

 Clustering in anomalous files of independent particles (20102011)
Highlights of [1]:
A previously undescribed variant of the famous process of file dynamics (the diffusion of classical hard spheres in a quasi one dimensional channel) made of anomalous, independent, particles (whose jumping times are taken independently from, ψ_{α}(t)~t^{1α}, 0<α<1), exhibits a unique and exciting behavior: formation of clusters. We characterize this phenomenon mathematically, enabling a precise control through α, and prove that it’s stable through many numerical tests. We think that the clustering in this system may explain the mysterious phenomenon of rafts in biological membranes and can be used in regulating biological channels.
[1] O. Flomenbom
Clustering in anomalous files of independent particles
EPL 94, 58001 (2011).
 New results in single file dynamics (20082010)
 How enzyme works? (20032005)
r=r_{0}l^{a}, 0≤a≤1,
where l is a macroscopic length scale. We have derived the following formula for the mean square displacement (MSD) [1]:
$<\; r2>\; ~$r_{0} ^{(a1)} < r ^{2} _{free} >^{(1+a)/2}. (1)
Here < r ^{2} > _{free} is the scaling law for a free particle, so our result holds for any underlying dynamics. This formula shows explicitly how the particles’ density affects the tagged particle’s diffusion, thus enables to enhance very accurately its propagation while adjusting the power a. We have also found that for a normal diffusion file,
the probability density function (PDF) of the tagged particle is Gaussian in position for any value of a.
Now, equation (1) holds when all particles are the same. For a heterogeneous file with a distribution of diffusion coefficients,
W(D)~D^{– g}, 0≤g≤1,
the MSD scales as [2],
< r ^{2} > ~ t^{ m }, m = [1g ] / [2/(1+a)g ]. (2)
The PDF is still a Gaussian in position.
In [3], we look on hetereogeneousrenewalanomalous files. A renewal anomalous file is a file in which the effective waiting time PDF for individual jumps for a sphere is of the form:
y(t)~t^{1 a }, 0<a≤1,
for large t, and all the particles attemp to jump at the same time. There are several schemes that exhibit this scaling for y(t), yet each one of them has different dynamical properties. In a renewalanomalous file, we can use the results for the MSD in normal dynamics with the substitution,
t→t^{ α }. (3)
We also find that in an anomalous file of independent particles, the dynamics are much slower than in its renewal counterpart.
[1] O. Flomenbom, A. Taloni
On single file and less dense processes
Europhys. Lett. 83, 20004p1p6 (2008).
[2] O. Flomenbom
Dynamics of heterogeneous hard spheres in a file
Phys. Rev. E 82, 031126 (2010).
[3] O. Flomenbom
Renewalanomalousheterogeneous files
Phys. Lett. A 374, 4331 (2010).
To fully utilize RD forms in the analysis of the data, we developed a toolbox that builds a RD form from a twostate trajectory. See Software descriptions for details.
2018 (1)
47 Are SocioEconoPhysical Models Better to Explain Biases in Societies? RAPS 2(2), (2018)
2017 (4,5)
46 Ophir Flomenbom, and Jelena Mazaj , Customizing Crowdfunding Approaches to Replace “Biased” Funding Rep. Adv. Phys. Sci. 01, 1771001 (2017) 45 Arnab Chatterjee, Gul Unal Coban, and Ophir Flomenbom, Introduction – Commentary on the Special Issue Rep. Adv. Phys. Sci. 01, 1703001 (2017) 44 Ophir Flomenbom, The Income Gini of Fairness Rep. Adv. Phys. Sci., 01, 1740004 (2017) 43 Alessandro Taloni,ab Ophir Flomenbom,c Ramón CastañedaPriego*d and Fabio Marchesonie Single file dynamics in soft materials Soft Matter, 2017,13, 1096110642 Yekbun Adigüzel1, Ophir Flomenbom2, *, †, Gul Unal Coban3 From the Physiocrats to Fairness in Nations Rep. Adv. Phys. Sci. 01, 1750001 (2017)
2016 (3)
41 Ophir Flomenbom , Larysa Baraban, Vyacheslav Misko
Commentary on the Special Issue Continuation on “Single File Dynamics and Generalizations in Interdisciplinary Sciences”
Biophysical Reviews and Letters 11, 1 (2016)
40 Ophir Flomenbom ,Gul Unal Coban2 Yekbun Adiguzel3
Commentary on “Biophysical Economics” and Evolving Areas
Biophysical Reviews and Letters 11, 55 (2016)
39. Ophir Flomenbom
MFPT in Single file dynamics
Biophysical Reviews and Letters 11, 39 (2016)
2015 (3)
38. Fredrick Sachs, Ophir Flomenbom ,
“How to get more from less”,
Physics of Life Reviews, 13, 150 (2015) ; doi:10.1016/j.plrev.2015.03.006
37. Ophir Flomenbom , Alessandro Taloni, Ramon CastanedaPriego, Fabio Marchesoni, Francois Peeters
Single file dynamics’ solutions, perspectives and the soft matter relation
abstract (2015)
36. Ophir Flomenbom
The society deciders model and fairness in nations
BIOPHY. REV. LETT. (2015) ; DOI: 10.1142/S1793048015500046
2014 (3)
35. O. Flomenbom
Advanced properties in Single File Dynamics, &: Slow files in 1D & higher dimensions.
Majorana Centre, Conference on Single file dynamics in biophysics, physics & related fields & extensions in higher dimensions, BOOKLET (2014).
34. Ophir Flomenbom, Ramon Castaneda – Priego, Francois Peeters
Introduction to the Special Issue on Single File Dynamics advances in biophysics, physics & related fields, & extensions in higher dimensions Biophys Rev. Lett. 9, 301 (2014)
33. O. Flomenbom
Single File Dynamics Advances and a Focus on Biophysical Relevance
Biophys Rev. Lett. 9, 307 (2014).
2013 (3)
32. Ophir Flomenbom, Kelly Velonia, Mircea Cotlet
Introduction to the Special Issue on Measuring & Solving Single Molecules
Biophys Rev. Lett. 8(3), 103 (2013)
31. O. Flomenbom
MATHEMATICAL TREATMENTS THAT SOLVE SINGLE MOLECULES
Biophys Rev. Lett. 8(3), 109136 (2013).
30. O. Flomenbom
Solving single molecules:
filtering noisy discrete data made of photons and other type of observables
arXiv; http://arxiv.org/abs/1306.2435
text,supplemtary information
2012 (1)
29. O. Flomenbom
Fairness in society
arXiv:1112.0262
This project will appear with new results & new title during 2014/2015
2011 (3)
28. O. Flomenbom
Heterogeneous walkers in Rich Environments
A book, ISBN: 9783844315769 (2011).
Publishing with LAMBERT Academic Publishing .
27. O. Flomenbom
Clustering in anomalous files of independent particles
EPL 94, 58001 (2011).
arXiv:1103.4082 26. O. Flomenbom
Making it possible: constructing a reliable mechanism from a finite trajectory
Adv. Chem. Phys. 146, 367 (2011).
arXiv:0912.3952
2010 (2)
25. O. Flomenbom
Renewalanomalousheterogeneous files
Phys. Lett. A 374, 4331 (2010).
arXiv:1008.2323
24. O. Flomenbom
Dynamics of heterogeneous hard spheres in a file
Phys. Rev. E 82, 031126 (2010).
Draft of the paper, arXiv:1002.1450
2009 (1)
23. O. Flomenbom
The rule for a subdiffusive particle in an extremely diverse environment
Phys. Lett. A 373, 14051408 (2009).
arXiv:0805.4054
2008 (4)
22. O. Flomenbom, A Taloni
On single file and less dense processes
Europhys. Lett. 83, 20004p1p6 (2008).
arXiv:0802.1516
21. O. Flomenbom, and R. J. Silbey
Toolbox for analyzing finite twostate trajectories
Phys. Rev. E 78, 066105 (2008).
arXiv:0802.1520
20. O. Flomenbom, and R. J. Silbey
Universal properties of mechanisms from twostate trajectories
J. Chem. Phys. 128, 114902 (2008). Selected by and appeared on the Virtual Journal of Biological Physics Research.
19.O. Flomenbom, and R. J. Silbey
Unique mechanisms from finite twostate trajectories
E. Barkai, F. L. H. Brown, M. Orrit & H. Yang Eds. THEORY AND EVALUATION OF SINGLEMOLECULE SIGNALS,(October, 2008). arXiv:0706.2328
2007 (2)
18. O. Flomenbom, and R. J. Silbey
Path PDFs for semiMarkovian random walks
Phys. Rev. E 76, 041101 (2007).
arXiv:0706.3211
17. O. Flomenbom, and R. J. Silbey
Properties of the generalized master equation: Green’s functions
and probability density functions in the path representation
J. Chem. Phys. 127, 034102 (2007).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.
2006 (3)
16. O. Flomenbom, J. Klafter, and R. J. Silbey
Comment on “Path Summation Formulation of the Master Equation”
Phys. Rev. Lett. 97, 178901 (2006).
15. O. Flomenbom, J. Hofkens, K. Velonia, et al
Correctly validating results from single molecule data:
The case of stretched exponential decay in the
catalytic activity of single lipase B molecules
Chem. Phys. Lett. 432, 371–374 (2006).
14. O. Flomenbom, and R. J. Silbey
Utilizing the information content in twostate trajectories
Proc. Natl. Acad. Sci. USA 103, 1090710910 (2006).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.
13. O. Flomenbom and J. Klafter
On the relationships between kinetic schemes
and twostate single molecule trajectories
J. Chem. Phys. 123, 064903 (2005).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.
12. O. Flomenbom and J. Klafter
Uncorrelated twostate single molecule trajectories
from reducible kinetic schemes
Acta Phys. Pol. B 36, 15271535 (2005).
qbio/0501029
11. O. Flomenbom and J. Klafter
Closedform solutions for continuous time
random walks on finite chains
Phys. Rev. Lett. 95, 098105 (2005).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.
10. O. Flomenbom and J. Klafter
Stretched exponential decay and correlations
from twostate single molecule trajectories,
L. B. Kish, K. Lindenberg, Z. Gingl Eds.
Noise in complex systems and stochastic dynamics III,
Proceedings of SPIE 5845, 156164 (2005).
9. O. Flomenbom, J. Klafter, and A. Szabo
What can one learn from twostate single molecule trajectories?
Biophys. J. 88, 37803783 (2005).
qbio/0502006
8. O. Flomenbom, K. Velonia, D. Loos, et al
Stretched exponential decay and correlations in the catalytic
activity of fluctuating single lipase molecules
Proc. Natl. Acad. Sci. USA 102, 23682372 (2005).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.
7. K. Velonia, O. Flomenbom, D. Loos, et al
Single Enzyme Kinetics of CALB Catalyzed Hydrolysis
Angew. Chem. Int. Ed. 44, 560564 (2005), cover.
6. O. Flomenbom, R. J. Amir, D. Shabat, and J. Klafter
Some New Aspects of Dendrimer Applications
J. Lumin. 111, 315325 (2005).
condmat/0410436
5. O. Flomenbom, R. J. Amir, D. Shabat, and J. Klafter
Dendrimer – Based Devices: Antennae and Amplifiers
D. L. Andrews Ed., Energy Harvesting Materials, (2005).
4. O. Flomenbom and J. Klafter
Resonant activation in discrete systems
Phys. Rev. E. 69, 051109 (2004).
3. O. Flomenbom and J. Klafter
Translocation of a Single Stranded DNA Through
a Conformationally Changing Nanopore
Biophys. J. 86, 35763584 (2004).
2. O. Flomenbom and J. Klafter
Single Stranded DNA Translocation Through a Fluctuating Nanopore
J.T. Fourkas, P. Levitz, M. Urbakh, K.J. Wahl Eds.
Dynamics in Small Confining Systems,
MRS Proceedings 790, P7.4.1P7.4.6 (2004).
qbio/0501014
1. O. Flomenbom and J. Klafter
Single stranded DNA translocation through a nanopore:
A master equation approach
Phys. Rev. E 68, 041910 (2003).
Selected by and appeared on the
Virtual Journal of Biological Physics Research.