15, 16, vortices in superconductors17, 18,
active membranes19 and nucleoprotein filaments20.Comment: https://www.weizmann.ac.il/complex/tlusty/papers/NaturePhys2006.pd
Conformational Proofreading: The Impact of Conformational Changes on the Specificity of Molecular Recognition
To perform recognition, molecules must locate and specifically bind their targets within a noisy biochemical environment with many look-alikes. Molecular recognition processes, especially the induced-fit mechanism, are known to involve conformational changes. This raises a basic question: Does molecular recognition gain any advantage by such conformational changes? By introducing a simple statistical-mechanics approach, we study the effect of conformation and flexibility on the quality of recognition processes. Our model relates specificity to the conformation of the participant molecules and thus suggests a possible answer: Optimal specificity is achieved when the ligand is slightly off target; that is, a conformational mismatch between the ligand and its main target improves the selectivity of the process. This indicates that deformations upon binding serve as a conformational proofreading mechanism, which may be selected for via evolution
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