7,484 research outputs found
The speed of range shifts in fragmented landscapes
Peer reviewedPublisher PD
The difficulty of folding self-folding origami
Why is it difficult to refold a previously folded sheet of paper? We show
that even crease patterns with only one designed folding motion inevitably
contain an exponential number of `distractor' folding branches accessible from
a bifurcation at the flat state. Consequently, refolding a sheet requires
finding the ground state in a glassy energy landscape with an exponential
number of other attractors of higher energy, much like in models of protein
folding (Levinthal's paradox) and other NP-hard satisfiability (SAT) problems.
As in these problems, we find that refolding a sheet requires actuation at
multiple carefully chosen creases. We show that seeding successful folding in
this way can be understood in terms of sub-patterns that fold when cut out
(`folding islands'). Besides providing guidelines for the placement of active
hinges in origami applications, our results point to fundamental limits on the
programmability of energy landscapes in sheets.Comment: 8 pages, 5 figure
Field theory for a reaction-diffusion model of quasispecies dynamics
RNA viruses are known to replicate with extremely high mutation rates. These
rates are actually close to the so-called error threshold. This threshold is in
fact a critical point beyond which genetic information is lost through a
second-order phase transition, which has been dubbed the ``error catastrophe.''
Here we explore this phenomenon using a field theory approximation to the
spatially extended Swetina-Schuster quasispecies model [J. Swetina and P.
Schuster, Biophys. Chem. {\bf 16}, 329 (1982)], a single-sharp-peak landscape.
In analogy with standard absorbing-state phase transitions, we develop a
reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model.
The field theory representation of the reaction-diffusion system is
constructed. The proposed field theory belongs to the same universality class
than a conserved reaction-diffusion model previously proposed [F. van Wijland
{\em et al.}, Physica A {\bf 251}, 179 (1998)]. From the field theory, we
obtain the full set of exponents that characterize the critical behavior at the
error threshold. Our results present the error catastrophe from a new point of
view and suggest that spatial degrees of freedom can modify several mean field
predictions previously considered, leading to the definition of characteristic
exponents that could be experimentally measurable.Comment: 13 page
Micrographia of the twenty-first century: from camera obscura to 4D microscopy
In this paper, the evolutionary and revolutionary developments of microscopic imaging are overviewed with a perspective on origins. From Alhazen’s camera obscura, to Hooke and van Leeuwenhoek’s two-dimensional optical micrography, and on to three- and four-dimensional (4D) electron microscopy, these developments over a millennium have transformed humans’ scope of visualization. The changes in the length and time scales involved are unimaginable, beginning with the visible shadows of candles at the centimetre and second scales, and ending with invisible atoms with space and time dimensions of sub-nanometre and femtosecond. With these advances it has become possible to determine the structures of matter and to observe their elementary dynamics as they unfold in real time. Such observations provide the means for visualizing materials behaviour and biological function, with the aim of understanding emergent phenomena in complex systems
4D ultrafast electron diffraction, crystallography, and microscopy
In this review, we highlight the progress made in the development of 4D ultrafast electron diffraction (UED), crystallography (UEC), and microscopy (UEM) with a focus on concepts, methodologies, and prototypical applications. The joint atomic-scale resolutions in space and time, and sensitivity reached, make it possible to determine complex transient structures and assemblies in different phases. These applications include studies of isolated chemical reactions (molecular beams), interfaces, surfaces and nanocrystals, self-assembly, and 2D crystalline fatty-acid bilayers. In 4D UEM, we are now able, using timed, single-electron packets, to image nano-to-micro scale structures of materials and biological cells. Future applications of these methods are foreseen across areas of physics, chemistry, and biology
Self-assembly scenarios of patchy colloidal particles
The rapid progress in precisely designing the surface decoration of patchy
colloidal particles offers a new, yet unexperienced freedom to create building
entities for larger, more complex structures in soft matter systems. However,
it is extremely difficult to predict the large variety of ordered equilibrium
structures that these particles are able to undergo under the variation of
external parameters, such as temperature or pressure. Here we show that, by a
novel combination of two theoretical tools, it is indeed possible to predict
the self-assembly scenario of patchy colloidal particles: on one hand, a
reliable and efficient optimization tool based on ideas of evolutionary
algorithms helps to identify the ordered equilibrium structures to be expected
at T = 0; on the other hand, suitable simulation techniques allow to estimate
via free energy calculations the phase diagram at finite temperature. With
these powerful approaches we are able to identify the broad variety of emerging
self-assembly scenarios for spherical colloids decorated by four patches and we
investigate and discuss the stability of the crystal structures on modifying in
a controlled way the tetrahedral arrangement of the patches.Comment: 11 pages, 7 figures, Soft Matter Communication (accepted
Spatial multi-level interacting particle simulations and information theory-based error quantification
We propose a hierarchy of multi-level kinetic Monte Carlo methods for
sampling high-dimensional, stochastic lattice particle dynamics with complex
interactions. The method is based on the efficient coupling of different
spatial resolution levels, taking advantage of the low sampling cost in a
coarse space and by developing local reconstruction strategies from
coarse-grained dynamics. Microscopic reconstruction corrects possibly
significant errors introduced through coarse-graining, leading to the
controlled-error approximation of the sampled stochastic process. In this
manner, the proposed multi-level algorithm overcomes known shortcomings of
coarse-graining of particle systems with complex interactions such as combined
long and short-range particle interactions and/or complex lattice geometries.
Specifically, we provide error analysis for the approximation of long-time
stationary dynamics in terms of relative entropy and prove that information
loss in the multi-level methods is growing linearly in time, which in turn
implies that an appropriate observable in the stationary regime is the
information loss of the path measures per unit time. We show that this
observable can be either estimated a priori, or it can be tracked
computationally a posteriori in the course of a simulation. The stationary
regime is of critical importance to molecular simulations as it is relevant to
long-time sampling, obtaining phase diagrams and in studying metastability
properties of high-dimensional complex systems. Finally, the multi-level nature
of the method provides flexibility in combining rejection-free and null-event
implementations, generating a hierarchy of algorithms with an adjustable number
of rejections that includes well-known rejection-free and null-event
algorithms.Comment: 34 page
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