Invited talks
Zdzisław Burda
Jagellonian University, Kraków, Poland
Maximal entropy random walk
We discuss a new class of random walk processes which maximize entropy. This maximal entropy random walk is equivalent to generic random walk if it takes place on a regular lattice, but it is not if the underlying lattice is irregular. In particular, we consider a lattice with weak dilution. We show that the stationary probability of finding a particle performing maximal entropy random walk localizes in the largest nearly spherical region of the lattice which is free of defects. This localization phenomenon, which is purely classical in nature, is explained in terms of the Lifshitz states of a certain random operator.
Jörn Dunkel
University of Oxford, Oxford, United Kingdom
Nonlocal observables and lightconeaveraging in relativistic thermodynamics
The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred class of hyperplanes in spacetime. (ii) There exist different, seemingly equally plausible ways of defining heat and work in relativistic systems. These ambiguities led, for example, to various proposals for the Lorentz transformation law of temperature. Traditional "isochronous" formulations of relativistic thermodynamics are neither theoretically satisfactory nor experimentally feasible. I will discuss how these deficiencies can be resolved by defining thermodynamic quantities with respect to the backwardlightcone of an observation event. This approach also allows for a straightforwardextension of thermodynamics to general relativity. Theoretical considerations are illustrated through threedimensional relativistic manybody simulations.
Marcin Fiałkowski
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Polymerinduced phase separation and ordering in ionic surfactants
I will present a new and simple method of inducing phase separation
and further ordering in solutions of ionic surfactants. In this method
the phase separation is obtained either by addition of polyelectrolytes
or nonionic polymers along with inorganic salt. The system separates
into surfactantrich and polymerrich phase. The resulting
surfactantrich phase exhibits the hexagonal ordering. The method of the
induction of the phase separation is versatile and facilitates formation
of surfactantrich ordered phases in a broad range of surfactant mass
fractions. The surfactantrich phases can be employed as templates to
fabricate structural functional materials.
Andrzej Fuliński
Jagellonian University, Kraków, Poland
Firstpassage times and related characteristics of anomalous diffusion
Tools which enable the identification of anomalous diffusion and its exponent α in
experimental or simulation series of data are discussed. Among others, the concept of
bounded average firstpassagetime <θ_{L}>_{T} to the absorbing barrier L,
averaged over finite time interval T is introduced, which corresponds to real data much
better than standard MFPT, the more that the latter is divergent in many cases.
<θ_{L}>_{T} scales as L^{2/α}. This scaling (and some other ones) is
illustrated by simulations of anomalous Brownian motion driven by thermal noise, and by
intermittent chaotic generator.
Robert Hołyst
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Viscosity in polymer solutions at nano and macroscale
We measured a viscosity of poly(ethylene glycol) (PEG 6000, 12000,
20000) in water using capillary electrophoresis and fluorescence
correlation spectroscopy with nanoscopic probes of different diameters
(from 1.7 nm up to 114 nm). For a probe of diameter smaller than the
radius of gyration of PEG (e.g. rhodamine B or lyzozyme) the measured
nanoviscosity was orders of magnitude smaller than the macroviscosity.
For sizes equal to (or larger than) the polymer radius of gyration,
macroscopic value of viscosity was measured. Mathematical relation for
macro and nanoviscosity was found as a function of PEG radius of
gyration, Rg, correlation length in semidilute solution, x , and size of
a probe, R. For R<Rg the nanoviscosity (normalized by water viscosity)
is given by exp(b(R/x)^{a}) and for R>Rg both nano and macroviscosity
follow the same curve exp(b(Rg/x)^{a}) , where b and the exponent a are
two constants close to unity. This mathematical relation was shown to
describe equally well rhodamine (of size 1.7 nm) in PEG 20000 and
macroviscosity of PEG 8 000 000 whose radius of gyration exceeds 200 nm.
Additionally, for smallest probes (rhodamine B and lyzozyme) we have
verified using capillary electrophoresis and fluorescence correlation
spectroscopy that the StokesEinstein (SE) relation holds providing that
we use size dependent viscosity in the formula. SE relation is correct
even in PEG solution of very high viscosity (three orders of magnitude
larger than that of water).
M. Howard Lee
Department of Physics, University of Georgia, Athens, GA USA
Ergometric theory of the ergodic hypothesis
The ergometric theory of the ergodic hypothesis is a physical theory for
Hermitian many body systems. It is applicable to both quantum and
classical macroscopic ensembles. The basic elements of the theory which
determine whether a dynamical variable (say A) of a system is ergodic
are the existence of the thermodynamic limit and the delocalizability
of perturbed energy coupled to dynamical variable A. In several recent
papers the workings of the ergometric theory have been demonstrated.
The ergodic theory of the ergodic hypothesis is a mathematical theory
developed over the years by Birkhoff, Khinchin and other mathematicians,
primarily applicable to classical many body problems. The essential
elements of the ergodic theory are invariant measures, transitivity and
chaos. We show that these elements are also contained in the ergometric
theory. It will be illustrated through several many body models.
Hyunggyu Park
Korea Institute for Advanced Study, Seoul, Korea
Collective synchronization in a large population of random frequency oscillators
The synchronization transition of coupled random frequency oscillators is revisited.
The Kuramoto model (global coupling) is shown to exhibit a meanfieldtype continuous
phase transition in both phase and frequency synchronization.
On the other hand, locally coupled oscillators in d space dimensions reveal two types of
synchronization transitions: meanfield behavior at d>4, and aggregation of compact synchronized
domains in three and four dimensions. In the latter case, there exists no ordering in phase
synchronization, but only in frequency synchronization, which shows an abrupt change at the
transition. We also discuss over sampletosample fluctuations as well as temporal fluctuations,
which dominate the finitesizescaling behavior near the transition.
Dmitry Postnov
Saratov State University, Saratov, Russia
Noisecontrolled pattern formation in "firediffusefire" model of neural tissue
Beside the wellknown coupling between neurons via the chemical and
electrical synapses, there are another communication pathways in the
brain tissue, that can significantly alter the network dynamics.
According to the conventional approach the extracellular environment has
fixed ionic concentrations. However, in many cases the extracellular
concentration of potassium ions can not be regarded as constant. That
represents specific chemical pathway for neurons to influence each other
and can influence strongly the behavior of a single neuron as well as
large ensembles. The "potassium accumulation hypothesis" is still
debating mechanism for the onset of epileptic seizures.
We address this problem by studying the dynamics of simplified model
systems based on excitable units each being an extension of
FitzHughNagumo model. For a a single such unit embedded in the
extracellular matter that leads to a number of noiseinduced effects,
like selfmodulation of firing rate. In the spatially extended situation
various patterns appear ranging from spirals and traveling waves to
oscillons and inverted structures depending on the parameters of the
medium.
Francesc Sagués
Universitat de Barcelona, Barcelona, Spain
Dynamical regimes of individually actuated paramagnetic colloids
I will report on different dynamical regimes in a softmatter system consisting of a
dispersed solution of micronsize paramagnetic colloidal particles. The system is actuated from outside with
an external magnetic field either precessing or simply rotating. Two situations will be considered, depending
on whether the particles are floating on a free surface or over a ferromagnetic structured garnet film. The anisotropy in
the shape of the particles will be also taken into account by reporting forcing conditions of either spherical or ellipsoidal particles.
Different scenarios of transport will be unveiled from localized to superdiffusive and ballistic. Experiments will be presented, together
with numerical simulations based on overdamped dynamic equations.
Lutz SchimanskyGeier
Humboldt Universitat, Berlin, Germany
Increase of coherence in excitable systems by delayed feedback
The control of coherence and spectral properties of noiseinduced
oscillations by timedelayed feedback is studied in a FitzHughNagumo
system which serves as a paradigmatic model of excitable systems. A
semianalytical approach based on a discrete model with waiting time
densities is developed which allows one to predict quantitatively the
increase of coherence measured by the correlation time, and the
modulation of the main frequencies of the stochastic dynamics in
dependence on the delay time. The analytical meanfield approximation
is in good agreement with numerical results for the full nonlinear
model.
[1] T. Prager, H.P. Lerch, L. SchimanskyGeier and E. Schöoll, J. Phys. A:
Math. Theor. 40, 111 (2007).
Gerhard Schmid
Augsburg University, Augsburg, Germany
Entropic particle transport
We demonstrate that transport in the presence of entropic barriers
exhibits peculiar characteristics which makes it distinctly different
from that occurring through energetic barriers. The constrained dynamics
yields a scaling regime for the particle current and the diffusion
coefficient in terms of the ratio between the work done to the particles
and available thermal energy [1,2]. The problem is analyzed under the
perspective of the FickJacobs equation which accounts for the effect of
the lateral
confinement by introducing an entropic barrier in a one dimensional
diffusion. The validity of this approximation, being based on the
assumption of an instantaneous equilibration of the particle
distribution in the crosssection of the structure, is analyzed by
comparing the different time scales that characterize the problem. A
validity criterion is established in terms of the shape of the structure
and of the applied force [2,3].
Moreover, we investigate the role of entropic barriers for the
phenomenon of "Stochastic Resonance" [4]. This Entropic Stochastic
Resonance (ESR), characteristic of smallscale systems, constitutes a
useful mechanism for manipulation and control of single molecules and
nanodevices.
[1] D. Reguera, G. Schmid, P. S. Burada, J. M. Rubi, P. Reimann, and
P. Hanggi, Entropic transport: Kinetics, scaling and control mechanisms,
Phys. Rev. Lett. 96, 130603 (2006).
[2] P. S. Burada, G. Schmid, P. Talkner, P. Hänggi, D. Reguera, and J.
M. Rubi, Entropic Particle Transport in periodic channels,
Biosystems 93, 1622 (2008).
[3] P. S. Burada, P. Hänggi, F. Marchesoni, G. Schmid, and P. Talkner,
Diffusion in confined geometries, ChemPhysChem 10: 4554 (2009)  Review
[4] P. S. Burada, G. Schmid, D. Reguera, M. H. Vainstein, J. M. Rubi,
and P. Hänggi,
Entropic Stochastic Resonance, Phys. Rev. Lett. 101, 130602 (2008).
B. Spagnolo, A. A. Dubkov, S. Spezia, L. Curcio, N. Pizzolato, A. Fiasconaro, D. Valenti,
A. La Cognata, P. Caldara, P. Lo Bue, E. Peri, S. Colazza
University of Palermo, Palermo, Italy
State University of Nizhni Novgorod, Russia
Environmental noise and nonlinear relaxation in biological systems
We investigate the role of the environmental noise in three biological systems: (i) an ecosystem described by a Verhulst model with a multiplicative Lévy noise; (ii) polymer translocation, and (ii) individuals of Nezara viridula. Specifically the transient dynamics of the Verhulst model perturbed by arbitrary nonGaussian white noise is investigated as a first biological system. For Cauchy stable noise, exact results for the probability distribution of the population density and nonlinear relaxation are derived. We find a transition induced by the multiplicative Lévy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics, and a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity. (ii) The noise driven translocation of short polymers in crowded solutions is analyzed as a second biological system. The polymer dynamics is simulated in a twodimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated and correlated noise source, and an oscillating electric field. We find a nonmonotonic behaviour of the mean first passage time and the most probable translocation time, of the polymer centre of inertia, as a function of the polymer length at low noise intensity: Moreover the mean first translocation time of the polymer centre of inertia shows a resonant activation behavior. Finally we report on experiments on the response of Nezara viridula individuals to subthreshold signals plus noise in their mating behavior. We analyzed the insect response by directionality tests and different noise intensity levels performed on a group of male individuals. The percentage of insects which react to the subthreshold signal, shows a nonmonotonic behavior, characterized by the presence of a maximum, for increasing levels of the noise intensity. This is the signature of the nondynamical stochastic resonance phenomenon. By using a "soft" threshold model we find that the maximum of the output cross correlation occurs in the same range of noise intensity values for which the activating behavioral has a maximum.
Karina Weron
Wrocław University of Technology, Wrocław, Poland
Over and undershoot compound subordination. Anomalous diffusion  relaxation consequences
The subordination form of the diffusion front resulting from the clusteringjump continuoustime random walk is presented. The jumpwaiting and waitingjump schemes, leading to different twopowerlaw relaxation processes, are discussed and shown to be related to over and undershoot compound subordination, respectively.
Ryszard Zygadło
Jagellonian University, Kraków, Poland
Thermodynamical quantities and relativity
Selected problems concerning transformational properties
of thermodynamical quantities and relativistic diffusion will be commented.
Karol Życzkowski
Jagellonian University, Kraków, Poland
On statistics of scientific citations and performance indices
Some current attempts to define performance indices based on
the number of scientific citations are reviewed. A scheme of evaluating
an impact of a given scientific article based on importance of papers quoting it is investigated. Introducing a weight of a given citation
dependent on the previous record of the author of the citing paper
we define the weighting factor of a given scientist. These weighting factors, defined by the components of the normalized leading eigenvector of the matrix describing the citation graph, allow us
to define weighted number of citations, weighted impact factor of a journal or weighted Hirsch index of an individual scientist or
of an entire scientific institution.
[1] K. Zyczkowski, Citation graph, weighted impact factors and performance indices,
preprint arxiv:0904.2110
Talks
Sighart F. Fischer and Wolfgang Dietz
Technische Universität München, München, Germany
Universal powerlaw model for the random fluctuations in the fluorescence of Cd Se/ZnS quantum dots
The fluorescence intermittency of quantum dots like Cd Se/Zns is interpreted in terms of uncorrelated nonadiabatic charge separation and charge recombination events. It is shown that light induced randomness in the charge transfer couplings can lead to a power law behaviour of the fluorescing "on""off" waiting time distributions in a well defined long time limit.
The universal exponent of 1.5 is derived for a large class of coupling distributions, which do not approach zero for arbitary small couplings. Deviations from this universal behaviour and the time window of its applicability are discussed in relation to other models (see for example the review of F. Cichos et al. Current Opinion in Colloid & Interface Science 2007, 12, 272284). The inclusion of multi channel charge separation events can give rise to larger or smaller exponents in the limit of sparce manifolds. Comparison with observed fluorescing time distributions, which show aging under continuous excitation conditions, is also discussed.
Piotr Garbaczewski
University of Opole, Opole, Poland
Lévy flights in confining potentials
We analyze confining mechanisms for Lévy flights. Two classes of
stochastic jumptype processes are considered: those driven by
Langevin equation with Lévy noise and those, named topological
Lévy processes (occurring in systems with topological complexity
like folded polymers or complex networks), whose Langevin
representation is unknown. Both classes of processes stay in affinity and
may share common stationary probability density, even if their
detailed dynamical behavior look different.
Danuta Makowiec, R. Gał±ska, A. Rynkiewicz and J. WdowczykSzulc
University of Gdańsk, Gdańsk, Poland
Multifractal estimators of shorttime autonomic control of the heart rate
Understanding of real world phenomena needs to incorporate the fact that
observations on different scales each carry essential information.
Multifractal formalism is tested if it can work as a robust estimator of
monofractal properties when scaling interval is consistent with
lowfrequency (LF) band of power spectral analysis used in estimates of
heart rate variability. Tests with fractional Brownian motions are
performed to validate two popular multifractal methods: Wavelet Transform
Modulus Maxima (WTMM) and Multifractal Detrended Fluctuation Analysis.
Only WTMM method passes the tests when scaling is limited to LF band. Then
WTMM method is applied in analysis of shorttime control processes
driving the heart rate. The significant difference is found between
multifractal spectra describing healthy hearts and hearts suffering from
left ventricle systolic dysfunction.
Igor M. Sokolov
Humboldt Universitat, Berlin, Germany
Nonergodicity in continuoustime random walk models.
We discuss nonergodicity (i.e. difference in the ensemble and time averages) in continuous time random walks (CTRW) on different substrates: simple CTRW on a homogeneous infinite lattice, CTRW in a bounded domain and CTRW on a fractal structure, all corresponding to subordination of an ergodic process of normal or anomalous diffusion to a nonergodic one. While in all these cases the ensemble averaging gives rise to the well defined, deterministic behavior, the time averaged quantities show universal fluctuations and do not lead to a deterministic limit even in the case of averaging over very long time intervals. Additional ensemble averaging of these time averages yields a deterministic behavior, which however differs from the ensembleaveraged result (in the absence of timepreaveraging). We discuss physical implication of the results, especially with respect to clear discrimination between subdiffusion caused by the presence of energetic or chemical traps and the one due to geometic disorder and crowding, as well as cases of subdiffusion of mixed origin.
[1] A. Lubelski, I.M. Sokolov and J. Klafter, Nonergodicity mimics inhomogeneity in single particle tracking, Phys. Rev. Lett. 100, 250602 (2008)
[2] T. Neusius, I.M. Sokolov and J.C. Smith, Subdiffusion in timeaveraged, confined random walks, Phys. Rev. E 80, 011109 (2009)
[3] Y. Meroz, I.M. Sokolov and J. Klafter, Subdiffusion of mixed origins: When ergodicity and nonergodicity coexist, submitted
Davide Valenti, Nicola Pizzolato and Bernardo Spagnolo
University of Palermo, Palermo, Italy
Moment equations in a system of three interacting species subject to colored noise
We study the effects of the colored noise on a LotkaVolterra system of three interacting species, namely two preys and one predator, in a twodimensional domain. The three species are affected by an external multiplicative time correlated noise, which accounts for environment fluctuations. Moreover, the interaction parameter between the two preys is a dichotomous stochastic process, which determines two dynamical regimes corresponding to different biological conditions. First, we study the noise effects on the three species dynamics in a single site. Afterwards, by a mean field approach we obtain, in Gaussian approximation, the moment equations for the species densities. Within this formalism we analyze the effect of the external colored noise on the spatially extended system. We find that the multiplicative noise does not affect the time behavior of the 1st order moments. Conversely, the 2^{nd} order moments are strongly dependent both on the intensity and correlation time of the multiplicative noise. Finally, we compare our results with those obtained by a discrete time approach based on a model of coupled map lattice.
Posters
Giuseppe Augello, Davide Valenti and Bernardo Spagnolo
University of Palermo, Palermo, Italy
Transient dynamics of short Josephson junctions under the influence of nonGaussian noise
We investigate the effects of nonGaussian white noise source on the transient dynamics of short Josephson junctions. The noise signal is simulated generating standard stable random variables with characteristic function described by Lévy index α and asymmetry parameter β. We study the lifetime of the superconductive state as a function both of the frequency of the external driving bias current and the noise intensity for different values of index α. We compare our results with those obtained in the presence of Gaussian white noise. We find the presence of noise induced effects such as resonant activation and noise enhanced stability.
Przemysław Borys
Silesian University of Technology, Gliwice, Poland
Stochastic model of a newborn's physical development
According to Vojta principles, newborn's physical development is genetically determined.
The development must go through well defined subsequent stages to achieve the final walk
and sit abilities. A frequent question of parents is how long will the development take
if the baby has some deficiencies, i.e. achievement of a certain state is delayed. Doctors
usually don't give the answer being aware of large uncertainty margins and having poor skills
in statistics to describe their predictions. In this work I try to present a model that
predicts this time based upon the development data in Vojta results and Munich Functional
Development Diagnostics. I also take into account the plasticity of the neural system that
decreases with age.
Teodor Buchner
Warsaw University of Technology, Warszawa, Poland
Dynamics of coupled rotators kicked with delay
We analyze a simple nonlinear system  a pair of mutually kicking rotators theoretically and numerically. Classification of synchronization states is supplied by theoretical analysis and verified by numerical experiment. As such a system is a toy model for cardiorespiratory synchronization, it is discussed how well can it mimic the original physiological phenomenon.
Pasquale Caldara, Alessandro Fiasconaro and Bernardo Spagnolo
University of Palermo, Palermo, Italy
Role of the multiplicative noise in a system with a metestable state
The interaction of a system with environment can be modelized with a stochastic variable that affects the
evolution of the system. This noisy interaction can be described by additive and/or multiplicative noise sources.
This kind of situation is ubiquitous in both natural [1, 2] and humanmade complex systems [3], which are open
systems. In population dynamics, for example, the noise can break the symmetry of the dynamical behaviour of
two interacting species system [4]. Metastability is quite general problem in physics and we can find examples in
condensed matter and in the study of the decaying of false vacuum states in quantum field theory [5, 6, 7]. Here
we study a model system characterized by an asymmetric bistable potential with a metastable state in the presence
of both additive and multiplicative noise sources. The role of both noise sources on the lifetime of the metastable
state will be analyzed. The effective potential of our model system allows us to analyze how the noiseenhanced
stability phenomenon [8, 9] is affected by both additive and multiplicative noise sources. This model is also
suitable to describe the essential physics of a nonequilibrium Ising lattice. We find a non monotonic behaviour of
the mean escape time that arises in the presence of both additive and multiplicative noise for certain ranges of the
parameters that can be seen as "islands of metastability".
[1] P. Sura et al., Jour. Atm. Sci. 62 1391 (2005).
[2] L. SchimanskyGeier, D. Abbott, A. Neiman, C. Van Den Broeck, Noise in complex systems and stochastic
dynamics, Proceedings of SPIE 5114, (2003).
[3] R. N. Mantegna and H.E. Stanley An Introduction to Econophysics Correlations and Complexity in Finance
Cambridge University Press, 2000.
[4] B. Spagnolo, D. Valenti, A. Fiasconaro, Noise in ecosystems: a short review, Mathematical Biosciences and
Engineering 1, 185 (2004).
[5] P. G. Debenedetti, F.H. Stillinger, Nature 410, 267 (2001).
[6] M. Gleiser, R.C. Howell, Phys. Rev. Lett. 94, 151601 (2005).
[7] P. I. Hurtado, J. Marro, P.L. Garrido J. Stat. Phys. 133, 29 (2008).
[8] N. Agudov and B. Spagnolo, Noise enhanced stability of periodically driven metastable states, Phys. Rev. E
64, 035102(R) (2001).
[9] A. A. Dubkov, N. V. Agudov and B. Spagnolo, Noise enhanced stability in uctuating metastable states , Phys.
Rev. E 69, 0611031 0611037 (2004).
Joanna DeperasStandyło
Jagellonian University, Kraków, Poland
Effect of LET and Track structure on cellcycle delay and statistical distribution of chromosome aberrations.
Investigations of the genetic effects of particle exposure are
of particular interest in relevance for application of particle beams in therapy and prediction of radiation risk in space. The key issue in understanding biophysical effects of radiation is the difference in energy deposition following irradiation with photons and heavy charged particles (Ritter 2000, Nasonova 2001, Nasonova 2004, Tenhumberg 2007, Peng 2009). Following microdosimetric concepts, distribution of imparted energy can be estimated from the knowledge of range and stopping powers of penetrating charged particles in an irradiated object. For particles, the energy is inhomogeneously deposited along the trajectory of an ion penetrating the matter with a local dose distribution within a particle track following the 1/r2 dependence.
In contrast, in the case of Xrays, the energy deposition is spatially uniform.
Due to the high local energy deposition within the particle track,
a traversal of a single ion through a cell nucleus can result in multiple chromatin breaks. This lesion “clustering” determines nonPoisson distribution of aberrations among cells. Additionally, contributions to damge coming from independent individual tracks give rise to
a compound distribution well approximated by a mixed statistics (Virsik and Harder, 1981, GudowskaNowak 2005, 2007).
We have analyzed chromosome aberration data obtained for human lymphocytes exposed to Xrays and C (LET = 175 keV/μm and 29keV/μm) and Feions (LET = 155 keV/μm). For cytogenetic analysis lymphocytes were collected in metaphase at 48,60,72 and 84 postirradiation. For the timecourse analysis a modified mathematical approach proposed by Scholz (1998) has been used. To account for the different kinetics of high and lowLET induced damage, the total amount of aberrations induced within the entire population has been determined. For each subgroup of aberrant cells the flux through mitosis was analyzed revealing correlation between delay in mitosis and number of aberrations carried by a cell. This observation is of particular importance for the proper estimation the biological efficiency of C ions and health risks associated with radiation exposure.
[1] E. GudowskaNowak, A. Kleczkowski, E. Nasanova, M. Scholz, S. Ritter, Int. J. Radiat. Biol., Vol. 81, No. 1 (2005), pp. 2332.
[2] E. Nasanova, E. GudowskaNowak, S. Ritter, G. Kraft, Int. J. Radiat. Biol., Vol. 77, No. 1 (2001), pp. 5970.
[3] S. Ritter, E. Nasanova, E. GudowskaNowak, M. Scholz, G. Kraft, Int. J. Radiat. Biol., Vol. 76, No. 2 (2000), pp.149161.
[4] E. Nasanova, K. Fussel, S. Berger, E. GudowskaNowak, S. Ritter, Int. J. Radiat. Biol., Vol. 80, No. 9 (2004), pp. 621634.
[5] S. Tenhumberg, E. GudowskaNowak, E. Nasanova, S. Ritter, Int. J. Radiat. Biol., Vol. 83, No. 8 (2007), pp. 501513.
[6] E. GudowskaNowak, R. Lee, E. Nasanova, S. Ritter, M. Scholz, Advances in Space Research 39 (2007), pp. 10701075.
[7] Y. Peng, T.B. Borak, S.D. Bouffler, R.L. Ullrich, M.M. Weil, J. S. Bedford, Radiat. Res. 171 (2009), pp. 484493.
[8] R. Virsik, D. Harder, Radiat. Res. 85 [1] (1981), pp. 1323.
[9] M. Scholz, S. Ritter, G. Kraft, Int. J. Radiat. Biol., Vol. 74, No. 3 (1998), pp. 325331.
Bartłomiej Dybiec
Jagellonian University, Kraków, Poland
Anomalous diffusion: temporal nonMarkovianity and weak ergodicity breaking
Traditionally, discrimination between Markovian and nonMarkovian process is based on the definition. If the process is Markovian, its transition probability does not depend on the history of the process and it fulfills the SmoluchowskiChapmanKolmogorov equation. A practical verification of these two criteria can be not always possible or fully conclusive. Therefore, we present an additional method which can be used to confirm the simplest version of Markovianity. This method is based on properties of sums of independent random variables. We apply the presented method to prove the increment dependent character of an anomalous process combining long waiting times with long jumps. Such a process, despite being nonMarkovian in nature, due to a competition between long waiting times and long jumps can reveal ``normal'' behavior. We also demonstrate that this anomalous process breaks the ergodicity in the weak sense. Finally, we apply the suggested method to some experimental time series proving their Markovian nature for small time scales.
[1] B. Dybiec, J. Stat. Mech. P08025 (2009).
Daniela Froemberg and Igor M. Sokolov
Humboldt Universitat, Berlin, Germany
Boundary value problems under subdiffusion
We investigate boundary value problems for subdiffusion which can be
solved within the Green functions approach, including the case when the
particles degrade at a certain rate, which corresponds to the simplest
possible chemical reaction.
Here we use the reactionsubdiffusion equations with nondecoupling
reaction and transport terms derived earlier.
Although these equations appear complicated at first glance,
it turns out that the methods for the solution of the corresponding linear
reactiondiffusion equations can easily be adopted to the anomalous case.
Simon Fugmann and Igor M. Sokolov
Humboldt Universitat, Berlin, Germany
Rupture dynamics of a bond in a grafted chain
We consider the equilibrium relaxation properties in a grafted homopolymer chain. We calculate mean first passage times of monomer distances (bonds) within the framework of the Wilemski Fixman approximation. We show that these times crucially depend on the length of the chain and the position of the bond in the chain. Close to the grafted end we observe an increase of the mean first passage time, which grows with the chain length and is the stronger the softer the bonds are. Close to the free terminal the typical passage times are lowered to a chain length independent value. Based on these results we discus the effect of spacer molecules in polymer rupture experiments performed at a constant loading rate.
Tomasz Gradowski, Maciej Mrowiński and Robert Kosiński
Warsaw University of Technology, Warszawa, Poland
Cooperation in peertopeer networks
The Internet has become one of the most important means of
communication of our century. Every second it is being used worldwide
to deliver an unimaginable amount of content. A substantial part of
this traffic can be attributed to the so called peertopeer networks
in which users can exchange data directly, without the assistance of
any intermediate server (there may be some servers involved in
establishing the connection). While used mostly for illegal file
sharing, peertopeer networks are an effective way of distributing
files to a large group of users at virtually no cost for the
publisher. Unlike centralized serverbased solutions, peertopeer
networks are as reliable (in terms of file availability) as their
users and cooperation between the file sharers plays a crucial role in
spreading files over the network. In our work we use simple models to
study the cooperative and dynamical phenomena in peertopeer
networks. By extensive numerical simulations and analytical
calculations based on the master equation we study the efficiency and
stability of this file sharing mechanism. We look for critical
parameters that determine the dynamics of such systems and discuss
ways of preventing freeriding (users who download files without
sharing them).
Saverio Bivona, Giovanni Bonanno, Riccardo Burlon, Davide Gurrera and Claudio Leone
University of Palermo, Palermo, Italy
Forecasting by seasonal and longmemory stochastic models
The idea of using a mathematical model to describe the behaviour of a physical phenomenon is well established, but in many problems we have to consider a timedependent phenomenon in which there are many unknown factors and for which it is not possible to write a deterministic model. Nevertheless, it may be possible to derive a stochastic model. The models for time series that are needed for example to achieve optimal forecasting and control are in fact stochastic models, but the choice of the suitable kind of model is never straightforward. In the present work, we test the modelling and forecasting ability of two different kinds of stochastic models: seasonal autoregressive integrated moving average models and autoregressive fractionally integrated moving average models. As an example, we employ wind speed data, but a like analysis could be developed in other fields, like for example econophysics, social sciences, engineering, natural sciences (including biology).
Robert Kosiński and Andrzej Grabowski
Central Institute for Labour Protection  National Research Institute, Warszawa, Poland
Warsaw University of Technolog, Warszawa, Poland
Percolation in online networks
We study bond and site percolation in four real social networks: two Internet society of friends consisting of over 10^{6} and 10^{7} people, over 10^{6} users of music community website and over 5×10^{6} users of gamers community server. We study the properties of those systems (e.g. the network components size distribution) in function of fraction p of nodes or links that retained in network. We have calculated critical fraction p_{C} at which the percolation transition takes place and giant component emerges.
Robert Hołyst and Marek Litniewski
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Heat transfer at the nanoscale: evaporation of nanodroplets
We demonstrate [1] using molecular dynamics simulations of the LennardJones fluid that the evaporation process of nanodroplets is limited by the heat transfer. The temperature is continuous at the liquidvapor interface if the vapor/liquid density ratio is higher than about 0.05 and discontinuous if it is lower. The temperature in the vapor has a scaling form T(r,t) = T[r/R(t)], where R(t) is the radius of evaporating droplet at time t and r is the distance from its center. Mechanical equilibrium establishes very quickly, and the pressure difference obeys the Laplace law during evaporation.
[1] R. Holyst and M. Litniewski, Phys. Rev. Lett. 100, 055701 (2008)
Agnieszka Jurlewicz, Justyna Trzmiel, Joanna Janczura and Marek Teuerle
Wrocław University of Technology, Wrocław, Poland
Twopowerlaw relaxation processes in gallium doped Cd_1xM_xTe
We present the results concerning dielectric response of gallium doped Cd_0.99M_0.01Te:Ga, revealing stochastic origins of the observed nonDebye patterns of the corresponding relaxation processes. We detect the twopowerlaw behavior of the measured permittivity with m and n, the low and highfrequency exponents, respectively, that satisfy m<1n. To explain the empirical results we propose the stochastic diffusion scenario leading to the generalized MittagLeffler relaxation function.
Ewelina Kalwarczyk
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Polymerinduced phase separation in solutions of ionic surfactants
We present a new method to induce phase separation in solutions of ionic surfactants. In this method, the phase separation is obtained either by addition of polyelectrolytes or nonionic polymers along with inorganic salt. As a result, the system separates into polyelectrolyterich (or nonionic polymer rich) and surfactantrich phase. Four types of the mixtures were investigated: (i) anionic surfactants and anionic polyelectrolytes, (ii) cationic surfactants and cationic polyelectrolytes, (iii) cationic surfactants and nonionic polymers, and (iv) anionic surfactants and nonionic polymers. We found that the addition of polyelectrolyte with the charge of the same sign as that of surfactant can induce the phase separation in a wide range of surfactant concentrations. The addition of nonionic polymers induces the phase separation only in solutions of cationic surfactants. Moreover, the addition of nonionic polymers induces the phase separation only for relatively high total content of polymer and surfactant in the mixture. We found however that the addition of inorganic salt to the mixture of cationic surfactant and nonionic polymer triggers the phase separation even for a small concentrations of surfactant. In our experiments, water as well as mixtures of water and polar solvents were employed as solvents. Based on the optical microscopy studies we found that the surfactantrich phase represents hexagonal ordering.
Tomasz Kalwarczyk
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Tracing of single nano objects as a tool for viscosity measurements in polymer solutions
We measured[1] the viscosity of poly(ethylene glycol) (PEG 6000, 12 000, 20 000) in water using
capillary electrophoresis and fluorescence correlation spectroscopy with nanoscopic probes of differ
ent diameters (from 1.7 to 114 nm). For a probe of diameter smaller than the radius of gyration of
PEG (e.g. rhodamine B or lyzozyme) the measured nanoviscosity was orders of magnitude smaller
than the macroviscosity. For sizes equal to (or larger than) the polymer radius of gyration, macro
scopic value of viscosity was measured. A mathematical relation for macro and nanoviscosity was
found as a function of PEG radius of gyration, R_{g} , correlation length in semidilute solution, ξ, and
probe size, R. For R < R_{g} , the nanoviscosity (normalized by water viscosity) is given by exp(b(R/
ξ)^{a} ), and for R > R_{g} , both nano and macroviscosity follow the same curve, exp(b(R/ξ)^{a} ), where a
and b are two constants close to unity. This mathematical relation was shown to equally well describe
rhodamine (of size 1.7 nm) in PEG 20 000 and the macroviscosity of PEG 8 000 000, whose radius of
gyration exceeds 200 nm. Additionally, for the smallest probes (rhodamine B and lysozyme) we have
verified, using capillary electrophoresis and fluorescence correlation spectroscopy, that the Stokes
Einstein (SE) relation holds, providing that we use a sizedependent viscosity in the formula. The SE
relation is correct even in PEG solutions of very high viscosity (three orders of magnitude larger than
that of water).
[1] R. Holyst, A. Bielejewska, J. Szymanski, A. Wilk, A. Patkowski, J. Gapinski, A. Zywocinski, T. Kalwarczyk, E. Kalwarczyk, M. Tabaka, N. Ziebacz, and S. A. Wieczorek, Phys. Chem. Chem. Phys. 2009.
Tadeusz Kosztołowicz and Katarzyna D. Lewandowska
Jan Kochanowski University, Kielce, Poland
Medical University of Gdańsk, Gdańsk, Poland
Subdiffusion in a composite medium
We study a system with two infinitely thin partially permeable walls
divided this system into three homogenous parts. In each part there are
different values of subdiffusion coefficients and subdiffusion parameters.
The system is described by the linear differential equations with
fractional time derivative. We derive the Greens functions for this system
which have an universal character and allow one to calculate the
concentration profiles for any initial conditions. We also discuss the
properties of the concentrations found for the system where initially
concentration was unzero only in the one part.
Andrzej Krawiecki
Warsaw University of Technology, Warszawa, Poland
Stochastic resonance in systems on hierarchical and modular networks
Stochastic resonance in two exemplary complex systems in which the structure of interactions between coupled units is that of modular or hierarchical networks is investigated. The first system consists of threshold elements coupled to form a hierarchical RavaszBarabasi network. The second one is the Ising model on two weakly coupled scalefree networks. In both cases, under ceratin conditions, structural stochastic multiresonance occurs, i.e., signaltonoise ratio or spectral power amplification exhibit multiple maxima as functions of the input noise intensity or temperature, respectively. The appearance of multiresonance is directly related to the complex structure of interactions.
Monika Krasowska and Zbigniew J. Grzywna
Silesian University of Technology, Gliwice, Poland
Thermodynamical aspects of generalzed fractal dimension case of cancer cell lines metastasis
The generalized fractal dimension ($D_q$) and its Legendre transform ($f(\alpha)$, partitioned iterated function system semifractals (PIFSSF) and lacunarity, were used to analyze quantitative differences in secretory membrane activities. Two rat prostate cancer cell lines (MatLyLu and AT2) as well as two human breast cancer cell lines (MDAMB231 and MCF7) were analyzed. MatLyLu and MDAMB231 showed the strong metastatic membrane potential whereas AT2 and MSF7 showed the weak metastatic membrane potential. Based on the previous [1, 2] we can conclude, that the vesicle patterns differ depending on the metastatic potential of cancer cells and can be characterized using generalized fractal dimension particularly $D_0$, $D_1$, $D_{1}$, and $\Delta D$. Generally this tools can be potentially useful in cancer diagnostics. In this presentation we have shown thermodynamical aspects of generalized fractal dimension in case of cancer cell lines metastasis.
[1] M. Krasowska, Z. J. Grzywna, M. Mycielska and M. B. A. Djamgoz, Eur. Biophys. J. 33, 535, (2004).
[2] M. Krasowska, Z. J. Grzywna, M. Mycielska and M. B. A. Djamgoz, Eur. Biophys. J., DOI:10.1007/s002490090516z.
Angelo La Cognata, Davide Valenti, Alexander A. Dubkov and Bernardo Spagnolo
University of Palermo, Palermo, Italy
State University of Nizhni Novgorod, Russia
Dynamics of a LotkaVolterra system in the presence of nonGaussian noise sources
We consider a LotkaVolterra system of two competing species subject to multiplicative αstable Lévy noise. The interaction parameter between the species is a random process which obeys a stochastic differential equation with a generalized bistable potential in the presence both of a periodic driving term and an additive αstable Lévy noise. We study the species dynamics, which is characterized by two different dynamical regimes, exclusion of one species and coexistence of both ones, analyzing the role of the Lévy noise sources.
Katarzyna D. Lewandowska and Tadeusz Kosztołowicz
Medical University of Gdańsk, Gdańsk, Poland
Jan Kochanowski University, Kielce, Poland
The scaling method to study the subdiffusion and subdiffusionreaction equations
We consider a (sub)diffusionreaction system of two initially separated
substances A and B reacting according to the formula \lambda_A A+\lambda_B
B \rightarrow P(inert). To study the normal diffusion equation one usually
uses the scaling method. However, this method cannot be applicable to the
subdiffusionreaction system due to the specific properties of fractional
derivative. We propose modified scaling method and use it to study the
subdiffusionreaction system.
Adam Lipowski
Adam Mickiewicz University, Poznań, Poland
Prisoner's dilemma on reinforcing weighted networks
We examine a directed weighted network of agents playing the prisoner's
dilemma game. Network weights (that determines probabilities of who
plays with whom) depends on the accumulated payoff obtained from playing
the game between a pair of agents. Simulations show that such a network
evolves towards a randomgraphlike structure. In a version of the model
where weights depends also on the total payoff accumulated by a given
agent, the network evolves towards scalefreelike structure. Wealth
distribution and kinetics of these two versions of the model are also
much different.
Krzysztof Małysiak and Zbigniew J. Grzywna
Silesian University of Technology, Gliwice, Poland
Ionic strength influence on the potassium ion channel rate of Ninactivation
Ninactivation is the process in which one of the four, charged Nendings of the potassium ion channel protein binds to its allosteric centre, plugs the channel's pore and stops the ion transport. Apart from this scenario, it has been experimentally shown that Ninactivation can be recovered for the channels with its Nendings removed, by delivering them into the bathing solution. We develop the Langevintype model for the random walk of inactivating Nendings in electrostatic field, at different ionic strengths of the bathing solution. Model's output is directly compared with the measurement of an ensemble averaged transchannel current. In conclusions we point and discuss important differences between two mentioned modes of Ninactivation that cannot be easily distinguished in experiment.
Patrycja Nitoń, Andrzej Zywocinski, Robert Hołyst, Robert Kieffer and Carsten Tschierske
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Cardinal Stefan Wyszyński University, Warszawa, Poland
MartinLutherUniversity HalleWittenberg, Halle, Germany
Reversible aggregation of bolaamphiphiles with partially fluorinated lateral chains at the air/water interface
We present the results for four new compounds from the group of partially fluorinated Xshaped bolaamphiphiles. Three of them are partially fluorinated and the forth one is left in hydrogenated form for comparison. The compounds of this type have broad medical applications (e.g. gene delivery) because of their liquidcrystalline properties, strong interaction with air/water interface and tendency to selforganization. The fluorinated bolaamphiphiles exhibit an unusual reversibility of Langmuir isotherms even though compressed at maximum rate of compression up to a total collapse of the film. The subsequent compressiondecompression cycles follow perfectly the first isotherm proving also a very good reproducibility of the isotherms. Fluorination of the lateral chains is the key property here, since the hydrogenated compound does not exhibit such perfect reversibility of the isotherm.
Anna OchabMarcinek
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Extrinsic noise passing through a MichaelisMenten reaction: Universal response of a genetic switch
The study of biochemical pathways usually focuses on a small section of the protein interaction network. Fluctuations in such a system are not only generated intrinsically by molecular dynamics, but also extrinsically, by interactions of the system with the rest of the network and its environment.
Concentration fluctuations of a substance outside the studied system can enter it through a nonlinear uptake reaction which acts as a nonlinear filter. Varying the intensity of the input noise varies the mean of the output noise after the passage through the filter, which causes a change of stability properties of the system. Using an analytical method of small noise expansion, I prove that when weak and rapid noise enters the system through a reaction of MichaelisMenten type (reaction rate function monotonically increasing and concave), then the steady states of the system always shift to the right as noise intensity increases.
I demonstrate this by an example of two different models of lac operon. The bistable switch responds to fluctuations in extracellular TMG/lactose concentration in an asymmetric manner because of the displacement of its bistability region to the right: As noise intensity increases, uninduction becomes easier and induction becomes more difficult.
The steadystate displacement due to weak and rapid extrinsic noise passing through a nonlinear filter is a universal phenomenon: It is independent of the kinetics of the system but it only depends on the filtering function. The calculation method presented enables even qualitative predictions of this effect, only by inspection of the experimental data.
Krzysztof Pawełek, John J. Kozak and Zbigniew J. Grzywna
Silesian University of Technology, Gliwice, Poland
University of Chicago, Chicago, USA
Synchronous vs. asynchronous motion of K+ in the KcsA selectivity filter
The difference of synchronous vs. asynchronous motion of the K+ ions and water molecules in the selectivity filter of the KcsA bacterial channel is studied by recently proposed Markovian model. Five different cases are taken into account: the simplest system without any interactions, the system with only repulsive interactions between K+ ions or only attractive interactions between K+ ions and the carbonyl groups lining the channel, the system with electrostatic potential added to the membrane and in the last case, the system, in which all interactions are turned on. The degree of asynchronicity in K+ ions and water molecules motion is taken quantitatively by "an asynchronicity factor". Considering the simplest system with excluded volume effects only, the difference in mean passage time through the channel is in the range 50%75%. In the other cases the difference is also important and can not be neglected.
Dominique Persano Adorno, Nicola Pizzolato, Davide Valenti and Bernardo Spagnolo
University of Palermo, Palermo, Italy
Complex dynamics of leukemic cells under intermittent therapy
The evolutionary dynamics of cancerous cell populations in a model of Chronic Myeloid Leukemia (CML) is investigated. A Monte Carlo approach is applied to model the cancer development and progression by simulating the stochastic evolution of initially healthy cells which can experience genetic mutations and modify their reproductive behavior, becoming leukemic clones. Front line therapy for the treatment of this kind of tumor is achieved by tyrosine kinase inhibitors, namely imatinib (Gleevec) or, more recently, dasatinib or nilotinib. Despite they represent the first example of a successful molecular targeted therapy, the development of resistance to these drugs is observed in a proportion of patients, especially those with advancedstage CML. In the present work, we simulate an imatiniblike treatment of CML by modifying the fitness and the death rate of cancerous cells and describe the several scenarios in the evolutionary dynamics of blood cells as a consequence of the efficacy of the different modeled therapies. In our model, resistant cancerous cells, which are insensitive to the therapy, are generated from leukemic cells by a stochastic process of genetic mutation. We study how the patient response to the therapy changes when the drug is assumed with an intermittent time scheduling. Of course the best results, in terms of a permanent disappearance of the leukemic phenotype and containment of resistance, are achieved with a continuous therapy. However, our findings demonstrate that an intermittent therapy could also represent a valid choice in patients with high risk of toxicity, despite the retard on the complete restoring of healthy cells. The description of this biological system in terms of a complex system of evolving cells contributes to an overall understanding of the cancer dynamics.
Monika Pyzalska, Piotr Korczyk and Piotr Garstecki
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Upscaling microfluidics
The idea to conduct reactions within droplets in microfluidic channels has been
intensively exploited in the recent years due to the following, attractive
characteristics: i) fast (millisecond) mixing that is either difficult or impossible to
achieve in singlephase microfluidics, ii) lack of dispersion of time of residence that is
inherent to single phase flowthrough reactors iii) ease of controlling the kinetics of
reactions via the simple correspondence between the time of residence and the
position in the channel, and iv) efficient convection from the bulk of the droplets to
their (extended in ratio to volume) surface that provides for efficient phase transfer.
The intrinsically small throughput of these systems is preferable for analytical
purposes, yet for applications in synthesis it constitutes a significant drawback.
A potential solution lies in up scaling of the channels of millimetric cross
sections. We have investigated experimentally the answers to the question of how
much can the microfluidic systems be enlarged while preserving the attractive
features of flow at the microscale. In our poster we will present results from
characterization the formation of droplets, the rate of mixing in droplets and the rate
of phase transfer in systems with increasing crosssections of the channels (up to 2
mm, and in particular cases even larger).
Pawel Romanczuk
Humboldt Universitat, Berlin, Germany
Effective diffusion and quasideterministic transport of Brownian particles in a spatiotemporally oscillating potential
We consider overdamped Brownian dynamics in an temporally oscillating and spatially periodic potential. We analyze the nondirected diffusive transport which shows oscillation induced enhancement of the effective diffusion and present an approximate formula for the effective diffusion
coefficient. Furthermore we analyze the effect of the oscillating potential on directed transport due to the application of a constant force. We show via numerical simulations the existence of an optimal force at which the deterministic dynamics is in resonance with the potential oscillations
giving rise to directed transport with extremely low dispersion and discuss a simplified theoretical description of the observed effect.
Aleksandra Rybak, Monika Krasowska, Krzysztof Małysiak and Zbigniew J. Grzywna
Silesian University of Technology, Gliwice, Poland
Structure morphology problems in the air separation by magnetic membranes
Study of transport processes through membranes is a difficult problem, especially, if structuremorphology aspects have to be taken into account. In this
work we are analyzing the complex behavior of nonclassical membrane systems. Considered system is being studied basing on the phenomenological (ideal
Fickian or nonideal), and molecular (random walk on a fractal lattice) approach. Comparison with experimental data for the case of oxygen and nitrogen
diffusing through magnetic membranes is also presented.
Marta Siek, Agnieszka Kamińska and Piotr Garstecki
Cardinal Stefan Wyszyński University, Warzsawa, Poland
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Generation of polymerencapsulated microbubbles in a microfluidic flowfocusing system
Microfluidics is a technique for precise handling of small quantities of fluids. In recent years microfluidics has been demonstrated to provide useful tools for preparation of emulsions and foams. For example, it is possible to form highly monodisperse droplets, bubbles, or structured (multiple) droplets.
Bare bubbles, even if prepared almost ideally monodisperse, are unstable  they undergo coalescence, Ostwald ripening and dissolution of the gas into the surrounding liquid  until saturation. There are different ways to increase the stability of bubbles, by e.g. creation of a shell typically composed of either a protein (e.g., denatured albumins) or a surfactant such as phospholipids or a polymer like a poly (acrylic acid), present at the surface of the bubble.
Gas microbubbles, stabilized by a surfactant or polymer coating, have become well established over the past 2030 years as the most effective type of contrast agent available for ultrasound radiography. More recently, their potential for use in therapeutic applications including targeted drug delivery, gene therapy and focused ultrasound surgery has also been investigated. Providing a high degree of control over microbubble size, composition, stability and uniformity is needed.
We demonstrate formation of monodisperse bubbles in a microfluidic flowfocusing device, and stabilization of these bubbles by building a polymer (poly (acrylic acid)) coating around them, all in situ in the same device and process.
Susane E. L. Silva, Mendeli H. Vainstein, and Fernando A. Oliveira
University of Brasilia, Brasilia, Brazil
Breaking in polymeric chains
Extensive simulations call atention to the anomalous dynamics of breaking of anharmonic chains and its connection with basic principles of statistical mechanics[1, 2]. The dynamics of a set of rectilinear chains was followed solving simultaneously a set of coupled Langevin equations. The
problem addressed here is that of calculating the breaking strength of a polymer fibril immersed
in a fluid. This problem has technological interest due the use of petrol additive [3]. Long chains
are better for drag reduction; however they are weak and have a small lifetime, which is the reason
one needs to change the motor oil frequently, since successive breaking reduces the chain to small
ineffective parts. Many essential biological processes for life depend on the reaction of various bonds
to an applied force. One such example is how leukocytes recognize invading pathogenic organisms
in blood vessels [4]. Atomic force microscope (AFM) [5, 6] and biomembrane force probe (BFP)
[79] are now being used to determine the energy landscape of those complex molecules, as well as
scaling laws [10, 11]. We present here a short review of those ideas and their implications, and we
also discuss the state of art of the theory.
[1] F. A. Oliveira and P. L. Taylor, J. Chem. Phys. 101 10118 (1994).
[2] F. A. Oliveira, Phys. Rev. B 52 1009 (1995).
[3] A. Maroja, F. A. Oliveira, M. Ciesla and L. Longa, Phys. Rev. E 63 061801 (2001).
[4] R. Merkel, Phys. Rep. 346 343 (2001).
[5] Y.S. Lo, Y.J. Zhu, and T. P. B. Jr, Lagmuir 17 3741 (2001).
[6] O. H. Willemsen, M. M. E. Snel, A. Cambi, J. Greve, B. G. D. Grooth, and C. G. Figdor, Biophys 79 3267 (2000).
[7] R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans Nature (London) 397 50 (1999).
[8] E. Evans, A. Leung, D. Hammer, and S. Simon Proc. Natl. Acad. Sci. U.S.A. 98 3784 (2001).
[9] E. Evans, Biophys. Chem. 82 83 (1999).
[10] C. L. Dias, M. Dube, F. A. Oliveira, and F. A. Oliveira, Phys. Rev. E, 72 011918 (2005).
[11] S. E. L. Silva, M. H. Vainstein and F. A. Oliveira, to be published.
Stefano Spezia, Dominique Persano Adorno, Nicola Pizzolato and Bernardo Spagnolo
University of Palermo, Palermo, Italy
Nonlinear temperature and field dependence of electron spin depolarization in GaAs semiconductors
In this work we investigate the influence of temperature and transport conditions on
the electron spin relaxation in ntype GaAs bulk semiconductors. The electron
transport, including the evolution of the spin polarization vector, is simulated by a
Monte Carlo procedure which keeps into account all the possible scattering phenomena
of the hot electrons in the medium. Electronspin states in semiconductor structures
relax by scattering with imperfections, other carriers and phonons. Spin relaxation
lengths and times are computed through the D'yakonovPerel process since this is the
more relevant spin relaxation mechanism in the regime of interest (10<T<300 K). The
decay of the initial spin polarization of the conduction electrons is calculated as a
function of the distance under the presence of a static electric field varying in the
range 0.013 kV/cm. We find that the electron spin relaxation distance and time have a
nonmonotonic dependence on both the lattice temperature and the electric field
amplitude. We discuss the behaviour of the electron spin relaxation lengths and times,
showing the best conditions to achieve extended functionality in spinbased devices,
to be exploited on future information processing systems.
Anna Strzelewicz and Zbigniew J. Grzywna
Silesian University of Technology, Gliwice, Poland
On the measures of coupling in isothermal mass transport through magnetic membranes
It is known from the theory of linear nonequilibrium thermodynamics, that when several species are simultaneously diffusing, the flow of one species influences the flow of another, i.e. there are cross effects between diffusing species. In the paper we consider the diffusional system consisted of two components gas, permeating through a planar membrane of thickness l, where external (magnetic) field affects one component transport. An operational activity of magnetic field is coverd by drift term in the transport equation. An influence of the two components on each other transport (coupling) could be measured by the "influence factor IF". We have introduced a couple of different quantitative measures of IF. It turned out however, that in our case IF is small (weak coupling) and, as a first approximation, we can use two independent PDEs for N_{2} and O_{2}, respectively i.e. D_{12}=D_{21}=0 in the set.
Marcin Tabaka
Institute of Physical Chemistry, Polish Academy of Sciences, Warszawa, Poland
Accurate genetic switch in escherichia coli: novel mechanism of regulation by corepressor
Understanding a biological module involves recognition of its structure and the dynamics of its principal components. In this report we present an analysis of the dynamics of the repression module within the regulation of the trp operon in Escherichia coli. We combine biochemical data for reaction rate constants for the trp repressor binding to trp operator and in vivo data of a number of tryptophan repressors (TrpRs) that bind to the operator. The model of repression presented in this report greatly differs from previous mathematical models. One, two or three TrpRs can bind to the operator and repress the transcription. Moreover, reaction rates for detachment of TrpRs from the operator strongly depend on tryptophan (Trp) concentration, since Trp can also bind to the repressor–operator complex and stabilize it. From the mathematical modeling and analysis of reaction rates and equilibrium constants emerges a highquality, accurate and effective module of trp repression.
This genetic switch responds accurately to fast consumption of Trp from the interior of a cell. It switches with minimal dispersion when the concentration of Trp drops below a thousand molecules per cell.
Natalia Ziębacz, Stefan A. Wieczorek, Tomasz Szymborski, Piotr Garstecki and Robert Hołyst
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Cardinal Stefan Wyszyński University, Warszawa, Poland
Thousandfold acceleration of phase decomposition in polymer / liquid crystal blends
Smallangle light scattering measurements were carried out on 5CB/PS (4cyano4'npentylbiphenyl/polystyrene) and 8CB/PS (4cyano4'noctylbiphenyl/polystyrene) mixtures during phase separation in the AC electric field. The size of polymer domains in LC matrix was determined as a function of time, film composition, amplitude and frequency of applied external electric field. For 5CB/PS and 8CB/PS, in the absence of electric field or in a high frequency (>30 Hz) electric field, we found diffusion growth of domains, L(t)~t^{α}, in time t with exponent α=0.3±0.04. In the low frequency electric field (<30 Hz) the phase separation process in the isotropic phase was accelerated more than one order of magnitude for moderate fields of amplitude 3V/μm. For 5CB/PS and 8CB/PS mixtures in the AC field of frequency 2 Hz and amplitude 3.3V/μm we found exponential growth of the domain's size L(t)~exp(bt). We gave a set of experimental evidence that ion impurities in liquid crystals are responsible for the acceleration of the phase separation process in liquid crystal/polymer mixtures.
Xia Xin
Institute of Physical Chemistry Polish Academy of Sciences, Warszawa, Poland
Incorporation of carbon nanotubes into lyotropic liquid crystal induced by phase separation
We incorporated carbon nanotubes (CNTs) including singlewalled carbon nanotubes (SWNTs) and multiwalled carbon nanotubes (MWNTs) into nonionic surfactant ndodecyl octaoxyethene monoether (C12E6) lyotropic liquid crystal (LLC) phase formed spontaneously by phase separation in the presence of nonionic hydrophilic polymer poly (ethylene glycol) PEG 20000. The properties of LLC/CNTs composites were investigated by polarized optical microscopy, Raman spectra and smallangle Xray scattering measurements. The results obtained clearly indicated that SWNTs have been successfully incorporated into the lytropic hexagonal upper phase formed by C12E6 without destroying the LLC matrix and MWNTs are more difficult to be incorporated into LLC matrix compared with SWNTs due to their larger tube diameter. Moreover, the incorporation of CNTs can also induce interesting changes of the host LLC phase, which is also of great fundamental interest. So, the effects of temperature, concentrations of CNTs, C12E6 and PEG 20000 on the properties of LLC/CNTs composites were also observed. The results showed that all of these factors can significantly influence the properties of LLC/CNTs composites.
