||Phase separation phenomena in bilayer lipid membranes
Abstract: A significant feature of many biological membranes is
that the two layers, or leaflets, of their bilayer
structure have different chemical compositions. Specifically
the two layers contain different lipids and also have different
concentrations of cholesterol. In particular, it may happen that
the composition of one layer is such that it would be expected to phase
separate into a fluid cholesterol-rich phase and a fluid cholesterol-poor
phase, but the composition of the other layer favors miscibility.
What will happen? What effect do the two layers have on each
I will report on a study of these questions using a model based on
a Landau free energy. The model includes the fact that the presence
of cholesterol favors increased orientational ordering of the lipid
hydrocarbon chains (i.e. reduction of the average number of
gauche C-C bonds). It also includes the entropy of mixing
and molecule-molecule interactions that produce phase
separation, typified by a critical temperature and a critical
concentration. An essential feature is that the two leaflets
are coupled by a free energy term that promotes orientational
ordering in the hydrocarbon chains of one layer if the other
layer orders. The model is analyzed to obtain phase diagrams for
The dominant result is that phase separation in one leaflet drives
phase separation in the other leaflet at the same temperature,
although the difference between the separated phases in the
second layer is weaker. In principle a further liquid-liquid
phase separation is possible at lower temperature. The special
case of coupled layers having the same composition is also
||The Quantum Smoluchowski Equation|
Abstract: In this talk I will briefly discuss how the strong friction limit in quantum
mechanics leads to the low temperature version of the classical Smoluchowski
equation based on an exact description of dissipative quantum systems . This
in turn also shows that recent derivations by means of high temperature master
equations are not consistent. As a specific application the phase diffusion of
overdamped Josephson junctions is considered  and the changeover from
coherent Cooper pair tunneling to Coulomb blockade
discussed. Some recent extensions of this descriptions are addressed.
- J. Ankerhold, P. Pechukas, and H. Grabert, Phys. Rev. Lett. 87, 086802
- J. Ankerhold, Europhys. Lett. 61, 301 (2003).
||The unreasonable effectiveness of equilibrium-like theory for
interpreting non-equilibrium experiments
Abstract: There has been great interest in applying the results of statistical
mechanics to single molecule experiements. Recent work has
highlighted so-called non-equilibrium work-energy relations and
Fluctuation Theorems that take on an equilibrium-like (time
independent) form. Here I give a very simple heuristic example where
an equilibrium result (the barometric law for colloidal particles)
arises from theory describing the thermodynamically non-
equilibrium phenomenon of a single colloidal particle falling through
solution due to gravity. This simple description arises from the
fact that the particle, even while falling, is in mechanical
equilibrium (gravitational force equal the viscous drag force) at
every instant. The results are generalized using Onsager's least
dissipation approach for stochastic processes to derive time
independent equations that hold for thermodynamically non-equilibrium
(and even non-stationary) systems. These equations offer great
possibilities for rapid determination of thermodynamic parameters
from single molecule experiments.
The benefit of hydrodynamic interactions
Abstract: We experimentally and theoretically investigate the collective behavior of
three colloidal particles that are driven by a constant force along a toroidal
trap. Due to hydrodynamic interactions, a characteristic limit cycle is
observed. When we additionally apply a periodic sawtooth potential, we find a
novel caterpillar-like motional sequence that is dominated by hydrodynamic
interactions and promotes the surmounting of potential barriers by the
|Sergey M. Bezrukov
||Static and dynamic disorder in protein
folding: Fluctuating ion channels
Abstract: By analyzing fluctuations in biochemical processes, it is
possible to reveal their important kinetic features that are usually hidden in
average rates. This is particularly true for a variety of modern techniques that
can probe the functioning of proteins on a single-molecule level. Among the new
questions to address is that of static and dynamic disorder in protein folding.
While static disorder is seen as time-persistent deviations of individual reaction
rates from their ensemble average, dynamic disorder can often be observed as rate
variations with time. I discuss these phenomena using recent single-molecule
enzymology experiments with a special emphasis on the channel-forming membrane
|Chris Van Den Broeck
||From Brownian motor to Brownian
Abstract: Onsager symmetry implies that a Brownian motor, driven by
a temperature gradient, will also perform a refrigerator function upon loading.
We analytically calculate the corresponding heat flux for an exactly solvable
microscopic model and compare it with molecular dynamics simulations.
We show that, by a combination of the motor and refrigeration
function, it is in principle possible to achieve Carnot effiency.
- C. Van den Broeck, R. Kawai and P. Meurs, Phys. Rev. Lett. 93, 090601 (2004).
- C. Van den Broeck, P. Meurs and R. Kawai, New J. Phys. 7, 10 (2005).
- C. Van den Broeck, Phys. Rev. Lett. 95, 190602 (2005).
- C. Van den Broeck, Carnot efficiency revisited, to appear Adv. Chem. Phys..
- C. Van den Broeck and R. Kawai, From Brownian motor to Brownian
||Novel Coupling of
Nonlinear Elements for Fun and Profit
||Langevin approach to anomalous diffusion in fixed potentials: Recent
results and perspectives
Abstract: The direct derivation of closed fractional diffusion equation for
probability density from Langevin equation with white Levy noise,
based on the theory of infinitely divisible distributions, is proposed
. Describing the Markovian anomalous diffusion in the form of Levy
flights, this equation gives a good opportunity to investigate a
probabilistic and time characteristics of anomalous diffusion in
different smooth potential profiles. We review recently obtained
results regarding the stationary probability distributions, the rate
of barrier crossing, and the features of resonant activation
phenomenon for Levy flights. We derive also the exact equation to
compute the mean lifetime (nonlinear relaxation time) for arbitrary
smooth potential and solve it for the metastable cubic potential. The
exact expression for the mean lifetime obtained by integration of the
solution mentioned is used to analyze the peculiarities of noise
enhanced stability (NES) phenomenon  in the case of anomalous
diffusion. In conclusion, some perspectives of further investigations
in this area are discussed.
- A.A. Dubkov, B. Spagnolo, Fluct. Noise Lett. 5, L267 (2005).
- A.A. Dubkov, N.V. Agudov, and B. Spagnolo, Phys. Rev. E 69, 061103 (2004).
||Several generalizations of
the Smoluchowski equation
Abstract: We will give first an historical overview of several generalizations including
internal coordinates and distances which were first given by Debye, Huckel,
Onsager and Falkenhagen. Further we will discuss applications to electrolytes,
polymers etc., and also give some overview on the statistical derivations by
means of projection operators etc.. In the last part we will give new
Smoluchowski-type equations for active Brownian particles.
||Noise-induced enantiomer separation in a microfluidic channel
Two different molecules that are mirror images of each other,
the so-called enantiomers, can possess very different functional
properties in biological systems or as pharmaceuticals.
For this reason, separation and analysis of enantiomers is of
great importance. Recently, Kostur et al.  proposed a new
separation scheme for enantiomers based on spatially variable
vorticity of the flow in a microfluidic device.
We investigate the motion of enantiomers in fluid flows through
microchannels without vortices. We show that two different
enantiomers can have different migration velocities along the channel,
resulting in their separation. In discussing the underlying physical
mechanism we identify the presence of thermal noise as an
- M. Kostur et al., Phys. Rev. Lett. 96, 014502 (2006).
||Smoluchowski Rate Equation Approach to Cluster Size
Distribution: Beyond Mean-Field
Abstract: Cluster nucleation and growth by aggregation is the central feature of many
physical processes, from polymerization and gelation in polymer science,
flocculation and coagulation in aerosol and colloidal chemistry, percolation
and coarsening in phase transitions and critical phenomena, agglutination and
cell adhesion in biology, to island nucleation and thin-film growth in
materials science. Detailed information about the kinetics of aggregation is
provided by the time-dependent cluster-size distribution, a quantity which can
be measured experimentally. Based on the von Smoluchowski rate equations,
considerable theoretical effort has been made toward a better understanding of
the mechanisms determining the scaling properties of aggregation phenomena.
While the standard rate-equation approach has been successful in predicting the
scaling behavior of average quantities such as the total cluster density, when
there are significant spatial fluctuations it gives predictions which
are in significant disagreement with both experiments and kinetic Monte Carlo
simulations. This failure can be traced to the fact that the usual mean-field
approach does not include correlations between the size of an island and its
local environment. Such correlations are especially important in lower
dimensions, such as in cluster growth on surfaces. In this talk I will present
a new method for calculating the cluster-size distribution which solves the long lasting problem of determining the correlations between the size of an
island and that of its capture zone. Applying this method to submonolayer
epitaxial growth, we show that by coupling a set of evolution equations for the
capturezone distributions with a set of rate equations for the island densities
one may obtain accurate predictions for the time and size-dependent rates of
monomer capture. In particular, we show that by using this method one can
obtain excellent results for the capture numbers and island-size dis
tributions in irreversible growth on both one- and two dimensional substrates.
|Henrik K. Flyvbjerg
||Cell motility as persistent random motion:
theories from experiments
Abstract: Cell migration is essential in many physiological and
pathological processes and in emerging medical technologies
that depend on it for colonization of biomaterials.
Quantitative migration studies rely on motility models
for data interpretation. Finding no model in the literature
that captures the nature of our data, we used the data
to capture the nature of suitable models. An analysis
of trajectories followed by motile human keratinocytes
and fibroblasts lead to cell-type-specific motility models.
These models show that cells have memory, and apparently
reflect the cells' different roles in the organism.
The method of analysis is general and may be applied to
other motile cell-types and organisms.
||Asymmetries and anomalous phenomena in ionic transport through nanochannels
Abstract: Biological and synthetic nanochannels exhibit two essential biophysical
properties: selective ion conduction and the ability to gate open in response to
appropriate stimulus. Both these properties are related to several untypical modes of
behavior of the diffusional and conduction currents, absent in the normal
(electro-)diffusion. We present our recent results concerning some of such anomalous
||Smoluchowski coagulation equation in
modeling polymerization processes
The Smoluchowski coagulation equation was derived back in 1916.
It is usually linked with diffusivity and size of aggregating particles. In its contemporary form it reads:
where ci is the number (concentration) of clusters of size i (i = 1, 2, ...)
and the coagulation kernel Ki,j contains all the physics of the aggregation process.
In 1944 Stockmayer used eq.
to derive the size distribution of (macro)molecules formed in a polymerization process.
Ki,j was then the rate coefficient at which molecules of size i reacted with those of size j.
At present, the idea behind the Smoluchowski coagulation equation has been applied for various
types of polymerization process. Its application revealed the significance of the so-called time
correlations in the polymerization processes and their effect on the size distribution of polymer molecules.
The method of using eq. (1) in polymer science will be outlined and its application in particular processes,
e.g. for reducing molecular dispersity in hyperbranched polymerization.
||Quantum Brownian motion and Quantum Brownian motors
||Evaporation/condensation in a microscale
Abstract: The evaporation/condensation processes are studied in the framework of
diffuse interface hydrodynamics supplemented by the van der Waals
equation of state. The processes are studied in the time scale from
picoseconds to microseconds and in the length scale from tenth of
nanometers to micrometers. The evaporation process proceeds
quasistationary, governed by the heat flow along the temperature
gradients. Condensation is never quasistationary. It proceeds two orders
of magnitude faster than evaporation. Simple formula for evaporation
rate of a liquid droplet is derived and compared with full solution of
hydrodynamic equations. It shows that mass transfer during evaporation
follows the heat flow. Finally it will be shown that vapor bubbles can
be used, during condensation, as a high-temperature (2000 K for argon)
fast (50 ps) microreactors at low temperature (280 K) of a surrounding
fluid. This fact will bring the subject close to the sonoluminescence
||Searching a circular DNA strand: a stochastic approach
We introduce and explore a stochastic model of an enzyme searching for a target site on a circular DNA strand. The enzyme performs a local scan of the strand and occasionally, according to a given exponential rate, randomly relocates its position on the strand. The local scanning corresponds to a one-dimensional continuous motion on the strand, whereas the relocation corresponds to a 3D motion in the medium containing the strand.
An analysis of the model proposed for general scanning and relocation mechanisms is carried out, and closed-form analytic formulae for the mean and Laplace transform of the overall search duration are computed. Thereafter, an asymptotic analysis for long DNA strands is conducted, yielding the limiting probability distribution of the overall search duration. The asymptotic analysis is further generalized to encompass the cases of parallel and massively-parallel searches performed by an ensemble of independent enzymes.
The general results obtained are applied to the following examples of local scanning mechanisms:(i) directed linear motion, (ii)Brownian motion, (iii)fractional Brownian motion, and (iv) fractional Lévy motion. For these examples the asymptotically optimal relocation rates are calculated.
||Ergodic hypothesis in Hermitian many-body problems
The ergodic hypothesis (EH) says that the time and ensemble averages of a
dynamical quantity are the same. The studies of its validity by ergodic
theory or quasi-ergodic theory are far removed from physics. A more
physically based study is to do the time averages and to compare it the
ensemble average. This would be the most direct and clearest way of
testing EH. Why has it not been done earlier?
To do time averaging, one must know the time evolution of a dynamical
variable by solving the Heisenberg equation of motion, itself no simple
task. But now there are general solutions by the recurrence relations
method. Thus the time averaging can be achieved. As a result, a new
ergodic condition has been formulated and the physical mechanisms that
underly EH have been found.
Reactions between diffusive species in constrained geometries have long
been known to exhibit kinetics that differ profoundly from mean
field behavior, reflecting the importance of spatial and temporal
fluctuations in these systems. When the reactive species are
subdiffusive, the kinetics are yet again entirely different. We further
explore these kinetics when the subdiffusive reactants are subject to
competing decay processes, e.g., when the reactants have an intrinsically
||Breakdown of photon transport due to Anderson localization
Constructive interference between reciprocal multiple scattering paths of
waves in disordered media gives rise to coherent backscattering and
Anderson localization. We report on optical coherent backscattering and
time resolved transmission experiments on very turbid powders of high index
colloidal particles. These samples have photon transport mean free paths l*
close to or smaller than the wavelength 2pi/k and very weak absorption so
that multiple scattering paths lengths up to 10m (> 10^7 scattering events)
can be analyzed. We find a slowing down of the photon diffusion constant
at long times which scales with kl* [1,2] in quantitative agreement with
predictions of scaling theory of localization [3,4].
 M.Störzer, P.Gross, C.M.Aegerter, G.Maret, Phys.Rev.Lett. 96, 063904 (2006)
 C.M.Aegerter, M.Störzer, G.Maret, submitted (2006)
 E.Abrahams, P.W.Anderson, D.C.Licciardello, T.V.Ramakrishnan,
Phys.Rev.Lett. 42, 673 (1979)
 R.Berkovitz, M.Kaveh, J.Phys.Cond.Mat. 2, 307 (1990)
|Maciej A. Nowak
||Brownian Walks of Large Matrices
Abstract: We briefly discuss the method of free random variables, its relation
to probability theory and to random matrices and we point at possible
applicatons in a context of the stochastic diffusion theory.
In order to demonstrate this approach, we apply the formalizm of free
random variables for the cases of additive matrix diffusion and
for matrix analogues of multiplicative Brownian walks.
||Two level system perturbed by
noise: the Random Matrix Theory Approach
Abstract: By using the random matrix approach we solve analytically the model of an effective
two-level system coupled to a noise reservoir represented by a random Wishart-Cauchy matrix.
We compare the calculated spectral properties of the system with the numerically simulated results
and outline possible applications of the model in the field of condensed phase reactions.
||Centenary of Marian Smoluchowski's kinetic theory of
the Brownian motion
Abstract: Seminal ideas developed by Marian Smoluchowski in his 1906 papers on the
diffusion and on the Brownian motion present the most creative application of
the probability theory to the description of physical phenomena.
||Weizmann Institute of Science
||Hamiltonian theory of stochastic acceleration
Abstract: Stochastic acceleration, defined in terms of a stochastic equation of motion for the acceleration, is derived from a
Hamiltonian model. A free particle is coupled bilinearly to a harmonic bath through the particle's momentum and coordinate.
Under appropriate conditions, momentum coupling induces velocity diffusion which is not destroyed by the spatial coupling.
Spatial-momentum coupling may induce spatial subdiffusion. The thermodynamic equilibrium theory presented in this Letter
does not violate the second law of thermodynamics, although the average velocity squared of the particle may increase in
time without bound.
|Harald A. Posch
||From diffusion to the colour of the sky:
Marian Smoluchowski's scientific roots and his impact on statistical physics
Abstract: Already during his studies in Vienna, Marian Smoluchowski was
strongly affected by the fierce debate, which raged about the existence
of atoms, and which, at the end of the 19th century, was preparing the
grounds for a new science, theoretical physics. Ultimately, the probabilistic
approach he pioneered already in his early work was decisive for the
acceptance of the atomistic point of view. It also had a profound
influence on the evolution of statistical physics as a whole. We demonstrate
the implications of his work with a few examples.
|Jose Miguel Rubi
||Fick-Jakobs kinetics for entropic transport
in quasi-onedimensional structures
Abstract: We study nonlinear transport processes through quasi-onedimensional
structures, as pores, ion channels and zeolites, exhibiting changes in their shape
along the propagation direction. The constrained dynamics of the particles is
analyzed by means of the Fick-Jakob equation for the probability distribution which
assumes that particles evolves through entropic barriers. Our analysis reveals that
entropic transport is distinctly different from that occurring though energy
barriers. Applications to different dynamic situations are presented.
||Noise-mediated rhythms in active media
I consider two scenarios of noise-mediated oscillatory regimes in extended
active media. The first situation corresponds to the well-known BZ reaction in
its photosensitive version. By forcing it with a spatiotemporally distributed
noise we obtain a sustained target-like pattern of wave propagation from an
otherwise (in absence of noise) purely excitable condition. Experimental,
theroretical and numerical results will be briefly summarized (1).
In the second scenario we propose a moel to explain the phenomenon known as
plankton blooms. It is based on the coupling of an activator-inhibitor dynamics
for two plankton populations with a turbulent flow field simulated in terms of
a stochastic velocity field (2).
- S. Alonso et al., PRL 87, 078302 (2001); S. Alonso et al., PRE 65, 066107
- R. Reigada et al., Proc. R. Soc. Lond. B, 270, 875 (2003)
||Anomalous transport in geological formations: Theory and observations|
Abstract: Anomalous transport of chemical tracers has been observed at field and laboratory scales, in
a wide variety of porous and fractured geological formations. Quantification of this widespread phenomenon has been
a long-standing problem. These formations are heterogeneous on a very wide range of spatial scales and the difficulty in
capturing the complexities of tracer plume migration patterns suggests that local heterogeneities cannot be "averaged out"
even on small scales (as has been the practice). Recently, a theory developed within the continuous time random walk (CTRW)
framework, based on a picture of transport as a sequence of particle transfer rates, has been demonstrated, via laboratory-
and field-scale observations, to provide an effective means to quantify this anomalous transport. In highly disordered systems
we show that statistically rare, slow transition rates limit transport. Hence, the key step is to retain the entire range of
these transitions with a pdf (r,t), where r is a transition step displacement and t is the transfer time, instead of upscaling
from mean local rates. The present application is shown to be a uniquely rich example of anomalous transport as the tracer
plume and breakthrough curves can be measured directly. It has generated a new level of confirmation and further development
of the theory. Most importantly, we have now developed the CTRW within the framework of partial differential equations (pde)
and generalize its applicability to non-stationary domains (e.g., extended field sites) and interactions with "immobile states"
(matrix effects). These pde's are non-local in time as they incorporate a memory function M(t), based on r (r,t), and the
Laplace space form of them can be solved by both analytical and conventional numerical methods. We show that physical models
of M(t) encompass full tracer (plume) dynamics with multirate mass transport, fractional-derivative- and
advective-dispersion- equations as specialized cases.
||Low randomness in
ratchets and steppers
Abstract: We introduce the diffusion coefficient and the Peclet-number as a
measure of quality for transport in ratchets and for the motion of
steppers. We calculate both for simple discrete ratchet models and
give conditions which reduce randomness of the transport. In addition
periodic forcing can be used to synchronize the motion of Brownian
steppers which corresponds to a state with low randomness.
J. A. Freund, and L. Schimansky-Geier, Phys. Rev. E 60, 1304 -1309 (1999).
B. Lindner, M. Kostur, and L. Schimansky-Geier, Fluctuations and Noise
Letters 1, R25 (2001).
B. Lindner and L. Schimansky-Geier, Phys.Rev.Lett. 89, 230602 (2002).
T Prager, L Schimansky-Geier and I M Sokolov, J. of Physics: Cond.
Matter 17, 3661 (2005)
|Michael F. Shlesinger
||Stretched Times and Divergent
Time Scales Near the Glass Transition
|Igor M. Sokolov
||Response, fluctuations and reactions in
Abstract: Many physical systems showing subdiffusive behavior can be described within
a framework of continuous time random walks (CTRW) with waiting time
distributions lacking the mean. The corresponding random processes are not
homogeneous in time. For example, the behavior of the system depends on the
time elapsed from the instant when the system was prepared, the effect
typically quoted as aging. More complicated aging effects arise in systems
under influence of time-dependent fields and in reacting systems, where
products of reaction are introduced into the system later in course of
reaction. We discuss here the general problem of kinetic equation
description of CTRW and related systems and illustrate the situation by
several results pertinent to response of such systems to external fields,
field-induced fluctuation effects and to behavior of reactions in systems
||Lifetime of metastable states and suppression
of noise in interdisciplinary physical models
Abstract: Metastability is a generic feature of many nonlinear systems, and the problem
of the lifetime of metastable states involves fundamental aspects of
nonequilibrium statistical mechanics. The investigation of noise-induced
phenomena in far from equilibrium systems is one of the approach used to
understand the behaviour of physical and biological complex systems. The
enhancement of the lifetime of metastable states due to the noise and the
suppression of noise through resonant activation phenomenon will be discussed
in models of interdisciplinary physics: (i) dynamics of an overdamped Josephson
junction; (ii) transient regime of the noisy FitzHugh-Nagumo model; (iii)
||Long-time behavior of
driven Smoluchowski processes with metastable states
|Horacio S. Wio
||Stochastic resonance in extended systems: general
nonequilibrium potential framework
Abstract: Many phenomena related to Stochastic resonance (SR) occur
in extended systems, a fact that together with the possible
technological applications, motivated many recent studies
showing the possibility of achieving an enhancement of the
system's response by means of the coupling of several units
in what conforms an extended medium. In a series of papers
 we have studied the SR phenomenon in extended systems,
when transitions between two different spatial patterns
occurs (i.e. bistability). This was done exploiting the
concept of non-equilibrium potential (NEP) : a Lyapunov
functional of the associated deterministic system that, for
non-equilibrium systems, plays a role similar to that of a
thermodynamic potential in equilibrium. Such NEP characterize
the global properties of the dynamics: attractors, relative
stability of these attractors, height of the barriers
separating attraction basins. In addition, it allows us to
evaluate the transition rates among the different attractors.
Here I will report on how some known forms of the NEP, for
scalar as well as many component systems, could be exploited
in order to analyze SR in extended systems. I will discuss,
from the NEP's viewpoint, several aspects: the effect of the
NEP's symmetry, of density-dependent coupling, the role played
by local and non-local couplings, as well as the possibility of
other related phenomena like the so called "system-size SR".
I will also show a way to evaluate the amplification factor
as a measure of the SR response in extended systems.
 H.S.Wio, Phys.Rev. E 54, 3045 (1996); F.Castelpoggi,
H.S.Wio, Europhys.Lett. 38, 91 (1997) and Phys.Rev. E 57,
5112 (1998); S.Bouzat, H.S.Wio, Phys. Rev. E 59, 5142
(1999); B.von Haeften, R.Deza, H.S.Wio, Phys.Rev.Lett.
84, 404 (2000); H.S.Wio, S.Bouzat, B.von Haeften,
[Proc. STATPHYS21: 21st IUPAP International Conf. on
Statistical Physics], Physica A 306C, 140 (2002);
B.von Haeften, et al, Phys. Rev. E 69, 021107 (2004);
B.von Haeften, G.G. Izus and H.S.Wio, Phys. Rev. E 72
(2), 021101 (2005).
 R.Graham, in "Instabilities and Nonequilibrium Structures",
Eds.E.Tirapegui and D.Villaroel (D.Reidel, Dordrecht, 1987);
H.S. Wio, in "4th. Granada Seminar in Computational Physics",
Eds. P. Garrido and J. Marro (Springer-Verlag, Berlin, 1997),
|Wojbor A. Woyczynski
||Large scale structure of the universe and scaling
limits for clasical and anomalous conservation laws
Abstract: Burgers turbulence is one of the accepted formalisms for the adhesion model of
the large-scale distribution of matter in the Universe. Variational methods can
be used to establish evolution, in the scaling limit, of the quasi-Voronoi
tesselation structure of shock fronts dependent on random potentials and
initial data. Self-similar solutions can also play an important role in studies
of anomalous conservation laws.
||Atomic physics meets condensed matter physics
||The intertwining of structure and dynamics in liquid crystals|
Abstract: Molecular organization (structure) and dynamics are strictly coupled in
liquid crystals (LC), as shown, for instance, by the classical Nordio-Smoluchowski stochastic
equation for the molecular reorientation of a molecule in uniaxial nematics [1,2],
where the phase structure enters with an effective anisotropic molecular field.
This equation has been generalized in many ways, e.g. to more complex biaxial and, recently,
chiral solutes and phases . However, while these equations are invaluable in analyzing
experimental data for a variety of techniques, the number of structural and dynamical
parameters they require rapidly increases, making their predictive power relatively limited.
On the other hand computer simulations of liquid crystals have made important progresses and
molecular  and atomistic  resolution models have become increasingly important.
In particular reasonable predictions of the nematic-isotropic transition temperatures from
atomistic molecular dynamics now start to become feasible for realistic systems .
Here we shall discuss how state of the art computer simulations can now be used to provide
some important information that complements stochastic models, and how the two approaches can
to some extent be combined. In particular we shall show some recent examples for the structure
and dynamics of the popular nematic 4-pentyl, 4'-cyano biphenyl 5CB .
- see, e.g., A. Ferrarini, P. L. Nordio and G. J. Moro, in The Molecular Dynamics of Liquid Crystals,
edited by G. R. Luckhurst and C. A. Veracini (Kluwer, Dordrecht, 1994) p. 41 and references
- W. Haase and S. Wrobel, Relaxation Phenomena (Springer-Verlag, Berlin, 2003).
- D. Frezzato, G. J. Moro and C. Zannoni, J. Chem. Phys. 122, 164904 (2005).
- C. M. Care and D. J. Cleaver, Rep. Prog. Phys. 68, 2665 (2005).
- M. R. Wilson, Internat. Rev. Phys. Chem. 24, 421 (2005).
- R. Berardi, L. Muccioli and C. Zannoni, ChemPhysChem, 5, 104 (2004).
- G. Tiberio, L. Muccioli, R. Berardi, C. Zannoni, A. Ferrarini, M. Cestari, G. Moro, to be submitted (2006)
If you are not an invited speaker, you may present a poster.
|Michael Alania*, Renata Modzelewska, Anna Wawrzyńczak-Szaban
||Einstein – Smoluchowski equation and problem of
galactic cosmic ray time-dependent modulation
Abstract: We developed a time-dependent model based on the Parker's
transport equation to describe a propagation of galactic cosmic rays (GCR) in the interplanetary space.
The model is five dimensional - time t and rigidity R dependent partial differential equation in
the spherical coordinate system (r, q, j). We numerically solve this 5-D partial differential equation
assuming that the scattering of GCR particles in the irregularities (turbulence) of the interplanetary
magnetic field (IMF) can be considered as a Brownian motion and the Einstein-Smoluchowski relation is
||On the mathematics of Ball and Chain models
||Spontaneous oscillations of a two-phase flow in a
Abstract: We study pressure-driven flow of a liquid containing droplets of another
fluid through a network of microchannels. The droplets flow into the network
at constant frequency, at intervals T.
When a droplet arrives at the point in which the channel branches into two,
it enters the channel where the volumetric flow is larger. However,
the presence of droplets in channel affects its hydrodynamic resistance,
so that two subsequent droplets do not have to choose the same way.
This system displays two paradigm features of non-linear systems:
amplification of the sligthest difference between the inflow into the branches
to a binary choice of the trajectory, and the feedback between subsequent
choices through the long range interactions transmitted via the distribution
of pressure in the system.
We investigate the dynamics of this system for large occupancies of
the network by the droplets.
For many simple networks we observe that the system achieves
a stationary state and the number of droplets in each channel stabilizes
at a constant level (with fluctuations not greter than few droplets).
Surprisingly, there are also networks for which the stationary state
does not exist. Instead, we observe spontaneous oscillations of the number
of droplets in the channels, with an amplitude much larger than one
droplet and a period much longer than T.
|Carmen Schmitt, Bartłomiej Dybiec, Peter Hänggi, Clemens Bechinger,
||Stuttgart, Kraków, Augsburg
||Experimental study of resonant activation
Abstract: Resonant activation is a generic effect for the barrier crossing dynamics of temporally
modulated energy landscape. Here the escape of a Brownian particle over a periodically modulated
double-well potential barrier is investigated experimentally and numerically. The problem
of resonant activation is revisited with the attention on the effect of periodic modulation of the
barrier on optimal value of the mean escape time in the system. The experimental measurements
of the resonant activation phenomenon in a colloidal system are accompanied with computer simulations.
||Extinction statistics in N random interacting species
Abstract: An N-species Lotka-Volterra system randomly interacting in the presence of a
multiplicative noise is analyzed. The investigation is focused on the
statistical properties of the extinction times of the populations. The role of
the external noise on the extinction statistics is studied.
|Agnieszka Gil-świderska, Renata Modzelewska, Michael V. Alania
||On the 27–day variation of the galactic cosmic
rays intensity and anisotropy
Abstract: We propose a new model to describe the-27 day variations of the galactic
cosmic ray (GCR) intensity and anisotropy based on the Parker’s transport
equation. In the model are included the heliolongitudinal asymmetries of the
solar wind velocity and the interplanetary magnetic field (IMF) turbulence
among other classical processes responsible for the GCR modulation in the
interplanetary space. We found that the distinction of the amplitudes of the
GCR intensity and anisotropy in different the positive (A>0) and the negative
(A<0) polarity epoch is caused by the heliolongitudinal asymmetry of the GCR
particles convection due to drift in the regular heliospheric magnetic field.
We estimated an influence of the character of the radial decay of the
heliolongitudinal asymmetries of the solar wind velocity and the IMF turbulence
on the expected amplitudes of the 27-day variations of the GCR intensity and
anisotropy. The theoretical calculations are compared with the exper
imental results obtained by neutron monitors data for different the A>0 and
A<0 epoch of solar cycle. We believe that the proposed model is compatible to
describe the-27 day variations of the GCR intensity and anisotropy in the
energy range of 5-50GeV.
||Active Stochastic Quantization
Abstract: Stochastic quantization provides an interesting connection between
quantum field theory and statistical mechanics, with new applications
especially in gauge field theories. Euclidean quantum field theory is
viewed as the equilibrium limit of a statistical system coupled to a
thermal reservoir; the Euclidean Green functions become identical to
Active stochastic quantization is a proposed generalization of this
quantization scheme by employing active brownian motion.
|Adam Kleczkowski, Piotr Kleczkowski
||Monte-Carlo Methods for Shaping Time-Frequency Areas for the
Selective Mixing of Sounds
Abstract: The method of Selective Mixing of Sounds is an innovative technology
in audio engineerging. It is a non-linear process in which we attempt to
reduce the information from several tracks of audio during the otherwise
routine operation of mixing these tracks to a single track in a musical
recording. The most conceptually challenging element of the method is a
procedure of determining areas of the time-frequency plane in which a single
track is dominating. The procedure needs to take into account the
information about the energy transmitted in each track at a given
time-frequency combination. However, using local information only leads to
high distortions of the signal and rapid switching among tracks. A smoothing
technique is necessary to produce large and compact areas of dominance by a
single instrument. The smoothing also needs to preserve shapes important for
the perception of tone colour, sound attack and decay and other features,
characteristic for different instruments. The choice of a particular method
has a major effect on the overall quality of the sound. We propose a range
of novel methods, based on an iterative Monte-Carlo approach. While
computationally expensive, these methods are very flexible. The approach
focuses here on a single time-frequency event and uses a set of
deterministic or probabilistic rules to assign to it a particular track. The
selection depends not only on the properties of all tracks at the event, but
also on its neighborhood. The rules are then applied sequentially to all
events, either in a systematic or random order. The procedure is then
repeated until the required level of smoothing is achieved. In this way, the
selection of a dominant track for any given time-frequency event is based on
a large number of events. This allows preservation of some characteristic
details of an instrument, while selecting the most important signal for each
area of the time-frequency plane.
|Robert Kosiński, Andrzej Grabowski
||Properties of evolving directed network with local rules and intrinsic variables
Abstract: We present a model of evolution of directed network, based on local rules. It generates a complex network with the
properties of real systems, like scale-free distribution of outgoing and ingoing connectivity. Each node is characterised by
intrinsic variable S, and number of outgoing links kout. As a result of network evolution, the number of nodes and links, as
well as their location, change in time. For critical values of control parameters a transition to a scale-free network is
observed. Our model reproduce also others nontrivial properties of real networks, e.g. large clustering coefficient and lack
of correlations between age of a node and its connectivity.
Krystian Kubica*, Stanisława Koronkiewicz, Sławomir Kalinowski
||Monte Carlo model of the induction of lipid membrane
Abstract: The phenomenon of electroporation is preceded by induction and expansion of
defects, responsible for the pre-pore excitation. We examine the mechanism of
the induction of the field-driven defects by Monte-Carlo simulations. The study
is based on the improved Pink model, which includes explicit interactions
between polar heads and energy of interactions between the heads and the field.
No anomalous deformation of the molecules is allowed. The study, provided for
bilayer dipalmitoyl-phosphatidylcholine (DPPC) membrane in the gel (300 K) and
fluid (330 K) phases, shows dependence of the membrane conformational and
energetical state on the value of electric field. We observe that the electric
field affects the number of molecules in the gel and in the fluid states. In
the layer at the negative potential, when the transmembrane voltage is above
Uc ~ 280 mV, lipid heads abruptly reorient and the number of local
spots with fluid conformation increases. The other layer slightly tends to tighten its structure, producing additional mechanical stress
between layers. Lipids showed complete insensivity to electric field within
physilogical limits, U < 70 mV.
|Tadeusz Kosztołowicz*, Katarzyna D. Lewandowska**, Michał Penkowski**
||Application of hyperbolic subdiffusion equation to
study the electrochemical impedance
Abstract: We use the hyperbolic subdiffusion equation with fractional time derivatives
(generalized Cattaneo equation) to study the transport process of electrolytes
in gels and porous medium. In particular, we apply the equation to obtain, for
a process with non-vanishing relaxation time, the formula of electrochemical
impedance in a spatially restricted sample. Comparing the theoretical formulas
with the experimental Cole-Cole plots of impedance, we find the parameters
describing the transport (such as subdiffusion parameters and relaxation times)
for the investigated materials.
|Małgorzta Krawczyk, Krzysztof Kułakowski
||Formation of DNA networks - computer simulations|
Abstract: Continuous search for potential applications of DNA is motivated by special
features of the DNA molecules. In particular, it is possible to construct
networks of DNA [1,2]. Here we report results of the computer simulation of a
formation of networks from two kinds of molecules: linear and branched
(Y-shaped). The simulation is performed on a basis of two-dimensional
Our aim is to analyze the distribution of the pore size in the network, as
dependent on the concentration of DNA in the system. Here we demonstrate, that
the obtained distribution does not depend on the density of the branched
- Seeman N.C., TIBTECH 17 (1999) 437
- M.J.Krawczyk and K.Kulakowski, Lecture Notes in Computer Science (2006), in print.
|Natalia Kruszewska, Adam Gadomski
||How to get 2D model biopolymer polycrystals based on a
mesoscopic Smoluchowski-type dynamics supplemented by computer experiment?
Abstract: Based on a Smoluchowski-type model, formulated in a phase space of the linear
object's size (relevant stochastic variable) in terms of the mesoscopic
nonequilibrium thermodynamics (MNET)  as a guiding formalism, we are looking
for its basic trends and characteristic features in a suitably designed
computer experiment . It turns out that the basic and most interesting
trends are recovered, although both ways, i.e. MNET and computer model, are
sometimes able to see things for their own in a profitable way. It implies that
both approaches are useful in examining, e.g. biopolymer polycrystals termed
- D. Reguera, J.M. Rubi, J.M.G. Vilar, J. Phys. Chem. B 109, 2005
- N. Kruszewska, A. Gadomski, Conference of the Condensed Matter Division,
poster Dy 46.83, 2006
- A. Gadomski, Ber. Bunsenges. Phys. Chem. 100 134, 1996.
||Effects of vibratonal nonequilibrium on fast
nonadiabatic processes of energy and charge transfer
Abstract: Considerable developments in ultrafast laser spectroscopy
offer a powerful tool for studying the very initial stages of photosynthesis.
These involve the energy transfer within an antenna system followed by the primary
electron transfer in a reaction centre and last no longer than few picoseconds.
Of a similar rate are processes of vibrational relaxation which, consequently,
have to be taken into account in the correct description of the phenomenon.
In a few recent papers, this was done by numerical solving of a complex system
of quantum master equations. Here, a simplified formalism is proposed combining
transition processes with diffusion in an energy space. Analytical formulae for
effective rate constants for the transitions are derived and a transient kinetics is considered.
The model explains a peculiar temperature and wavelength dependence of pomp-probe spectra observed.
|| Molecular dynamics study on the influence of the quencher concentration on the rate of simple
The influence of quencher concentration on the rate of the reaction: A+B –> C+B (B – quencher) is analyzed by
performing large scale computer simulations [1,2]. The reagents are represented by identical soft spheres. Two different
types of systems are considered: simple liquids at high and moderate density described by deterministic MD and very low
density systems in which the spheres are immersed in the Brownian medium. It is shown that the excess in the rate coefficient
caused by the finite quencher concentration is not universal and manifests specific behavior depending on considered system.
For the deterministic systems the excess is positive for short times and negative in the long time limit. For the Brownian
systems the excess is always positive and, except for very short times, constant. It is also shown that the relative excess
in the surviving probability for a very wide range of time can be described by an universal quadratic function of the
ncentration. A very strong correlation between the excess in relative value of spatial correlations between the reagents and
the excess in the rate coefficient is observed. It is also shown that the A-A and A-C interactions have some influence on the
excess values. A simple model for this effect is presented.
- M. Litniewski, J. Chem. Phys. 123, 124506 (2005)
- M. Litniewski, J. Chem. Phys. in press
- M. Kostur et al., Phys. Rev. Lett. 96, 014502 (2006).
|Krzysztof Małysiak, Zbigniew Grzywna
||On the Ball and Chain Model by Simple Diffusion
||Smoluchowski's consideration of limits of the second law of thermodynamics is topical again
Abstract: Thoughts of great scientists, on the one hand, seem obvious and, on the other hand, keep topicality during a long time. The point of view by Marian Smoluchowski on the second law of thermodynamics expounded in  seems obvious for physicists of 20 century although it is written in this paper that most scientists of 19 century rejected the atomic-kinetic theory of heat. Smoluchowski was first who argued why the perpetuum mobile is not possible in spite of the persistent equilibrium motion, for example, of Brownian particles. This argumentation repeated by Richard Feynman in his well known consideration of the ratchet/pawl combination  seems indubitable. Nevertheless the problem of limits of the second law is topical now as well as the century ago [3,4]. The argumentation by Smoluchowski is based on a firm foundation: any equilibrium motion can not be ordered because of chaotic equilibrium motion of all. This equality of universal motion prevent a breach of symmetry because
of an direct equilibrium motion. The postulate on impossibility of any direct equilibrium motion seems self-evident because of the equality of directions in space. Nobody could make doubt of the equal probability of motion in opposite directions since if anybody says that a right direction has higher probability than opposite one he should explain why no left. But even this self-evident postulate is violated in quantum systems . It will be explained in the present work on the example of the experimental result considered in  why the Bohr’s quantization violates symmetry of equilibrium motion and challenges the second law.
- M. Smoluchowski, “Gultigkeitsgrenzen des zweiten Hauptsatzes der Warmetheorie,” in Vortrage uber kinetische Theorie der Materie und der Elektrizitat (Mathematische Vorlesungen an der Universitat Gottingen, VI). Leipzig und Berlin, B.G.Teubner, 1914, pp.87-105; translation “Validity limits of the second law of thermodynamics” in Usp. Fiz. Nauk 93, 724-748 (1967).
- R.P Feynman, R. B Leighton, M. Sands, The Feynman Lectures on Physics, Addison-Wesley, Reading, Mass. (1963).
- Daniel Sheehan, Eds. Quantum Limits to the Second Law. AIP Conference Proceedings 643, Melville, New York, 2002.
- V. Capek and D. Sheehan, Challenges to the Second Law of Thermodynamics. Theory and Experiment. Springer, 2005.
- A.V. Nikulov, "Brownian Motion and Intrinsic Breach of Symmetry", the talk at the 13th General Meeting of the European Physical Society "Beyond Einstein - Physics for the 21th Century", Bern, Switzerland, 11-15 July 2005; “Symmetry Breaking and the Law of Entropy Increase”, Symmetry: Culture and Science, 16, 47-69, (2005).
- J. Berger “The Chernogolovka experiment”, Physica E 29, 100-103, 2005.
Ewa Gudowska-Nowak, Alessandro Fiasconaro, Bernardo Spagnolo
||Co-occurrence of resonant
activation and noise-enhanced stability in the Michaelis-Menten
Abstract: We investigate a stochastic version of a simple enzymatic reaction
which follows the generic Michaelis-Menten kinetics. At
sufficiently high concentrations of reacting species, the
molecular fluctuations can be approximated as a realization of a
Brownian dynamics for which the model reaction kinetics takes on
the form of a stochastic differential equation. After eliminating
a fast kinetics, the model can be rephrased into a form of a
one-dimensional overdamped Langevin equation. We discuss physical
aspects of environmental noises acting in such a reduced system,
pointing out the possibility of coexistence of dynamical regimes
where noise-enhanced stability and resonant activation phenomena
can be observed together.
|Rafał Orlik, Antoni C. Mitus, A.Z. Patashinski, M. Ratner
||Local structure percolation in 2D Lennard-Jones liquid
Abstract: The concept of precolation on lattices is generalized onto the case of locally ordered but globally disordered systems. These ideas are applied to a 2D Lennard-Jones liquid simulated using molecular dynamics method. We find that local solid-like structures precolate close to the liquidus line.
|Otto Riefert, Antoni C. Mitu´s,
||On local solid-like order in 2D Lennard-Jones liquid
Abstract: The concentration of local solid-like structure in 2D Lennard-Jones liquid is analyzed
using earlier proposed probabilistic analysis. The line (narrow domain) where this concentration
becomes negligible is found, and constitutes a natural continuation in the pressure-temperature
thermodynamic plane of the gas-liquid coexistence line. The question of related anomalies of
physical parameters is briefly discussed.
|Piotr Romiszowski, Andrzej Sikorski, Piotr Adamczyk
||Structure of polymer chains in an adsorbing slit. a
Computer simulation study
Abstract: The aim of the study was the investigation of polymer molecules located between
two parallel and impenetrable attractive surfaces. The chains were constructed of united atoms
(segments) and were restricted to knots of a simple cubic lattice. Each polymer consisted of three
chains of equal length emanating from a common origin (a uniform star). Since the chains were at good
solvent conditions the only interaction between the segments of the chain was the excluded volume
effect. The properties of the model chains were determined by means of Monte Carlo simulations with a
sampling algorithm based on chain's local changes of conformation. The influence of the chain length,
the size of the slit and the strength of adsorption on the structure of the system were studied.
The differences and similarities in the structure (tails, trains, loops and bridges) for different
adsorption regimes and size of the slit were shown and discussed. The dynamic behavior of the chain's
structural elements was also studied.
||Statistical description of a non-Brownian suspension
|Julian Sienkiewicz, Piotr Fronczak, Janusz A. Hołyst
||Discrete effects on average path length scaling in
Abstract: We show that, depending on the network's average degree, mean distance in
scale-free and random complex networks may exhibit deviations from well known
scaling laws such as dependence on logarithm of network's size or logarithm of
degrees product. It can be shown both analiticly and using numerical
simulations that this behavior has its origin in discretization of path length
distributions. A discussion about relevance of this feature to applications of
real-world complex networks is presented.
|Andrzej Sikorski, Dominik Gront
||Thermodynamic properties of polypeptide chains.
Parallel tempering monte carlo simulations
Abstract: A coarse-grained model of polypeptide chains was designed and studied.
The chains consisted of united atoms that represented amino acid residues. The united
atoms were located at the positions of alpha carbons and were restricted to a 
type lattice. Two kinds of united atoms were defined: hydrophilic and hydrophobic ones.
The sequence of united atoms in the chain was assumed to be characteristic for a-helical
proteins (the helical septet). The force field used consisted of the long-range contact
potential between a pair of residues and the local potential preferring conformational
states, which were characteristic for a-helices. In order to study the thermodynamics
of our model we employed the Parallel Tempering (the Replica Exchange) Monte Carlo
sampling scheme combined with the Multihistogram method. The optimal set of
temperatures for the Parallel Tempering simulations was found by an iterative procedure.
Starting from energy observations at different temperatures we computed the density of
states for the system. Then, it was possible to recalculate any parameter of interest
(such as the radius of gyration or energy components) as a continuous function of the
temperature via averaging over the canonical ensemble. The influences of the temperature
and the force field on the properties of coil-to-globule transition were also studied.
|Marek Siłuszyk, K. Iskra, M. V. Alania*
||Long-period modulation of the galactic cosmic rays
intensity and the interplanetary magnetic field turbulence
Abstract: To study the relationship between the temporal changes of the interplanetary
magnetic field (IMF) turbulence and the rigidity spectrum of the galactic
cosmic ray (GCR) intensity variations data of neutron monitors and of the IMF
were used. The calculations were performed for the four ascending and four
descending phases of solar activity (1960-2002) including the positive (A>0)
and the negative (A<0) polarity periods of solar magnetic cycle. The soft
rigidity spectrum of the GCR intensity variations for the maximum epoch and the
hard one for the minimum epoch obtained by the worldwide network of neutron
monitors data we ascribe to the essential rearrangement of the structure of the
interplanetary magnetic field (IMF) turbulence in the range of the frequencies
(10-6 – 10-5)Hz throughout the 11-year cycle of solar activity. There is
not found any difference between the changes of the rigidity spectrum of the
11-year variations of the GCR intensity for different the A>0
and the A<0 polarity epoch. Taking account a strong relationship between the
energy range of the IMF turbulence and the rigidity spectrum of the GCR
intensity variations we conclude that the structure of the IMF turbulence
significantly changes versus solar activity, while it does not change versus
the A>0 and the A<0 polarity epoch of solar magnetic cycle. We propose the
rigidity spectrum exponent of the GCR intensity variations as a new index to study the 11-year variations of GCR intensity and to estimate the state of the
energy range of the IMF turbulence.
P. F. Góra
||Chaos in Newtonian iterations: Searching for zeros which are not there
Abstract: We show analytically that Newtonian iterations
have a positive topological entropy. In a specific example of
"solving" the equation x2+1=0, we
analytically find the invariant density and show how this problem relates
to that of a piecewise linear map.
||Nanorheology of surfactant micellar solutions from
Abstract: The Fluorescence Correlation Spectroscopy was used to determine the diffusion
coefficients of proteins and dye molecules in the buffered solutions of C12E6
nonionic surfactant. The viscosity of the solution was extracted from the
Einstein-Stokes relation. We showed that dynamics of proteins in the solution
is heterogenous and consequently viscosity felt by the protein depends on its
size, L, equal to twice the hydrodynamic radius. In the case of small proteins
(e.g. lysozyme, L=3.8 nm) the nanoviscosity is order of magnitude smaller than
the macroviscosity. From the size dependence of viscosity found in our
experiments we estimated that in the case of our system we reach the
macroscopic viscosity for L~20 nm. This means that the system becomes
homogenous (for diffusion) at the length scale larger than 20 nm.
||Stochasticity in gene expression
Abstract: Biochemical reactions that take place at the level of a single cell typically
include small numbers of molecules (e.g. 10-400). The complex inner structure
of the cell makes up for heterogenous distribution of these molecules. Spatial
fluctuations of the concentration of the reagents may introduce noise into
biochemical pathways. We apply GFRD method to simulate genetic pathway of
tryptophan regulation in Escherichia coli.
|Davide Valenti*, L. Schimansky-Geier**, X. Sailer**, and B. Spagnolo*
||Moment Equations in a Lotka-Volterra extended system
with time correlated noise
Abstract: A spatially extended Lotka-Volterra system of two competing species in the
presence of two correlated noise sources is analysed: (i) an external
multiplicative time correlated noise which mimics the interaction between the
system and the environment; (ii) a dichotomous stochastic process, whose jump
rate is a periodic function, which represents the interaction parameter between
the species. The moment equations for the species densities are derived in
Gaussian approximation using a mean field approach. Within this formalism we
study the effect of the external time correlated noise on the ecosystem
dynamics. Finally we compare these results with those obtained studying the
system dynamics within a coupled map lattice model.
|Aleksander Weron, Marcin Magdziarz
||Fractional stable noise. From Statistical Physics to
Abstract: The starting point is the unique BRW (1998) decomposition of every
self-similar stable noise into three independent components: mixed fractional
motion, harmonizable and evanescent processes. We will analize the asymptotic
dependence structure of fractional Ornstein-Uhlenbeck type noise and detect
long and short range dependence.
Some applications to anomalous diffusion as well as to option pricing
in the context of term structure (Vasicek model) will be presented in
|Maciej Wołoszyn, Bartłomiej J. Spisak
||One-dimensional systems with correlated disorder in
Abstract: We consider the localization properties of electrons in one-dimensional systems
with correlated disorder. The phase space formalism based on the
quasi-distribution functions is applied to the description of such systems. The
Renyi-Wehrl entropy is calculated from the Husimi function and used for
reconstructing the localization properties.
|Aleksander Woziński, Jan Iwaniszewski
||Surmounting fluctuating barriers in the presence of Kangaroo multiplicative noise