scholarly journals SPONTANEOUS SCALING EMERGENCE IN GENERIC STOCHASTIC SYSTEMS

1996 ◽  
Vol 07 (05) ◽  
pp. 745-751 ◽  
Author(s):  
SORIN SOLOMON ◽  
MOSHE LEVY

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range (α < –2.) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents α > −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.


1996 ◽  
Vol 07 (04) ◽  
pp. 595-601 ◽  
Author(s):  
MOSHE LEVY ◽  
SORIN SOLOMON

Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.



2020 ◽  
Vol 14 (3-4) ◽  
pp. 186
Author(s):  
Andrew Gustar

This paper investigates the processes leading to musical fame or obscurity, whether for composers, performers, or works themselves. It starts from the observation that the patterns of success, across many historical music datasets, follow a similar mathematical relationship known as a power law, often with an exponent approximately equal to two. It presents several simple models which can produce power law distributions. An examination of these models' transience characteristics suggests parallels with some historical music examples, giving clues to the ways that success and obscurity might emerge in practice and the extent to which success might be influenced by inherent musical quality. These models can be seen as manifestations of a more fundamental process resulting from the law of maximum entropy, subject to a constraint on the average value of the logarithm of the success measure. This implies that musical success is a multiplicative quality, and suggests that musical markets operate to strike a balance between familiarity (socio-cultural importance) and novelty (individual importance). The common power law exponent of two is seen to emerge as a consequence of the tendency for musical activity to be spread evenly across the log-success bands.



2020 ◽  
Vol 52 (10) ◽  
Author(s):  
M. Normann ◽  
J. A. Valiente Kroon

AbstractWe use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and perfect fluid. We also provide a discussion of self-gravitating elastic matter. The frame is Fermi–Walker propagated and coordinates are chosen such as to satisfy the Lagrange condition. We show the propagation of the constraints of the Einstein-matter system.



2020 ◽  
Author(s):  
Lucian Chan ◽  
Garrett Morris ◽  
Geoffrey Hutchison

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.



2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.



2021 ◽  
Vol 11 (2) ◽  
pp. 787
Author(s):  
Bartłomiej Ambrożkiewicz ◽  
Grzegorz Litak ◽  
Anthimos Georgiadis ◽  
Nicolas Meier ◽  
Alexander Gassner

Often the input values used in mathematical models for rolling bearings are in a wide range, i.e., very small values of deformation and damping are confronted with big values of stiffness in the governing equations, which leads to miscalculations. This paper presents a two degrees of freedom (2-DOF) dimensionless mathematical model for ball bearings describing a procedure, which helps to scale the problem and reveal the relationships between dimensionless terms and their influence on the system’s response. The derived mathematical model considers nonlinear features as stiffness, damping, and radial internal clearance referring to the Hertzian contact theory. Further, important features are also taken into account including an external load, the eccentricity of the shaft-bearing system, and shape errors on the raceway investigating variable dynamics of the ball bearing. Analysis of obtained responses with Fast Fourier Transform, phase plots, orbit plots, and recurrences provide a rich source of information about the dynamics of the system and it helped to find the transition between the periodic and chaotic response and how it affects the topology of RPs and recurrence quantificators.



2000 ◽  
Vol 122 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Hui He ◽  
Mohamad Metghalchi ◽  
James C. Keck

A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modification of the characteristic temperatures for different motion mode has been made which improves the agreement with the exact values for simple cases. The properties of branched alkanes up to 2,3,4,-trimthylpentane have been calculated and the results are in good agreement with the experimental data. A relatively small number of parameters are needed in this model to estimate the sensible thermodynamic properties of a wide range of species. The model may also be used to estimate the properties of molecules and their isomers, which have not been measured, and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations. [S0195-0738(00)00902-X]



Author(s):  
X. Lachenal ◽  
P. M. Weaver ◽  
S. Daynes

Conventional shape-changing engineering structures use discrete parts articulated around a number of linkages. Each part carries the loads, and the articulations provide the degrees of freedom of the system, leading to heavy and complex mechanisms. Consequently, there has been increased interest in morphing structures over the past decade owing to their potential to combine the conflicting requirements of strength, flexibility and low mass. This article presents a novel type of morphing structure capable of large deformations, simply consisting of two pre-stressed flanges joined to introduce two stable configurations. The bistability is analysed through a simple analytical model, predicting the positions of the stable and unstable states for different design parameters and material properties. Good correlation is found between experimental results, finite-element modelling and predictions from the analytical model for one particular example. A wide range of design parameters and material properties is also analytically investigated, yielding a remarkable structure with zero stiffness along the twisting axis.



Radiocarbon ◽  
2012 ◽  
Vol 54 (3-4) ◽  
pp. 449-474 ◽  
Author(s):  
Sturt W Manning ◽  
Bernd Kromer

The debate over the dating of the Santorini (Thera) volcanic eruption has seen sustained efforts to criticize or challenge the radiocarbon dating of this time horizon. We consider some of the relevant areas of possible movement in the14C dating—and, in particular, any plausible mechanisms to support as late (most recent) a date as possible. First, we report and analyze data investigating the scale of apparent possible14C offsets (growing season related) in the Aegean-Anatolia-east Mediterranean region (excluding the southern Levant and especially pre-modern, pre-dam Egypt, which is a distinct case), and find no evidence for more than very small possible offsets from several cases. This topic is thus not an explanation for current differences in dating in the Aegean and at best provides only a few years of latitude. Second, we consider some aspects of the accuracy and precision of14C dating with respect to the Santorini case. While the existing data appear robust, we nonetheless speculate that examination of the frequency distribution of the14C data on short-lived samples from the volcanic destruction level at Akrotiri on Santorini (Thera) may indicate that the average value of the overall data sets is not necessarily the most appropriate14C age to use for dating this time horizon. We note the recent paper of Soter (2011), which suggests that in such a volcanic context some (small) age increment may be possible from diffuse CO2emissions (the effect is hypothetical at this stage and hasnotbeen observed in the field), and that "if short-lived samples from the same stratigraphic horizon yield a wide range of14C ages, the lower values may be the least altered by old CO2." In this context, it might be argued that a substantive “low” grouping of14C ages observable within the overall14C data sets on short-lived samples from the Thera volcanic destruction level centered about 3326–3328 BP is perhaps more representative of the contemporary atmospheric14C age (without any volcanic CO2contamination). This is a subjective argument (since, in statistical terms, the existing studies using the weighted average remain valid) that looks to support as late a date as reasonable from the14C data. The impact of employing this revised14C age is discussed. In general, a late 17th century BC date range is found (to remain) to be most likelyeven ifsuch a late-dating strategy is followed—a late 17th century BC date range is thus a robust finding from the14C evidence even allowing for various possible variation factors. However, the possibility of a mid-16th century BC date (within ∼1593–1530 cal BC) is increased when compared against previous analyses if the Santorini data are considered in isolation.



2017 ◽  
Vol 25 (2) ◽  
pp. 207
Author(s):  
Eros Rosilah Rosilah

Learning Social Studies (IPS) is a compulsory subject taught. Learning IPS has a very wide range of material. Reality on the ground results of test scores of fourth grade students of SDN Babakan Tarogong 5 in social studies subject of natural resources, economic activity and technological advances in the district / city and province is still very low. This is due to social studies learning not meet minimum completeness, because the strategy used so far have not matched the learning process. The purpose of this study to determine the activities of students in participating in learning by using learning strategies of problem solving. The results of this research has reached the average value of the class.Keyword : Natural resources, economic activities, technological progress.



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