1
|
Dongiovanni P, Meroni M, Aiello G, D’Amato A, Cenzato N, Casati S, Damiani G, Fenoglio C, Galimberti D, Grossi E, Prati D, Lamorte G, Bianco C, Valenti L, Soggiu A, Zapperi S, La Porta CAM, Del Fabbro M, Tartaglia GM. Salivary proteomic profile of young healthy subjects. Front Mol Biosci 2023; 10:1327233. [PMID: 38099196 PMCID: PMC10720708 DOI: 10.3389/fmolb.2023.1327233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Accepted: 11/21/2023] [Indexed: 12/17/2023] Open
Abstract
Background: The incidence of noncommunicable diseases (NCDs) has been rapidly ramped up worldwide. Hence, there is an urgent need to non-invasively detect NCDs possibly by exploiting saliva as a 'liquid biopsy' to identify biomarkers of the health status. Since, the absence of standardized procedures of collection/analysis and the lack of normal ranges makes the use of saliva still tricky, our purpose was to outline a salivary proteomic profile which features healthy individuals. Methods: We collected saliva samples from 19 young blood donors as reference population and the proteomic profile was investigated through mass-spectrometry. Results: We identified 1,004 proteins of whose 243 proteins were shared by all subjects. By applying a data clustering approach, we found a set of six most representative proteins across all subjects including Coronin-1A, F-actin-capping protein subunit alpha, Immunoglobulin J chain, Prosaposin, 78 kDa glucose-regulated protein and Heat shock 70 kDa protein 1A and 1B. Conclusion: All of these proteins are involved in immune system activation, cellular stress responses, proliferation, and invasion thus suggesting their use as biomarkers in patients with NCDs.
Collapse
Affiliation(s)
- P. Dongiovanni
- Medicine and Metabolic Diseases, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - M. Meroni
- Medicine and Metabolic Diseases, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - Gilda Aiello
- Department of Human Science and Quality of Life Promotion, Telematic University San Raffaele, Rome, Italy
| | - A. D’Amato
- Department of Pharmaceutical Sciences, University of Milan, Milan, Italy
| | - N. Cenzato
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - S. Casati
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - G. Damiani
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - C. Fenoglio
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - D. Galimberti
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
- Neurodegenerative Diseases Unit, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - E. Grossi
- Villa Santa Maria Foundation, Tavernerio, Italy
| | - D. Prati
- Biological Resource Center, Department of Transfusion Medicine, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - G. Lamorte
- Biological Resource Center, Department of Transfusion Medicine, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - C. Bianco
- Biological Resource Center, Department of Transfusion Medicine, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - L. Valenti
- Biological Resource Center, Department of Transfusion Medicine, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - A. Soggiu
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
| | - S. Zapperi
- Department of Physics, Center for Complexity and Biosystems, University of Milan, Milan, Italy
| | - C. A. M. La Porta
- Department of Environmental Science and Policy, Center for Complexity and Biosystems, University of Milan, Milan, Italy
| | - M. Del Fabbro
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
- SC Maxillo-Facial Surgery and Dentistry, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| | - G. M. Tartaglia
- Department of Biomedical, Surgical and Dental Sciences, University of Milan, Milan, Italy
- SC Maxillo-Facial Surgery and Dentistry, Fondazione IRCCS Cà Granda Ospedale Maggiore Policlinico, Milan, Italy
| |
Collapse
|
2
|
Lennartz-Sassinek S, Zaiser M, Main IG, Manzato C, Zapperi S. Emergent patterns of localized damage as a precursor to catastrophic failure in a random fuse network. Phys Rev E 2013; 87:042811. [PMID: 23679477 DOI: 10.1103/physreve.87.042811] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2013] [Indexed: 11/07/2022]
Abstract
We study the failure of disordered materials by numerical simulations of the random fuse model. We identify emergent patterns of localized damage prior to catastrophic failure by statistically averaging the density of damage around the eventual failure nucleation point. The resulting pattern depends on fracture density and obeys the same scaling relations as would be expected for the stress field generated by a critical crack nucleating in a finite, disorder-free effective medium of varying size. The growth of this critical crack absorbs preexisting clusters according to a well-defined scaling relation. Unfortunately, in single model runs such precursory signals are not obvious. Our results imply that reliable and accurate prediction of failure in time-independent, microscopically brittle random materials in a real case is inherently problematic, and degrades with system size.
Collapse
Affiliation(s)
- S Lennartz-Sassinek
- School of Engineering and School of Geosciences, University of Edinburgh, Edinburgh, EH9 3JL, United Kingdom.
| | | | | | | | | |
Collapse
|
3
|
Abstract
AbstractIt has been recently observed that synthetic materials subjected to an external elastic stress give rise to scaling phenomena in the acoustic emission signal. Motivated by this experimental finding we develop a mesoscopic model in order to clarify the nature of this phenomenon. We model the synthetic material by an array of resistors with random failure thresholds. The failure of a resistor produces an decrease in the conductivity and a redistribution of the disorder. By increasing the applied voltage the system organizes itself in a stationary state. The acoustic emission signal is associated with the failure events. We find scaling behavior in the amplitude of these events and in the times between different events. The model allows us to study the geometrical and topological properties of the micro-fracturing process that drives the system to the self-organized stationary state.
Collapse
|
4
|
Baldassarri A, Dalton F, Petri A, Zapperi S, Pontuale G, Pietronero L. Brownian forces in sheared granular matter. Phys Rev Lett 2006; 96:118002. [PMID: 16605874 DOI: 10.1103/physrevlett.96.118002] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2005] [Indexed: 05/08/2023]
Abstract
We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting in the system performs a Brownian motion. The same assumption has been utilized, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.
Collapse
Affiliation(s)
- A Baldassarri
- Dipartimento di Fisica, Università La Sapienza, Piazzale le Aldo Moro 2, 00185 Roma, Italy
| | | | | | | | | | | |
Collapse
|
5
|
Alava MJ, Zapperi S. Comment on "Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone". Phys Rev Lett 2004; 92:049601-049602. [PMID: 14995418 DOI: 10.1103/physrevlett.92.049601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/15/2003] [Indexed: 05/24/2023]
Affiliation(s)
- M J Alava
- Laboratory of Physics, Helsinki University of Technology, FIN-02015 HUT, Finland
| | | |
Collapse
|
6
|
Dickman R, Alava M, Muñoz MA, Peltola J, Vespignani A, Zapperi S. Critical behavior of a one-dimensional fixed-energy stochastic sandpile. Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:056104. [PMID: 11736011 DOI: 10.1103/physreve.64.056104] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/25/2001] [Revised: 07/09/2001] [Indexed: 05/23/2023]
Abstract
We study a one-dimensional fixed-energy version (that is, with no input or loss of particles) of Manna's stochastic sandpile model. The system has a continuous transition to an absorbing state at a critical value of the particle density, and exhibits the hallmarks of an absorbing-state phase transition, including finite-size scaling. Critical exponents are obtained from extensive simulations, which treat stationary and transient properties, and an associated interface representation. These exponents characterize the universality class of an absorbing-state phase transition with a static conserved density in one dimension; they differ from those expected at a linear-interface depinning transition in a medium with point disorder, and from those of directed percolation.
Collapse
Affiliation(s)
- R Dickman
- Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, Minas Gerais, Brazil
| | | | | | | | | | | |
Collapse
|
7
|
Abstract
We investigate flux front penetration in a disordered type-II superconductor by molecular dynamics simulations of interacting vortices and find scaling laws for the front position and the density profile. The scaling can be understood by performing a coarse graining of the system and writing a disordered nonlinear diffusion equation. Integrating numerically the equation, we observe a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.
Collapse
Affiliation(s)
- S Zapperi
- INFM sezione di Roma 1, Dipartimento di Fisica, Università La Sapienza, P.le A. Moro 2, 00185 Roma, Italy
| | | | | |
Collapse
|
8
|
Abstract
The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated 'dislocation dynamics' simulations have proved very effective in the study of dislocation patterning, and have led to macroscopic constitutive laws of plastic deformation. Yet, a statistical analysis of the dynamics of an assembly of interacting dislocations has not hitherto been performed. Here we report acoustic emission measurements on stressed ice single crystals, the results of which indicate that dislocations move in a scale-free intermittent fashion. This result is confirmed by numerical simulations of a model of interacting dislocations that successfully reproduces the main features of the experiment. We find that dislocations generate a slowly evolving configuration landscape which coexists with rapid collective rearrangements. These rearrangements involve a comparatively small fraction of the dislocations and lead to an intermittent behaviour of the net plastic response. This basic dynamical picture appears to be a generic feature in the deformation of many other materials. Moreover, it should provide a framework for discussing fundamental aspects of plasticity that goes beyond standard mean-field approaches that see plastic deformation as a smooth laminar flow.
Collapse
Affiliation(s)
- M C Miguel
- The Abdus Salam International Centre for Theoretical Physics, PO Box 586, 34100 Trieste, Italy.
| | | | | | | | | |
Collapse
|
9
|
Vespignani A, Dickman R, Munoz MA, Zapperi S. Absorbing-state phase transitions in fixed-energy sandpiles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:4564-4582. [PMID: 11088996 DOI: 10.1103/physreve.62.4564] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/1999] [Revised: 06/02/2000] [Indexed: 05/23/2023]
Abstract
We study sandpile models as closed systems, with the conserved energy density zeta playing the role of an external parameter. The critical energy density zeta(c) marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics in random media.
Collapse
Affiliation(s)
- A Vespignani
- The Abdus Salam International Centre for Theoretical Physics (ICTP), P.O. Box 586, 34100 Trieste, Italy
| | | | | | | |
Collapse
|
10
|
Durin G, Zapperi S. Scaling exponents for barkhausen avalanches in polycrystalline and amorphous ferromagnets. Phys Rev Lett 2000; 84:4705-4708. [PMID: 10990776 DOI: 10.1103/physrevlett.84.4705] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/1999] [Indexed: 05/23/2023]
Abstract
We investigate the scaling properties of the Barkhausen effect by recording the noise in several soft ferromagnetic materials: polycrystals with different grain sizes and amorphous alloys. We measure the Barkhausen avalanche distributions and determine the scaling exponents. In the limit of vanishing external field rate, we can group the samples in two distinct classes, characterized by exponents tau = 1.50+/-0.05 or tau = 1.27+/-0.03, for the avalanche size distributions. We interpret these results in terms of the depinning transition of domain walls and obtain an expression relating the cutoff of the distributions to the demagnetizing factor which is in quantitative agreement with experiments.
Collapse
Affiliation(s)
- G Durin
- Istituto Elettrotecnico Nazionale Galileo Ferraris and INFM, Corso M. d'Azeglio 42, I-10125 Torino, Italy
| | | |
Collapse
|
11
|
Alencar AM, Hantos Z, Peták F, Tolnai J, Asztalos T, Zapperi S, Andrade JS, Buldyrev SV, Stanley HE, Suki B. Scaling behavior in crackle sound during lung inflation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 60:4659-63. [PMID: 11970328 DOI: 10.1103/physreve.60.4659] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/1998] [Revised: 07/14/1999] [Indexed: 04/18/2023]
Abstract
During slow inflation of lung lobes, we measure a sequence of short explosive transient sound waves called "crackles," each consisting of an initial spike followed by ringing. The crackle time series is irregular and intermittent, with the number of spikes of size s following a power law, n(s) proportional, variants(-alpha), with alpha=2.77+/-0.05. We develop a model of crackle wave generation and propagation in a tree structure that combines the avalanchelike opening of airway segments with the wave propagation of crackles in a tree structure. The agreement between experiments and simulations suggests that (i) the irregularities are a consequence of structural heterogeneity in the lung, (ii) the intermittent behavior is due to the avalanchelike opening, and (iii) the scaling is a result of successive attenuations acting on the sound spikes as they propagate through a cascade of bifurcations along the airway tree.
Collapse
Affiliation(s)
- A M Alencar
- Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
| | | | | | | | | | | | | | | | | | | |
Collapse
|
12
|
Ivashkevich EV, Povolotsky AM, Vespignani A, Zapperi S. Dynamical real space renormalization group applied to sandpile models. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 60:1239-51. [PMID: 11969882 DOI: 10.1103/physreve.60.1239] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/1997] [Indexed: 04/18/2023]
Abstract
A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.
Collapse
Affiliation(s)
- E V Ivashkevich
- Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia
| | | | | | | |
Collapse
|
13
|
Zapperi S, Ray P, Stanley HE, Vespignani A. Avalanches in breakdown and fracture processes. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 59:5049-57. [PMID: 11969461 DOI: 10.1103/physreve.59.5049] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/1998] [Indexed: 04/18/2023]
Abstract
We investigate the breakdown of disordered networks under the action of an increasing external-mechanical or electrical-force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first-order transition. The scaling laws suggest an analogy with the behavior expected in spinodal nucleation.
Collapse
Affiliation(s)
- S Zapperi
- PMMH-ESPCI, 10 Rue Vauquelin, 75231 Paris Cedex 05, France
| | | | | | | |
Collapse
|
14
|
Muñoz MA, Dickman R, Vespignani A, Zapperi S. Avalanche and spreading exponents in systems with absorbing states. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 59:6175-9. [PMID: 11969602 DOI: 10.1103/physreve.59.6175] [Citation(s) in RCA: 82] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/1998] [Indexed: 04/18/2023]
Abstract
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the state-of-the-art exponents for directed percolation, dynamical percolation, and other universality classes. This collection of results should help to elucidate the connections of self-organized criticality and systems with absorbing states. In particular, some nonuniversality in avalanche exponents is predicted for systems with many absorbing states.
Collapse
Affiliation(s)
- M A Muñoz
- The Abdus Salam International Centre for Theoretical Physics (ICTP), P.O. Box 586, 34100 Trieste, Italy
| | | | | | | |
Collapse
|
15
|
Suki B, Andrade JS, Coughlin MF, Stamenović D, Stanley HE, Sujeer M, Zapperi S. Mathematical modeling of the first inflation of degassed lungs. Ann Biomed Eng 1998; 26:608-17. [PMID: 9662153 DOI: 10.1114/1.126] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
The pressure-volume (P-V) relationship of degassed lungs during the first inflation is different from that in consecutive inflations. We developed a mathematical model of the P-V curve of the first inflation by assuming that (1) central airways are open leading to many subtrees of n generations that are initially closed; (2) an airway opens when inflation pressure reaches the opening threshold pressure of that segment; and (3) the opening threshold pressures do not depend on airway generation. In this model, airway opening occurs in cascades or avalanches. To test the model which contains only two parameters, n and a pressure, P(low), at which at least one subtree completely opens, we measured the first inflation P-V curves of 15 excised and degassed rabbit lungs. By fitting these data, we found that n=17+/-5, P(low)=23+/-4 cmH2O, and that there is a wide distribution of threshold pressures for airways with diameters <2 mm. Analysis of the P-V curve in a lung which was lavaged with a liquid of constant surface tension and in which airways are presumably open demonstrated that the distribution of threshold pressures is narrow, and hence no avalanches occur during inflation. We conclude that in normal lungs the first inflation is dominated by avalanche behavior of airway opening providing information on the global distribution of threshold pressures and the average site of airway closure.
Collapse
Affiliation(s)
- B Suki
- Department of Biomedical Engineering, Boston University, MA 02215, USA.
| | | | | | | | | | | | | |
Collapse
|
16
|
Suki B, Alencar AM, Sujeer MK, Lutchen KR, Collins JJ, Andrade JS, Ingenito EP, Zapperi S, Stanley HE. Life-support system benefits from noise. Nature 1998; 393:127-8. [PMID: 9603516 DOI: 10.1038/30130] [Citation(s) in RCA: 164] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
|
17
|
Vespignani A, Zapperi S, Loreto V. Renormalization of Nonequilibrium Systems with Critical Stationary States. Phys Rev Lett 1996; 77:4560-4563. [PMID: 10062569 DOI: 10.1103/physrevlett.77.4560] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
18
|
Zapperi S, Stanley HE. Self-organized branching processes: Avalanche models with dissipation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 54:2483-2488. [PMID: 9965358 DOI: 10.1103/physreve.54.2483] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
19
|
Kutnjak-Urbanc B, Zapperi S, Milosevic S, Stanley HE. Sandpile model on the Sierpinski gasket fractal. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1996; 54:272-277. [PMID: 9965069 DOI: 10.1103/physreve.54.272] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
20
|
|
21
|
Loreto V, Pietronero L, Vespignani A, Zapperi S. Renormalization group approach to the critical behavior of the forest-fire model. Phys Rev Lett 1995; 75:465-468. [PMID: 10060028 DOI: 10.1103/physrevlett.75.465] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
22
|
Vespignani A, Zapperi S, Pietronero L. Renormalization approach to the self-organized critical behavior of sandpile models. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995; 51:1711-1724. [PMID: 9962830 DOI: 10.1103/physreve.51.1711] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
23
|
Pietronero L, Vespignani A, Zapperi S. Renormalization scheme for self-organized criticality in sandpile models. Phys Rev Lett 1994; 72:1690-1693. [PMID: 10055676 DOI: 10.1103/physrevlett.72.1690] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|