45 research outputs found
Stability of ecosystems enhanced by species-interaction constraints
Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures-a constant row sum in the interaction matrix-prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse-a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure-limiting the total interactions for each species-is biologically plausible
Using the uncertainty principle to design simple interactions for targeted self-assembly
We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification is achieved by a combination of heat kernel smoothing and Gaussian screening of the interaction potential in real and reciprocal space. We use this method to analytically design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The derived interactions are simple enough to narrow the gap between theory and experimental implementation of theory based designed self-assembling materials
Chiral surfaces self-assembling in one-component systems with isotropic interactions
We show that chiral symmetry can be broken spontaneously in one-component
systems with isotropic interactions, i.e. many-particle systems having maximal
a priori symmetry. This is achieved by designing isotropic potentials that lead
to self-assembly of chiral surfaces. We demonstrate the principle on a simple
chiral lattice and on a more complex lattice with chiral super-cells. In
addition we show that the complex lattice has interesting melting behavior with
multiple morphologically distinct phases that we argue can be qualitatively
predicted from the design of the interaction.Comment: 4 pages, 4 figure
Novel self-assembled morphologies from isotropic interactions
We present results from particle simulations with isotropic medium range
interactions in two dimensions. At low temperature novel types of aggregated
structures appear. We show that these structures can be explained by
spontaneous symmetry breaking in analytic solutions to an adaptation of the
spherical spin model. We predict the critical particle number where the
symmetry breaking occurs and show that the resulting phase diagram agrees well
with results from particle simulations.Comment: 4 pages, 4 figure
Designing isotropic interactions for self-assembly of complex lattices
We present a direct method for solving the inverse problem of designing
isotropic potentials that cause self-assembly into target lattices. Each
potential is constructed by matching its energy spectrum to the reciprocal
representation of the lattice to guarantee that the desired structure is a
ground state. We use the method to self-assemble complex lattices not
previously achieved with isotropic potentials, such as a snub square tiling and
the kagome lattice. The latter is especially interesting because it provides
the crucial geometric frustration in several proposed spin liquids.Comment: 4 pages, 3 figure
Renormalization of cellular automata and self-similarity
We study self-similarity in one-dimensional probabilistic cellular automata
(PCA) using the renormalization technique. We introduce a general framework for
algebraic construction of renormalization groups (RG) on cellular automata and
apply it to exhaustively search the rule space for automata displaying dynamic
criticality. Previous studies have shown that there exists several exactly
renormalizable deterministic automata. We show that the RG fixed points for
such self-similar CA are unstable in all directions under renormalization. This
implies that the large scale structure of self-similar deterministic elementary
cellular automata is destroyed by any finite error probability. As a second
result we show that the only non-trivial critical PCA are the different
versions of the well-studied phenomenon of directed percolation. We discuss how
the second result supports a conjecture regarding the universality class for
dynamic criticality defined by directed percolation.Comment: 14 pages, 4 figure
Identification of metastable states in peptide's dynamics
A recently developed spectral method for identifying metastable states in Markov chains is used to analyse the conformational dynamics of a four residue peptide Valine-Proline-Alanine-Leucine. We compare our results to empirically defined conformational states and show that the found metastable states correctly reproduce the conformational dynamics of the system
Universality of striped morphologies
We present a method for predicting the low-temperature behavior of spherical
and Ising spin models with isotropic potentials. For the spherical model the
characteristic length scales of the ground states are exactly determined but
the morphology is shown to be degenerate with checkerboard patterns, stripes
and more complex morphologies having identical energy. For the Ising models we
show that the discretization breaks the degeneracy causing striped morphologies
to be energetically favored and therefore they arise universally as ground
states to potentials whose Hankel transforms have nontrivial minima.Comment: 4 pages, 4 figure
A method for estimating the interactions in dissipative particle dynamics from particle trajectories
We introduce a method for determining the functional form of the stochastic
and dissipative interactions in a dissipative particle dynamics (DPD) model
from projected phase space trajectories. The DPD model is viewed as a coarse
graining of a detailed dynamics that displays a clear time scale separation.
Based on the Mori-Zwanzig projection operator method we derive a consistency
equation for the stochastic interaction in DPD. The consistency equation can be
solved by an iterative boot strapping procedure. Combined with standard
techniques for estimating the conservative interaction, our method makes it
possible to reconstruct all the forces in a coarse grained DPD model. We
demonstrate how the method works by recreating the interactions in a DPD model
from its phase space trajectory. Furthermore, we discuss how our method can be
used in realistic systems with finite time scale separation
On the microscopic foundation of dissipative particle dynamics
Mesoscopic particle based fluid models, such as dissipative particle
dynamics, are usually assumed to be coarse-grained representations of an
underlying microscopic fluid. A fundamental question is whether there exists a
map from microscopic particles in these systems to the corresponding
coarse-grained particles, such that the coarse-grained system has the same bulk
and transport properties as the underlying system. In this letter, we
investigate the coarse-graining of microscopic fluids using a Voronoi type
projection that has been suggested in several studies. The simulations show
that the projection fails in defining coarse-grained particles that have a
physically meaningful connection to the microscopic fluid. In particular, the
Voronoi projection produces identical coarse-grained equilibrium properties
when applied to systems with different microscopic interactions and different
bulk properties.Comment: First revisio