scholarly journals MONTE CARLO SIMULATION OF THE RISE AND THE FALL OF LANGUAGES

2005 ◽  
Vol 16 (05) ◽  
pp. 781-787 ◽  
Author(s):  
CHRISTIAN SCHULZE ◽  
DIETRICH STAUFFER
Keyword(s):  
Phase Transition ◽  
Monte Carlo Simulation ◽  
Scaling Law ◽  
Biological Evolution ◽  
Mutation Rates ◽  
Random Mutation ◽  
Simple Scaling ◽  
Log Normal ◽  
Sharp Phase Transition ◽  
Fixed Population

Similar to biological evolution and speciation, we define a language through a string of 8 or 16 bits. The parent gives its language to its children, apart from a random mutation from zero to one or from one to zero; initially all bits are zero. The Verhulst deaths are taken as proportional to the total number of people, while in addition languages spoken by many people are preferred over small languages. For a fixed population size, a sharp phase transition is observed: For low mutation rates, one language contains nearly all people; for high mutation rates, no language dominates and the size distribution of languages is roughly log-normal as for present human languages. A simple scaling law is valid.

scholarly journals Hierarchy and extremes in selections from pools of randomized proteins

2016 ◽  
Vol 113 (13) ◽  
pp. 3482-3487 ◽  
Author(s):  
Sébastien Boyer ◽  
Dipanwita Biswas ◽  
Ananda Kumar Soshee ◽  
Natale Scaramozzino ◽  
Clément Nizak ◽  
...  
Keyword(s):  
High Throughput Sequencing ◽  
Scaling Law ◽  
Natural Populations ◽  
Value Theory ◽  
Darwinian Evolution ◽  
Future Evolution ◽  
Synthetic Protein ◽  
Simple Scaling ◽  
Protein Libraries

Variation and selection are the core principles of Darwinian evolution, but quantitatively relating the diversity of a population to its capacity to respond to selection is challenging. Here, we examine this problem at a molecular level in the context of populations of partially randomized proteins selected for binding to well-defined targets. We built several minimal protein libraries, screened them in vitro by phage display, and analyzed their response to selection by high-throughput sequencing. A statistical analysis of the results reveals two main findings. First, libraries with the same sequence diversity but built around different “frameworks” typically have vastly different responses; second, the distribution of responses of the best binders in a library follows a simple scaling law. We show how an elementary probabilistic model based on extreme value theory rationalizes the latter finding. Our results have implications for designing synthetic protein libraries, estimating the density of functional biomolecules in sequence space, characterizing diversity in natural populations, and experimentally investigating evolvability (i.e., the potential for future evolution).

scholarly journals Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals

2018 ◽  
Vol 115 (31) ◽  
pp. 7884-7889 ◽  
Author(s):  
Daniel A. Sanchez ◽  
Zhaohe Dai ◽  
Peng Wang ◽  
Arturo Cantu-Chavez ◽  
Christopher J. Brennan ◽  
...  
Keyword(s):  
Scaling Law ◽  
New Physics ◽  
Adhesion Energy ◽  
Work Of Adhesion ◽  
Fourth Power ◽  
Layered Systems ◽  
Simple Scaling ◽  
Dynamics Simulations ◽  
2D Crystals ◽  
Good Agreement

Layered systems of 2D crystals and heterostructures are widely explored for new physics and devices. In many cases, monolayer or few-layer 2D crystals are transferred to a target substrate including other 2D crystals, and nanometer-scale blisters form spontaneously between the 2D crystal and its substrate. Such nanoblisters are often recognized as an indicator of good adhesion, but there is no consensus on the contents inside the blisters. While gas-filled blisters have been modeled and measured by bulge tests, applying such models to spontaneously formed nanoblisters yielded unrealistically low adhesion energy values between the 2D crystal and its substrate. Typically, gas-filled blisters are fully deflated within hours or days. In contrast, we found that the height of the spontaneously formed nanoblisters dropped only by 20–30% after 3 mo, indicating that probably liquid instead of gas is trapped in them. We therefore developed a simple scaling law and a rigorous theoretical model for liquid-filled nanoblisters, which predicts that the interfacial work of adhesion is related to the fourth power of the aspect ratio of the nanoblister and depends on the surface tension of the liquid. Our model was verified by molecular dynamics simulations, and the adhesion energy values obtained for the measured nanoblisters are in good agreement with those reported in the literature. This model can be applied to estimate the pressure inside the nanoblisters and the work of adhesion for a variety of 2D interfaces, which provides important implications for the fabrication and deformability of 2D heterostructures and devices.

Reliability Against Drifting Ice—An Adjunct to Monte Carlo Simulation

1991 ◽  
Vol 113 (3) ◽  
pp. 253-259
Author(s):  
A. B. Dunwoody
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Normal Family ◽  
Probability Distributions ◽  
Load Model ◽  
Ice Load ◽  
Ice Loads ◽  
Drifting Ice ◽  
Log Normal ◽  
Monte Carlo Simulation Program

A method is presented for the calculation of the reliability of a structure against drifting ice subject to restrictions on the form of the ice load model and on the form of the probability distributions of the ice feature characteristics. The ice load model must have the form that the ice load is proportional to the product of the characteristics of the impacting ice feature raised to individual powers. Results from a Monte Carlo simulation program are presented to demonstrate that the ice loads for a number of useful ice interaction scenarios can be modeled by an equation of this form. The probability distributions of the ice feature characteristics must be from the log-normal family. A realistic example using publicly available ice data and ice load model is presented.

scholarly journals Concentration-driven phase transition and self-assembly in drying droplets of diluting whole blood

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Anusuya Pal ◽  
Amalesh Gope ◽  
John D. Obayemi ◽  
Germano S. Iannacchione
Keyword(s):  
Phase Transition ◽  
Self Assembly ◽  
Whole Blood ◽  
Morphological Analysis ◽  
Hierarchical Structures ◽  
Contact Angle Measurement ◽  
Angle Measurement ◽  
Colloidal Systems ◽  
Functional Complexity ◽  
Sharp Phase Transition

Abstract Multi-colloidal systems exhibit a variety of structural and functional complexity owing to their ability to interact amongst different components into self-assembled structures. This paper presents experimental confirmations that reveal an interesting sharp phase transition during the drying state and in the dried film as a function of diluting concentrations ranging from 100% (undiluted whole blood) to 12.5% (diluted concentrations). An additional complementary contact angle measurement exhibits a monotonic decrease with a peak as a function of drying. This peak is related to a change in visco-elasticity that decreases with dilution, and disappears at the dilution concentration for the observed phase transition equivalent to 62% (v/v). This unique behavior is clearly commensurate with the optical image statistics and morphological analysis; and it is driven by the decrease in the interactions between various components within this bio-colloid. The implications of these phenomenal systems may address many open-ended questions of complex hierarchical structures.

Critical exponents and the universality class of a minesweeper percolation model

2020 ◽  
Vol 31 (09) ◽  
pp. 2050129
Author(s):  
Yuqi Qing ◽  
Wen-Long You ◽  
Maoxin Liu
Keyword(s):  
Phase Transition ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Critical Exponents ◽  
Critical Density ◽  
Universality Class ◽  
Percolation Model ◽  
System Configuration ◽  
Percolation Transition ◽  
Second Order Phase Transition

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

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