arXiv subjects

Martin Nilsson Jacobi

Publications and source records attributed to Martin Nilsson Jacobi.

At least 19 recordsLinked to original sources

arXiv2021

Complex ecological communities and the emergence of island species area relationships

It has been a century since the species-area relationship (SAR) was first proposed as a power law to explain how species richness scales with area. There have been many attempts to explain the origin of this predominant form. Apart from the power law, numerous empirical studies also report a semi-log form of the SAR, but very few have addressed its incidence. In this work, we test whether these relationships could emerge from the assembly of large random communities on island-like systems. We reformulate the generalized Lotka-Volterra model by introducing an area parameter that determines the species richness of the assembled communities. Our analysis demonstrates that the two most widely reported relationship forms can emerge due to differences in immigration rates and skewness towards weak interactions. We particularly highlight the incidence of the semi-log SAR for low immigration rates from a source pool, which is consistent with several previous empirical studies. The two SAR forms might show good fits to data over a large span of areas but a power-law overestimates species richness on smaller islands in remote archipelagoes.

q-bio.PE↗

arXiv2014

A Design Path for Hierarchical Self-Assembly of Patchy Colloids

Patchy colloids are promising candidates for building blocks in directed self-assembly. To be successful the surface patterns need to both be simple enough to be synthesized, while feature-rich enough to cause the colloids to self-assemble into desired structures. Achieving this is a challenge for traditional synthesis methods. Recently it has been suggested that the surface pattern themselves can be made to self-assemble. In this paper we show that a wide range of functional structures can be made to self-assemble using this approach. More generally we present a design path for hierarchical targeted self-assembly of patchy colloids. At the level of the surface structure, we use a predictive method utilizing universality of patterns of stripes and spots, coupled with stoichiometric constraints, to cause highly specific and functional patterns to self-assemble on spherical surfaces. We use a minimalistic model of an alkanethiol on gold as a model system and demonstrate that, even with limited control over the interaction between surface constituents, we can obtain patterns that causes the colloids themselves to self-assemble into various complex geometric structures. We demonstrate how variations of the same design path cause in-silico self-assembly of strings, membranes, cubic and spherical aggregates, as well as various crystalline patterns.

cond-mat.soft↗

arXiv2013

Predicting self-assembled patterns on spheres with multi-component coatings

Interactions between the components in many-body systems can give rise to spontaneous formation of complex structures. Usually very little is known about the connection between the interactions and the resulting structure. Here we present a theory for self-assembling pattern formation in multi-component systems, formulated as an analytic technique that predicts morphologies directly from the interactions in an effective model. As a demonstration we apply the method to a model of alkanethiols on spherical gold particles, successfully predicting its morphologies and transitions as a function of the interaction parameters. This system is interesting because it has been suggested to provide an effective route to produce patchy colloids.

cond-mat.soft↗

arXiv2012

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. We use this method to design isotropic interactions for self-assembly of complex lattices and of materials with functional properties. The interactions we derive are significantly simpler than those previously published, and it is realistic to discuss explicit experimental implementation of the designed self-assembling components.

cond-mat.soft↗

arXiv2012

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.

cond-mat.mtrl-sci↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

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.

cond-mat.mtrl-sci↗

arXiv2011

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.

cond-mat.soft↗

arXiv2011

A mixed basis approach in the SGP-limit

A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s^2) time, where s denotes the number of boundary elements. Several approximate eigenvalues and eigenfunctions to the diffusion operator are retrieved. The method is applied to 1-D and 2-D systems with Neumann boundary conditions.

physics.comp-ph↗

arXiv2010

Determining interaction rules in animal swarms

In this paper we introduce a method for determining local interaction rules in animal swarms. The method is based on the assumption that the behavior of individuals in a swarm can be treated as a set of mechanistic rules. The principal idea behind the technique is to vary parameters that define a set of hypothetical interactions to minimize the deviation between the forces estimated from observed animal trajectories and the forces resulting from the assumed rule set. We demonstrate the method by reconstructing the interaction rules from the trajectories produced by a computer simulation.

physics.bio-ph↗

arXiv2010

A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains

A spectral method for identifying lumping in large Markov chains is presented. Identification of meta stable states is treated as a special case. The method is based on spectral analysis of a self-adjoint matrix that is a function of the original transition matrix. It is demonstrated that the technique is more robust than existing methods when applied to noisy non-reversible Markov chains.

math.NA↗

arXiv2009

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.

cond-mat.soft↗

arXiv2009

Bottom-up derivation of an effective thermostat for united atoms simulations of water

In this article we derive the effective pairwise interactions in a Langevin type united atoms model of water. The interactions are determined from the trajectories of a detailed molecular dynamics simulation of simple point charge water. A standard method is used for estimating the conservative interaction, whereas a new "bottom-up" method is used to determine the effective dissipative and stochastic interactions. We demonstrate that, when compared to the standard united atoms model, the transport properties of the coarse-grained model is significantly improved by the introduction of the derived dissipative and stochastic interactions. The results are compared to a previous study, where a "top-down" approach was used to obtain transport properties consistent with those of the simple point charge water model.

physics.comp-ph↗

arXiv2008

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.

cond-mat.soft↗

arXiv2008

Inference of higher order substitution dynamics by Markov chain lumping

We apply Markov chain lumping techniques to aggregate codons from an empirical substitution matrix. The standard genetic code as well as higher order amino acid substitution groups are identified. Since the aggregates are derived from first principles they do not rely on system dependent assumptions made beforehand, e.g. regarding criteria on what should constitute an amino acid group. We therefore argue that the acquired aggregations more accurately capture the multi-level structure of the substitution dynamics than alternative techniques.

q-bio.QM↗

arXiv2008

A dual eigenvector condition for strong lumpability of Markov chains

Necessary and sufficient conditions for identifying strong lumpability in Markov chains are presented. We show that the states in a lump necessarily correspond to identical elements in eigenvectors of the dual transition matrix. If there exist as many dual eigenvectors that respect the necessary condition as there are lumps in the aggregation, then the condition is also sufficient. The result is demonstrated with two simple examples.

math.PR↗

arXiv2008

Effective thermostat induced by coarse-graining of SPC water

We investigate how the transport properties of a united atoms fluid with a dissipative particle dynamics thermostat depend on the functional form and magnitude of both the conservative and the stochastic interactions. We demonstrate how the thermostat strongly affects the hydrodynamics, especially diffusion, viscosity, and local escape times. As model system we use SPC water, from which projected trajectories are used to determine the effective interactions in the united atoms model. The simulation results support our argument that the thermostat should be viewed as an integral part of the coarse-grained dynamics, rather than a tool for approaching thermal equilibrium. As our main result we show that the united atoms model with the adjusted effective interactions approximately reproduce the diffusion constant and the viscosity of the underlying detailed SPC water model.

physics.chem-ph↗