scholarly journals Minimal Energy Configurations of Finite Molecular Arrays

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 158
Author(s):  
Pablo Negrón-Marrero ◽  
Melissa López-Serrano
Keyword(s):  
Minimum Energy ◽  
Triangular Array ◽  
Intermolecular Potential ◽  
Regular Tetrahedron ◽  
Stable States ◽  
Homogeneous Solutions ◽  
Multiple Stable States ◽  
Repulsive Forces ◽  
Secondary Bifurcations ◽  
Energy Configurations

In this paper, we consider the problem of characterizing the minimum energy configurations of a finite system of particles interacting between them due to attractive or repulsive forces given by a certain intermolecular potential. We limit ourselves to the cases of three particles arranged in a triangular array and that of four particles in a tetrahedral array. The minimization is constrained to a fixed area in the case of the triangular array, and to a fixed volume in the tetrahedral case. For a general class of intermolecular potentials we give conditions for the homogeneous configuration (either an equilateral triangle or a regular tetrahedron) of the array to be stable that is, a minimizer of the potential energy of the system. To determine whether or not there exist other stable states, the system of first-order necessary conditions for a minimum is treated as a bifurcation problem with the area or volume variable as the bifurcation parameter. Because of the symmetries present in our problem, we can apply the techniques of equivariant bifurcation theory to show that there exist branches of non-homogeneous solutions bifurcating from the trivial branch of homogeneous solutions at precisely the values of the parameter of area or volume for which the homogeneous configuration changes stability. For the triangular array, we construct numerically the bifurcation diagrams for both a Lennard–Jones and Buckingham potentials. The numerics show that there exist non-homogeneous stable states, multiple stable states for intervals of values of the area parameter, and secondary bifurcations as well.

Trapped liquid drop in a microchannel: Multiple stable states

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
Zhengjia Wang ◽  
Cheng-Chung Chang ◽  
Siang-Jie Hong ◽  
Yu-Jane Sheng ◽  
Heng-Kwong Tsao
Keyword(s):  
Liquid Drop ◽  
Stable States ◽  
Multiple Stable States

scholarly journals Population dynamics of synthetic Terraformation motifs

2016 ◽  
Author(s):  
Ricard V. Solé ◽  
Raúl Montañez ◽  
Salvador Duran Nebreda ◽  
Daniel Rodriguez-Amor ◽  
Blai Vidiella ◽  
...  
Keyword(s):  
Habitat Degradation ◽  
Ecological Engineering ◽  
Ecological Interactions ◽  
Stable States ◽  
Population Extinction ◽  
Intensive Exploitation ◽  
Engineering Designs ◽  
Synthetic Organisms ◽  
Multiple Stable States ◽  
Catastrophic Shifts

Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation, and human-driven habitat degradation. Such threats are pushing ecosystems to the brink of collapse. Because of a general presence of multiple stable states, including states involving population extinction, and due to intrinsic nonlinearities associated with feedback loops, collapse can occur in a catastrophic manner. Such catastrophic shifts have been suggested to pervade many of the future transitions affecting ecosystems at many different scales. Many studies have tried to delineate potential warning signals predicting such ongoing shifts but little is known about how such transitions might be effectively prevented. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. Four classes of such ecological engineering designs orTerraformation motifshave been defined in a qualitative way. Here we develop the simplest mathematical models associated with these motifs, defining the expected stability conditions and domains where the motifs shall properly work.

Modelling of interactions in solutions: alkali halides in DMSO

1979 ◽  
Vol 57 (5) ◽  
pp. 538-551 ◽  
Author(s):  
Peeter Kruus ◽  
Barbara E. Poppe
Keyword(s):  
Reasonable Agreement ◽  
Minimum Energy ◽  
Alkali Halides ◽  
Ion Pair ◽  
Point Of View ◽  
Ion Solvation ◽  
Solvation Energies ◽  
Solvent Molecules ◽  
A Charge ◽  
Energy Configurations

A model of solutions of alkali halides in DMSO is developed. Each ion is described by a radius, a charge, a polarizability, and an exponential repulsion parameter. Each molecule is described by a polarizability, charges, 6-12 energy parameters, and 6-12 distance parameters centered on each of the 10 atoms in the molecule. The model is applied to calculate (i) the vaporization energy of solvent molecules, (ii) single ion solvation energies and configurations of the solvating molecules, and (iii) the energy as a function of reaction coordinate for the formation of an ion pair. The energies and configurations are obtained by allowing the systems to relax to minimum energy configurations by allowing motion of the molecules. The results of (i) give a vaporization energy 60% of the experimental. The results of (ii) give solvation energies in reasonable agreement with the experimental, and configurations which are reasonable from the point of view of mobilities of ions. The results of (iii) show the presence of a distinct solvent separated ion pair which actually has an energy lower than the contact ion pair. Advantages and problems involved in using this approach to model solutions are discussed.

scholarly journals Multiple stable states of tree cover in a global land surface model due to a fire-vegetation feedback

2016 ◽  
Vol 43 (12) ◽  
pp. 6324-6331 ◽  
Author(s):  
G. Lasslop ◽  
V. Brovkin ◽  
C. H. Reick ◽  
S. Bathiany ◽  
S. Kloster
Keyword(s):  
Land Surface ◽  
Land Surface Model ◽  
Tree Cover ◽  
Surface Model ◽  
Stable States ◽  
Vegetation Feedback ◽  
Global Land ◽  
Multiple Stable States

scholarly journals Clusters, columns, and lamellae—minimum energy configurations in core softened potentials

Soft Matter ◽  
2008 ◽  
Vol 4 (7) ◽  
pp. 1396 ◽  
Author(s):  
Gernot J. Pauschenwein ◽  
Gerhard Kahl
Keyword(s):  
Minimum Energy ◽  
Energy Configurations

scholarly journals How adaptive immunity constrains the composition and fate of large bacterial populations

2018 ◽  
Vol 115 (32) ◽  
pp. E7462-E7468 ◽  
Author(s):  
Madeleine Bonsma-Fisher ◽  
Dominique Soutière ◽  
Sidhartha Goyal
Keyword(s):  
Stochastic Dynamics ◽  
Phage Genome ◽  
Population Level ◽  
Abundance Distribution ◽  
Stable States ◽  
Bacterial Populations ◽  
Multiple Stable States ◽  
Time Invariant ◽  
Microbial Systems ◽  
Rank Abundance

Features of the CRISPR-Cas system, in which bacteria integrate small segments of phage genome (spacers) into their DNA to neutralize future attacks, suggest that its effect is not limited to individual bacteria but may control the fate and structure of whole populations. Emphasizing the population-level impact of the CRISPR-Cas system, recent experiments show that some bacteria regulate CRISPR-associated genes via the quorum sensing (QS) pathway. Here we present a model that shows that from the highly stochastic dynamics of individual spacers under QS control emerges a rank-abundance distribution of spacers that is time invariant, a surprising prediction that we test with dynamic spacer-tracking data from literature. This distribution depends on the state of the competing phage–bacteria population, which due to QS-based regulation may coexist in multiple stable states that vary significantly in their phage-to-bacterium ratio, a widely used ecological measure to characterize microbial systems.

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