Abstract: Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot... more Abstract: Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century.
Networks portray a multitude of interactions through which people meet, ideas are spread and infe... more Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society1–5. Identifying the most efficient 'spreaders' in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people6–10.
Randomly packing spheres of equal size into a container consistently results in a static configur... more Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of∼ 64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit.
Abstract An important issue in the study of cities is defining a metropolitan area, because diffe... more Abstract An important issue in the study of cities is defining a metropolitan area, because different definitions affect conclusions regarding the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSAs), based on rules attempting to capture the notion of city as a functional economic region, and it is performed by using experience.
3D computer simulations and experiments are employed to study random packings of compressible sph... more 3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous transition in which the stress vanishes as f2fc b, where f is the (solid phase) volume density. The value of fc depends on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings).
A variety of systems such as granular materials, compressed emulsions, or molecular glasses, exhi... more A variety of systems such as granular materials, compressed emulsions, or molecular glasses, exhibit a nonequilibrium transition from a fluidlike to a solidlike state. When the constituent particles of such systems are so crowded that they are in close contact with one another, the whole system experiences a sudden dynamical arrest, which is referred to as the glass or jamming transition [1–3].
Fluctuation-dissipation FD relations are commonly used in equilibrium systems, derived from the n... more Fluctuation-dissipation FD relations are commonly used in equilibrium systems, derived from the notion that small perturbations and Brownian fluctuations produce the same response in a given system 1. Mobility, the constant of proportionality between a particles drift speed and a constant external force, is extracted from velocity statistics of particles in a given system. Diffusivity, calculated from fluctuation displacements of particles in a system over time, represent the Brownian motion.
Abstract The human brain has been studied at multiple scales, from neurons, circuits, areas with ... more Abstract The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology.
We develop the concept of frequency dependent effective mass,~ Mš! Ž, of jammed granular material... more We develop the concept of frequency dependent effective mass,~ Mš! Ž, of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of~ Mš! Ž provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium.
We illustrate the general principle that in biophysics, econophysics and possibly even city growt... more We illustrate the general principle that in biophysics, econophysics and possibly even city growth, the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data. Specifically, we discuss recent work on DNA sequences, heartbeat intervals, avalanche-like lung inflation, urban growth, and company growth. Although our main focus is on data, we also discuss statistical mechanical models.
Abstract. We present extensive computational results for the effective temperature, defined by th... more Abstract. We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation.
Abstract In this opening introductory paper, we discuss the possibility that scale-invariant corr... more Abstract In this opening introductory paper, we discuss the possibility that scale-invariant correlations may be a feature of biological and possibly even social systems. We illustrate this possibility by reviewing recent work at Boston University. Specifically, we focus first on the apparent scale-invariant correlations in non-coding deoxyribonucleic acid (DNA) and show that this feature can be used to distinguish coding and non-coding DNA.
ABSTRACT The distribution of the population of cities has attracted a great deal of attention, in... more ABSTRACT The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail, because available data need to rely on the “legal” rather than “economic” definition of cities for medium and small cities. To remedy this difficulty, in this work we construct cities “from the bottom up” by clustering populated areas obtained from high-resolution data.
Abstract: We derive the continuum equation for a discrete model for ion sputtering. We follow an ... more Abstract: We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking the continuum limit, we arrive at the Kuramoto-Sivashinsky equation with a stochastic noise term.
Experimentally it is known that the bulk modulus K and shear modulus m of a granular assembly of ... more Experimentally it is known that the bulk modulus K and shear modulus m of a granular assembly of elastic spheres increase with pressure p faster than the p13 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p.
In this work we study the percolation phase transition of a family of scale-free networks previou... more In this work we study the percolation phase transition of a family of scale-free networks previously introduced to explain the emergence of fractality and self-similarity in complex networks. This model introduces a parameter, e, that allows for tuning the level of fractality in the network. When e= 0 the network is a pure fractal, when e= 1 it is a pure small-world network.
Abstract: We propose a new method to generate a sequence of random numbers with long-range power-... more Abstract: We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.
Recently the growth of rough interfaces has witnessed an explosion of theoretical, numerical, and... more Recently the growth of rough interfaces has witnessed an explosion of theoretical, numerical, and experimental studies, fueled by the broad interdisciplinary aspects of the subject [1—6]. Applications can be as diverse as imbi-bition in porous media, Quid-Quid displacement, fire &ont motion, and the motion of Qux linesin superconductors [7-17].
Abstract The emergence of universal properties such as the scale-free property self-similarity, a... more Abstract The emergence of universal properties such as the scale-free property self-similarity, and modularity, as key features of complex networks raises the fundamental question of the governing growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological and social networks, as well as computers in the Internet, is of interest to the specialist and the laymen alike, as it promises to uncover the origins of collective behavior.
Size segregation of granular mixtures 1–7 is known to occur when mixtures are exposed to external... more Size segregation of granular mixtures 1–7 is known to occur when mixtures are exposed to external periodic perturbations. A much-studied size segregation phenomenon is known as the ''Brazil nut effect''8–12 and occurs when, upon vibration, larger grains rise on a bed of finer grains. Axial size segregation in alternating bands consisting of small and large grains occurs when a mixture of grains is placed in a horizontal rotating cylinder 13–16.
Abstract: Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot... more Abstract: Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century.
Networks portray a multitude of interactions through which people meet, ideas are spread and infe... more Networks portray a multitude of interactions through which people meet, ideas are spread and infectious diseases propagate within a society1–5. Identifying the most efficient 'spreaders' in a network is an important step towards optimizing the use of available resources and ensuring the more efficient spread of information. Here we show that, in contrast to common belief, there are plausible circumstances where the best spreaders do not correspond to the most highly connected or the most central people6–10.
Randomly packing spheres of equal size into a container consistently results in a static configur... more Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of∼ 64%. The ubiquity of random close packing (RCP) rather than the optimal crystalline array at 74% begs the question of the physical law behind this empirically deduced state. Indeed, there is no signature of any macroscopic quantity with a discontinuity associated with the observed packing limit.
Abstract An important issue in the study of cities is defining a metropolitan area, because diffe... more Abstract An important issue in the study of cities is defining a metropolitan area, because different definitions affect conclusions regarding the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSAs), based on rules attempting to capture the notion of city as a functional economic region, and it is performed by using experience.
3D computer simulations and experiments are employed to study random packings of compressible sph... more 3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous transition in which the stress vanishes as f2fc b, where f is the (solid phase) volume density. The value of fc depends on whether the grains interact via only normal forces (giving rise to random close packings) or by a combination of normal and friction generated transverse forces (producing random loose packings).
A variety of systems such as granular materials, compressed emulsions, or molecular glasses, exhi... more A variety of systems such as granular materials, compressed emulsions, or molecular glasses, exhibit a nonequilibrium transition from a fluidlike to a solidlike state. When the constituent particles of such systems are so crowded that they are in close contact with one another, the whole system experiences a sudden dynamical arrest, which is referred to as the glass or jamming transition [1–3].
Fluctuation-dissipation FD relations are commonly used in equilibrium systems, derived from the n... more Fluctuation-dissipation FD relations are commonly used in equilibrium systems, derived from the notion that small perturbations and Brownian fluctuations produce the same response in a given system 1. Mobility, the constant of proportionality between a particles drift speed and a constant external force, is extracted from velocity statistics of particles in a given system. Diffusivity, calculated from fluctuation displacements of particles in a system over time, represent the Brownian motion.
Abstract The human brain has been studied at multiple scales, from neurons, circuits, areas with ... more Abstract The human brain has been studied at multiple scales, from neurons, circuits, areas with well-defined anatomical and functional boundaries, to large-scale functional networks which mediate coherent cognition. In a recent work, we addressed the problem of the hierarchical organization in the brain through network analysis. Our analysis identified functional brain modules of fractal structure that were inter-connected in a small-world topology.
We develop the concept of frequency dependent effective mass,~ Mš! Ž, of jammed granular material... more We develop the concept of frequency dependent effective mass,~ Mš! Ž, of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of~ Mš! Ž provide signatures of the dissipation of acoustic modes, elasticity, and aging effects in the granular medium.
We illustrate the general principle that in biophysics, econophysics and possibly even city growt... more We illustrate the general principle that in biophysics, econophysics and possibly even city growth, the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data. Specifically, we discuss recent work on DNA sequences, heartbeat intervals, avalanche-like lung inflation, urban growth, and company growth. Although our main focus is on data, we also discuss statistical mechanical models.
Abstract. We present extensive computational results for the effective temperature, defined by th... more Abstract. We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation.
Abstract In this opening introductory paper, we discuss the possibility that scale-invariant corr... more Abstract In this opening introductory paper, we discuss the possibility that scale-invariant correlations may be a feature of biological and possibly even social systems. We illustrate this possibility by reviewing recent work at Boston University. Specifically, we focus first on the apparent scale-invariant correlations in non-coding deoxyribonucleic acid (DNA) and show that this feature can be used to distinguish coding and non-coding DNA.
ABSTRACT The distribution of the population of cities has attracted a great deal of attention, in... more ABSTRACT The distribution of the population of cities has attracted a great deal of attention, in part because it sharply constrains models of local growth. However, to this day, there is no consensus on the distribution below the very upper tail, because available data need to rely on the “legal” rather than “economic” definition of cities for medium and small cities. To remedy this difficulty, in this work we construct cities “from the bottom up” by clustering populated areas obtained from high-resolution data.
Abstract: We derive the continuum equation for a discrete model for ion sputtering. We follow an ... more Abstract: We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking the continuum limit, we arrive at the Kuramoto-Sivashinsky equation with a stochastic noise term.
Experimentally it is known that the bulk modulus K and shear modulus m of a granular assembly of ... more Experimentally it is known that the bulk modulus K and shear modulus m of a granular assembly of elastic spheres increase with pressure p faster than the p13 law predicted by effective medium theory (EMT) based on Hertz-Mindlin contact forces. To understand the origin of these discrepancies, we perform numerical simulations of granular aggregates under compression. We show that EMT can describe the moduli pressure dependence if one includes the increasing number of grain-grain contacts with p.
In this work we study the percolation phase transition of a family of scale-free networks previou... more In this work we study the percolation phase transition of a family of scale-free networks previously introduced to explain the emergence of fractality and self-similarity in complex networks. This model introduces a parameter, e, that allows for tuning the level of fractality in the network. When e= 0 the network is a pure fractal, when e= 1 it is a pure small-world network.
Abstract: We propose a new method to generate a sequence of random numbers with long-range power-... more Abstract: We propose a new method to generate a sequence of random numbers with long-range power-law correlations that overcomes known difficulties associated with large systems. The new method presents an improvement on the commonly-used methods. We apply the algorithm to generate enhanced diffusion, isotropic and anisotropic self-affine surfaces, and isotropic and anisotropic correlated percolation.
Recently the growth of rough interfaces has witnessed an explosion of theoretical, numerical, and... more Recently the growth of rough interfaces has witnessed an explosion of theoretical, numerical, and experimental studies, fueled by the broad interdisciplinary aspects of the subject [1—6]. Applications can be as diverse as imbi-bition in porous media, Quid-Quid displacement, fire &ont motion, and the motion of Qux linesin superconductors [7-17].
Abstract The emergence of universal properties such as the scale-free property self-similarity, a... more Abstract The emergence of universal properties such as the scale-free property self-similarity, and modularity, as key features of complex networks raises the fundamental question of the governing growth process according to which these structures evolve. The possibility of a unique growth mechanism for biological and social networks, as well as computers in the Internet, is of interest to the specialist and the laymen alike, as it promises to uncover the origins of collective behavior.
Size segregation of granular mixtures 1–7 is known to occur when mixtures are exposed to external... more Size segregation of granular mixtures 1–7 is known to occur when mixtures are exposed to external periodic perturbations. A much-studied size segregation phenomenon is known as the ''Brazil nut effect''8–12 and occurs when, upon vibration, larger grains rise on a bed of finer grains. Axial size segregation in alternating bands consisting of small and large grains occurs when a mixture of grains is placed in a horizontal rotating cylinder 13–16.
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